Seismological tools for geothermal
exploration and monitoring
vorgelegt von
M. Sc.
Tania Andrea Toledo Zambrano
ORCID: 0000-0002-6870-2194
an der Fakultät VI - Planen Bauen Umwelt
der Technischen Universität Berlin
zur Erlangung des akademischen Grades
Doktor der Naturwissenschaften
-Dr. rer. nat.-
genehmigte Dissertation
Promotionsausschuss:
Vorsitzender: Prof. Dr. Thomas Neumann
Gutachterin: Prof. Dr. Charlotte Krawczyk
Gutachter: Prof. Dr. Hansruedi Maurer (ETH Zürich)
Gutachterin: Prof. Dr. Maren Brehme (TU Delft)
Gutachter: Dr. Philippe Jousset (GFZ Potsdam)
Tag der wissenschaftlichen Aussprache: 13. April 2021
Berlin 2021
A las mujeres de mi vida: María, Tania, Ana
Acknowledgements
Building this thesis has been a great challenge I could have hardly accomplished without
the support system of colleagues, friends, and family. I have been incredibly blessed to be
accompanied by all of you throughout the highs and lows of this adventure called PhD. In
that sense, I like to think of this thesis not as mine but as ours.
To Charlotte Krawczyk: Lotte, I am grateful for your constant support and dedication not
only to me but to the entire group. In the last years I have scarcely met someone as dedicated
and hardworking as you. You are somewhat of an inspiration to me of what it means to be a
woman in science. Although fully committed to various tasks, you took the time to discuss
with me how to move forward with my work. I am grateful to you for pushing me to order my
ideas and to exercise seeing the bigger picture in the things I do. I think this is something I
will carry with me from this day on, so thank you.
To Philippe Jousset: Thank you for your support, creativity, and unceasing good humor
throughout the past 4 years. Despite the many commitments, you made sure to be available
to discuss any doubts or crazy ideas I had. I am very grateful for your trust in my capacity
and judgement. At times I thought you trusted me too much but I am now happy you did
because it pushed me to think independently and accomplish things I previously did not think
I would be capable of. As part of your scientific children group, I am happy to consider you
not only a supervisor but also a friend.
To Hansruedi Maurer: Thank you for your sustained guidance and support over the last
4+ years. From my seeking of your advice upon the end of my master program, to the quick
responses to any doubts I had along the way. You have been very present and available one-call
away. On our video conferences, I was continuously amazed at your efficiency and your ability to
spot details from my slides without seeing the processing. This encouraged me to meticulously
reason things through and constantly ask myself the question why. Thank you for trusting me
and for taking so much time to help me become a researcher. It has been such a pleasure to
work and learn so much from you.
To my GFZ colleagues working for the GEMex Project: Katrin Kieling, Anna Jentsch,
David Bruhn. You have been my project dream team: from the direction and organizational
aspects including the equipment handling for the fieldwork campaign, to the open data and
knowledge sharing. Frankly, this work could have never reached the quality it has today
without your valuable contributions. I left every project meeting feeling proud to belong to
such well-rounded and hardworking group, and I look forward to a future project together
again.
To Emmanuel Gaucher, Anne Obermann, Joana Martins, Arie Verdel: Thank you for your
trust in my capacity and for the time you took to share with me your expertises. I have been
incredibly lucky to collaborate and learn so much from you. Working with you has been like
tickling the brain. I left every meeting with you feeling both excited and motivated to continue
learning. Thus, I look forward to working closely with you in the future.
To my Mexican colleagues: Thank you for the nice collaborations and for the fun and
efficient field campaign. I was happy to work with such flexible and optimistic group that looks
beyond the obstacles to find suitable solutions on the go.
To Kemal Erbas: Thank you for your enthusiasm, openness, and trust in my ideas. Despite
my being a young researcher, you took my proposals seriously and allowed me to explore
them without hesitation. Your energy was always contagious and I enjoyed our work dynamic
together with Malte and David. Thank you also for your motivation when I was low and for
encouraging me to believe more in myself.
To Malte Metz and David Naranjo: Thank you for the enthusiastic, eager to learn, and
hands-on dynamic you brought into our work group. Working with you was very encouraging
and did not feel like work at all. I learned so much from/and with you, and I look forwards to
see what you work on in the future.
To Michael Weber: Thank you for sharing your wisdom with me over the last years. From
casually dropping on my desk the latest paper I needed to read for my research to the many
deep conversations about life and where to go in the future. In every situation when I thought
I have reached a dead end, you somehow managed to find solutions. And you even made it
seem so easy! Thanks to you, I shall always keep in mind to make a task list wherever I go.
Thank you for believing and nurturing not only the researcher in me but the human being as
well.
To Anke Lerch (the Career Center and the Welcome Center teams): Thank you for our
many conversations, your guidance, and the thought-provoking questions about the future.
I am very grateful for your work guiding young researchers like me, and for the constant
reminders to look after the person beyond the scientist.
To my dear GFZ colleagues: Thank you for making my experience at the GFZ a very
enjoyable one, and for the delightful conversations over coffee breaks and over our famous
Mahlzeit.
To all my friends: In particular to Sr. Gabriela, Femia, Rahel, Mauro, Lydia for your
constant calls and messages of support reminding me of the heart behind the brain. It was a
joy to have you so close to me despite the distance. You never failed to let me know you were
there for me through this challenging journey and beyond, so thank you.
To my amazing roommates: Not only were you feeding me during the last strides of my
PhD, you managed to make me laugh when I thought I was done for good. Thank you for
your friendships and for encouraging me to look forward to the future.
A mi familia: En especial a mi mamá y a mi abuelita. Doy gracias a Dios por el regalo de
ustedes, su optimismo, humor y fortaleza. You are at my core, and I am who I am because of
you. Thank you for reminding me to focus on the good, to smile, and to always enjoy and be
grateful for the ride.
vi
Zusammenfassung
Wichtige Aspekte der geothermischen Exploration und Nutzung sind die Bewertung und
Reduzierung der natürlichen und/oder induzierten Seismizität, die Abbildung und Ressourcen-
bewertung eines geothermischen Reservoirs, sowie die Überwachung der Auswirkungen der
Explorationsaktivitäten. In dieser Arbeit werden die Analysen und Anwendungen verschiedener
seismologischer Methoden zur Planung, Erkundung und Überwachung geothermischer Felder
vorgestellt. Die untersuchten und hier weiterentwickelten Methoden umfassen das Design für
den Aufbau und die Bewertung mikroseismischer Netzwerke, die lokale Erdbebentomographie,
die Ambient-Noise-Tomographie und die Coda-Wellen-Interferometrie. Diese Techniken werden
angewendet, um die geothermischen Felder Los Humeros (Mexiko), Theistareykir (Island) und
Reykjanes (Island) zu untersuchen.
Die Geometrie seismologischer Arrays ist essentiell für eine gute Bestimmung seismischer
Ereignisse mit kleinen Lokationsungenauigkeiten. Ein sequenzieller Algorithmus zum Design
des Arrays, der eine Qualitätskennzahl auf der Grundlage des D-Kriteriums verwendet, wurde
benutzt, um das seismische Netzwerk in Theistareykir zu erweitern und die Geometrie des
Reykjanes-Netzwerks zu testen. Unter der Annahme von mittleren Ablesefehlern von t
p
=0.2
s und t
s
=0.4 s für P- und S- Wellen verbessert das erweiterte Theistareykir-Netzwerk die
berechneten Hypo-Zentren um 0.2 km innerhalb des neuen Netzes. Das Reykjanes-Netz könnte
andererseits um bis zu 18 Stationsstandorte reduziert werden und dennoch vergleichbare
Lokationsgenauigkeiten erzielen. Diese Studie zeigte die Wichtigkeit vor den eigentlichen
Feld-Experimenten Tests möglicher Array-Designs durchzuführen um die Kosten für ein
geothermisches Projekt (erforderliche Anzahl von Sensoren) zu optimieren und gleichzeitig
gute Lokationen für erwartete seismische Ereignisse zu erhalten (Nutzen/Kostenverhältniss).
Um die seismischen Strukturen der geothermischen Felder Los Humeros und Theistareykir
zu charakterisieren, wurden an beiden Standorten eine lokale Erdbebentomographie und eine
Ambient-Noise-Tomographie berechnet. Eine lokale Erdbebentomographie ist in Gebieten
mit hoher Seismizität und guter Strahlenabdeckung (Erdbeben/Stationsgeometrie) möglich.
Eine Ambient-Noise-Tomographie hängt nur von einer guten und ausreichend dichten
Stationsverteilung ab. Mit den Ergebnissen dieser Studien wurden dann erstmals die seismischen
Strukturen und die Dynamik dieser beiden produzierenden Felder ermittelt.
Die Seismizitätsverteilung in Los Humeros wurde verwendet, um Strukturen und potenzielle
Verbesserungen in der Durchlässigkeit einiger Störungszonen zu charakterisieren. Das abge-
leitete Vp-Modell wurde mit Bohrloch-Daten und Ultraschall-Messungen an Gesteinsproben
kombiniert, um die Grenzen verschiedener geologischer Einheiten abzuschätzen. Das Vp/Vs-
Modell wurde dann in Kombination mit Widerstandsdaten und Oberflächen-CO
2
-Messungen
verwendet, um die Geometrie der leitfähigen Tonkappe abzuleiten (Vp/Vs
≤
1.65 und
Widerstand
≤
10 Ωm), um Fluide zu identifizieren (reduzierte Vp Werte, Vp/Vs
≥
1.71 und
Widerstände zwischen 10-60 Ωm) und um gasführende Bereiche zu lokalisieren (Vp/Vs
≤
1.55
und hohe CO
2
-Konzentrationen). Eine ähnliche Studie wurde in Theistareykir durchgeführt,
wo das Vs-Modell mit Widerstandsdaten kombiniert wurde, um magmatische und/oder
hydrothermale Körper zu identifizieren (Vs
≤
-7 %, Widerstände
≤
30 Ωm). Eine wichtige
Schlussfolgerung aus diesen Studien ist, dass die Kombination von seismischen Eigenschaften
mit zusätzlichen geologischen und/oder geophysikalischen Daten Mehrdeutigkeiten vermeidet
und robuste Interpretationen der Dynamik und Struktur eines geothermischen Reservoirs
liefert.
Weiterhin wurde eine Coda-Wellen-Interferometrie-Technik (Dehnungsmethode) auf zwei
Jahre Ambient-Noise-Daten im Geothermiefeld Theistareykir angewendet, um mögliche
Geschwindigkeitsänderungen aufgrund der Nutzung des Feldes zu überwachen. Hier waren
die Auswirkungen der Injektions- und Produktionsveränderungen auf das ∆
v/v
-Verhältnis
sehr gering und nur eine kleine, möglicherweise produktionsbedingte, langfristige Geschwin-
digkeitsreduktion wurde festgestellt (-0.05 %/Jahr innerhalb des Produktionsbereichs im
Vergleich zum regionalen Wert von -0.04 %/Jahr). Solche Beobachtungen sind für die sichere
langfristige Ausbeutung von geothermischen Feldern von großer Bedeutung. Obwohl es noch
keine Standardpraxis ist, ist die Berechnung dieser Änderungen weiterhin sehr nützlich, um
aseismische Prozesse vor potenziell ausgelösten/induzierten großen seismischen Ereignissen zu
steuern, sie ergänzen weiterhin die mikroseismische Überwachung.
Mit diesen Ergebnissen trägt die vorgelegte Arbeit zu den Bemühungen der Internationalen
Energieagentur bei, die Nutzung von Geothermie zu entwickeln und zu erhöhen.
viii
Abstract
Important aspects of geothermal exploration and exploitation are the assessment and mitigation
of natural and/or induced seismicity, the imaging and resource assessment of a geothermal
reservoir and the monitoring of the effects of the exploitation activities. With this thesis
the analysis and application of various seismological tools for the planning, exploration, and
monitoring of geothermal fields are given. The methods explored and further developed
include survey design for microseismic network construction and assessment, local earthquake
tomography, ambient noise tomography, and coda wave interferometry. These techniques
were applied to study Los Humeros (Mexico), Theistareykir (Iceland) and Reykjanes (Iceland)
geothermal fields.
The geometry of seismological arrays is essential for high quality seismic event retrieval
and minimal location errors. A sequential survey design algorithm that uses a quality measure
based on the D-criterion was applied to extend the seismic network at Theistareykir and
to qualify the geometry of the Reykjanes network. Assuming mean picking errors of t
p
=
0.2 s and t
s
=0.4 s, the extended Theistareykir network presented an improvement of
∼
0.2 km for the computed hypocentral components of seismic events located within the new
network. Conversely, we estimated that the Reykjanes network could spare up to 18 of its
station locations and obtain comparable location errors nonetheless. This study showed the
importance of prior survey design experiments to optimize the expenses for a geothermal
project (required number of sensors) while obtaining good location estimates of expected
seismic events (benefit/cost relations).
To characterize the seismic structures at Los Humeros and Theistareykir geothermal fields,
a local earthquake tomography and an ambient noise tomography were computed at both
locations, respectively. A local earthquake tomography is feasible in areas with high seismicity
and good ray coverage (earthquake/station geometries). On the other hand, an ambient noise
tomography depends on a good and sufficiently dense station distribution. With the results
of these studies, the seismic structures and the dynamics of these two producing fields were
obtained for the first time.
The seismicity distribution at Los Humeros was used to characterize structures and
potential permeability enhancements in some of the existing faults. The retrieved Vp model
was combined with available well log data and ultrasonic pulse measurements of collected
rock samples to estimate the boundaries of different geologic units. The Vp/Vs model was
then used in combination with resistivity data and surface CO
2
measurements to deduce the
geometry of the conductive clay cap (Vp/Vs
≤
1.65 and resistivities
≤
10 Ωm), to identify
fluid (Vp reduction, Vp/Vs
≥
1.71, and resistivities between
∼
10-60 Ωm), and to locate gas
bearing regions (Vp/Vs
≤
1.55 and high surface CO
2
concentrations). A similar study was
carried out at Theistareykir, where the Vs model was combined with resistivity data to identify
magmatic and/or hydrothermal bodies (Vs
≤
-7 %, resistivities
≤
30 Ωm). An important
conclusion from these studies is that the combination of seismic properties with additional
geological and/or geophysical data avoids ambiguities and provides robust interpretations of
the dynamics and structure of a geothermal reservoir.
Finally, a coda wave interferometry technique (stretching method) was applied to two
years of ambient noise records at the Theistareykir geothermal field with the aim to monitor
possible velocity changes due to the exploitation activities. Here, the effects of the injection and
production changes were very small on the computed ∆v/v ratio and only a small long-term
velocity reduction (possibly due to production) was detected (-0.05 %/year at the producing
field compared to a regional -0.04 %/year). Such observations are also very relevant for the safe
long-term continuation of exploitation activities. Although not yet a standard practice, the
computation of these changes is very useful to control aseismic processes prior to potentially
triggered/induced large seismic events and is complementary to microseismic monitoring.
With these results, this thesis contributes to the efforts of the International Energy Agency
to develop and increase the use of geothermal energy.
x
Table of Contents
Title Page i
Zusammenfassung vii
List of Figures xv
List of Tables xxiii
1 Introduction 1
1.1 Generalcontext.................................... 1
1.2 Geothermal resources and their assessment . . . . . . . . . . . . . . . . . . . . 1
1.3 Passive seismic as a tool for exploration and monitoring of geothermal resources 2
1.4 Objectives and outline of the thesis . . . . . . . . . . . . . . . . . . . . . . . . . 3
1.5 Listofpublications.................................. 4
I Methods and concepts 5
2 Seismic wave propagation, ray, and inversion theory 7
2.1 The elastic wave equation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
2.2 TheGreen’sfunction................................. 8
2.3 Introduction to ray theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
2.3.1 Theshootingmethod ............................ 9
2.3.2 Thebendingmethod............................. 10
2.3.3 The pseudo-bending method . . . . . . . . . . . . . . . . . . . . . . . . 12
2.3.4 The finite difference method . . . . . . . . . . . . . . . . . . . . . . . . . 12
2.4 Introduction to inverse theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
2.4.1 The linear inverse problem . . . . . . . . . . . . . . . . . . . . . . . . . 14
2.4.2 Nonlinearinversion.............................. 15
2.4.3 Analysis of the solution robustness . . . . . . . . . . . . . . . . . . . . . 15
2.4.3.1 Data resolution matrix . . . . . . . . . . . . . . . . . . . . . . 15
2.4.3.2 Model resolution matrix . . . . . . . . . . . . . . . . . . . . . . 16
2.4.3.3 Spread function . . . . . . . . . . . . . . . . . . . . . . . . . . 16
2.4.3.4 Model covariance matrix . . . . . . . . . . . . . . . . . . . . . 16
xi
TABLE OF CONTENTS
3 Earthquake location and survey design 17
3.1 Basic principles of earthquake location . . . . . . . . . . . . . . . . . . . . . . . 17
3.1.1 Earthquake location by iterative methods . . . . . . . . . . . . . . . . . 18
3.2 Experimental survey design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18
3.2.1 The D-criterion ............................... 19
3.2.2 Optimization approaches for survey design . . . . . . . . . . . . . . . . . 19
4 Principles for local earthquake tomography 23
4.1 The coupled 1D velocity model and earthquake location problem . . . . . . . . 23
4.2 3D travel time tomography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24
4.2.1 Model parametrization . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24
4.2.2 Forward and inverse calculations . . . . . . . . . . . . . . . . . . . . . . 25
5 Ambient seismic noise tomography and coda wave interferometry 27
5.1 Originsofambientnoise............................... 27
5.2 Green’s function reconstruction . . . . . . . . . . . . . . . . . . . . . . . . . . . 28
5.3 Ambient noise travel time surface wave tomography . . . . . . . . . . . . . . . 30
5.3.1 Properties of Surface waves . . . . . . . . . . . . . . . . . . . . . . . . . 31
5.3.2 Ambient noise surface wave tomography . . . . . . . . . . . . . . . . . . 31
5.4 Noise-basedmonitoring ............................... 32
5.4.1 Stretching technique . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33
5.4.2 Moving window cross-spectral analysis . . . . . . . . . . . . . . . . . . . 33
5.4.3 Comparison of both methods . . . . . . . . . . . . . . . . . . . . . . . . 34
II Applications 35
6 Optimized experimental network design for microseismicity location and
monitoring 37
6.1 Introduction...................................... 38
6.2 Background theory and synthetic examples . . . . . . . . . . . . . . . . . . . . 41
6.2.1 Basic principles of earthquake location and inverse theory . . . . . . . . 41
6.2.2 Experimental survey design: The D-criterion ............... 42
6.2.3 Eventdetectability.............................. 43
6.2.4 Test Case A: survey design for a single source . . . . . . . . . . . . . . . 44
6.2.5 Test Case B: small multi-event survey design . . . . . . . . . . . . . . . 46
6.2.6 Test Case C: large multi-event survey design . . . . . . . . . . . . . . . 48
6.3 Case study I: Theistareykir geothermal field . . . . . . . . . . . . . . . . . . . . 48
6.3.1 Experimental design setup, results and discussion . . . . . . . . . . . . . 50
6.3.2 Theistareykir experimental survey design . . . . . . . . . . . . . . . . . 51
6.3.3 Spatial quality measure distribution . . . . . . . . . . . . . . . . . . . . 53
6.3.4 Earthquake location accuracies . . . . . . . . . . . . . . . . . . . . . . . 53
6.4 Case study II: Reykjanes seismic data and network performance . . . . . . . . 55
6.4.1 Seismic network quality . . . . . . . . . . . . . . . . . . . . . . . . . . . 57
6.5 Discussion....................................... 61
xii
TABLE OF CONTENTS
6.5.1 D-optimality ................................. 61
6.5.2 Linearized destruction sequential survey design . . . . . . . . . . . . . . 61
6.5.3 Detectability ................................. 62
6.5.4 Design and qualification of seismic arrays . . . . . . . . . . . . . . . . . 62
6.6 Conclusions...................................... 63
7 Local earthquake tomography of a geothermal field 65
7.1 Geologic and tectonic setting . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67
7.2 Seismic monitoring and data processing . . . . . . . . . . . . . . . . . . . . . . 69
7.2.1 Seismicnetwork ............................... 69
7.2.2 Local earthquake detection . . . . . . . . . . . . . . . . . . . . . . . . . 69
7.3 1Dvelocitymodel .................................. 70
7.4 3Dseismictomography ............................... 74
7.4.1 Model parametrization . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75
7.4.2 Regularization ................................ 77
7.4.3 Model quality and uncertainty . . . . . . . . . . . . . . . . . . . . . . . 77
7.5 Resultsanddiscussion................................ 83
7.5.1 1Dvelocitymodel .............................. 83
7.5.2 Seismicity distribution . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83
7.5.3 Vpstructure ................................. 84
7.5.4 Vp/Vsstructure ............................... 85
7.6 Conclusions...................................... 92
Appendix 7.A Station corrections associated with the 1D velocity model . . . . . . 94
Appendix 7.B Tradeoff test sample for a single model parametrization . . . . . . . 96
Appendix 7.C Diagonal elements of the MRM (RDE) . . . . . . . . . . . . . . . . . 96
Appendix7.D Spreadvalues............................... 96
Appendix 7.E Model statistics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97
8 Seismic interferometry for imaging and monitoring a geothermal field 101
8.1 Introduction......................................102
8.2 Geologic setting and seismic network . . . . . . . . . . . . . . . . . . . . . . . . 103
8.2.1 Geologic and tectonic setting . . . . . . . . . . . . . . . . . . . . . . . . 103
8.2.2 Seismicnetwork ...............................105
8.3 Dataprocessing....................................105
8.4 Ambient noise tomography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105
8.4.1 Group velocity dispersion analysis . . . . . . . . . . . . . . . . . . . . . 105
8.4.2 2D group velocity tomography . . . . . . . . . . . . . . . . . . . . . . . 106
8.4.3 Modelquality.................................109
8.4.4 Retrieval of 3-D Vs model . . . . . . . . . . . . . . . . . . . . . . . . . . 111
8.5 Determination of time-lapse changes . . . . . . . . . . . . . . . . . . . . . . . . 111
8.5.1 Waveform stretching . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 112
8.6 Interpretation and discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . 115
8.6.1 Ambient noise tomography . . . . . . . . . . . . . . . . . . . . . . . . . 115
8.6.2 Time-lapsechanges..............................115
xiii
TABLE OF CONTENTS
8.7 Conclusions......................................116
III Discussions and Conclusions 121
9 Discussions of results 123
9.1
Optimized experimental network design for microseismicity location and
monitoring ......................................123
9.1.1 Survey design experiments at Reykjanes and Theistareykir (Iceland) . . 124
9.1.2 General considerations for survey design experiments . . . . . . . . . . . 124
9.1.2.1 Quality measure choice . . . . . . . . . . . . . . . . . . . . . . 124
9.1.2.2 Optimization choice . . . . . . . . . . . . . . . . . . . . . . . . 125
9.1.2.3 Detectability............................125
9.1.2.4 Outlooks ..............................125
9.2 Passive seismic imaging for the exploration of geothermal fields . . . . . . . . . 125
9.2.1 Local earthquake tomography at Los Humeros geothermal field . . . . . 126
9.2.2 Joint interpretation at Los Humeros geothermal field . . . . . . . . . . . 126
9.2.3 Ambient noise tomography at the Theistareykir geothermal field . . . . 127
9.2.4 Joint interpretation at the Theistareykir geothermal field . . . . . . . . 127
9.2.5 Advantages and disadvantages of the methods . . . . . . . . . . . . . . . 128
9.2.6 Multi-parameter interpretations . . . . . . . . . . . . . . . . . . . . . . . 128
9.3 Coda wave interferometry for monitoring geothermal fields . . . . . . . . . . . . 129
9.3.1 The Theistareykir case study . . . . . . . . . . . . . . . . . . . . . . . . 129
9.3.2
Importance of coda wave interferometry for monitoring geothermal
operations...................................129
10 Conclusions 131
References 133
Appendix A Contributions to the publications 151
Appendix B Statutory declaration 155
xiv
List of Figures
2.1
Schematic representation of the shooting method. Aand Brepresent the source
and receiver positions, respectively, located in a medium with velocity
V
(
x, z
).
The angle projection at the source of ray 1 is iteratively adjusted until the
ray passes as close as possible to the receiver position (ray 3). Modified from
Rawlinson and Sambridge (2003) .......................... 10
2.2
Schematic representation of the bending method. Aand Brepresent the source
and receiver positions, respectively, located in a medium with velocity
V
(
x, z
).
The geometry of ray 1 is iteratively adjusted until it satisfies Fermat’s principle
(ray 3). Modified from Rawlinson and Sambridge (2003)............. 11
2.3
Schematic representation of the pseudo bending method. Aand Brepresent the
source and receiver positions, respectively, located in a medium with velocity
V
(
x, z
). First, an initial guess with three points is provided (ray 0). Then,
the center of ray 0 is updated to better satisfy the ray equation (ray 1). Each
line segment is halved and their mid points updated once more (ray 2). This
process is carried out iteratively until a convergence criterion is satisfied (ray 3).
Modified from Rawlinson and Sambridge (2003).................. 12
2.4
The finite difference method proposed by Vidale (1988) to find the first arrival
travel time field assuming a continuous velocity medium. See text for details.
Modified from Rawlinson and Sambridge (2003).................. 13
3.1
Survey design example for an event at 3 km depth with M
L
0.8. a) 5 stations
setup. b) 115 stations setup. The colorbar shows the order of placed stations.
c) Design quality Θof the survey setup for each number of placed stations. The
dashed red line represents station point 4, and the horizontal dashed black line
the limit of Θ= 3.4 (see figure inset). Taken from Toledo et al. (2020b) . . . . 21
4.1
Various types of model parametrization: a) constant velocity blocks, b) grid of
velocity nodes, c) triangulated velocity grid for constant velocity gradient cells
(White, 1989). Taken from Rawlinson and Sambridge (2003)........... 25
5.1
Illustration of the time reversal principle. a) Point Cis a source that emits a
signal recorded at Aand B. b) Point Bemits a signal that is mirrored by Cand
recorded by A. Triangles mark the receiver positions, and the stars correspond
to the source locations. Modified from Obermann (2014). ............ 28
xv
LIST OF FIGURES
5.2
Synthetic illustration of the stretching (a, c) and MWCS methods (b, d). a)
Comparison of a reference (gray lines) with respect to stretched (black lines)
waveforms. c) Correlation coefficients for each stretched waveform in a). b)
Comparison of a reference waveform (gray lines) with respect to fixed moving
window segments (black lines). d) Linear regression for the obtained best time
shifts with respect to time. The maximum associated
ϵ
is, in both cases, 5%.
Taken from Nakata et al. (2019)........................... 33
6.1
Test case A. Survey design example for an event at 3 km depth with M
L
0.8.
a) 5 stations setup. b) 115 stations setup. The colorbar expresses the order of
placed stations. c) Design quality or "goodness" of the survey setup for each
number of placed stations. The dashed red line represents station point 4, and
the horizontal dashed black line the limit of Θ=3.4................ 45
6.2
Test case B. Survey design example for three events 3 km deep. Events have
M
L
0.8 (center), 0.6 (top), and 0.5 (bottom left). a) 12 stations setup. b) 231
stations setup. The colorbar expresses the order of placed stations. c) Total
design quality or "goodness" of the survey setup after progressively placing
stations. d) Design quality contribution per event for the whole experiment.
The dashed red line represents station point 12, and the horizontal dashed black
line the limit of Θevent =3.4. ............................ 47
6.3
Test case C. Survey design example for multiple events of M
L
0.5 located at 3 km
depth. Pink points indicate epicenter locations and triangles stand for station
locations. The colorbar expresses the order of placed stations. a) 100 stations
setup. b) 598 stations setup. c) Total design quality or "goodness" of the survey
setup after progressively placing stations. d) Design quality contribution per
event for the whole experiment. The dashed red line represents station point
100, and the horizontal dashed black line the limit of Θevent = 3.4. . . . . . . . 49
6.4
Initial receiver positions and synthetic epicenters defined prior to the design study.
50
6.5
Synthetic earthquake catalog specifications. a) 1D P- and S-wave velocity profiles
from the SIL system (Bjarnason et al., 1993). c) Event depth distribution. The
red line indicate the depth above which 95 %of events are located. This limit
is also known as the brittle-ductile boundary. d) Magnitude distribution of the
synthetic earthquake catalog. b value = 2.16 . . . . . . . . . . . . . . . . . . . 51
6.6
a) 23 stations network. b) 135 stations network. The colorbar expresses the
order of the added stations. c) Total design quality of the survey setup after
progressively adding stations. d) Design quality contribution per event for the
whole experiment. The dashed red line on the left indicates the limit for the
initial 12 stations, and the red line on the right the limit for a 23 stations
network. The horizontal dashed black line indicates the limit of Θevent = 3.4. . 52
xvi
LIST OF FIGURES
6.7
Measures of design quality or network goodness according to event position and
magnitude. The first column indicates values associated to events of M
L
0.5,
the second to M
L
0.8. White triangles mark the starting station positions. The
red triangles stand for the added stations after the design experiment. a) and
b) show a 3D view, c) and d) depict a depth slice at 3 km, and e) and f) an YZ
profile cutting at y = 37.5 km. . . . . . . . . . . . . . . . . . . . . . . . . . . . 54
6.8
Accuracies of hypocentral coordinates for events at 3 km depth. The first
column indicates events of M
L
0.5 and the second of M
L
0.8. Red triangles
markstationpositions................................. 56
6.9
Mean inversion errors for events at 3 km depth and magnitudes a) M
L
0.5 and
b) ML0.8........................................ 57
6.10
Location accuracy and error differences between the original (12) and final (23)
station networks for events in the synthetic earthquake catalog of Fig. 6.5 . . . 58
6.11
a) Seismic events, seismometers, and OBS positions. b) EW profile. Topography
is ignored for its rather small variation. . . . . . . . . . . . . . . . . . . . . . . 59
6.12
a) 1D Vp velocity model (Jousset et al., 2016). b) Maximum detection distances.
59
6.13
Reykjanes network quality. a) Order of importance of the Reykjanes seismic
stations. b) Total design quality of the survey setup after progressively adding
stations. c) Design quality contribution per event for the whole experiment.
The dashed red lines indicate the limits of 50%, 60%, 70%, 80%, and 90%stations.
60
6.14 Location accuracies given by a station number reduction . . . . . . . . . . . . . 61
7.1
a) Surface geology, b) main structures and well locations at LHVC (modified
from Carrasco-Núñez et al., 2017a; Norini et al., 2015). c) Locations of the
Trans-Mexican Volcanic Belt (TMVB) and LHVC (red triangle). . . . . . . . . 68
7.2
Topographic map and temporary seismic network at Los Humeros geothermal
field. Blue and red triangles mark the positions of three component short-
period (Mark L-4C-3D) and three-component broadband (Trillium Compact
120s) sensors, respectively. The reference station for the 1D inversions (also
a three-component broadband Trillium Compact 120s sensor) is marked as a
red circle. Several indentified and inferred structures are delineated in black
(modified from Carrasco-Núñez et al., 2017a; Norini et al., 2015). . . . . . . . . 70
7.3
Distribution of the detected local earthquakes after a nonlinear localization in
a homogeneous 3D volume with a P-wave velocity of 3.5 km/s and a Vp/Vs
ratio of 1.73. Triangles mark the station positions and dark solid lines indicate
structures inferred at the surface. Red stars mark the positions of three injection
wells. C1, C2, and C3 indicate the positions of three main seismic clusters.
Depths are defined relative to sea level. . . . . . . . . . . . . . . . . . . . . . . 71
7.4
Results of the 1D inversions using Velest. The 35 best a) P-wave and b) S-wave
final velocity models (gray lines). Heat maps for the same c) P-wave and d)
S-wave set of final models. The yellow lines indicate all initial velocity models
used. The selected minimum 1D models are indicated in black lines in panels a)
and b), and in red lines in panels c) and d). . . . . . . . . . . . . . . . . . . . . 72
xvii
LIST OF FIGURES
7.5
Minimum 1D model showing: a) the selected Vp and Vs models along with 2
available models (Lermo et al., 2008; Löer et al., 2020), b) the resulting Vp/Vs
ratio, and c) the earthquake distribution over depth after the 1D inversion.
Solid lines indicate the depth intervals with best sensitivity for each model. . . 73
7.6
Ray path distribution after the 1D inversion: a) map view, b) N-S, and c) E-W
projections. Seismic stations are represented as purple triangles, local events as
green circles. The projections of three injection wells are marked as red lines in
the cross sections. Dark solid lines in the map view indicate structures inferred
at the surface, and the gray lines correspond to topographic contours. . . . . . 74
7.7
Model parametrization and DWS distribution at different depth levels for an
initial (unrotated) inversion grid. Panels a) and c) show two depth slices for
the Vp model DWS distribution at -2.6 km and -1.10 km depth. Panels b) and
d) show the depth slices for the Vp/Vs model DWS distribution at -2.6 km and
-1.10 km depth. Darker shading indicates regions of higher ray density. Gray
crosses indicate node positions. . . . . . . . . . . . . . . . . . . . . . . . . . . . 76
7.8
Cross sections A1-A1’ and B1-B1’ for the Vp model DWS distribution (Figure
7.7). Darker shading indicates regions of higher ray density. Black crosses
indicate the node positions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77
7.9 Nodes of the 228 inversion grids used to estimate the average velocities. . . . . 78
7.10
Averaged DWS distribution at different depth levels. Panels a) and c) show two
depth slices for the Vp model DWS distribution at -2.6 km and -1.10 km depth.
Panels b) and d) show the depth slices for the Vp/Vs model DWS distribution
at -2.6 km and -1.10 km depth. Darker shading indicates regions of higher ray
density. ........................................ 79
7.11 RMS misfit variation for the 228 inverted models. . . . . . . . . . . . . . . . . . 80
7.12
Checkerboard recovery. Panels a), c), and e) show three depth slices for the
recovered Vp anomalies at -2.6 km, -2.10 km, and -1.10 km depth. Panels b),
d), and f) show the recovered Vp/Vs anomalies at -2.6 km, -2.10 km, and -1.10
km depth. The red and blue squares mark the positions of the synthetic high
and low velocity anomalies. Gray areas mark the regions where the DWS is less
thanorequalto5. .................................. 81
7.13
Cross sections A2-A2’, B2-B2’, C2-C2’, and D2-D2’ (Figure 7.12) for the
retrieved Vp and Vp/Vs model variations. Panels a), c), e), and g) show the
recovered Vp anomalies, and panels b), d), f), and h) show the recovered Vp/Vs
anomalies of the checkerboard test. Gray areas mark the regions where the
DWS is less than or equal to 5. . . . . . . . . . . . . . . . . . . . . . . . . . . . 82
7.14
Vp model variations with respect to the minimum 1D velocity model at different
depth levels. Panels a), b), c), and d) show depth slices for the resulting
Vp model variations at -2.60 km, -2.10 km, -1.60 km, and -1.10 km depth,
respectively. Green circles mark the location of earthquakes +/- 150 m away
from slice. Dashed red lines indicate the boundary at which spread values are
less than or equal to 1.5. Gray areas mark the regions where the DWS is less
thanorequalto5. .................................. 88
xviii
LIST OF FIGURES
7.15
Cross sections for the Vp model variations (Figure 7.14). Green circles mark
the locations of earthquakes +/- 200 m away from the slice. Dashed red lines
indicate the boundary at which spread values are less than or equal to 1.5.
Gray areas mark the regions where the DWS is less than or equal to 5. Dashed
gray lines indicate different absolute velocity levels, and solid gray lines mark
approximate unit boundaries. Approximate locations of main structures are
indicated in black. Vertical green lines indicate the positions of neighboring
injectionwells. .................................... 89
7.16
Vp/Vs structure at different depth levels. Panels a), b), c), and d) show depth
slices for the resulting Vp/Vs model at -2.60 km, -2.10 km, -1.60 km, and -1.10
km depth, respectively. Green circles mark the locations of earthquakes +/-
150 m away from the slice. Dashed red lines indicate the boundary at which
spread values are less than or equal to 1.5. Gray areas mark the regions where
the DWS is less than or equal to 5. . . . . . . . . . . . . . . . . . . . . . . . . . 90
7.17
Cross sections for the Vp/Vs model (Figure 7.16). Green circles mark the
locations of earthquakes +/- 200 m away from the slice. Dashed red lines
indicate the boundary at which spread values are less than or equal to 1.5. Gray
areas mark the regions where the DWS is less than or equal to 5. Approximate
locations of main structures are indicated in black. Vertical green lines indicate
the positions of neighboring injection wells. . . . . . . . . . . . . . . . . . . . . 91
7.18
a) P-wave and b) S-wave station corrections associated with the 1D velocity
models. Topographic lines are indicated in gray and main structures are shown
inblack......................................... 94
7.19
Tradeoff curves for a) Vp and b) Vp/Vs to select the optimal damping values.
The parameters selected were 7 and 10 for Vp and Vp/Vs models, respectively. 96
7.20
Average RDE distribution at different depth levels. Panels a), c), and e) show
three depth slices for the Vp model RDE distribution at -2.6 km, -2.10 km, and
-1.10 km depth. Panels b), d), and f) show the depth slices for the Vp/Vs model
RDE distribution at -2.6 km, -2.10 km, and -1.10 km depth. Darker shading
indicates higher resolution values. . . . . . . . . . . . . . . . . . . . . . . . . . . 98
7.21
Averaged spread distribution at different depth levels. Panels a), c), and e) show
three depth slices for the Vp model spread distribution at -2.6 km, -2.10 km,
and -1.10 km depth. Panels b), d), and f) show the depth slices for the Vp/Vs
model spread distribution at -2.6 km, -2.10 km, and -1.10 km depth. Darker
shading indicates regions with less smearing. . . . . . . . . . . . . . . . . . . . 99
7.22
Standard deviation distribution at different depth levels associated with the
averaged models. Panels a), c), and e) show three depth slices for the Vp
model standard deviation distribution at -2.60 km, -2.10 km, and -1.10 km
depth. Panels b), d), and f) show the depth slices for the Vp/Vs model standard
deviation distribution at -2.60 km, -2.10 km, and -1.10 km depth. Pink circles
mark the locations of earthquakes +/- 150 m away from the slice. Dashed blue
lines indicate the boundary at which spread values are less than or equal to 1.5.
Gray areas mark the regions where the DWS is less than or equal to 5. . . . . . 100
xix
LIST OF FIGURES
8.1
a) Map of Iceland and location of the Theistareykir geothermal field. The rift
fissure swarms GOR (Grímsey Oblique-Rift), HFF (Húsavík-Flatey Fault), and
DL (Dalvík Lineament) of the TFZ (Tjörnes Fracture Zone) are shown with
blue lines. The fissure swarm Th (Theistareykir)/Má (Mánáreyjar) of the NRZ
(Northern Rift Zone) is shown with a yellow line. b) Main exploitation area.
The location of injection and production wells are marked with yellow and white
circles, respectively. Approximate well deviations are shown as black lines. c
) Temporary (red triangles) and permanent (blue and green triangles) seismic
networks at the Theistareykir geothermal field. The location of panel b) is
shown with white dashed lines. The yellow dashed lines indicate the region
showninFigure8.7. .................................104
8.2
a) Full set of picked Rayleigh wave dispersion curves. b) Number of
measurements per period. The vertical red lines indicate the limits of the
measurements used in this study. . . . . . . . . . . . . . . . . . . . . . . . . . . 106
8.3
Raypath (a, c) and ray density (b, d) maps for periods of 2 and 5 s. Raypaths
in a) and c) are colored with their associated measured group velocity. The
chosen cell size is
∼
3.5 x 3.5 km. Black triangles indicate the seismic stations
positions and the gray lines correspond to topographic contours. . . . . . . . . 107
8.4
Rayleigh wave group velocity maps at a) 2, b) 3, c) 4, and d) 5 s. Initial
velocities used in each inversion are shown in the upper right corner. Black
triangles indicate the seismic stations positions and the gray lines correspond
totopographiccontours................................108
8.5
Spatial resolution (a, c) and resolution shift (b, d) at 2 and 5 s. The red lines
indicate the 80 %contour levels of the MRM associated to three cells points
(red crosses). Black triangles indicate the seismic stations positions and the
gray lines correspond to topographic contours. . . . . . . . . . . . . . . . . . . 110
8.6
a) Example of synthetic local dispersion curves and b) their associated 1D Vs
models. The local (data) dispersion curve is represented as a thick black line.
Lines are colored according to their corresponding misfit. c) Best fitting 1D Vs
profiles for each grid cell (gray lines). The 1D model that is routinely used for
earthquake locations in Iceland (SIL model, Stefánsson et al., 1993) is shown
witharedline. ....................................112
8.7
Vs depth slices. Resistivity contour lines are taken from Karlsdóttir et al.
(2012). Black triangles indicate the seismic stations positions and the gray lines
correspond to topographic contours. White circles represent the location of
injection and production wells, and the approximate well deviations are shown
with black lines. The location of these maps are shown with yellow dashed lines
inFigure8.1c. ....................................113
8.8
Velocity changes computed with the stretching technique for the ACs of stations
a ) SKI and b) TH05. The color scale represents the associated CC. Results
for 2, 5, and 10 day stacks are shown in the upper, middle, and lower panels,
respectively.......................................118
xx
LIST OF FIGURES
8.9
Velocity changes computed for all available ACs. Results for a) 2, b) 5, and c) 10
day stacks times. Line colors represent three station groups: station neighboring
the injection site (red), stations close to the production sites (blue, located
within 8.1c), stations far from the exploitation zone (orange). We discarded
∆v
v
values with CC
≤
0.35. d) Linear regressions of the velocity variation averages
for stations inside and outside the exploitation area. e) Total production (red)
and injection (blue) rates at the geothermal field, and local seismicity rates
(pink) from the 1 January 2018 to 15 July 2018 (taken from Naranjo (2020)).
The gray boxes highlight the fluctuations I, II, and III. See main text for more
details..........................................119
8.10
(a, c) Spectrograms and (b, d) velocity variation averages (2-day stack window)
for stations inside and outside the exploitation area (within 8.1c). The sinusoidal
trend has been removed for both curves. e) Total production (red) and injection
(blue) rates at the geothermal field, and local seismicity rates (pink) from 1
January 2018 to 15 July 2018 (taken from Naranjo (2020)). The gray boxes
highlight the fluctuations I, II, and III. See main text for more details. . . . . . 120
xxi
List of Tables
1.1 Seismological tools explored in this thesis . . . . . . . . . . . . . . . . . . . . . 3
7.1
Approximate mean P- velocities obtained from laboratory measurements of
different core and outcrop rock samples. Modified from Bär and Weydt (2019) 86
7.2 Station corrections associated to the minimum 1D velocity model . . . . . . . . 95
xxiii
1
Introduction
1.1 General context
The Industrial Revolution started in the late eighteenth and early nineteenth century with
the replacement of manual labor by machinery operated mainly with fossil fuels. Since then,
scientists have pointed out to the rapid increase of greenhouse gases emissions (40%more CO
2
compared to pre-industrial times) leading to a critical rise of global temperatures (IPCC, 2013,
2014).
In a world with increasing energy demands, clean alternatives have become essential for
climate change mitigation and policy making (e.g. the Paris Agreement of 2015). Promising
sources to meet these demands include geothermal energy and heat production. According
to the International Energy Agency (2011), if implemented, developed, and encouraged,
geothermal energy could contribute ca 3.5%(1400 TWh per year) of the global electricity
production by 2050, thus preventing the emission of almost 800 megatons (Mt) of CO
2
per
year. In addition, the generated geothermal heat could contribute ca 3.9%(1600 TWh thermal
energy) of the projected global heat energy by 2050. To meet these targets, the International
Energy Agency recommends, among others, the development of databases, protocols, and tools
for geothermal resource assessment, management, and monitoring.
1.2 Geothermal resources and their assessment
A geothermal resource requires a circulating fluid, heat, and adequate rock permeability to
extract energy. Temperatures of at least 120
◦
C and permeability rates of
≥
50 L/s at depths of
at least 3 km are necessary in Europe for deep geothermal, for example, to achieve economic
power production (Hirschberg et al., 2015; Huenges and Ledru, 2010). Similarly, temperatures
above 70
◦
C at depths of 2-3 km are needed for direct heating purposes (Hirschberg et al.,
2015). Hirschberg et al. (2015) advice, however, to distribute this service to nearby end users
to limit the energy loss due to transportation.
There are two types of geothermal resources (International Energy Agency, 2011):
1
1. Introduction
•
Hydrothermal resources: These systems make use of the natural high rock permeability
and existing aquifers for their economic exploitation. They are common near plate
boundaries and are often associated to active volcanism and seismicity (Hamza et al.,
2008; International Energy Agency, 2011).
•
Hot rock resources: These are hot and dry systems with limited permeability. For their
exploitation to be profitable, their permeability must be first significantly enhanced so
that fluid circulation between injection and production wells can be achieved. The rock
volume is stimulated to create and open fractures by hydraulic fracturing, hence the
common name enhanced geothermal systems (EGS).
The successful exploitation of a geothermal reservoir requires a thorough priory resource
assessment. This involves estimating the underground temperature, the presence and extent of
fluids (mainly for hydrothermal systems), the degree of permeability (e.g. fracturing, faulting,
and anisotropy), and the 3D geometry of the resource (Hirschberg et al., 2015). To this purpose,
several geophysical prospecting surveys are usually a prerequisite in the exploration phase
of a geothermal target. These techniques include, among others, magneto telluric (MT) (e.g.
Benediktsdóttir et al., 2019; Karlsdóttir et al., 2012), gravity (e.g. Portier et al., 2020), and
active and passive seismic (e.g. Martins et al., 2020b; Muksin et al., 2013; Toledo et al., 2020a)
surveys.
1.3 Passive seismic as a tool for exploration and monitoring
of geothermal resources
Passive seismic imaging uses natural and/or induced seismicity or, conversely, the continuously
recorded ambient seismic noise to characterize the 3D geometry of the reservoir and its seismic
properties. Seismic properties such as the compressional P-wave (Vp) velocity, the shear
S-wave (Vs) velocity, and the Vp/Vs ratio can be used as tools to derive lithologies, changes of
fluid content, rock porosity, and temperature of geothermal systems (e.g. Calò and Dorbath,
2013; De Matteis et al., 2008; Jousset et al., 2011; Martins et al., 2020b; Muksin et al., 2013;
Toledo et al., 2020a). These seismic properties are to be assessed, however, in complementarity
with other geophysical and geological methods for robust interpretations. Additionally, in
seismically active geothermal settings, the study of local seismicity helps defining the geometry
of existing faults and possible fluid pathways in the subsurface.
In addition to their imaging potential, passive seismic techniques have proven to be robust
tools for monitoring time-lapse changes of geothermal systems. Monitoring procedures include
the observation of Vp and Vs variations (e.g. Calò and Dorbath, 2013), and changes in micro-
seismicity (M
L≤
2.0) levels detected with sensitive seismic networks. The latter is relevant
during the stimulation phase of an EGS (hydraulic fracturing), as well as in any sort of
fluid injection or re-injection activity which can cause the rise of underground fluid pressure.
Although microseismicity is considered beneficial for reservoir characterization, when the
earthquake magnitudes are large enough, they risk being felt by surrounding communities, or
worse, cause structural damage. Such effects could contribute to a field’s closure due to a lack
of social acceptance. Risk mitigation approaches include, for instance, the implementation of
2
1.4 Objectives and outline of the thesis
traffic light systems where geothermal operations are controlled in attention to the detected
seismicity (e.g. Bommer et al., 2006; Häring et al., 2008).
A more recent approach for monitoring geothermal systems is the study of the variations
in the coda of surface waves retrieved from the cross-correlation of seismic ambient noise
(e.g. Hillers et al., 2015; Sánchez-Pastor et al., 2019). This technique has previously been
successful in monitoring changes in the medium properties of volcanoes and active fault zones
(e.g. Obermann et al., 2013; Sens-Schönfelder and Wegler, 2006), and is particularly useful in
less seismically active areas. In addition, the changes in the coda wave could potentially reveal
aseismic processes which can help understand the underground stress evolution (Bourouis and
Bernard, 2007).
1.4 Objectives and outline of the thesis
This thesis contributes to the efforts of the International Energy Agency (2011) by applying and
extending several existing and novel passive seismic methods in support of the exploration and
monitoring of various geothermal fields. The experiences gained throughout these studies then
bring about a set of recommendations for the geothermal resource assessment and monitoring
of future sites.
The seismology methods explored in this thesis are presented in several chapters and take
part in various peer-reviewed publications. They are summarized in Table 1.1.
Table 1.1: Seismological tools explored in this thesis
Methodology Purpose
Survey design theory for
seismic network construction
and assessment
Exploration and monitoring planning
Local earthquake tomography Exploration
Ambient noise tomography Exploration
Coda wave interferometry Monitoring
The underlying theory and principles of the methods are presented in Part I. Chapter 2
provides an introduction to seismic wave propagation, ray, and inversion theory, Chapter 3
describes the main concepts of the earthquake location problem and survey design theory,
Chapter 4 introduces the main principles for local earthquake tomography, and Chapter 5
presents the concepts for ambient seismic noise tomography and coda wave interferometry.
Then, Part II consists in the application of these techniques to three case studies. They
are outlined as follows:
•
Chapter 6: The study and application of a survey design algorithm for constructing
(Theistareykir - NE Iceland) and evaluating (Reykjanes - SW Iceland) seismic networks
dedicated for microseismicity retrieval (Toledo et al., 2020b).
•
Chapter 7: The use of local seismicity for imaging the Vp and Vp/Vs ratio structures of
a producing geothermal field in Mexico (Los Humeros). Final interpretations were made
taking into account available geological, geophysical, and petrophysical data (Toledo
et al., 2019, 2020a).
3
1. Introduction
•
Chapter 8: The use of seismic ambient noise for imaging the Vs structure and monitoring
temporal velocity changes of a producing geothermal field in Iceland (Theistareykir)
(Toledo et al., 2021).
Finally, Part III discusses the obtained results (Chapter 9) and concludes with recommen-
dations for future studies (Chapter 10).
1.5 List of publications
The list of publications associated to this thesis are:
•
Chapter 6: Optimized experimental network design for earthquake location problems:
Applications to geothermal and volcanic field seismic networks, Journal of Volcanology
and Geothermal Research, 2020, (391) by Tania Toledo, Philippe Jousset, Hansruedi
Maurer, Charlotte Krawczyk (Postprint)
•
Chapter 7: Local Earthquake Tomography at Los Humeros Geothermal Field (Mexico),
Journal of Geophysical Research: Solid Earth, 2020, 125, by Tania Toledo, Emmanuel
Gaucher, Philippe Jousset, Anna Jentsch, Christian Haberland, Hansruedi Maurer,
Charlotte Krawczyk, Marco Calò, Ángel Figueroa (Postprint)
with its associated data publication:
Dataset of the 6G seismic network at Los Humeros, 2017-2018. GFZ Data Services.
Other/Seismic Network, 2019, by Tania Toledo, Emmanuel Gaucher, Malte Metz, Marco
Calò, Angel Figueroa, Joel Angulo, Philippe Jousset, Katrin Kieling, Erik Saenger.
•
Chapter 8: Ambient seismic noise monitoring and imaging at the Theistareykir geothermal
field (Iceland), in preparation, 2021, by Tania Toledo, Anne Obermann, Philippe Jousset,
Arie Verdel, Joana Martins, Kemal Erbas, Anette Mortensen, Charlotte Krawczyk
4
Part I
Methods and concepts
5
2
Seismic wave propagation, ray, and
inversion theory
This chapter provides a brief introduction to the elastic wave equation and the seismic wave
types as described in Shearer (2009) and Bormann et al. (2012). Later, I describe the main
concepts of ray theory following Lee and Stewart (1981) and Rawlinson and Sambridge (2003),
and inverse theory according to Menke (2012). These concepts are used throughout this thesis
to design and qualify seismic networks, locate seismicity in an investigation area, and compute
tomographies.
2.1 The elastic wave equation
Seismic waves can be approximated as elastic waves that travel through the Earth, with
a propagation velocity that depends on the medium’s elasticity and the wave type. For a
continuous medium the equation of motion is written as:
ρ∂2ui
∂t2=∂τij
∂j +fi(2.1)
where
ρ
,
ui
,
τij
, and
fi
correspond to the material density, the displacement, the stress tensor,
and the body force term, respectively. iand jare numbers between 1 and 3 corresponding to
the cartesian directions x, y, and z. Assuming a homogeneous isotropic media, the equation of
motion outside the source region becomes:
ρü= (λ+ 2µ)∇∇ · u−µ∇ × ∇ × u(2.2)
where
λ
and
µ
are the Lamé parameters, and
u
and
ü
are the displacement vector and its
second time derivative, respectively. The first term of Eq. 2.2 contains a divergence or scalar
product (
∇ · u
) which describes a shear and a volume change. The second term contains a
curl or rotation term (
∇ × u
) which represents a pure shear motion (change of shape without
7
2. Seismic wave propagation, ray, and inversion theory
modifying the volume). The displacement vector
u
can be decomposed as the sum of a rotation
free urand a divergence free udterms:
u=ur+ud(2.3)
If we apply the divergence and curl to Eq. 2.2, we obtain:
∂2(∇ · u)
∂2t=λ+ 2µ
ρ∇2(∇ · ur)(2.4)
and
∂2(∇ × u)
∂2t=µ
ρ∇2(∇ × ud)(2.5)
Eqs. 2.4 and 2.5 refer to the solutions of the wave equation for the two body waves types:
the compressional (P-) and the shear (S-) waves. Their velocities are defined as:
Vp=√λ+ 2µ
ρ(2.6)
and
Vs=õ
ρ(2.7)
The P-wave is faster than the S-wave, and is also referred to as the primary wave. The
S-wave is also known as the secondary wave. It can be differentiated as polarized in the
horizontal (SH waves) and vertical planes (SV waves), and travels only through solids. This
property is particularly useful in geothermal contexts, where the identification of fluids and
fluid pathways is necessary for characterizing a prospect reservoir.
The presence of the Earth’s free surface gives way to two surface wave types: the Rayleigh
and the Love waves. Rayleigh waves propagate in the horizontal direction with an elliptical
and retrograde particle motion (P-SV). Love waves are faster than Rayleigh waves and consist
of pure SH waves and a particle motion perpendicular to the direction of propagation. The
amplitudes of both surface wave types decrease with depth and their velocities are slower than
those of body waves.
2.2 The Green’s function
The Green’s functions (G) are the solutions to the wave equation for
δ
-function sources
activated at (x0, t0) and evaluated at a point (x, t). It is expressed by:
∂2G
∂t2(x, t;x0, t0)−c2∆G(x, t;x0, t0) = δ(x−x0)δ(t−t0)(2.8)
where a δ-function is defined as
δ(x) = {∞x= 0
0x= 0 (2.9)
8
2.3 Introduction to ray theory
The Green’s function between two points represents the wave propagation between them
and contains the information of the medium response.
2.3 Introduction to ray theory
The seismic ray method is a high frequency approximation of the wave equation for body waves
propagating in smoothly varying media. Assuming the seismic energy is originated by a point
source (e.g. earthquake), a seismic wave propagates away from such point along wavefronts
(planes perpendicular to the direction of propagation). Seismic rays are then defined as the
normals to such wavefronts and pointing in the direction of the wave propagation. In ray
theory, only one point on the wavefront is tracked rather than the complete wavefield.
For a heterogeneous earth model, travel times between a source and a receiver are obtained
by solving the Eikonal equation describing the wave propagation:
(∇t)2= [s(r)]2(2.10)
where
∇t
is the travel time gradient, s(
r
) represents the medium slowness, and
r
is the
position vector (x, y, z). For an isotropic medium of slowness s(
r
), the travel time tneeded for
a ray to travel from source point A (
rA
=(
xA, yA, zA
)) to receiver point B (
rB
=(
xB, yB, zB
))
along raypath Lis given by:
tAB =∫L
s(r)dl (2.11)
where dl represents the differential path length. The ray equation can be derived from the
Eikonal equation as:
∂
∂l (s(r)∂r
∂l )=∇(s(r)) (2.12)
Eq. 2.12 is typically used to derive the ray propagation path of a seismic wave.
There are several methods to derive ray path geometries to provide accurate travel time
estimates. These include, among others, ray tracing (e.g. Červený, 1987, 2001), finite difference
solutions to the Eikonal equation (e.g. Moser, 1989; Podvin and Lecomte, 1991; Vidale, 1988),
and the application of network/graph theory using Fermat’s principle (e.g. Moser, 1991). In
this work, I summarize the main principles of three ray tracing methods (shooting, bending,
and pseudo-bending) and the finite difference method. These techniques are later used in
Chapter 3 and Chapter 4 to estimate ray path geometries and travel times for earthquake
locations and seismic tomography.
2.3.1 The shooting method
Provided that the medium velocity and source and receiver locations are known, the shooting
method consists in iteratively adjusting the initial projection ray angle (from the source) until
the ray end reaches the receiver as close as possible (Figure 2.1).
9
2. Seismic wave propagation, ray, and inversion theory
Figure 2.1:
Schematic representation of the shooting method. Aand Brepresent the source and
receiver positions, respectively, located in a medium with velocity
V
(
x, z
). The angle projection at
the source of ray 1 is iteratively adjusted until the ray passes as close as possible to the receiver
position (ray 3). Modified from Rawlinson and Sambridge (2003)
For a constant velocity model, the ray path is a straight line that connects the source and
receiver, and the travel time varies linearly with the ray distance. In the case of a layered
model, the ray trajectories follow Snell’s Law at the interfaces between the layers:
sin θi
vi
=sin θr
vr
(2.13)
where
θi
and
θr
are the incident and refracted angles, and
vi
and
vr
are the layer velocities
where the incident and refracted rays are contained.
For the 3D case, the ray paths are obtained by solving the following set of equations
(Sambridge and Kennett, 1990):
∂x
∂t =vsin θicos θa
∂y
∂t =vsin θisin θa
∂z
∂t =vcos θi
∂θi
∂t =−cos θi(∂v
∂x cos θa+∂v
∂y sin θa)+∂v
∂z sin θi
∂θa
∂t =1
sin θi(∂v
∂x sin θa−∂v
∂y cos θa)
(2.14)
where
θi
and
θa
are the incident and azimuthal angles, respectively. The travel time is
then obtained by numerical integration of Eq. 2.11.
2.3.2 The bending method
The bending method (Figure 2.2) consists in iteratively adjusting the ray path geometry until
finding the true ray path which satisfies Fermat’s principle (the ray must follow a minimum
time path).
10
2.3 Introduction to ray theory
Figure 2.2:
Schematic representation of the bending method. Aand Brepresent the source and
receiver positions, respectively, located in a medium with velocity
V
(
x, z
). The geometry of ray 1
is iteratively adjusted until it satisfies Fermat’s principle (ray 3). Modified from Rawlinson and
Sambridge (2003)
For a continuous 3D velocity model, the ray path is obtained by solving a modified version
of Eq. 2.11 (Julian and Gubbins, 1977):
t=∫qB
qA
sFdq (2.15)
where the position vector
r
in Eq. 2.11 is now expressed as a function of qas
r
= x(q) +
y(q) + z(q). Then:
F=dl
dq =√˙x2+ ˙y2+ ˙z2(2.16)
where
˙x
,
˙y
, and
˙z
are the differentials with respect to q. The ray path is then obtained by
solving the Euler-Lagrange system of equations (Julian and Gubbins, 1977):
d
dq
∂
∂˙x(sF) = ∂
∂x (sF)
d
dq
∂
∂˙y(sF) = ∂
∂y (sF)
∂F
∂q = 0
(2.17)
where in this case q = l/L. The system of equations 2.17 is nonlinear but can be linearized
by assuming:
x1(q) = x0(q) + ξ0(q)(2.18)
For an initial ray path
x0
(
q
)that crosses the source and receiver, the equations are now
solved iteratively for perturbation
ξ0
(
q
), such that the estimated ray path
x1
(
q
)is improved
(Julian and Gubbins, 1977).
11
2. Seismic wave propagation, ray, and inversion theory
2.3.3 The pseudo-bending method
Um and Thurber (1987) developed a faster modified version of the bending method. Starting
with a ray with three points linearly interpolated, the middle point is updated such that the
travel time is minimized (Figure 2.3). Then, each line segment is halved and the middle points
are updated once more. This procedure continues until the change in travel time between
iterations satisfies a convergence criterion.
Figure 2.3:
Schematic representation of the pseudo bending method. Aand Brepresent the
source and receiver positions, respectively, located in a medium with velocity
V
(
x, z
). First, an
initial guess with three points is provided (ray 0). Then, the center of ray 0 is updated to better
satisfy the ray equation (ray 1). Each line segment is halved and their mid points updated once
more (ray 2). This process is carried out iteratively until a convergence criterion is satisfied (ray
3). Modified from Rawlinson and Sambridge (2003)
2.3.4 The finite difference method
The finite difference consists in progressively integrating travel times along the velocity nodes
of a parameterized medium. Consider, for example, the Eikonal equation for the 2D case:
(∂t
∂x)2
+(∂t
∂z )2
= [s(x, z)]2(2.19)
If the travel time to source point A(Figure 2.4) is
t0
, then the travel time to points
Bi
can
be calculated as (Vidale, 1988):
tBi=t0+h
2(sBi+sAi)(2.20)
where his the even distance between the nodes, and
sBi
and
sAi
are the slowness at points
Bi
and
Ai
, respectively. If the travel times to
A
(
t0
),
B1
(
t1
), and
B2
(
t2
) are known, then the
travel time to
C1
(
t3
) can be approximated by substituting the following differential terms
into Eq. 2.19:
∂t
∂x =1
2h(t1+t3−t0−t2)
∂t
∂z =1
2h(t2+t3−t0−t1)
(2.21)
12
2.4 Introduction to inverse theory
Figure 2.4:
The finite difference method proposed by Vidale (1988) to find the first arrival travel
time field assuming a continuous velocity medium. See text for details. Modified from Rawlinson
and Sambridge (2003)
Finally, the travel time in C1(t3) is given by:
t3=t0+√2(h¯s)2−(t2−t1)2(2.22)
where
¯s
is the mean velocity of the four nodes. The travel times to the next set of grid
points is determined by progressively solving equations along squares of increasing size around
the source point. This method is called the expanded square formalism. For the extended 3D
derivation see Vidale (1990).
Unlike ray tracing methods, this approach does not explicitly determine the ray path. One
common way to obtain it is to first compute the travel time gradient
∇t
across the medium
(Podvin and Lecomte, 1991), and then follow it back from receiver to source (backtracing).
2.4 Introduction to inverse theory
Inverse theory is a set of mathematical methods used to derive useful information of the
physical world from observed data (Menke, 2012). In relation to geothermal exploration, this
information includes accurate earthquake locations and the seismic structure of a geothermal
field.
In contrast to the forward problem, where data is predicted using a known model and
model parameters:
model parameters →model →data prediction
the inverse problem aims to estimate some model parameters from observed data:
data →model →model parameters
In matrix form, the linear discrete notation can be written as:
Forward problem: d=Gm (2.23)
13
2. Seismic wave propagation, ray, and inversion theory
Inverse problem: m=G−gd(2.24)
where
d
,
m
, and
G
denote the data vector, the model parameters, and the model,
respectively.
G
corresponds to the true physical processes in the subsurface when it relates
the true model parameters
mtrue
with
dobs
. Similarly, a set of estimated data
dest
can be
calculated using model parameters mest.
There are several approaches for solving the inverse problem. Back-projection techniques
(e.g. Gilbert, 1972; Gordon et al., 1970), gradient methods (e.g. Eberhart-Phillips, 1993; Menke,
2012; Thurber, 1983), and global optimization (Mosegaard and Sambridge, 2002; Sambridge
and Mosegaard, 2002) are among common inversion techniques. In this thesis, I only introduce
the damped least squares approach (gradient method), given it is the inversion technique used
in Chapter 6 and Chapter 7.
2.4.1 The linear inverse problem
The usual procedure to solve the inverse problem is to iteratively compute
dest
, compare it
to
dobs
, and update
mest
such that the misfit between
dest
and
dobs
is minimized (Tarantola,
2005).
Then mest is given by:
mest =G−gdobs (2.25)
where
G−g
is the generalized inverse (Menke, 2012). In a purely over-determined problem
(more data points than model parameters), it is defined as:
G−g= (GTG)−1GT(2.26)
where GTis the transpose of G.
In the case of an under-determined problem (more model parameters than data points):
G−g=GT(GGT)−1(2.27)
Underdetermined problems have infinite number of solutions with no inconsistencies.
If a problem is simultaneously over- and under-determined due to more data points than
model parameters and trade-offs between the model parameters, it is called a mixed-determined
problem. The solution to these problems is:
mest = (GTG+γI)−1GTd(2.28)
where
γ
corresponds to a damping factor (Levenberg, 1944; Marquardt, 1963), and Iis
an identity matrix. The reader is referred to Menke (2012) and Lee and Stewart (1981) for
extended derivations. Eq. 2.28 is also known as the damped least squares solution.
14
2.4 Introduction to inverse theory
2.4.2 Nonlinear inversion
In the case of nonlinear functions
g
=
g
(
m
), the inverse problem can be solved by first
linearizing g. This is achieved by expanding it into Taylor series and omitting the higher order
terms. Then the linearized set of functions is:
g(m)i=g(minit)i+Gik + ∆mk(2.29)
where
i
and
k
are the indexes for the data points and model parameters, respectively, and
∆
mk
=
mk−minit
k
. In this case, Gis also known as the Jacobi matrix and it contains the
sensitivities or partial derivatives with respect to the model parameters.
The inverse problem is then solved by iteratively adjusting vector ∆
m
such that the
estimated and observed data are as close as possible. In other words, starting the first iteration
with minit:
mest
i=0 =minit (2.30)
the next iterations are given as:
mest
i+1 =mest
i+G−g∆d(2.31)
where ∆d=dobs −g(mest).
2.4.3 Analysis of the solution robustness
There are several methods to assess the quality of the solution post-inversions. Within inversion
theory, these include the analysis of the data resolution matrix, the model resolution matrix,
the model covariance matrix, the spread function, among others (Menke, 2012).
2.4.3.1 Data resolution matrix
Starting with the forward calculation of
dest
, one can retrospectively analyze how well it fits
the data dobs:
dest =Gmest =G[G−gdobs]=[GG−g]dobs =Ndobs (2.32)
where the square matrix
N
is also known as the data resolution matrix. If for example
N
=
I
, then
dest
=
dobs
, and the prediction error is zero. The diagonal elements of the data
resolution matrix are also called the data importance. They indicate how much weight a datum
has for its own prediction.
It is worth noting that
N
depends only on
G
, which describes the model and the experiment
design. Therefore, this matrix can be explored beforehand in the experiment design phase to
maximize the benefit of the recovered data.
15
2. Seismic wave propagation, ray, and inversion theory
2.4.3.2 Model resolution matrix
The model resolution matrix characterizes whether the model parameters can be resolved
independently. Starting with the inverse formulation, mest and mtrue are related by:
mest =G−gdobs =G−g[Gmtrue]=[G−gG]mtrue =Rmtrue (2.33)
where the square matrix
R
is also known as the model resolution matrix. The diagonal
values of
R
indicate the resolution of each model parameter and range from 0 to 1. If
R
=
I
,
each model parameter is uniquely determined. Non-zero off-diagonal elements in the matrix
indicate trade-offs between the model parameters.
2.4.3.3 Spread function
To better understand the trade-offs between the different model parameters, one can have a
closer look at the off-diagonal elements of
R
. The spread function measures the size of these
diagonal elements and it is given by:
spread(R) =
M
∑
i=1
M
∑
j=1
w(i, j)R2
ij (2.34)
where for the (i, j) element of matrix
R
,
w
(
i, j
)corresponds to a weighting factor that
measures its physical distance with respect to the diagonal element. When
R
=
I
, then
spread
(
R
)
= 0.
2.4.3.4 Model covariance matrix
The covariance matrix relates how the data errors are "mapped" into the calculated model
parameters
mest
. Assuming uncorrelated data with equal variance
σ2
d
, the model covariance
for the least squares solution is given by:
cov m=σ2
d[GTG]−1(2.35)
If the data errors have a Gaussian distribution, then the square root of the diagonal
elements of cov mcorrespond to the errors in the model parameters.
16
3
Earthquake location and survey design
The deployment of local seismic networks is a common practice to retrieve, monitor, and
mitigate natural and/or induced seismicity among several applied fields including underground
storage, oil and gas, and geothermal energy exploitation. Although considerable efforts
are dedicated to the development of standardized data-acquisition and inversion techniques,
adequate survey design analysis are rarely performed prior to the deployment of a network.
Nevertheless, the success of a microseismicity study relies on well constrained event locations,
which can be improved beforehand with the network configuration choice.
This chapter introduces the main concepts of earthquake location and survey design to
construct and qualify optimal seismic networks for microseismicity retrieval.
3.1 Basic principles of earthquake location
Hypocenter determination is an ongoing field of research given its potential to provide
information on the active processes in the subsurface (e.g. Maxwell, 2009; Wilkinson et al.,
2004). A wide range of techniques have been proposed for the earthquake location problem
including: ray based (Aki and Richards, 1980; Kissling et al., 1994), grid search methods
(Lomax, 2005; Sambridge and Kennett, 1986, 2001), wave-field back-propagation (McMechan,
1982; Witten and Artman, 2011), waveform stacking (Cesca and Grigoli, 2015; Kao and Shan,
2007), among others.
Ray based methods are, however, more commonly used due to their simplicity, fast
computation, and available inversion packages. Many of these methods are based on Geiger’s
algorithm (Geiger, 1912), where the source location is derived by carrying out an inversion that
iteratively minimizes observed and synthetic arrival times of body waves (Aki and Richards,
1980). The locations accuracies rely, among others, on the network geometry, the number of
available phases, and the accurate picking of these wave phases (Pavlis, 1986).
17
3. Earthquake location and survey design
3.1.1 Earthquake location by iterative methods
The location of an earthquake is a classical nonlinear problem which typically involves the
adjustment of model parameters
mest
(event position coordinates
xo
,
yo
,
zo
, and origin time
to
) such that they satisfy the observed data
dobs
(P- and S- wave arrival times
tp
and
ts
) in
relation to a mapping operator G. The damped least squares solution is given by:
mest =m0+ (GTG+γI)−1GT∆d(3.1)
Oftentimes, the square matrix
GTG
is near singular and the inversion stability depends on
its ability to be inverted. In the event location problem, kernel
G
is built with the sensitivities
of travel times with respect to the hypocentral coordinates -source point A (x
A
, y
A
, z
A
)- and
the origin time (Lee and Stewart, 1981):
G=
∂t
∂x ⏐⏐⏐A=−sdx
dl ⏐⏐⏐A
∂t
∂y ⏐⏐⏐A=−sdy
dl ⏐⏐⏐A
∂t
∂z ⏐⏐⏐A=−sdz
dl ⏐⏐⏐A
∂t
∂t0⏐⏐⏐A= 1
(3.2)
where:
cos αA=dx
dl ⏐⏐⏐⏐A
; cos βA=dy
dl ⏐⏐⏐⏐A
; cos γA=dy
dl ⏐⏐⏐⏐A
(3.3)
αA
,
βA
, and
γA
are also known as the instantaneous direction angles of the ray at point
A. scorresponds to the medium slowness at point A and dl represents the differential ray
path length. The sensitivities of matrix
G
are directly related to the survey design and are
calculated in this work using Podvin and Lecomte (1991) finite-difference time-field calculations
and a back-raytracing routine (See Section 2.3).
3.2 Experimental survey design
The main goal of experimental survey design is the selection of a network geometry (or data
subset) that would maximize the information (benefit) gathered from the inversions at a
minimum acquisition and/or computational cost (e.g. Maurer et al., 2010).
The benefit of an inversion can be directly quantified with the information or eigenvalue
content (
λi
:
i
= 1
, ..., N
) of matrix
GTG
(Curtis et al., 2004). Errors in the data propagate
into
mest
with
λi
factors. In other words, the propagation error can become very large if a
λi
is very small, making the inversion unstable altogether. Mathematically, the goodness of
matrix GTGcan, therefore, be expressed in terms of non-zero eigenvalues.
18
3.2 Experimental survey design
From Section 2.4.3.4, we know that the inversion accuracy is given by the model covariance
matrix:
cov m=σ2
d[GTG]−1(3.4)
In the earthquake location problem,
σ2
d
corresponds to the variance of onset-time
determination. The eigenvalues of matrix (
GTG
)
−1
provide the shape of the location confidence
ellipsoid, and the confidence volume is proportional to 1/det(
GTG
) (Buland, 1976; Flinn,
1965). Previous works for determining optimum network geometries (Kijko, 1977; Rabinowitz
and Steinberg, 1990) rely on the confidence ellipsoid as an indicator for goodness of network
performance (Hardt and Scherbaum, 1994).
3.2.1 The D-criterion
A wide range of options have been proposed to quantify the goodness of a dataset (Curtis,
1999a; Maurer et al., 2010). In this work I base this quantity in terms of
GTG
, also known
as the approximate Hessian matrix. Not only is this matrix contributing to the solution’s
model covariance (and hence on the event location precision), but its ability to be inverted
determines the success of model parameter reconstruction.
One popular quality measure for the earthquake location problem is the determinant of
GTG
, also known as the D-criterion. The main benefit of this measure is its sensibility to the
entire eigenvalue spectrum (Hardt and Scherbaum, 1994; Kijko, 1977; Rabinowitz and Steinberg,
1990). Several quality measures based on the D-criterion have been proposed and tested by
e.g. Curtis (1999a) and Maurer et al. (2010). In this work I chose a modified version of the
multi-source function defined by Rabinowitz and Steinberg (1990) as:
Θ =
N
∑
i=1
γilog (1
det(GT
iGi) + δ)(3.5)
where Nstands for the total number of earthquakes, and
γi
corresponds to a weighting factor
assigned to each event i. In a Bayesian framework, weights
γi
can also be considered as prior
probabilities for the hypocenters (Chaloner and Verdinelli, 1995). In this study the weights
reflect a combination of a prior probability and an event importance (Steinberg and Rabinowitz,
2003). A small value
δ
is introduced in Eq. 3.5 to stabilize the optimization procedure for cases
where the determinant would be zero (under-determined case). By minimizing the objective
function Θone would in some sense also minimize the confidence volumes of the studied
seismic events.
3.2.2 Optimization approaches for survey design
Having chosen a quality measure, the remaining components to construct the sensitivities of
matrix G(Eq. 3.2) are:
1. Target earthquake locations
These can be defined by analyzing the previous seismological history in a target region.
2. A representative velocity model
19
3. Earthquake location and survey design
3. Potential sensor locations
The potential deploying areas are defined by detectability (e.g. minimum detecting
magnitudes) and accessibility.
Then, the aim of survey design is to find the optimal source-receiver configuration, such
that the quality measure Θis minimized. There are several approaches for the optimization
including the use of global optimizers like simulated annealing (e.g. Kraft et al., 2013), Bayesian
statistical experimental design (e.g. Coles and Curtis, 2011a), and sequential survey design
(e.g. Curtis et al., 2004; Guest and Curtis, 2009). The latter, although does not guarantee
global optimality, is flexible and faster to compute and allows addressing benefit (Θ)/cost
(number of stations) concepts.
Sequential design consists in stepwise removing (destructive) or adding (constructive)
seismic stations at a location that effectively minimizes Θ. In a destructive sequential design
framework,
G
is first constructed with of all possible sensitivity entries, namely all detecting
station positions. Then, Θvalues are calculated after removing each recording sensor. These
values are then compared and the position associated to the minimum Θvalue (possibly
redundant information) is removed. This process is carried out in a step-wise fashion depleting
the potential deploying area. In the end, each station position has an assigned "order" of
importance number.
To demonstrate the use of this scheme, Figure 3.1a shows the construction of a 5 station
network for locating a single event at 3 km depth (pink point). After defining a detection
radius (dashed red circle), the deploying area is fully populated with potential station locations
(Figure 3.1b). The station positions are then removed in each step when effectively minimizing
the objective function Θ. Notice how in the station placement, locations close and far away
from the seismic source have higher importance (must be located first). In fact, the geometry
in Figure 3.1a resembles a quadripartite, which is also seen in Rabinowitz and Steinberg (1990)
and Hardt and Scherbaum (1994). Figure 3.1c shows the benefit/cost curve of the experiment.
Note how Θis vastly reduced after installing only four stations. Adding more stations after
that also reduces the objective function, however in a much smaller proportion.
This destructive sequential survey design approach is applied in Chapter 6 to extend a
seismic network dedicated for the microseismicity monitoring of a producing geothermal field
(Theistareykir in NE Iceland), and to qualify the geometry of an already deployed temporary
network (Reykjanes in SW Iceland).
20
3.2 Experimental survey design
a)
0 20 40 60 80
x (km)
0
10
20
30
40
50
60
70
80
y (km)
1
1.5
2
2.5
3
3.5
4
4.5
5
23
4
1
5
b)
0 20 40 60 80
x (km)
0
10
20
30
40
50
60
70
80
y (km)
10
20
30
40
50
60
70
80
90
100
110
c)
0 20 40 60 80 100
Number of stations placed
-5
0
5
10
15
20
25
30
Event design quality contribution [ event]
02468
0
1
2
3
4
5
Figure 3.1:
Survey design example for an event at 3 km depth with M
L
0.8. a) 5 stations setup.
b) 115 stations setup. The colorbar shows the order of placed stations. c) Design quality Θof the
survey setup for each number of placed stations. The dashed red line represents station point 4,
and the horizontal dashed black line the limit of Θ= 3.4 (see figure inset). Taken from Toledo
et al. (2020b)
21
4
Principles for local earthquake
tomography
Local earthquake tomographies are classical coupled inverse problems, where the earthquake
location and 3D velocity models are derived using the arrival times of body waves (P- and S-
waves). They are typically obtained by first computing the joint inversion of a 1D velocity
model and earthquake locations. Then, this so called minimum 1D velocity model is used as
an initial estimate for a 3D joint inversion (e.g. Muksin et al., 2013; Thurber, 1983).
In this chapter, I first describe the formulation for the coupled 1D velocity model and
earthquake location problem according to Kissling et al. (1994). Then I introduce the 3D local
earthquake tomography formulation following Rawlinson and Sambridge (2003) and Thurber
(1983).
4.1 The coupled 1D velocity model and earthquake location
problem
The travel times of body waves
t
can be expressed as a nonlinear function of station coordinates
st, the hypocentral parameters h, and the velocity model v:
t(st,h,v)(4.1)
As described in Chapter 2, an a priori velocity model can be used to calculate synthetic
travel times
test
. The difference between
tobs
(observed travel times) and
test
(∆
t
) can then
be expanded as a function of the difference between estimated and true model parameters.
Applying a first-order Taylor expansion to Eq. 4.1 (Kissling et al., 1994):
∆t=tobs −test =
4
∑
k=1
∂t
∂hk
∆hk+
N
∑
n=1
∂t
∂vn
∆vn+e(4.2)
23
4. Principles for local earthquake tomography
where ∆
hk
and ∆
vn
are the hypocentral and velocity model parameter perturbations,
respectively. In matrix notation, the coupled relation between hypocenter and velocity model
parameters can be written as (Kissling et al., 1994):
∆t=tobs −test =Hh+Mm+e(4.3)
where:
H: matrix containing the partial derivatives of travel times with respect to the
hypocentral parameters
M: matrix containing the partial derivatives of travel times with respect to the velocity
model parameters
h: vector of hypocentral parameter perturbations
m: vector of velocity parameter perturbations
e: vector of travel time error
Then, Eq. 4.3 can be solved using the damped least squares inversion method detailed in
Section 2.4.1 and the travel times computed with the shooting method described in Section
2.3.1. This is the approach adopted in the Velest software (Kissling et al., 1994; Maurer, 1993).
Velest calculates the damped least squares solution for a set of earthquakes and a multilayered
velocity model of fixed thicknesses. A scalar term associated to each station is also provided
in the inversion to account for deviations due to near surface velocities below the stations
(station corrections).
To avoid being trapped in a local minimum, Kissling et al. (1994) advise the computation
of several inversions using different initial velocity models. Finally, the minimum 1D velocity
model corresponds to the final model with lowest associated RMS (root-mean-square) error.
4.2 3D travel time tomography
After obtaining the minimum 1D velocity model, the classical steps for retrieving 3D
tomographic images are (Rawlinson and Sambridge, 2003):
•Model parametrization
•Forward calculation
•Inversion
•Solution quality
The software I used to compute a local earthquake tomography for Los Humeros geothermal
field (Mexico) in Chapter 7 is called SIMUL2000 (Eberhart-Phillips, 1990; Eberhart-Phillips
and Michael, 1998; Evans et al., 1994; Thurber, 1983).
4.2.1 Model parametrization
Prior to an inversion, a region must be discretized into smaller cells or grid points
(model parameters) from which the final velocity values can be computed. Various model
24
4.2 3D travel time tomography
parametrization types include constant velocity blocks, velocity node grids, and triangulated
velocity grids (Figure 4.1). To calculate the velocity values at any point (x, y, z), SIMUL2000
uses a grid of velocity nodes (Figure 4.1b) interpolated with the function (Thurber, 1983):
V(x, y, z) =
2
∑
i=1
2
∑
j=1
2
∑
k=1
V(xi, yj, zk)(1−⏐⏐⏐⏐
x−xi
x2−x1⏐⏐⏐⏐)(1−⏐⏐⏐⏐
y−yj
y2−y1⏐⏐⏐⏐)(1−⏐⏐⏐⏐
z−zk
z2−z1⏐⏐⏐⏐)(4.4)
where xi,yj, and zkcorrespond to the eight grid points that surround point (x, y, z).
Then, to maximize the recovered information, an adequate model parametrization is
suggested by Evans et al. (1994) and Husen et al. (2000, 2003) as a grid with as small as
possible node spacing, that maintains a fairly homogeneous ray density.
Figure 4.1:
Various types of model parametrization: a) constant velocity blocks, b) grid of
velocity nodes, c) triangulated velocity grid for constant velocity gradient cells (White, 1989).
Taken from Rawlinson and Sambridge (2003)
4.2.2 Forward and inverse calculations
Similar to the 1D model case, the travel time residuals of the linearized system can be written
as (Thurber, 1983):
∆t=tobs −test =
4
∑
k=1
∂t
∂hk
∆hk+
N
∑
n=1
∂t
∂vn
∆vn+e(4.5)
where in this case the model parameters v
n
are the nodes of a 3D velocity grid. The
sensitivities of travel times with respect to the hypocentral parameters (
∂t/∂hk
) are given by
Eq. 3.2. The partial derivatives of travel times with respect to the velocity parameters involve
the integrals along the ray path:
∂t
∂vn
=∫station
source
−{1
V(x, y, z)}2∂V (x, y, z)
∂vn
dl (4.6)
where
vn
is the nth velocity parameter and dl is a ray segment. In terms of slowness
sn= 1/vn;S(x, y, z)=1/V (x, y, z)and dividing the ray path into Msegments:
∂t
∂sn
=
M
∑
m=1
∂S(xm, ym, zm)
∂sn
L(4.7)
25
4. Principles for local earthquake tomography
where Lis the ray length, (
xm, ym, zm
) is the midpoint of the mth path segment, and
∂S/∂sncan be calculated using Eq. 4.4.
Ray geometries in Chapter 7 are obtained using the pseudo-bending method (Um and
Thurber, 1987) described in Section 2.3.3. SIMUL2000 uses the damped least squares approach
to solve the inverse problem (Section 2.4.1). Finally, the tomography quality in Chapter 7 is
assessed using a synthetic checkerboard test and a resolution matrix analysis (Section 2.4.3).
26
5
Ambient seismic noise tomography
and coda wave interferometry
In previous chapters I have mainly discussed concepts of classical earthquake seismology. These
techniques are, however, restricted to seismically active regions. Good resolution of a local
earthquake tomography is, for example, limited to areas with even ray coverage (homogeneous
distribution of local earthquakes and seismic stations). In practice, an adequate ray coverage
is difficult to control, especially in aseismic regions. Ambient seismic noise (AN) techniques
offer suitable alternatives to study these regions and increase the resolution by turning the
seismic stations into (virtual) sources.
In this chapter I provide an introduction to the origins of ambient noise and the
reconstruction of Green’s functions between receiver pairs. Then I describe the main principles
for ambient noise tomography (ANT) and ambient noise methods used for monitoring purposes
(CWI, coda wave interferometry).
5.1 Origins of ambient noise
The ambient noise field is generated by a wide range of forces of both anthropological and
natural origin. The sources producing the ambient noise field vary depending on the frequency
range under study (Bormann et al., 2012; Nakata et al., 2019).
At higher frequencies (1-10 Hz), the ambient noise is generally human-generated ("cultural"
noise) (e.g. Campillo et al., 2011; McNamara and Buland, 2004). Urban sources include cars,
trains, electrical grids, and machinery that operate in the neighborhood of a recording seismic
station. Other natural short-period noise sources include glacier calving (O’Neel et al., 2007)
and the effects of wind on the Earth’s surface (Withers et al., 1996).
Intermediate frequencies (0.03-1 Hz) are primarily dominated by ocean microseism (e.g.
Bromirski and Gerstopft, 2009; Díaz, 2016; Gutemberg, 1936). However, the noise in this
period range can also be affected by extra-tropical storms and tropical cyclones (Ebeling and
Stein, 2011; Sufri et al., 2014), and the presence of sea ice (Anthony et al., 2014; Grob et al.,
27
5. Ambient seismic noise tomography and coda wave interferometry
2011; Stutzmann et al., 2009). Two prominent peaks in this spectrum are also known as the
primary (0.05-1 Hz) and the secondary (0.1-0.3 Hz) microseism peaks. These peaks are mainly
dominated by fundamental mode surface waves of still debatable origin (Landès et al., 2010).
Finally, long period signals (0.002-0.03 Hz) are generally attributed to ocean infragravity
waves also called the Earth’s Hum. These waves are produced by storm-forced, shoreward-
directed winds (Ardhuin et al., 2015; Bromirski and Gerstopft, 2009; Nakata et al., 2019; Webb,
2007).
Given that oceanic and atmospheric processes have a strong influence on the ambient
seismic noise, it is not surprising that the ambient noise also experiences seasonal variations
(Landès et al., 2010).
5.2 Green’s function reconstruction
This section outlines the main concepts of the Green’s function retrieval using cross-correlation
and time reversal principles (Campillo and Paul, 2003; Derode et al., 2003a,b; Wapenaar, 2004;
Wapenaar and Fokkema, 2006). The description and analogies in this section are based on the
thesis of Obermann (2014).
Consider two receivers Aand B, and a source Cplaced in an inhomogeneous medium
(Figure 5.1). The signal emitted by source C(
e
(
t
)) is recovered in receivers A(
SA
(
t
)) and B
(
SB
(
t
)) as the convolution (*) of the signal with the impulse response of the medium (Green’s
function) between Aand C(hAC(t)) and Band C(hBC(t)):
SA=e(t)∗hAC(t)
SB=e(t)∗hBC(t)(5.1)
Figure 5.1:
Illustration of the time reversal principle. a) Point Cis a source that emits a signal
recorded at Aand B. b) Point Bemits a signal that is mirrored by Cand recorded by A. Triangles
mark the receiver positions, and the stars correspond to the source locations. Modified from
Obermann (2014).
28
5.2 Green’s function reconstruction
The correlation CAB between the signals recorded at Aand Bcan be then written as:
CAB(τ) = SA(t)∗SB(−t)
CAB(τ) = hAC (t)∗hBC(−t)∗f(t)(5.2)
where τis the correlation time and f(t)is given by:
f(t) = e(t)∗e(−t)(5.3)
By the principle of source-receiver reciprocity we know that the signal emitted from Bto
Cis identical to the signal travelling from Cto B. Therefore, hBC(t) = hCB(t)and:
CAB(τ) = hAC (t)∗hCB(−t)∗f(t)(5.4)
If we consider the case of Figure 5.1b where the point Bis now the source position and C
is a mirror point, the signal recorded at Awill be given by:
SA(t) = hBC(−t)∗hAC (t)(5.5)
where Eq. 5.2 and Eq. 5.4 are still dependent on point C.
The time reversal principle states that the back-propagation of a mirrored (in time) signal
recorded at a receiver concentrates back at the original source. If we simulate a series of points
Ci
(scatterers/mirror points) surrounding Aand B, and point Acorresponding to a source
emitting a signal in all directions, then the points
Ci
and
B
will record
hACi
(
t
)(and re-emit
hACi
(
−t
)) and
hAB
, respectively. If the number of mirror points
Ci
is very large, we can
assume that there is a time reversed wave that back-propagates to Aand is recorded at Bas
hAB
(
−t
). That is to say, this time reversal experiment is given by the sum of Green’s functions
between A and B in positive and negative lag times and is analogous to the cross-correlation
definition (Derode et al., 2003a,b; Obermann, 2014):
∑
Ci
hACi(t)∗hCiB(−t) = hAB(t) + hAB(−t)(5.6)
This translates in practice to the reconstruction of Green’s functions between different
receiver pairs from the cross correlation of ambient noise records (Campillo and Paul, 2003;
Wapenaar, 2004; Wapenaar and Fokkema, 2006). The reconstruction of the Green’s function
holds if the noise sources are evenly distributed around the receivers, and if the medium is
highly heterogeneous, such that the scatterers can act as mirrors or secondary sources.
In practice, the noise sources are not evenly distributed resulting many times in asymmetrical
correlograms (e.g. different amplitudes for the causal and acausal parts). This behavior implies
that the correlations have not converged to the Green’s functions. Hadziioannou et al. (2009)
points out, however, that a full convergence is not necessary for monitoring purposes.
In addition, the ambient noise wavefield is also "polluted" by the signal of earthquake
sources which do not comply with the requirements of Green’s function retrieval. To remove
these signals, and enhance the Green’s functions recovery, several authors propose different
pre-processing and stacking schemes. Some schemes include (Nakata et al., 2019): the
averaging of causal and acausal parts of correlograms, spectral whitening, time domain running
29
5. Ambient seismic noise tomography and coda wave interferometry
averages, frequency domain normalization (e.g. Bensen et al., 2007; Groos et al., 2012), one-bit
normalization (e.g. Cupillard et al., 2011; Hanasoge and Branicki, 2013; Larose et al., 2004;
Shapiro and Campillo, 2004), phase weighted stacking (e.g. Baig et al., 2009; Schimmel and
Paulssen, 1997; Schimmel et al., 2011), directional balancing (Curtis and Halliday, 2010),
Welch’s method of overlapping time windows (Seats et al., 2012; Welch, 1967), the application of
curvelet denoising filters (Stehly et al., 2011), and sequences of selection and noise suppression
filters (e.g. Boué et al., 2014; Nakata et al., 2015).
There are three main lines of research based on the study ambient noise: noise-based
seismic imaging, monitoring the continuous changes in the medium properties, and studies of
the spatio-temporal distribution of seismic sources. In this thesis, I apply methods for the first
two applications. Hence, their fundamentals are outlined in the next sections.
5.3 Ambient noise travel time surface wave tomography
This section gives an overview of seismic noise-based surface wave imaging based on the work
of Nakata et al. (2019).
The first ideas for using ambient noise for the purpose of imaging were introduced by Aki
(1957) and Claerbout (1968). However, the potential of this technique was not fully exploited
until the improvement of computational and storage capabilities. Sabra et al. (2005a); Shapiro
and Campillo (2004) were the first to extract surface waves from the cross-correlation of
ambient noise, which led to the first applications of noise-based passive seismic imaging in
California (Sabra et al., 2005b; Shapiro et al., 2005). Since then, this technique has been
widely exploited for imaging at various scales (e.g. Bensen et al., 2008; Mordret et al., 2015;
Obermann et al., 2016) and more recently for geothermal exploration by Granados et al. (2020);
Lehujeur et al. (2017); Martins et al. (2020b); Planès et al. (2020).
As described in the previous section, the Green’s function reconstruction holds if the
noise sources are evenly distributed around a medium, which is typically not the case in the
real world. As a matter of fact, most of the noise sources (atmospheric and ocean driven)
are located at the Earth’s surface. This results in the dominant reconstruction of surface
waves (mainly their fundamental modes) from the cross-correlations of ambient noise. The
inhomogeneous distribution of noise sources contribute to asymmetric correlograms (even for
the surface waves), which leads to difficulties in extracting their amplitude information (Stehly
et al., 2006). However, Garnier and Papanicolaou (2009) have shown that the travel time of
these waves can be effectively estimated even if the Green’s function have not fully converged.
Given that the main information recovered from cross-correlations are surface waves, it
is not surprising that the primary application for imaging is the ambient noise surface wave
tomography (ANSWT). Having obtained the travel time paths (N(N-1)/2) from Nstations
(virtual sources), tomographies can be obtained using traditional ray methods (Section 2.3
and Section 2.4.1).
30
5.3 Ambient noise travel time surface wave tomography
5.3.1 Properties of Surface waves
Surface waves propagate along the surface with their amplitudes decaying with depth.
Assuming, for example, a surface wave
usw
(
x, z, t, ω
)at a single frequency propagating in the
xdirection (Nakata et al., 2019):
usw(x, z, t, ω)≈ξ(z, ω) exp[i(ωt −k(ω)x)] = ξ(z, ω) exp[iω(t−x/C(ω))] (5.7)
where t,
ω
,
u
,
k
, and
ξ
correspond to time, frequency, depth, displacement, wavenumber,
and the eigenfunction representing the wave amplitude decay with depth, respectively. The
phase velocity C(ω)is given by:
C(ω) = ω
k(ω)(5.8)
and the group velocity U(ω)by:
U(ω) = (∂k(ω)
∂ω )−1
(5.9)
with both velocities being related by
U(ω) = C(ω)
1−ω
C(ω)
∂C
∂ω
(5.10)
Dispersion is an important property of surface waves, with wavenumbers (
k
) being dependent
on the frequency (
ω
) (Levshin et al., 1989). This translates in the energy of surface waves being
concentrated at the top-most layers, where
ξ
(
z, ω
)is largest (typically reaching a thickness of
half a wavelength). Higher frequencies sample the shallow subsurface, while larger frequencies
reach deeper levels. This behavior leads to the possibility of using surface group and phase
velocities at different frequencies (or periods) to constrain velocities at different depths.
For a single receiver pair, it is possible to measure 4 types of dispersion curves: phase
and group velocity propagations of Love and Rayleigh waves. The choice of the different
components account for different wave types. There are several ways to measure the dispersion
curves, with the frequency time analysis (FTAN Levshin et al., 1989) being a popular choice.
5.3.2 Ambient noise surface wave tomography
The most standard steps of ANSWT are (Nakata et al., 2019):
1. Pre-processing of the collected continuous seismic data
2. Cross-correlation computation between different station pairs
3.
Measuring group and/or phase travel times from the causal and acausal parts of
correlograms ZZ, RR, RZ, ZR for Rayleigh waves and TT for Love waves
4. Quality control and travel time selection prior to the inversions
5.
2D surface wave tomography: frequency dependent group and/or phase velocity maps
for Rayleigh and/or Love waves
31
5. Ambient seismic noise tomography and coda wave interferometry
6.
1D inversion of regionalized dispersion curves at every station location to construct a
final 3D Vs model. This step is also called time to depth conversion.
These are the steps also adopted in Chapter 8 to image the Theistareykir geothermal field
in Iceland, which has a limited earthquake-related ray coverage.
5.4 Noise-based monitoring
This section gives an overview of principles of seismic noise-based monitoring based on the
work of Nakata et al. (2019).
An application of seismic interferometry is the monitoring of structural and velocity changes
by measuring the distortions of so called "coda" waves (Sens-Schönfelder and Wegler, 2006;
Snieder, 2002). This technique is commonly known as coda wave interferometry (CWI) and
has been successfully applied in volcano monitoring (e.g. Brenguier et al., 2008b; Obermann
et al., 2013), observations of environmental conditions (e.g. Hillers et al., 2014; Mordret
et al., 2016), earthquake related observations (e.g. Brenguier et al., 2008a; Wegler and Sens-
Schönfelder, 2007), geotechnical applications (e.g. Planès and Larose, 2013), and more recently
for geothermal field monitoring (e.g. Hillers et al., 2015; Obermann et al., 2015; Sánchez-Pastor
et al., 2019; Taira et al., 2018).
The principle was first introduced by Poupinet et al. (1984) to measure velocity changes
from the coda of repeatable earthquakes (doublets or multiplets). They compared different
seismic events that occurred on the Calaveras Fault in California and noticed small phase shifts
in time which can be explained by velocity changes in the medium. The time-domain version
of this concept was later proposed by Snieder et al. (2002). This technique, though powerful,
requires the acquisition of repeatable signals (sources), which is oftentimes non feasible (e.g.
earthquakes and use of explosives). With the introduction of seismic interferometry the
technical and logistic efforts required to obtain repeating signals could finally be circumvented
thus allowing the use of ambient noise also for monitoring (Sens-Schönfelder and Wegler,
2006).
There are two common techniques used to quantify the velocity changes from coda waves:
the moving-window cross-spectral analysis introduced by Poupinet et al. (1984) and the
stretching method introduced by Sens-Schönfelder and Wegler (2006). Both of them are based
on the principle that small changes in the medium ∆
v
would result in small time shifts ∆
t
of
the arriving waves:
∆t
t=−∆v
v=ϵ(5.11)
where we refer the velocity change as an apparent velocity change due to the assumption
that it is homogeneous in space.
ϵ
is known as the relative travel time change and is constant
for all lapse times under the same assumption. To observe variations, both methods compare
a "current" correlogram (
ul
) to a reference signal (
uk
), typically constructed as the stacked
cross-correlation function over the entire recording period.
32
5.4 Noise-based monitoring
5.4.1 Stretching technique
The main idea behind the stretching technique is to stretch or compress the time axis of a
current correlogram (
ul
) by a factor
t→t
(1
±ϵ
)such that the correlation coefficient (
Ck,l
)
with respect to ukis maximized (Figure 5.2a,c):
Ck,l(ϵ) =
tmax
∑
t=tmin
uk(t)ul(t(1 ±ϵ))
√u2
k(t)u2
l(t(1 ±ϵ))
(5.12)
The stretching of a curve is simulated simply by modifying the sample interval by
dt
(1 +
ϵ
).
Then, the value 1
−Ck,l
(decorrelation) indicates the remaining waveform change that cannot
be explained with the simulated homogeneous velocity change (stretching).
Figure 5.2:
Synthetic illustration of the stretching (a, c) and MWCS methods (b, d). a)
Comparison of a reference (gray lines) with respect to stretched (black lines) waveforms. c)
Correlation coefficients for each stretched waveform in a). b) Comparison of a reference waveform
(gray lines) with respect to fixed moving window segments (black lines). d) Linear regression for
the obtained best time shifts with respect to time. The maximum associated
ϵ
is, in both cases,
5%. Taken from Nakata et al. (2019)
5.4.2 Moving window cross-spectral analysis
In contrast to using a long time window, the MWCS technique compares several short time
windows (with length
tw
and centered at
ti
) of a current correlogram (
ul
) with respect to a
33
5. Ambient seismic noise tomography and coda wave interferometry
reference
uk
. The waveform distortion if then given by the time shift ∆
t
required to match
the reference trace (Figure 5.2b). The similarity between
ul
and
uk
at a local time
ti
is given
by (Nakata et al., 2019, Chapter 9):
Ci
k,l(∆t) =
ti+tw/2
∑
t=ti−tw/2
uk(t)ul(1 ±∆t)
√u2
k(t)u2
l(1 ±∆t)
(5.13)
A linear function is then fitted with the collected time shifts ∆
tmax
(
ti
)that maximize
Ci
k,l
(∆
t
)(Figure 5.2d). The final ∆
t/t
is then obtained by measuring the slope of the linear
function.
5.4.3 Comparison of both methods
Hadziioannou et al. (2009) made a detailed comparison of both methods showing better results
for the stretching technique in noisy conditions. On the other hand, the stretching technique
can be biased by changes of frequency content (Zhan et al., 2013). In addition the MWCS
does not suffer from the amplitude changes that result from the assumption of stretching a
waveform.
In Chapter 8, I apply the stretching technique to 2 years of ambient noise seismic records
collected at the Theistareykir geothermal field (NE Iceland) to investigate possible changes in
the reservoir due to exploitation related activities.
34
Part II
Applications
35
6
Optimized experimental network
design for microseismicity location and
monitoring
This chapter focuses on the application of survey design tools described in Chapter 3 to extend
a seismic network dedicated for microseismicity monitoring at the Theistareykir geothermal
field (NE Iceland). The same principles were then used to qualify an existing network recording
microseismicity at the Reykjanes Peninsula (SW Iceland).
Optimized experimental network design for earthquake location problems:
Applications to geothermal and volcanic field seismic networks
Tania Toledo, Philippe Jousset, Hansruedi Maurer, Charlotte Krawczyk
Article published in Journal of Volcanology and Geothermal Research, 2020.
https://doi.org/10.1016/j.jvolgeores.2018.08.011
Abstract:
We constructed a network optimization scheme based on well-
established survey design tools to design and qualify local and regional
microseismic monitoring arrays dedicated for geothermal exploration and
volcano monitoring. The optimization routine is based on the traditional
minimization of the volume error ellipsoid of the linearized earthquake location
problem (D-criterion) with the twist of a sequential design procedure. Seismic
stations are removed one by one to obtain networks for constraining the
locations of multiple hypothetic earthquakes with varying local magnitudes.
The sequential approach is simple and allows the analysis of benefit/cost
relations. Cost curves are computed for all hypothetic events to reveal
the minimum optimal number of stations given specific design experiment
objectives.
The scheme is first demonstrated on three test design experiments. Later,
we use the routine to augment an existing seismic network for monitoring
37
6. Optimized experimental network design for microseismicity location and monitoring
microseismicity in a geothermal field in NE Iceland (Theistareykir). The
resulting 23 station network would become the backbone of a reservoir behavior
and exploitation activity study. Hypothetic event locations and magnitude
relations are taken from a previous regional seismicity study and coincide with
geothermal injection and production areas. Sensitivities are calculated with a
known 1D velocity model profile using a finite-difference back-ray tracer, and
body wave amplitudes are computed from known local magnitude relations.
Finally, expected earthquake location accuracies are calculated via multiple
Monte Carlo experiments.
The design routine is later used to qualify an existing seismic network
located in SW Iceland (Reykjanes). The seismic array is reduced to strategic
positions, and benefit and expected accuracies are quantified to observe
whether costs could have been optimized had a previous network design
experiment been performed.
Overall, we explore quick and flexible tools for designing and qualifying
networks for many applications at various scales.
6.1 Introduction
Since the mid 70s, the identification of economically attractive reservoirs and their exploitation
for geothermal heat energy have been the aim of numerous projects worldwide (Dyer et al., 2008;
Tester et al., 2006). Parameters such as heat source, reservoir, and preferential fluid pathways
geometries, the availability and characteristics of underground fluids, and the knowledge of
the recharge area are some of the main targets for the exploration of both conventional and
enhanced geothermal systems (EGS). These parameters rarely show surface manifestations,
and are therefore mostly assessed by geophysical techniques such as microseismic monitoring.
Several studies have shown that geothermal and volcanic systems are usually associated
with high levels of natural and/or induced microseismic activity (e.g. Soultz-sous-Forêts
(Cuenot et al., 2008), Hengill (Jousset et al., 2011), Basel (Majer et al., 2007), Merapi volcano
(Surono et al., 2012), Reykjanes (Blanck et al., 2018b, this issue), Krafla (Foulger et al., 1983)).
These events are good indicators of the active processes in the subsurface. Accurate event
location can potentially help identify the reservoir boundaries; the shape, size, position, and/or
growth of active fractures or faults (Philips et al., 2002); and, when correlating the seismicity
evolution with time, the migration patterns of injection fluids. Well-constrained events
also improve results of further seismic studies such as earthquake tomography, attenuation
and anisotropy structural analysis, and source mechanism determination with first arrival
wave polarity (e.g. Blanck et al., 2018b, this issue) for an overall better understanding of a
geothermal field and/or volcanic hazard assessment. In the best case scenario, high precision
micro-earthquake locations serve as guides for further drilling and development of a geothermal
field (e.g. Jousset et al., 2016). In a similar way, volcanic hazard studies can be enhanced with
better seismic event precision (e.g. Surono et al., 2012).
High precision hypocentral parameters are the aim of most passive microseismic studies and
considerable effort is currently dedicated to develop standardized data-processing and inversion
38
6.1 Introduction
techniques. These methods range from ray-based (e.g. Aki and Richards, 1980; Kissling et al.,
1994) and grid search methods (e.g. Lomax, 2005; Sambridge and Kennett, 1986, 2001), to
wave-field back-propagation (e.g. McMechan, 1982; Witten and Artman, 2011) and waveform
stacking (e.g. Cesca and Grigoli, 2015; Kao and Shan, 2007), among others. Ray-based or
arrival time inversion techniques with travel time picking are to this day the most common
choice in microseismic experiments given their formulation simplicity, their relatively fast
computation despite the large amounts of data, the availability of inversion packages, and the
proven results in numerous case studies. Several of these standard automated location routines
rely on Geiger’s algorithm (Geiger, 1912), where the location is derived by carrying out an
inversion that iteratively minimizes observed and synthetic travel times of body waves (Aki and
Richards, 1980). For simplicity and inversion stability, event location is usually first performed
using a 1D reference velocity model. This assumption can limit the location accuracy, given the
systematic biases that are introduced by 3D velocity changes. This effect is normally alleviated
by including source and/or station correction terms and/or jointly inverting the travel time
data for both hypocenters and velocity structure in local earthquake tomography studies (e.g.
Eberhart-Phillips (1990); Ellsworth (1977); Kissling et al. (1994); Michelini (1995); Roecker
(1981); Thurber (1992)).
It has been pointed out by several authors that the success, reliability, and accuracy of
the results strongly depend on acquired data quality mainly given by the number of available
phases, accurate picking (if needed) (Pavlis, 1986), and network geometry (Kijko, 1977;
Rabinowitz and Steinberg, 1990; Uhrhammer, 1980). Although we have limited influence on
the micro-earthquake occurrence, we can maximize the information content of an experiment
by designing optimal network configurations or by selecting an optimal subset of an existing
dense dataset (e.g. Maurer et al., 2010). Ideally one can think of improving results precision
by using a large number of seismometers, in practice however, geothermal exploration and
seismic monitoring in general is strongly constrained by budget. On top of that, no additional
information can ever compensate missing or inadequate data required for resolving a target
parameter, hence the critical importance of the survey design choice.
The usual procedure in geothermal exploration or volcano monitoring is to deploy a number
of seismometers (6 or more) covering a prospect area or volcano, and record continuously over
a period of time at sampling rates higher than 50 Hz. Often the seismic network is designed
following a heuristic approach with some basic guidelines: the expected microseismic events
should be located within the array forming an azimuthal gap of less than
∼
180
◦
(Valtonen
et al., 2013), and the average inter-station spacing should be of the average hypocentral depths.
In some cases, standard designs involve specific configurations required for existing inversion
and analysis tools. The later choice can be quite restrictive when encountering field and/or
instrumentation constrains. Heuristic design can also lead to difficulties in evaluating potential
error estimations. Several inversion tests would be needed to find an adequate design that
effectively minimizes potential errors, leading to a considerably large computational cost.
Alternative network design strategies have been introduced in the framework of experimental
design (ED) for a variety of applications (e.g. Coles and Curtis, 2011a; Curtis, 1999b; Glenn
and Ward, 1976; Jones and Foster, 1986; Kraft et al., 2013; Maurer and Boerner, 1998; Nuber
et al., 2017; Uhrhammer, 1980; Wilkinson et al., 2006). The main concept is to minimize (or
39
6. Optimized experimental network design for microseismicity location and monitoring
maximize) an objective function representing optimum network performance, which is in many
cases related to the eigenvalue content of the linearized inverse earthquake location problem.
One popular functional for the earthquake location problem is the D-criterion first implemented
by Kijko (1977) and later exploited by Rabinowitz and Steinberg (1990) to monitor a single
point source using the DETMAX algorithm (Mitchell, 1974). Later Steinberg et al. (1995)
extended these principles to obtain networks dedicated to monitor fault lines and multiple
seismic sources by introducing a multi-source objective function. The D-optimal concept
for event location network design is also implemented in the software program OPTINET
(Shimsoni et al., 1992).
The D-criterion is however only applicable in linearized design problems. Geoscientific
experiments on the other hand exhibit a complex non-linearity which only increases with the
number of optimizing parameters and observables. This makes nonlinear optimization still
very prohibitive at large scales due to its large computational demand, however some efforts in
this direction have been made with promising results. Coles and Curtis (2011a), for example,
presented a practical approach for fully non-linear Bayesian statistical experimental design
by introducing a generalization of the D-criterion which they called
DN
optimization. This
function benefits from linearized methods to make the optimization computationally feasible
in comparison to other non-linear approaches. They applied the algorithm to construct a
seafloor microseismic network for monitoring an offshore petroleum field and compared its
performance with a network acquired with linearized Bayesian sequential design, with better
results using their method.
Hardt and Scherbaum (1994) studied the potential for multi-purpose designs addressing
objectives such as tomography, focal mechanisms, and source-parameter estimation for an
aftershock experiment. Their work uses a simulated annealing approach (Kirkpatrick et al.,
1983) that reduces a synthetic temperature to search for the global minimum of the objective
function. Their results primarily point out that different research objectives require different
network configurations. Later Kraft et al. (2013) extended this algorithm to include the
possibility of using 3-D velocity models by adding a finite-difference ray tracer to compute
travel-times. They also introduce the construction of event detection thresholds by using the
Brune source model (Brune, 1970, 1971) to compute body-wave amplitudes and compare them
to local noise level amplitudes for augmenting a microseismic network in northern Switzerland
(Kraft et al., 2013).
Although global optimizers provide optimal configurations, its use may require extensive
computations as different initial configurations would be needed to check for the stability of
the solutions. Moreover, global optimizers can be quite restrictive when addressing changes in
the theoretical station positions due to field conditions, and many more calculations would be
then necessary to produce an alternative station configuration that accounts for these new
constrains. These facts motivated Curtis et al. (2004) to use a sequential design approach
for a 2D microseismic monitoring example with sources placed inside a borehole. The idea
consisted of removing receiver positions that represent redundant data in a stepwise fashion.
In this paper we shall explore a similar approach in 3D for constructing and qualifying passive
seismic networks for geothermal exploration purposes. This sequential optimization concept
40
6.2 Background theory and synthetic examples
not only reduces the computation time for network design but it also facilitates addressing the
benefit/cost question, which is oftentimes overlooked.
One main goal of this study is to apply fast and well-established linearized sequential survey
design tools to a new problem: constructing and qualifying microseismic arrays dedicated to
monitor geothermal operations. Therefore, after introducing a brief theoretical background for
earthquake location problems and relevant concepts of experimental design theory, we present
the used algorithm with the particular emphasis of treating large amounts of hypothetical
sources of varying local magnitudes to obtain optimal positions for a given number of seismic
stations. The chosen scheme is robust, simple, and addresses concepts like benefits and costs.
It is also particularly useful for qualifying and augmenting networks with existing stations. We
therefore first introduce three simple test cases to demonstrate the chosen approach. Later,
we present the two case studies where the algorithm was used to augment (Theistareykir case
study), and test the network quality of an existing array (Reykjanes case study).
Although global optimality cannot be guaranteed by sequential methods -whether the
metric used is linearized or non-linear-, the technique hereby explored arrives to quick designs
with good performance nonetheless. Linearized sequential design poses less computational
costs which makes these techniques more efficient in cases where quick designs are needed
such as post-earthquake aftershock studies. It could also provide a framework for potential
design-during-deployment (DDD).
The word "linearized" here and throughout this manuscript refers to the fact that the
quality metric used to assess each design relies on a linearized information measure. Hence,
even if a Bayesian formulation -which includes an a priori distribution of models- is used, such
a measure can only provide an approximation to the true measure of information expected
to be provided by each design. Whether or not the globally optimal experiment under that
information measure is found has nothing to do with the measure, and therefore has nothing
to do with linearization.
Global optimality can be obtained when using linearized design quality metrics if a global
optimization algorithm is used (such as a simple grid search over design space). By contrast,
Guest and Curtis (2009) use sequential methods to design experiments using fully nonlinearized
quality measures; so although for each design their quality metric will give a more robust
assessment of the amount of information than linearized metrics (but of course more costly to
evaluate), the sequential methods that they applied, while fast to converge, will not in general
find the globally optimal design under that metric.
6.2 Background theory and synthetic examples
6.2.1 Basic principles of earthquake location and inverse theory
Micro-earthquake location is a classical nonlinear inverse problem that aims to obtain a set of
model parameters
m
(event position coordinates
xo
,
yo
,
zo
, and origin time
to
) from observed
data
dobs
(P and S wave arrival times
tp
and
ts
) assuming a mapping operator
G
that relates
them. The linearized system of equations representing the forward problem is expressed as:
d=Gm (6.1)
41
6. Optimized experimental network design for microseismicity location and monitoring
where
G
corresponds to the true physical processes in the subsurface when it relates a true
model of the subsurface
mtrue
with
dobs
. In a similar fashion any set of predicted data
dest
can be calculated using an estimated set of model parameters
mest
assuming a known forward
operator or data kernel
G
. In the event location problem,
G
is comprised by the sensitivities of
travel times with respect to the hypocentral coordinates and the origin time. These sensitivities
are calculated in this work by using Podvin and Lecomte (1991) finite-difference time-field
calculations and a back-raytracing routine.
One usual procedure to tackle the inverse problem is to iteratively compute forward modeled
data
dest
and compare it to the observed dataset
dobs
such that the misfit between the two is
minimized (Tarantola, 2005). To achieve a better search of the global minima, the problem
is commonly solved by adding regularization constrains that tackle instabilities due to data
uncertainties (Levenberg, 1944; Marquardt, 1963). The damped least-squares solution to the
inverse problem of Eq. 6.1 is given by:
mest = (GTG+γI)−1GTd(6.2)
where
γ
corresponds to the damping factor, and Iis an NxN identity matrix with Nbeing
the number of model parameters contained in
m
(4 for this case). Square matrix
GTG
is often
near singular, and inversion stability strongly depends on its ability to be inverted. The reader
is referred to Menke (2012) and Lee and Stewart (1981) for extended relevant derivations.
6.2.2 Experimental survey design: The D-criterion
The main goal of experimental survey design is to select a network geometry or data subset
that would minimize the computational and/or acquisition costs while optimizing the benefit
of an inversion problem (Maurer et al., 2010). This benefit or "goodness" can best be described
in terms of the potential information content that can be obtained from a dataset, namely the
eigenvalue content (λi:i= 1, ..., N) of matrix GTG(Curtis, 2004).
One important property of eigenvalue content is its relationship to error propagation.
Errors in the data space propagate into the solution
mest
with an amplification of 1/
λi
, parallel
to their corresponding eigenvector. This means that for small eigenvalues the propagation error
can be quite large if not making the solution unstable altogether (ill-conditioned problem). As
a matter of fact, the covariance matrix of the solution to Eq. 6.2 is given by (Menke, 2012):
cov(m) = σ2(GTG)−1(6.3)
where
σ2
corresponds to the variance of onset-time determination. Assuming a constant
σ2
, the shape of the precision ellipsoid is given by eigenvectors and eigenvalues of 1/(
GTG
)
and its volume is proportional to 1/det(GTG) (Buland, 1976; Flinn, 1965).
Several design quality measures based on matrix
GTG
have been proposed, compared, and
analyzed in previous experimental design works (e.g. Curtis, 1999b, 2004; Maurer et al., 2010).
However one popular measure in earthquake location problems is given by the determinant of
GTG
, also known as the D-criterion due to its sensibility to the entire eigenvalue spectrum
(Hardt and Scherbaum, 1994; Kijko, 1977; Rabinowitz and Steinberg, 1990). After testing
different quality measures based on the D-criterion, we chose to work with a modified version
42
6.2 Background theory and synthetic examples
of the multi-source function defined by Rabinowitz and Steinberg (1990) for best results. We
thus define our quality measure Θas:
Θ =
N
∑
i=1
γilog (1
det(GT
iGi) + δ)(6.4)
where Nstands for the total number of earthquakes, and
γi
corresponds to a weighting
factor assigned to each event i(
γi
= 1 for all events studied in this work). In a Bayesian
framework, weights
γi
could be regarded as prior probabilities for the hypocenters (Chaloner
and Verdinelli, 1995). In this study however, the weights reflect a combination of a prior
probability and an event importance (Steinberg and Rabinowitz, 2003). We introduce a small
value
δ
in Eq. 6.4 to stabilize the optimization procedure for cases where the determinant
would be zero (under-determined case). With this objective function we would in some sense
minimize for the confidence ellipsoid volume of all events.
Sensitivities in
G
are solely related to the survey design. Hence the "goodness" of matrix
GTG
can be maximized by selecting the source-receiver configuration that would result in the
highest eigenvalue content (minimizing quality measure Θ). In a destructive sequential design
framework,
G
is first comprised of all possible sensitivity entries, namely all detecting station
positions. Later, Θvalues are calculated after removing each recording sensor. These values
are then compared and the position associated to the minimum Θvalue (possibly redundant
information) is removed. This process is carried out in a step-wise fashion depleting the
potential deploying area.
6.2.3 Event detectability
To address the design problem of defining this potential deploying area we examine the event
detectability in space (e.g. Coles and Curtis, 2011a; Hardt and Scherbaum, 1994; Kraft et al.,
2013). The original amplitude of a seismic phase is influenced mainly by the following factors:
magnitude, wave propagation effects (namely geometrical spreading and attenuation), and
source processes. The first two factors are addressed in this work only in an approximate
manner. Then, events are detected at a point only when their recorded amplitudes are greater
than the noise levels at that recording point.
We use the empirical local magnitude-attenuation relation used by the national seismic
network in Iceland (South Iceland Lowland or SIL system) to compute recorded amplitudes
(Jakobsdóttir, 2008):
ML= log10 A+ 2.1∗log10 ∆−4.8(6.5)
Eq. 6.5 is based on the maximum peak-to-peak amplitude in a 10 seconds interval around
the S-wave at all stations, where ∆represents the earthquake-station distance in km, and Ais
the maximum velocity amplitude of high-pass filtered waveforms with cutoff frequency at 2Hz
and a scaled response of a Lennartz 1Hz sensor and a Nanometrics RD3 digitizer.
To construct a detection radius, Ais chosen to match a minimum amplitude above an
expected noise level. In this work we assume rms noise amplitudes of around 42 nm/s
43
6. Optimized experimental network design for microseismicity location and monitoring
throughout the available space. This rms ground velocity amplitude (
vrms
) was obtained using
the following relation (Bormann, 1998):
vrms ≈√2· ⟨Pa/ω2⟩ · (f2−f1)(6.6)
where
Pa
corresponds to the most probable noise level at a given frequency interval obtained
from the probabilistic power spectral density (PPSD) for ground acceleration (McNamara and
Buland, 2004) at a given station. Then
⟨Pa/ω2⟩
corresponds to the mean converted ground
velocity function over a frequency range between
f1
and
f2
. Finally,
ω
stands for the angular
frequency. In this work we chose a seismic station located north to the Krafla region in Iceland
(Lees, 2004), computed its corresponding PPSD using ObsPy (Beyreuther et al., 2010), and
calculated the vrms associated to frequencies above 2 Hz.
Then we selected a large signal to noise ratio (SNR
≈
15) for detection threshold
construction. Authors like Hardt and Scherbaum (1994) point out that a SNR of 3 should be
enough to detect a seismic phase onset. However given that only the maximum amplitude in
a time window is taken into consideration for the detection, as well as the uncertainties of
lateral noise amplitude variations, we chose a much more conservative SNR value to construct
the detection thresholds. The potential deploying area would then correspond to the region
within this detection radius.
Detectability is not the main focus of this work and is therefore roughly addressed.
Amplitudes, noise, and magnitude values used are regarded as estimates only, and are merely
utilized to define a region to include stations for both the test cases and Case study I, which
corresponds to a region neighboring Krafla. It is advisable, where there would be available
preliminary seismic data, to compute laterally-variant noise estimates as done by Kraft et al.
(2013), as well as refining variable values of SNR. Hence, we recommend to update detection
models and repeat optimizations once more information on the target sites becomes available.
We have also not accounted for different radiation patterns given the typically unknown source
parameters in unexplored areas. We encourage to explore this variable when more information
is available.
6.2.4 Test Case A: survey design for a single source
To demonstrate the use of the destruction sequential survey design algorithm (DSSD), Fig. 6.1
shows the construction of a 5 (Fig. 6.1a) and a 115 (Fig. 6.1b) station network for locating a
single event of M
L
0.8 and 3 km depth in a homogeneous media of constant P-wave velocity
(V
p
) of 4 km/s. The possible station locations consist of the nodes of a triangular grid with
mean spacing of 3.5 km, obtained using the Persson and Strang (2004) open-source mesh
generator. The triangular mesh was chosen in accordance with the work of Kraft et al. (2013).
First, we construct the potential deploying area (region within dashed red lines in Fig.
6.1a and Fig. 6.1b) for the given event and the sensitivity matrix
G
for the total number of
recording sensors (115 for this case). Next, we remove one station and calculate the quality
value Θfor the remaining 114 station network. We put this station back into the network,
remove another station, and calculate Θagain. This process is carried out for all recording
stations to obtain a list of 115 Θvalues. Then we permanently remove the point with lowest
associated Θ, and assign to it the last placement number position (115 in this case). In
44
6.2 Background theory and synthetic examples
a)
0 20 40 60 80
x (km)
0
10
20
30
40
50
60
70
80
y (km)
1
1.5
2
2.5
3
3.5
4
4.5
5
23
4
1
5
b)
0 20 40 60 80
x (km)
0
10
20
30
40
50
60
70
80
y (km)
10
20
30
40
50
60
70
80
90
100
110
c)
0 20 40 60 80 100
Number of stations placed
-5
0
5
10
15
20
25
30
Event design quality contribution [ event]
02468
0
1
2
3
4
5
Figure 6.1:
Test case A. Survey design example for an event at 3 km depth with M
L
0.8. a)
5 stations setup. b) 115 stations setup. The colorbar expresses the order of placed stations. c)
Design quality or "goodness" of the survey setup for each number of placed stations. The dashed
red line represents station point 4, and the horizontal dashed black line the limit of Θ= 3.4.
other words we search for the station whose removal would worsen the network quality the
least, and would therefore be the last one we would need to place for optimally constraining
the hypocenter. Next, we repeat this procedure with the remaining 114 stations to look for
the second to last placement number position. This process is repeated until the total 115
available receivers are removed (triangles in Fig. 6.1b) and the full placement order sequence
is created (colorbar in Fig. 6.1a and Fig. 6.1b). Notice how when displaying the first 4 seismic
stations of the placement sequence (Fig. 6.1a), the distribution has a quadripartite geometry in
accordance with results of Rabinowitz and Steinberg (1990) and Hardt and Scherbaum (1994),
with the closest point to the epicenter as the very first station position. When further adding
a fifth sensor, notice how this receiver is placed again at a position close to the epicenter.
Given the proximity of this location to Station #1, this position can be regarded as redundant
information. In the framework of D-optimality this clustering or redundance can be interpreted
as a high regional importance (Kraft et al., 2013). In this particular case, the double positioning
45
6. Optimized experimental network design for microseismicity location and monitoring
is the result of no station candidate located right above the earthquake epicenter. It is for this
reason that the resulting station position sequence must be carefully assessed before ultimately
defining a network. Later, after displaying the entire sequence (Fig. 6.1b) we clearly see that
the first deployed stations (in darker blue) correspond to those close to the source and to those
bordering the detection radius limit.
Fig. 6.1c shows the variation of the design quality value Θafter using -nstation positions.
Low Θvalues indicate good array quality. This curve is a good representation of the benefit/cost
relations of the survey design problem. The cost is interpreted as the number of placed stations
and the benefit is defined by the value of Θitself, proportional to the logarithm of the resulting
confidence ellipsoid volume. Notice how this value decreases rapidly with the first 4 stations,
after which this decrease does not vary significantly. This means it takes only a few optimally
positioned stations to reach good network quality. We define a benefit threshold of Θ= 3.4
for this case (dashed blue line) to select a minimum number of stations (4). Using additional
receivers will further decrease the confidence ellipsoid volume and it would then be up to the
user to decide the number of needed stations to meet the objectives of an experiment, however
some attention must be given to potential station clustering. Notice also after placing enough
stations, this decrease is not significant, hence the benefit/cost curve tends to flatten with
large number of stations.
Though the proposed algorithm can potentially use both P-wave (Vp) and S-wave (Vs)
velocities for building the sensitivity matrix, we chose to work only with Vp. Errors in Vs
can considerably influence towards constructing a suboptimal station network. On one hand
Vs is typically lower than Vp, hence providing higher sensitivities to
tS
measurements. At
the same time, S-wave picks are often hard to acquire, especially in the presence of noisy
data. Gomberg et al. (1990) point out that although S-wave data can significantly improve
the accuracy of hypocenter location and reduce the trade-off between origin time and source
depth, incorrect estimates can also significantly degrade it. In this work we therefore consider
S-wave travel-time measurements merely as added values improving the location accuracies at
a later stage however not in the design experiment.
6.2.5 Test Case B: small multi-event survey design
In this example we will build a seismic network dedicated to constrain 3 known event targets
at a depth of 3 km with varying local magnitudes (M
L
0.8, 0.6, and 0.5). As an initial step,
and similar to the previous example, we construct the potential deploying areas for all three
events. On a second step, the multi-event quality measure Θis computed after removing each
recording station in the system, while carefully accounting for their contribution only to the
events that are detected by them. Values are then compared and the station that effectively
minimizes Θis removed. As in the previous exercise, this procedure is repeated until all 231
stations are removed.
Fig. 6.2a and Fig. 6.2b show the resulting 12 and 231 station networks, respectively.
Similar to Test Case A, the first stations of the placement order sequence are those close to the
event epicenters and those close to the detection boundaries (dark blue triangles). However,
no perfect quadripartite geometry is provided for all the events (Fig. 6.2a). This failure to
arrive to a perfect 4 station geometry occurs when potential deploying areas overlap (as is the
46
6.2 Background theory and synthetic examples
a)
0 20 40 60 80
x (km)
0
10
20
30
40
50
60
70
80
y (km)
Earthquake location
Added stations
Detection threshold
1
2
3
4
5
6
7
8
9
10
11
12
Event 1
Event 2
Event 3
2
1
3
4
5
6
7
8
9
10
11
12
b)
0 20 40 60 80
x (km)
0
10
20
30
40
50
60
70
80
y (km)
20
40
60
80
100
120
140
160
180
200
220
c)
20 40 60 80 100 120 140 160 180 200 220
Number of data.used stations
-10
0
10
20
30
40
50
60
Total design quality [ tot]
First station for Event
1
First station for Event
2
First station for Event
3
d)
0 50 100 150 200
Number of stations placed
-5
0
5
10
15
20
25
30
Event design quality contribution [ event]
Event1
Event2
Event3
8 10 12 14 16
0
1
2
3
4
5
Figure 6.2:
Test case B. Survey design example for three events 3 km deep. Events have M
L
0.8 (center), 0.6 (top), and 0.5 (bottom left). a) 12 stations setup. b) 231 stations setup. The
colorbar expresses the order of placed stations. c) Total design quality or "goodness" of the survey
setup after progressively placing stations. d) Design quality contribution per event for the whole
experiment. The dashed red line represents station point 12, and the horizontal dashed black line
the limit of Θevent = 3.4.
case of Event
1
and Event
2
). The multi-source objective function will naturally favor these
areas given that their contribution to more than one event will reduce Θmost (hence the
deep blue triangles all through this region in Fig. 6.2b). Overlapping areas will be even more
favored when these regions are considerably large. In these cases, stations would be very hardly
placed outside of them, yet it will keep the pattern of putting stations close and far from the
epicenters within them. The algorithm could then potentially return a poorer convergence to
a perfect quadripartite geometry. To obtain better geometries for particular events, one can
assign them higher weighting values γi(Eq. 6.4).
The benefit/cost curves, namely the total design quality values Θ
tot
and the individual
event contributions Θ
event
, are shown in Fig. 6.2c and Fig. 6.2d respectively. Design quality
curve Θ
tot
reveals two marked peaks which correspond to the points where the routine has
placed the first station at an event deploying area (e.g. station # 7 would be the first sensor
47
6. Optimized experimental network design for microseismicity location and monitoring
placed for Event
3
). The contribution of a single sensor at a deploying space yields Θ
event
= 30,
which is result of the sole influence of
δ
in an under-determined case (Eq. 6.4). An increase of
30 in Θ
tot
is also visible at these points, hence the peaks in the curve. Naturally, before this
first station is introduced no contribution to Θ
tot
or Θ
event
is made for this event. Placing a
second station would barely reduce this value of 30, for which Θ
tot
and Θ
event
hardly decrease
(still under-determined case). It is only after introducing the third and fourth stations at a
deploying space (reaching an even-determined case) that Θ
event
is reduced to a value between
3 and 4 (Fig. 6.2d). If we now define a benefit limit per curve of Θ
event
= 3.4 (dashed blue
line), we would then require the 12 stations shown in Fig. 6.2a.
6.2.6 Test Case C: large multi-event survey design
So far, we have addressed the network design for locating a single or very few known events, in
practice however, microseismicity studies for geothermal monitoring typically present hundreds
if not thousands of events. The next question is how to construct a seismic network for
optimizing a large number of earthquakes. Like the previous two cases we assume a constant
Vp of 4 km/s throughout the domain, but this time we introduce 1089 events of M
L
0.5 and
depth of 3 km placed in a grid-like manner every 2.5 km in xand ydirections.
Similar to the previous exercises we use the DSSD algorithm to construct the station
placement sequence and their associated quality curves. Fig 6.3a and Fig. 6.3b show the
resulting 100 and a 598 station networks, respectively, and Fig. 6.3c and Fig. 6.3d depict the
experiment design qualities Θ
tot
and Θ
event
. Notice the overall decreasing trend of Θ
tot
after
first reaching a maximum at
≈
26 stations. This is the point where most events have at least
one seismic station in their deploying area (≈60%of stations).
Once more, from the cost curve (Figure 6.3d) we may observe and select a number of
stations that would best constrain most of the 1089 events. It is important to note that
constraining all events will be very expensive and at times not realistic. More often than
not, we should be ready to sacrifice the benefit or location accuracies of some events for cost
reasons. In this case, we select 100 stations (Fig. 6.3a), given that most event cost curves reach
a benefit Θ
event ≤
3.4 (horizontal black dashed line in Fig. 6.3d). In the resulting network,
receivers are scattered in a quasi-regular way throughout the domain with few stations placed
at the boundaries. The overall station sequence presents a very similar quasi-regular behavior
in Fig. 6.3b.
6.3 Case study I: Theistareykir geothermal field
Theistareykir is a high temperature geothermal field located in NE Iceland that extends
from the Öxarfjördur Bay to the center of the country and is associated to the Baejarfjall
volcano (Fig. 6.4). It is characterized by a set of large normal faults that strike N22
◦
E with
maximum offset of around 200-300 meters, and various rift fissures (Sveinbjornsdottir et al.,
2013). This geothermal field has undergone intermittent exploration (1972-1974 and 1981-1984)
and monitoring (1991-2000) to assess its capabilities for drilling and production (Ármannsson,
2008), and is currently under the administration of Landsvirkjun, the national power company
of Iceland. Between 2002 to 2008 seven deep wells were drilled with depths of 1723 m to 2799
48
6.3 Case study I: Theistareykir geothermal field
a)
0 20 40 60 80
x (km)
0
10
20
30
40
50
60
70
80
y (km)
10
20
30
40
50
60
70
80
90
100
b)
0 20 40 60 80
x (km)
0
10
20
30
40
50
60
70
80
y (km)
50
100
150
200
250
300
350
400
450
500
550
c)
50 100 150 200 250 300 350 400 450 500 550
Number of data.used stations
-2000
0
2000
4000
6000
8000
10000
12000
14000
16000
18000
Total design quality [ tot]
d)
Figure 6.3:
Test case C. Survey design example for multiple events of M
L
0.5 located at 3 km
depth. Pink points indicate epicenter locations and triangles stand for station locations. The
colorbar expresses the order of placed stations. a) 100 stations setup. b) 598 stations setup. c)
Total design quality or "goodness" of the survey setup after progressively placing stations. d)
Design quality contribution per event for the whole experiment. The dashed red line represents
station point 100, and the horizontal dashed black line the limit of Θevent = 3.4.
m, and up to 8 additional wells were included by the end of 2017 (Landsvirkjun, 2016). Many
of these wells were drilled almost horizontally and the power plant is producing at a capacity
of 90 MW since spring 2018.
According to a Landsvirkjun report on seismic data recorded between November 1st 2016
and March 31st 2017 (Blanck et al., 2017a), most of the activity is clustered in the form of
vertical chimneys close to the production zone. The report shows a total of 140 earthquakes
located mainly at depths between 2 and 5 km with an array consisting of mainly 4 seismic
stations in the close vicinity: 1 from the national seismic array (SIL system) and 3 operated
by Iceland Geosurvey (ISOR) for Landsvirkjun. These events have mostly local magnitudes of
0.5 and higher, exhibiting a Gutenberg-Richter b-value relation of 2.16. Blanck et al. (2017a)
interpreted that the large amount of higher magnitude events could be the result of either a
strong crust at the site, or the side-effects of a small seismic network.
49
6. Optimized experimental network design for microseismicity location and monitoring
Figure 6.4: Initial receiver positions and synthetic epicenters defined prior to the design study.
6.3.1 Experimental design setup, results and discussion
To better understand the structures and behavior of the reservoir, a seismic network consisting
of 12 broadband stations will be augmented to monitor the Theistareykir geothermal field
(Fig. 6.4). This network is part of a larger deployment effort to monitor the exploitation
activity with an array of multi-parameter stations including gravimeters, GNSS receivers, and
seismic sensors (Jousset et al., 2018, EGU abstract). From the seismic stations depicted in
Fig. 6.4, seven are permanent stations belonging to the Icelandic Meteorological Office (IMO)
and Iceland Geosurvey (ISOR), and five stations belonging to the German Research Center
for Geosciences (GFZ) will be fixed at the gravimeter station positions. In this exercise an
additional 11 seismic station positions has been defined for a total of 23 receivers across the
geothermal field.
Following the proposed sequential survey design recipe, we first specify the target areas
where we may expect future microseismic events. These regions correspond to the production
and injection zones depicted by the red and blue cluster of points, respectively (Fig. 6.4).
As a next step we generate a synthetic earthquake catalog (196 events) using these points
as epicenters, and the depth and magnitude distributions of the catalog studied by Blanck
et al. (2017a) (Fig. 6.5). We chose to focus on local magnitudes between 0.5 and 0.8. Fig.
6.5a depicts the 1D P- and S-wave velocity profiles typically used by the IMO for earthquake
locations, though for the design experiment we shall once more only use the 1D P-wave velocity
profile.
As in the first test cases the domain is discretized to a 2D triangular grid with node
distances of roughly 3.5 km. After defining deploying areas for each event, we perform the
DSSD algorithm two times: the first time using only the 12 deployed stations as "potential
location points", and the second one right after, to account for the remaining positions in
the full deploying space. Results of the first survey design experiment provide an order of
importance of the fixed stations positions and determine which are the critical ones among
them. The second exercise is performed to augment the array.
50
6.3 Case study I: Theistareykir geothermal field
a)
01234567
Velocity (km/s)
0
1
2
3
4
5
6
Depth (km)
1D Vp(z) & Vs(z)
Vp
Vs
b)
Event depth distribution
0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4
No. Earthquakes [%]
0
1
2
3
4
5
6
Depth [km]
c)
0.5 0.55 0.6 0.65 0.7 0.75 0.8 0.85 0.9
ML
100
101
102
Earthquake instances
Figure 6.5:
Synthetic earthquake catalog specifications. a) 1D P- and S-wave velocity profiles
from the SIL system (Bjarnason et al., 1993). c) Event depth distribution. The red line indicate
the depth above which 95 %of events are located. This limit is also known as the brittle-ductile
boundary. d) Magnitude distribution of the synthetic earthquake catalog. b value = 2.16
6.3.2 Theistareykir experimental survey design
Fig. 6.6a and Fig. 6.6b show the resulting 23 and 135 (complete) station networks. Notice
how on the first network the selected stations are located at the outer limits of deploying areas
with smaller detection radii. However, few stations are anyways placed at the northwest of the
epicenters. According to Steinberg and Rabinowitz (2003), for velocities varying with depth,
receivers recording both direct and refracted waves are necessary for optimal location results.
It is also noticeable for the entire sequence of 135 stations (Fig. 6.6b) how, unlike the test cases,
the inner stations are selected first and the outermost positions last (corresponding to larger
event magnitudes). However within the innermost region, the behavior is similar to that of the
test cases, and stations are first located both close and further away from the epicenters. This
behavior is the result of having clustered events, with large or entirely overlapping deploying
areas. A possible solution to better consider the optimization of larger events is to assign them
a higher weighting value
γi
(Eq. 6.4). However, given the network objectives to potentially
51
6. Optimized experimental network design for microseismicity location and monitoring
a)
0 20 40 60 80
x (km)
0
10
20
30
40
50
60
70
80
y (km)
Earthquake location
Added stations
Detection threshold
13
14
15
16
17
18
19
20
21
22
23
b)
0 20 40 60 80
x (km)
0
10
20
30
40
50
60
70
80
y (km)
Earthquake location
Added stations
Detection threshold 20
40
60
80
100
120
c)
20 40 60 80 100 120
Number of data.used stations
-1000
0
1000
2000
3000
4000
5000
6000
Total design quality [ tot ]
d)
0 20 40 60 80 100 120
Number of stations placed
-5
0
5
10
15
20
25
30
Event design quality contribution [ event ]
10 20 30
0
2
4
6
Figure 6.6:
a) 23 stations network. b) 135 stations network. The colorbar expresses the order of
the added stations. c) Total design quality of the survey setup after progressively adding stations.
d) Design quality contribution per event for the whole experiment. The dashed red line on the
left indicates the limit for the initial 12 stations, and the red line on the right the limit for a 23
stations network. The horizontal dashed black line indicates the limit of Θevent = 3.4.
detect and locate much smaller earthquakes as well as the easier access to this much reduced
area, we have decided to keep γi= 1 for the earthquakes studied.
Similar to Test Case A, Fig. 6.6a presents few areas with some clustered stations (e.g. the
westernmost and the northern regions). Although one could argue that some of the additional
stations may represent redundant information, we have decided to keep them. In this exercise
we have assumed homogenous noise amplitudes and SNR, which might not be the case in
reality. Therefore, by keeping the additional stations we are in some sense attempting to
ensure traveltime recordings in these regions. We thus recommend to carry out a noise analysis
once more seismic data becomes available and assess if and which station positions can be
removed, and alternatively be placed elsewhere.
Fig. 6.6c and Fig. 6.6d depict the total Θ
tot
and individual Θ
event
design quality or cost
curves. Notice the marked decrease in both Θ
event
and Θ
tot
curves after introducing only one
52
6.3 Case study I: Theistareykir geothermal field
additional sensor (station # 13). When analyzing the curves for Θ
event
, we observe how after
introducing the initial 12 stations, most curves lie below a value of 3.4. The placement of
additional 11 stations results in Θ
event ≤
2 for almost all curves. Adding many more stations
would enhance the benefit much less significantly as the curves tend to flatten towards the
end. As a matter of fact, Θtot stops decreasing significantly after ≈35 stations.
6.3.3 Spatial quality measure distribution
If we now take the opposite problem where the station positions are fixed and a series of
hypocenters are located every 2.5 km in the xand ydirections, and every 0.5 km in the z
direction in a rectangular grid-like manner, we can estimate the "goodness" of the network
for constraining each of these additional points by computing their corresponding quality
measure Θ
event
. Therefore this exercise consists on the observation of the network benefit for
earthquakes in the region different from those in the catalog used in the design phase. Fig. 6.7
shows these design quality or "goodness" maps for events of magnitudes: M
L
0.5 (left column)
and M
L
0.8 (right column). Uncolored areas lie outside detectable bounds and are thus not
considered for the goodness calculation. Areas marking higher values of Θ
event
(colored in
yellow) correspond to points with few readings. Conversely, low values of Θ
event
indicate best
quality and hence lower error propagation in the inversion results (Eq. 6.2). Notice how for
both cases (3 km depth slice), the regions with low values Θ
event
lie within the array, and is
best where the network is denser especially right below the station positions in the center (Fig.
6.7c and Fig. 6.7d). This is to be expected given that these regions correspond to some of the
target event locations used for the network design. The extents of the high quality area (dark
blue) reach a radius of ∼20 km from the epicenters shown in Fig. 6.4.
In a similar way, we can observe how for a E-W profile (located at approximately the
domain center, y = 37.5 km) the area with best design quality has a rough semi-circular shape
and is best under the denser network region, with low values (best quality) roughly reaching 10
km below the surface for both cases (Fig. 6.7e and Fig. 6.7f). For both cases, the potentially
best invertible hypocenter locations match the injection and production areas, hence reaching
our goal for the Theistareykir survey design with a Θ
event ≈
2. Overall, goodness maps prove
good quick tools for providing a qualitative character of the inversion errors for points across
an area.
6.3.4 Earthquake location accuracies
As a final step, we analyze the effects of seismic array configuration on hypocenter location
accuracies. For this purpose, we follow a Monte Carlo approach proposed by Billings et al.
(1994) and calculate the standard deviation of resulting hypocentral parameters after the
least-squares inversion procedure of several perturbed P- and S- wave datasets. We define
these standard deviations as earthquake location accuracies. In this exercise, synthetic P- (t
P
)
and S-(t
S
) wave arrival times were contaminated with normally distributed errors with means
at 0.2 s and 0.4 s, respectively. Considered sources correspond to the same grid points of the
design quality map exercise, at a depth of 3 km. The velocity model used is shown in Fig.
6.5a. We subsequently invert for each dataset using a damping factor of 0.1. Initial values x
0
and y
0
were taken as the true values with normally distributed errors of 2 km, and z
0
was set
53
6. Optimized experimental network design for microseismicity location and monitoring
ML0.5
a)
ML0.8
b)
c) d)
e) f)
0 10 20 30 40 50 60 70 80
x (km)
0
10
20
30
40
50
60
70
80
y (km)
Depth below surface = 3.00 km
Station positions
0 5 10 15 20 25 30
Design quality
Figure 6.7:
Measures of design quality or network goodness according to event position and
magnitude. The first column indicates values associated to events of M
L
0.5, the second to M
L
0.8.
White triangles mark the starting station positions. The red triangles stand for the added stations
after the design experiment. a) and b) show a 3D view, c) and d) depict a depth slice at 3 km,
and e) and f) an YZ profile cutting at y = 37.5 km.
to 1.5 km. These values are used assuming that a previous automatic detection scheme has
been used and the inversions are merely a refinement step. This is usually the procedure in
microseismic problems.
54
6.4 Case study II: Reykjanes seismic data and network performance
Fig. 6.8 depicts the resulting accuracy or standard deviation maps after performing the
inversions. Notice how accuracies in xand yare slightly lower than accuracies in z. This is to
be expected as we have a 2D receiver configuration for a 3D problem. Events located inside
the array present resulting accuracies of around 0.3 km, 0.3 km, and 0.6 km for the x,y, and z
components respectively in both magnitude cases. The position errors in the inner regions
(difference between true and mean inverted values in Fig. 6.9a and Fig. 6.9b) are of around
half a kilometer. The areas external to the seismic network present higher accuracy values and
location errors, due to the fewer travel time readings and the limited azimuthal coverage. The
uncolored areas in Fig. 6.8 and Fig. 6.9 do not entirely match those provided by Fig. 6.7 given
that only points with at least 6 data entries were inverted to avoid non-converging results.
To further study the uncertainty improvements after introducing the new stations we
repeated the previous exercise, this time for the synthetic earthquake catalog used in the design
phase (Fig. 6.5). Hence, several synthetic travel time datasets were inverted for the original
12 and final 23 station networks. Their resulting accuracy and error differences are depicted
in Fig. 6.10. Notice how the accuracies have improved around 0.2 km for all hypocentral
components and location errors. The network symmetry around the epicenters contribute to
better epicentral estimates, whereas positions on top and far from them contribute to better
depth estimates (Steinberg and Rabinowitz, 2003).
Overall, inversion results are subject to changes depending on the initial values and travel
time (picking) errors. In this study we have overestimated these values, so better results should
be expected with lower picking errors. Errors in the velocity model were also not accounted
for in this analysis. All things considered, the resulting accuracies and errors are acceptable
for the seismic network purposes, therefore validating this final 23 station array as adequate.
6.4 Case study II: Reykjanes seismic data and network perfor-
mance
The Reykjanes peninsula is a region located in SW Iceland (Fig. 6.11a) characterized by high
volcanic and seismic activity resulting in a large number of high temperature geothermal areas
(Blanck et al., 2018b, this issue). A total of 6 fields are currently being exploited in this region
and are associated to four NE-SW oriented fissure swarms connected to 4 different volcanic
systems (Harðardottir et al., 2009). Particularly the Reykjanes field located at the tip of the
peninsula has a capacity of 100 MWe (Friðleifsson et al., 2018, this issue).
Within the framework of the IMAGE project (Integrated Methods for Advanced Geothermal
Exploration) a passive seismic array consisting of 86 on-land sensors and OBS distributed on
and around the peninsula was used to monitor the seismicity, and enhance and develop existing
and new passive seismic techniques for imaging geothermal fields (Fig. 6.11a). The array
consisted of 30 temporary on-land seismometers distributed in a concentric fashion around the
Reykjanes peninsula, 26 OBS surrounding the peninsula, 8 seismic stations handled by ISOR for
the permanent monitoring of the Reykjanes geothermal field, 15 stations of the Czech Academy
of Science (CAS) used for monitoring the Krýsuvík geothermal system, and 7 permanent
stations handled by the IMO as part of the national seismic network (Blanck et al., 2018b,
this issue). The array recorded from march 2014 to august 2015, and the resulting dataset
55
6. Optimized experimental network design for microseismicity location and monitoring
Accuracy -X
ML0.5 ML0.8
Accuracy -Y
Accuracy -Z
0 10 20 30 40 50 60 70 80
x (km)
0
10
20
30
40
50
60
70
80
y (km)
Accuracy -Y(km) Depth = 3.00 km
station locations
0 0.5 1 1.5 2 2.5
Accuracy (km)
Figure 6.8:
Accuracies of hypocentral coordinates for events at 3 km depth. The first column
indicates events of ML0.5 and the second of ML0.8. Red triangles mark station positions.
was used to study the regional seismicity and structures by means of re-localization and focal
mechanism analysis (Blanck et al., 2018b, this issue), travel time tomography (Jousset et al.,
2016), ambient noise analysis (Weemstra et al., 2016), and seismic interferometry (Martins
et al., 2020b; Verdel et al., 2016, this issue). Einarsson et al. (2018, this issue) additionally
analyzed the natural and exploitation related stress field changes of the region.
56
6.4 Case study II: Reykjanes seismic data and network performance
Mean inversion error
ML0.5
a)
ML0.8
b)
0 10 20 30 40 50 60 70 80
x (km)
0
10
20
30
40
50
60
70
80
y (km)
Error (km) Depth = 3.00 km
station locations
0 0.5 1 1.5 2 2.5 3 3.5 4
Error (km)
Figure 6.9:
Mean inversion errors for events at 3 km depth and magnitudes a) M
L
0.5 and b)
ML0.8.
6.4.1 Seismic network quality
A total of 2066 earthquakes were automatically detected with an STA/LTA approach after
which P- and S- wave arrivals were picked manually. An initial earthquake location was carried
out by Blanck et al. (2018b, this issue) using the 1D SIL velocity model (Bjarnason et al.,
1993), and later relocated the hypocenters using the model derived by Jousset et al. (2016)
shown in Fig. 6.12a. For the exercise of qualifying the network design we reduce the seismic
catalog to account only for events placed within the network and located with at least 3 P-
and 3 S- wave picks. The remaining 1981 seismic events are displayed as blue points in Fig.
6.11a and Fig. 6.11b. Seismic events are mostly distributed along the mid-ocean ridge, with
the majority located close to the Reykjanes peninsula tip (third cluster on the right). These
earthquakes reach a maximum depth of around 6km, marking the brittle-ductile boundary of
that region in accordance to a previous study by Kristjánsdóttir (2013). Fig. 6.12b depicts the
maximum station-event distance relationship per earthquake needed to construct theoretical
deploying areas. Notice how a significant number of events reach a maximum distance of around
10 km corresponding, in a large degree, to events located under the Reykjanes peninsula.
To assess the quality of the Reykjanes seismic array with respect to the located earthquakes
we ran the DSSD algorithm using the 86 station positions as hypothetic "location points". Fig.
6.13a illustrates the resulting order of importance of the receiver positions. As in previous
design exercises the routine has primarily selected stations located above most seismic events
(close to the Reykjanes peninsula tip), followed by some outer stations. Fig. 6.13b and Fig.
6.13c depict design qualities Θ
tot
and Θ
event
, respectively. Like before, cost curves decrease
progressively and become almost flat with the total number of stations. The quality Θ
event
limit for the total 86 sensors range from -1.83 to 8.4, corresponding to an average per event
57
6. Optimized experimental network design for microseismicity location and monitoring
a) b)
c) d)
Figure 6.10:
Location accuracy and error differences between the original (12) and final (23)
station networks for events in the synthetic earthquake catalog of Fig. 6.5
of 2.35 obtained from Θ
tot
. If we move to 80%of the seismic stations (71 sensors) the range
of Θ
event
is of -1.60 to 8.4 and a mean 2.41 per event from Θ
tot
. This means that some
∼
18
stations could be spared to provide similar confidence ellipsoid volumes, therefore hinting
the importance of a preliminary survey design experiment to optimize costs. In a similar
sense, these theoretical results highlight the importance of some of the OBS deployed (in dark
blue). OBS deployment was originally not contemplated in the project but by this study, their
eventual placement is justified.
Fig. 6.14 shows the resulting accuracies and expected errors of inverted datasets associated
to smaller arrays. The Vp/Vs ratio was taken at 1.78 (Blanck et al., 2018b, this issue). P- and
S- wave synthetic datasets were contaminated with normal distributed errors with means at
0.15 s and 0.30 s, respectively, and later inverted to obtain hypocentral parameter accuracies
and errors. It is clear once more how accuracies seem to remain stable from 80%stations on.
The 86 station network was nevertheless chosen to account for alternative seismic techniques
such as ambient noise tomography (Martins et al., 2020b, this issue). For this analysis we have
once more ignored effects of different source mechanisms, heterogeneous noise distribution,
58
6.4 Case study II: Reykjanes seismic data and network performance
a)
b)
3.6 3.8 4 4.2 4.4 4.6 4.8
Easting [m] 105
-3
-2
-1
0
1
Depth [m]
104
Figure 6.11:
a) Seismic events, seismometers, and OBS positions. b) EW profile. Topography is
ignored for its rather small variation.
a)
0 2 4 6 8 10 12 14
Vp (km/s)
0
5
10
15
20
25
Depth (km)
1D Vp(z)
b)
0 20 40 60 80 100 120
Maximum detection distance [km]
0
100
200
300
400
500
600
Instances
Figure 6.12: a) 1D Vp velocity model (Jousset et al., 2016). b) Maximum detection distances.
59
6. Optimized experimental network design for microseismicity location and monitoring
and sensor installation quality, though we encourage further studies accounting this additional
information.
a)
24 oW
30'
23 oW
30'
22 oW
30'
21 oW
24'
36'
48'
64 oN
12'
0 20 40 60 km
10
20
30
40
50
60
70
80
Added stations
Event Locations
b)
10 20 30 40 50 60 70 80
Number of used stations
0
1
2
3
4
5
6
Total design quality [ tot ]
10 4
c)
0 10 20 30 40 50 60 70 80
Number of stations placed
-5
0
5
10
15
20
25
30
Event design quality contribution [ event ]
Figure 6.13:
Reykjanes network quality. a) Order of importance of the Reykjanes seismic stations.
b) Total design quality of the survey setup after progressively adding stations. c) Design quality
contribution per event for the whole experiment. The dashed red lines indicate the limits of 50%,
60%, 70%, 80%, and 90%stations.
60
6.5 Discussion
45 50 55 60 65 70 75 80 85
Number of stations
0.1
0.2
0.3
0.4
0.5
0.6
Deviation [km]
RMS Accuracy x-
RMS Accuracy y-
RMS Accuracy z-
RMS Error (real position - inverted result)
Figure 6.14: Location accuracies given by a station number reduction
6.5 Discussion
The linearized sequential survey design hereby explored is a rather simple method for building
and qualifying seismic networks; however, it presents some drawbacks that must be addressed
to obtain optimal designs.
6.5.1 D-optimality
Results using the chosen objective function Θare very influenced by overlapping deploying
areas, favoring them when these are very large. While this behavior could favor locating
receivers that record as many possible events, it could also compromise the optimization of
single events. It is therefore of importance to first identify main target earthquakes to allocate
them high weighting factors
γi
(Eq. 6.4) prior to design. When no a priori accurate locations
are known, an experiment similar to the one shown in Fig. 6.3 can be used.
Another issue that must be considered when using the D-criterion is station clustering.
This phenomena is particularly likely in problems involving large number of stations to be
placed in reduced deploying areas (e.g. Case I), or when failing to place stations right above a
studied epicenter (e.g. Test Case A). Station clustering is the consequence of Θignoring model
error correlations. One way to account for this correlation is by introducing an inter-station
distance weight as performed by Hardt and Scherbaum (1994). In this work we decided to
overlook this correction, and interpret the clustering as regions of importance instead (e.g.
Kraft et al., 2013).
6.5.2 Linearized destruction sequential survey design
In this work, we have explored a linearized destruction sequential survey design algorithm
for its robustness, simplicity, and its ability to obtain optimal network configurations. A big
advantage of sequential routines is their ability to quickly take into account changes of station
positions (had they not been placed exactly at theoretical locations) and recompute design
experiments for new geometries. Additionally, sequential survey design allows for an intuitive
analysis of benefit/cost relations.
61
6. Optimized experimental network design for microseismicity location and monitoring
However, one disadvantage of destruction schemes comes with the computational expense
when dealing with large number of earthquakes and candidate station positions. With
destruction techniques one has to build the entire sequence/order of stations to obtain the
position of even a few of them. Construction algorithms on the other hand provide much faster
and cheaper results however possibly compromising global optimality. Given that at each
iteration a new station is placed, these algorithms require only as many iterations as stations
needed. This technique could then provide a framework for potential design-during-deployment.
However, one main drawback of construction design is its need for good initialization (setting
the first station position) which can seriously influence design optimality. Another sequential
design option with better global optimality is exchange design (Coles and Curtis, 2011b). These
algorithms scan through all observation points and replace station positions that extremize the
objective function. Although quite robust in achieving global optimality, this routine requires
twice as much computation than the previous two, given that each iteration needs two steps:
construction and deletion.
Overall, although global optimality cannot be guaranteed with linearized sequential design
approaches, these techniques provide fast optimal designs nonetheless. The simplicity of
these routines is particularly useful in cases that require quick designs like post-earthquake
aftershock studies, or simply building quick temporal networks. All the same, for cases requiring
permanent stations or extended monitoring we recommend alternative design approaches such
as global search algorithms like simulated annealing, and/or non-linear experimental design.
Although some of these schemes may represent higher computational demands, they do ensure
global optimality.
6.5.3 Detectability
Another key aspect to address in survey design is detectability. Detectability is very roughly
considered in this work, however it is critical for defining candidate points for deployment.
In our experiments we have considered homogeneous noise levels and SNR. In reality, these
values are laterally variant and are very much site-specific. Authors like Kraft et al. (2013) for
example calculated a first order ambient noise model to observe the lateral noise variations
in Switzerland. Then, they compared these values with phase amplitudes modeled using
Brune’s source model (Brune, 1970, 1971) to determine the detecting stations. This procedure
was possible given the availability of prior seismic data for this region. In practice, detailed
knowledge of lateral velocity variations, anisotropy, attenuation, site-specific noise, SNR levels,
etc. is largely unknown in unstudied areas. Hence the need of a seismic array in the first place.
Inevitably, we would in many cases rely on oversimplified models and assumptions that could
potentially lead to suboptimal designs. For this reason we recommend repeating optimization
experiments once more information on the target site becomes available, especially in cases
requiring permanent or extended monitoring. Survey design could in these cases be regarded
as an iterative procedure that improves with our knowledge of the target area.
6.5.4 Design and qualification of seismic arrays
Case study I offers a real case for constructing a small microseismic array in Theistareykir
geothermal field. This case however considers very clustered events as location targets which
62
6.6 Conclusions
directly affects station placement due to large deploying areas overlap. Nonetheless we have
judged that the region considered is appropriate for fieldwork conditions and therefore decided
not to assign higher
γi
values for larger events. With the introduced routine we have constructed
a 23 station network. The network performance was later tested by carrying out several Monte
Carlo experiments to calculate standard deviations of the inversion results with theoretical
noisy data. Monte Carlo experiments however can be very computationally expensive. For
this reason we discussed the use of "goodness maps" which are simply the spatial distribution
of quality measure Θ. These maps are much faster to compute and can qualitatively reveal
the extents of areas where events would be better constrained by the network.
Case study II uses the same design scheme to qualify an existing seismic array at the
Reykjanes peninsula. The algorithm is applied in the same fashion as in Case I, however with
the deployed stations as potential placement points. This approach results in the construction
of a station order of importance. We later tested the effects of removing least important
stations in the resulting location uncertainties. It was noticeable for the Reykjanes network,
that we would arrive to similar location uncertainties with only 71 stations out of 86. These
findings are of critical importance especially with constrained project budgets, hinting the
value of experimental survey design prior to deployment. On a similar tone, many seismic
experiments require moving stations to different positions at some point in time. Therefore
similar analysis can help identify which stations are crucial to the experiment and which can
be moved without affecting location uncertainties significantly.
6.6 Conclusions
We have successfully constructed and applied a DSSD algorithm for designing new optimized
seismic networks, and qualifying existing ones for geothermal studies in the framework of
sequential survey design based on the D-criterion. The DSSD scheme hereby explored uses
a 1D velocity model for sensitivity computations, and was first tested with simple test-cases
where concepts like benefit and cost were introduced. The routine was then applied to two
case studies, one for designing (Theistareykir) and a second one for qualifying (Reykjanes) an
existing seismic array.
After constructing a synthetic earthquake catalog in accordance with previously observed
seismic data, the Theistareykir network was augmented with the DSSD algorithm, from 12
to 23 sensors, reaching hypocentral accuracies of around
∼
0.5 km for normally distributed
picking errors of mean 0.2 s (for tP) and 0.4 s (for tS).
Finally the Reykjanes network was tested with the same algorithm to observe whether its
design was adequate for the recovered earthquake catalog. From the design quality values it
became apparent that up to
∼
18 stations could be spared for the survey, or conversely relocated
for better results. It is therefore of importance to conduct a survey design experiment prior to
deployment to obtain best possible location results. In this study we have not considered the
effects of variable seismic noise, for which a better detectability study could be carried out in
the future to refine results. Another interesting topic for future research is the building of a
multi-purpose network design for both velocity model and seismic event locations, and the use
of alternative non-linear quality metrics.
63
6. Optimized experimental network design for microseismicity location and monitoring
Acknowledgements
We gratefully acknowledge the help of M. Weber for the fruitful discussions and comments on
this paper. We are equally very grateful for the comments of two anonymous reviewers, whose
remarks vastly helped improving this manuscript.
This work received funding from the European Union’s Horizon 2020 research and innovation
program under grant agreement No. 727550 (GEMex project).
64
7
Local earthquake tomography of a
geothermal field
This chapter focuses on the calculation and interpretation of a local earthquake tomography at
the producing Los Humeros geothermal field in Mexico. In addition to the traditional inversion
method described in Chapter 4, resolution enhancement is explored in this publication by
inverting and averaging the inversion results of several initial parametrizations.
Local earthquake tomography at Los Humeros geothermal field (Mexico)
Tania Toledo, Emmanuel Gaucher, Philippe Jousset, Anna Jentsch, Christian Haberland,
Hansruedi Maurer, Charlotte Krawczyk, Marco Calò, Ángel Figueroa
Accepted for publication in Journal of Geophysical Research: Solid Earth.
©2020. The Authors.
This is an open access article under the terms of the Creative Commons Attribution License,
which permits use, distribution and reproduction in any medium, provided the original work
is properly cited.
https://doi.org/10.1029/2020JB020390
A passive seismic experiment using 25 broad-band and 20 short-period stations
was conducted between September 2017 and September 2018 at Los Humeros
geothermal field, an important natural laboratory for superhot geothermal
systems in Mexico. From the recorded local seismicity, we derive a minimum
1D velocity model and obtain 3D Vp and Vp/Vs structures of Los Humeros. We
improved the classical local earthquake tomography by using a post-processing
statistical approach. Several inversions were computed and averaged to
reduce artifacts introduced by the model parametrization and to increase the
resolution of the investigated region. Finally, the resulting Vp and Vp/Vs
structures and associated seismicity were integrated with newly acquired
geophysical and petrophysical data for comprehensive interpretation. The
recorded seismicity is mainly grouped in three clusters, two of which seem
65
7. Local earthquake tomography of a geothermal field
directly related to exploitation activities. By combining new laboratory
measurements and existing well data with our Vp model we estimate possible
geological unit boundaries. One large intrusion-like body in the Vp model,
together with neighboring high Vp/Vs anomalies hint at a region of active
resurgence or uplift due to the intrusion of new magma at the northern
portion of the geothermal field. We interpret high Vp/Vs features as fluid
bearing regions potentially favorable for further geothermal exploitation. Deep
reaching permeable faults cutting the reservoir unit could explain fluid flow
from a deeper local heat source in the area.
Introduction
Los Humeros Volcanic Complex (LHVC) is a superhot geothermal system located at the eastern
edge of the Trans-Mexican Volcanic Belt (TMVB), a volcanically active region favorable for
geothermal energy exploitation. It is one of the oldest producing fields in the region, with
more than 60 wells drilled up to
∼
3 km deep since the early 80s (Arellano et al., 2003; Cedillo-
Rodríguez, 1999; Gutierrez-Negrin and Izquierdo-Montalvo, 2010; Rocha-López et al., 2010).
Currently, it has an installed capacity of
∼
95 MW electric power and is administered by the
Comisión Federal de Electricidad (C.F.E.) (Romo-Jones et al., 2018). Temperatures as high as
400
◦
C have been measured in several producing wells at
∼
2.5 km depth. However geothermal
fluids at these temperatures are presently not being exploited. Despite the large number of
studies on the geochemical (e.g. Martinez and Alibert, 1994), geological (e.g. Carrasco-Núñez
et al., 2017a,b), structural (e.g. Norini et al., 2015), and geothermal (e.g. Gutierrez-Negrin and
Izquierdo-Montalvo, 2010) properties of the reservoir, a solid understanding of the conditions
and underground structures at depth is still rather sparse. Only a few deep probing geophysical
studies (resistivity 2D profiles and seismic surveys) in recent years have provided notions of the
local stress field and structures of the geothermal field (Arzate et al., 2018; Gutierrez-Negrin
and Quijano-Leon, 2004; Lermo et al., 2001, 2008, 2016; Norini et al., 2019; Urban and Lermo,
2013).
One objective of this study is to investigate the deeper structures of the geothermal system,
to locate and better understand the deep super-hot fluids for their exploitation. Passive seismic
methods are to this purpose widely exploited in geothermal prospecting (e.g. Calò and Dorbath,
2013; Jousset et al., 2011; Muksin et al., 2013). Seismic properties such as the compressional
P- (Vp) and shear S- (Vs) wave velocities, and the Vp/Vs ratio structures have proven reliable
tools to describe lithologies and possible variations due to changes in fluid composition, rock
porosity, and temperature (e.g. Gritto and Jarpe, 2014; Husen et al., 2004; Ito et al., 1979;
Mavko and Mukerji, 1995). These are key features in geothermal exploration and monitoring.
One conventional approach to obtain the seismic properties of a target area is the 3D
tomographic inversion of P- and S- wave arrival times from local earthquakes, as observed
in records of seismometers deployed in the area of interest. The 3D velocity structure is
typically obtained through a joint inversion of hypocenter locations and velocity structures
using an a priori parameterized 3D grid model of the subsurface. Classical tomographic
results are strongly influenced by the inversion grid or node spacing choice, and hence its
66
7.1 Geologic and tectonic setting
adequate selection is fundamental to retrieve the main features of the subsurface for reliable
interpretation. A too fine model could, for example, lead to poor resolution values and/or
artifacts such as grid oscillations, whereas a too coarse model (especially a coarse fixed
grid) could overlook smaller underground features. In addition, significant smearing can be
introduced when the chosen grid does not follow the orientation of the main anomalies. In
this work, we extend the conventional tomographic method of a single fixed model grid by
using a post-processing statistical approach. We compute and average several inversions using
different model parametrizations to achieve higher spatial accuracy, reduce the effects of poor
parametrization selection, and overall increase model resolution.
In this study, we image the 3D Vp and Vp/Vs structures, along with the seismicity
distribution at Los Humeros geothermal field. In the first part of this study, we compile
information on the geological and structural setting of Los Humeros area. Later, we describe
the passive seismic experiment and the data processing workflow followed to detect and locate
the local seismic events. We use the retrieved earthquake catalog to derive a new so-called
minimum 1D velocity model in part 3. In part 4, we compute and average the 3D tomography
of several parametrized models using the minimum 1D velocity model as initial input. Finally,
part 5 proposes a first interpretation of the obtained results in relation to existing geological
information and newly acquired petrophysical, geochemical, and geophysical data (Bär and
Weydt, 2019; Benediktsdóttir et al., 2019; Jentsch et al., 2020; Lucci et al., 2020; Urbani et al.,
2020).
7.1 Geologic and tectonic setting
LHVC is a Quaternary geological complex constituted by two nested calderas: the older (ca
460 ky) outer 18-20 km wide Los Humeros caldera, and the younger (70 ky) subordinate 5-8
km wide Los Potreros caldera (Calcagno et al., 2018; Carrasco-Núñez et al., 2017a,b, 2018),
where most of the injection and geothermal production activities take place (Figure 7.1).
An extensive fault network crosses the main production zone of the geothermal field and is
responsible for secondary permeability in the reservoir. Several faults (e.g. Los Humeros fault
and the Loma Blanca fault) favor fluid flow and present strong hydrothermal alteration at the
surface (Norini et al., 2015, 2019). The main fault system runs around 8 km in a NNW-SSE
direction, and includes the Maztaloya fault and Los Humeros fault. A second set of faults
parting from the main system runs N-S, NE-SW, and E-W. Both sets disappear at the surface
when approaching Los Potreros caldera rim (Figure 7.1).
From a geological perspective, Los Humeros geothermal field can be divided into four
distinct groups: (1) regional meta-sedimentary basement, (2) pre-caldera, (3) caldera, and
(4) post-caldera volcanic phases, which can be subdivided into nine local lithostratigraphic
units (Calcagno et al., 2018; Carrasco-Núñez et al., 2017b). Here, we briefly describe the
lithologies found in the four major groups. The lower portion of the basement, also called
the Teziultlán Massif, is mainly composed of old instrusive igneous and metamorphic rocks
(Paleozoic granites, greenschists, and granodiorites) (Quezadas-Flores, 1961; Viniegra, 1965;
Yáñez and García, 1982). These rocks are covered by an up to 3 km-thick Mesozoic sedimentary
basement mostly constituted of limestones, with some silts and shales. The basement is overlain
67
7. Local earthquake tomography of a geothermal field
Figure 7.1:
a) Surface geology, b) main structures and well locations at LHVC (modified from
Carrasco-Núñez et al., 2017a; Norini et al., 2015). c) Locations of the Trans-Mexican Volcanic
Belt (TMVB) and LHVC (red triangle).
by the pre-caldera group (10.5 – 0.155 Ma) mainly composed of andesitic, dacitic, and to
a minor extent, basaltic lavas also known as Teziutlán andesites. The Teziutlán volcanic
unit hosts the active geothermal reservoir and has a thickness larger than 1500 m in some
of the geothermal wells within LHVC (Arellano et al., 2003; Carrasco-Núñez et al., 2017a,b;
Cedillo-Rodríguez, 1997, 1999; Ferriz and Mahood, 2009; Gutierrez-Negrin and Izquierdo-
Montalvo, 2010; Lorenzo-Pulido, 2008; Norini et al., 2019; Yáñez and García, 1982). The
basalts and andesites are sealed above by low-permeability Quaternary ignimbrites of variable
thickness belonging to the caldera stage (Arellano et al., 2003; Cedillo-Rodríguez, 1997, 1999;
Gutierrez-Negrin and Izquierdo-Montalvo, 2010; Lorenzo-Pulido, 2008; Norini et al., 2019).
This unit is characterized primarily by eruptive events which resulted in the formation of Los
Humeros and Los Potreros calderas (Carrasco-Núñez and Branney, 2005; Carrasco-Núñez
et al., 2012; Ferriz and Mahood, 2009; Norini et al., 2019). The post-caldera stage (0.05 –
<0.003 Ma) was influenced by different intra-caldera eruptive phases (effusive and explosive).
Rhyodacitic, andesitic, and basaltic lavas as well as pyroclastic material (Carrasco-Núñez et al.,
2018) were produced by various monogenetic volcanic centers which are scattered between Los
Potreros and Los Humeros caldera rims (Norini et al., 2015, 2019). During that time, another
significant eruption took place which resulted in the 1.7 km oval shaped Xalapazco crater in
the south of the complex (Carrasco-Núñez et al., 2018).
68
7.2 Seismic monitoring and data processing
7.2 Seismic monitoring and data processing
7.2.1 Seismic network
From September 2017 to September 2018, we deployed and maintained a temporary seismic
network comprising 25 three-component broadband (Trillium Compact 120s) and 20 three-
component short-period (Mark L-4C-3D) sensors recording continuous seismic data at sampling
rates of 200 Hz and 100 Hz, respectively (Toledo et al., 2019). The array consisted of two
complementary sub-networks each configured to characterize shallow and deeper structures
using different seismic processing techniques (Figure 7.2). A denser (
∼
1.6-2 km inter-station
distance) pseudo-rhomboidal array was located mainly in the inner Los Potreros caldera
where previous studies have identified the occurrence of local seismicity (Gutierrez-Negrin and
Quijano-Leon, 2004; Lermo et al., 2001, 2008, 2016; Urban and Lermo, 2013), and where most of
the producing and injecting wells are located. This sub-network was primarily designed for local
microseismicity retrieval (Gaucher et al., 2019), local earthquake tomography, beamforming
of ambient noise (Löer et al., 2020), time-reverse imaging (Werner and Saenger, 2018), and
autocorrelation techniques (Verdel et al., 2019). The second much sparser network (
∼
5-10
km inter-station distance) was placed around the outer Los Humeros caldera and was mainly
intended for imaging deeper large-scale structures with techniques such as ambient noise
tomography (Granados et al., 2020; Martins et al., 2020a), among others.
7.2.2 Local earthquake detection
We focused the event detection mainly on Los Potreros caldera (Gaucher et al., 2019) using
Python tools based on the ObsPy library (Beyreuther et al., 2010). We calibrated a recursive
STA/LTA detection algorithm (Trnkoczy, 2012; Withers et al., 1998) on several days of the
recently acquired seismic dataset (2017-2018) and on a set of local seismic events recorded
between 2005 and 2006 by the permanent network operated by the C.F.E. (Lermo et al., 2008).
We exhaustively tested the detection performance through several days of the recent seismic
database using a wide range of parameter combinations. The optimum parameters selected
were a combination of bandpass filter between 10-30 Hz, STA and LTA windows of 0.2 s and 2
s, respectively, and on and off trigger thresholds of the computed STA/LTA function at 3.5
and 1.0, respectively. To account for the P- and S-wave arrivals, the STA/LTA function was
computed from a single amplitude trace determined by the square root of the sum of the 3
single component squared traces for each station. Finally, a detection was declared as such
when the triggering window of at least 5 stations from the dense sub-network coincided in time
(Trnkoczy, 2012; Withers et al., 1998). We reviewed each triggered detection and manually
picked P- and S-wave arrivals of local events and their associated empirical uncertainty range
using the Python Obspyck tool (Megies, 2016).
From a total of 1586 detections, 488 were identified as local events. After picking P- and
S- phases, these earthquakes were located using an oct-tree search (Lomax et al., 2000, 2009)
in a homogeneous 3D volume with a P-wave velocity of 3.5 km/s and a Vp/Vs ratio of 1.73
(Figure 7.3). Later, we re-selected the seismic events with a greatest angle without observation
(GAP) of less than 180
◦
, and at least 3 P- and 3 S- wave arrivals (333 events in total) for the
calculation of a minimum 1D velocity model and their relocation. The recorded seismicity is
69
7. Local earthquake tomography of a geothermal field
Figure 7.2:
Topographic map and temporary seismic network at Los Humeros geothermal field.
Blue and red triangles mark the positions of three component short-period (Mark L-4C-3D) and
three-component broadband (Trillium Compact 120s) sensors, respectively. The reference station
for the 1D inversions (also a three-component broadband Trillium Compact 120s sensor) is marked
as a red circle. Several indentified and inferred structures are delineated in black (modified from
Carrasco-Núñez et al., 2017a; Norini et al., 2015).
mostly located below the dense array within Los Potreros caldera, and mainly grouped into
three distinctive clusters, marked as C1, C2, and C3 in Figure 7.3.
7.3 1D velocity model
We use the retrieved travel time data from the filtered catalog (333 events with 2146 P-wave
and 2146 S-wave picks) as input for a joint inversion to determine the so-called minimum
1D Vp and Vs models, and the hypocenter relocations using the code Velest (Kissling et al.,
1994). The code Velest iteratively computes forward modeled data (predicted travel times),
using a ray tracer in an initial model (1D velocity model, hypocenter locations, and station
corrections), compares the synthetic data to the observed dataset and updates the model such
that the RMS (root-mean-squared) misfit between the two is minimized (Tarantola, 2005).
This procedure uses regularization parameters (damping factors) to tackle instabilities due to
data uncertainties (Levenberg, 1944; Marquardt, 1963) and continues until a maximum number
of iterations is reached.
The estimation of a minimum 1D model consists of a trial and error process in which
typically a broad range of plausible initial models is tested to ensure covering as many potential
70
7.3 1D velocity model
C3
C1
C2
C3
C1
C2
0 2 5
km
°3°2°1 0 1 2 3 4
Catalog Depth [km]
-3 -2 -1 0 1 2 3 4
Catalog depth [km]
a) b)
Figure 7.3:
Distribution of the detected local earthquakes after a nonlinear localization in a
homogeneous 3D volume with a P-wave velocity of 3.5 km/s and a Vp/Vs ratio of 1.73. Triangles
mark the station positions and dark solid lines indicate structures inferred at the surface. Red
stars mark the positions of three injection wells. C1, C2, and C3 indicate the positions of three
main seismic clusters. Depths are defined relative to sea level.
solutions as possible and select the best fitting model. This procedure is necessary because the
inversions are based on linearization and thus strongly depend on the initial model. In this
work, we performed the inversion of 10648 initial models with varying P-wave velocities at
the surface, vertical velocity gradients, and Vp/Vs ratios (thus also varying Vs models) over 5
iterations. The software Velest allows tracing rays to the true station elevations. However this
option poses the limitation of locating all stations within the first layer. With this in mind, we
set the uppermost layer thickness to more than 1 km, which corresponds to the approximate
elevation difference between the highest and lowest recording stations. The following layers
are then defined roughly every 0.5 km at shallow depths, and progressively increase to 1
and 2 km for deeper levels. The depth intervals were chosen taking into account well data
interpretation (Norini et al., 2015, 2019) and exhaustive testing. We define depths relative
to sea level throughout this manuscript. The uncertainty of P- and S-arrivals were defined
by the weighting factors 0, 1, 2, and 3 corresponding to the estimated picking uncertainties
of up to 0.03 s, 0.08 s, 0.12 s, and higher, respectively. Finally, we selected station DB13 as
the reference station given its location at approximately the center of the dense array and
geothermal field, and its high number of recorded P- and S- arrivals (red circle in Figure 7.2).
Figure 7.4a and Figure 7.4b depict all the initial (yellow lines) and the 35 resulting velocity
models with lowest associated RMS misfit values (gray lines) for Vp and Vs, respectively.
The misfit values for this set of best models range from 95.0 ms to 96.1 ms. Note the good
agreement for several layers of the resulting velocity models, particularly between -1.0 and
1.5 km depth where most of the seismicity is located. This coherence becomes less obvious at
71
7. Local earthquake tomography of a geothermal field
shallower and greater depths, where only a few hypocenters are located. Few models show
values with large deviations from the more obvious trend. We create a heat map with this
set of final models in Figure 7.4c and Figure 7.4d to better reveal the most frequent velocity
values in each layer. Finally we manually select the model with the lowest misfit value (black
lines in Figure 7.4a and Figure 7.4b) that best coincides with the main trend of most frequent
velocity values (red lines in Figure 7.4c and Figure 7.4d) as the minimum 1D velocity model.
Figure 7.4:
Results of the 1D inversions using Velest. The 35 best a) P-wave and b) S-wave final
velocity models (gray lines). Heat maps for the same c) P-wave and d) S-wave set of final models.
The yellow lines indicate all initial velocity models used. The selected minimum 1D models are
indicated in black lines in panels a) and b), and in red lines in panels c) and d).
Figure 7.5 depicts the resulting P- and S-wave velocity models, the associated Vp/Vs ratio
and the final event distribution for the selected minimum 1D velocity model. The model is
72
7.3 1D velocity model
best resolved between -2 to 2 km depth approximately, which is consistent with the hypocenter
distribution shown in Figure 7.5c. The seismic events are restricted up to approximately
4 km depth from the surface, with a maximum number of events between -0.5 and 0.2 km
depth. The seismicity presents a systematic shift towards
∼
0.5-0.8 km greater depths and
some improvements in clustering after the 1D inversion. Two velocity models proposed by
Lermo et al. (2008) (P-wave) and Löer et al. (2020) (S-wave) are marked in green and magenta,
respectively, in Figure 7.5a. The Vp model proposed by Lermo et al. (2008) was derived using
a seismic reflection profile and reaches an approximate depth of -0.5 km, below which a default
value of 5.18 km/s is assigned. The Vs model derived by Löer et al. (2020) was obtained using
three-component ambient noise beamforming and is most sensitive in the interval between -0.5
and 10 km depth. Notice the good correlation between the derived minimum 1D Vp model
and the model obtained by Lermo et al. (2008), especially between -2.0 and -0.5 km. Similarly,
there is a good agreement between the derived minimum 1D Vs model and the model obtained
by Löer et al. (2020) between -1.0 and 2.2 km depth.
The station delays associated with the selected minimum 1D velocity model are also
consistent with the local geology and are further described in Appendix 7.A.
Figure 7.5:
Minimum 1D model showing: a) the selected Vp and Vs models along with 2 available
models (Lermo et al., 2008; Löer et al., 2020), b) the resulting Vp/Vs ratio, and c) the earthquake
distribution over depth after the 1D inversion. Solid lines indicate the depth intervals with best
sensitivity for each model.
73
7. Local earthquake tomography of a geothermal field
7.4 3D seismic tomography
After selecting the reference 1D velocity model and hypocenter locations, we used the 3D travel
time inversion code SIMUL2000 (Eberhart-Phillips, 1990; Eberhart-Phillips and Michael, 1998;
Evans et al., 1994; Thurber, 1983) to estimate the 3D velocity structure of the geothermal field.
Forward calculations are computed using a pseudo bending method (Um and Thurber, 1987)
and inversions are performed using an iterative damped least-squares scheme. The software
SIMUL2000 allows for the simultaneous inversion of Vp and Vp/Vs ratio instead of Vs to
account for the generally lower resolution of Vs models due to larger uncertainties of S-wave
arrival determination, most of them being hampered by the coda of the P-wave (Thurber,
1993; Thurber and Eberhart-Phillips, 1999). Inversions in this section are computed using the
minimum 1D Vp model and a homogeneous Vp/Vs of 1.71 obtained from a Wadati diagram
analysis of the stacked events.
Distance [km]
Distance [km]
Depth [km]
Depth [km]
a) b)
c)
Figure 7.6:
Ray path distribution after the 1D inversion: a) map view, b) N-S, and c) E-W
projections. Seismic stations are represented as purple triangles, local events as green circles.
The projections of three injection wells are marked as red lines in the cross sections. Dark solid
lines in the map view indicate structures inferred at the surface, and the gray lines correspond to
topographic contours.
74
7.4 3D seismic tomography
7.4.1 Model parametrization
An appropriate model parametrization is suggested by Evans et al. (1994) and Husen et al.
(2000, 2003) as that with the finest possible node spacing, which allows inversions without
strong derivative weighted sum (DWS) heterogeneities. The DWS is a measure for ray density
which takes into account the number of crossing rays, ray-node separation and raypath length
in the vicinity of each node (Evans et al., 1994; Husen et al., 2000). Kissling et al. (2001) advise
taking into account both a priori information about the underground structure and resolution
capabilities of a dataset when selecting appropriate model parametrization. Accounting for
known subsurface features could lead to a too fine model node spacing which in turn could
result in lower resolution values and sparse imaging. On the other hand, a coarse model
parametrization, although yielding higher resolution values due to increased ray density, could
potentially overlook smaller features in the subsurface. To avoid this effect, some authors (e.g.
Abers and Roecker, 1991; Bijwaard et al., 1998) use uneven node spacing in their inversions.
This technique could, however, complicate interpretations given some velocity changes may be
inadvertedly interpreted as underground features. One methodology often used is a graded
inversion approach (Evans et al., 1994; Husen et al., 2003). Iterations are performed through
finer grids using a coarse model output as input for a new inversion with a finer grid.
Some novel post-processing techniques include the averaging and weighted averaging of
several inversion results using different initial model parametrizations (e.g. Calò et al., 2013;
Haberland et al., 2009). This technique helps enhancing velocity anomalies, reduces possible
smearing effects and model noise due to the parametrization choice, overcomes the fixed coarse
parametrization limitation of the inversion code, and improves the model resolution. In this
study, similar to Calò and Dorbath (2013), we compute several inversions using different model
parametrizations which we later average on a finer grid.
Figure 7.6 shows the event to station raypath configuration in the initial minimum 1D
velocity model. Raypaths are unevenly distributed and mostly located within Los Potreros
caldera, reaching
∼
1.5 km depth for the most part. Taking into account the raypath
configuration, we chose an initial lateral parametrization of 1 x 1 km
2
(Figure 7.7) and
0.5 km inter-node spacing with depth within Los Humeros caldera region (Figure 7.8). We
then progressively increased the node spacing in regions outside Los Humeros caldera and
below the seismicity. Figure 7.7 and Figure 7.8 show the DWS distribution after a 3D inversion
using the chosen grid. DWS values are, as expected, larger within the regions above the
seismic clusters (higher ray density), and extend to 0 to -1 km depth. After the inversion, the
seismicity presents a systematic shift towards
∼
0.5-0.8 km shallower depths which could be
attributed to initially setting the station delays of the minimum 1D model to zero. To avoid
decreases in retrieved velocity amplitudes, we fixed the hypocenter locations during the first
iteration and updated the new relocations after each velocity inversion (Husen et al., 2003).
We constructed several inversion grids starting off with the previous grid, and then rotated
it in 15◦steps. A similar procedure was carried out after displacing the inversion grid center
0.2 and 0.5 km towards the north, south, east, west, northwest, northeast, southeast, and
southwest. Figure 7.9 depicts the nodes of the 228 inversion grids used. Although Calò (2009)
proposes the use of fewer models to reach a decent benefit of the post-processing technique,
we opted for a larger number of inversions to yield a more statistically stable final model.
75
7. Local earthquake tomography of a geothermal field
Note that both Los Potreros and Los Humeros calderas are densely covered by nodes.
To construct a new averaging grid, we interpolated all outputs post inversion onto a regular
finer grid with 0.1 km spacing using the same interpolation scheme as applied in SIMUL2000
(Thurber, 1983). Then we averaged each point of the new grid. Figure 7.10 shows several
depth slices for the average DWS using the new grid. The covered gray areas (regions with
any ray density) become larger than when using a single initial inversion grid, which could
be attributed to both the averaging of DWS values, but also to taking into account model
parametrizations that favor different ray orientations.
Vp/Vs modelVp model
Depth: -2.60 km Depth: -2.60 km
Depth: -1.10 km Depth: -1.10 km
DWS
a) b)
c)
A1
A1A1
A1
B1 B1’ B1 B1’
B1 B1’ B1 B1’
A1’ A1’
A1’
A1’
d)
Figure 7.7:
Model parametrization and DWS distribution at different depth levels for an initial
(unrotated) inversion grid. Panels a) and c) show two depth slices for the Vp model DWS
distribution at -2.6 km and -1.10 km depth. Panels b) and d) show the depth slices for the Vp/Vs
model DWS distribution at -2.6 km and -1.10 km depth. Darker shading indicates regions of higher
ray density. Gray crosses indicate node positions.
76
7.4 3D seismic tomography
Model: Vp Section A1-A1’
Model: Vp Section B1-B1’
Depth [km]
Depth [km]
X [km]
a)
c)
DWS
X [km]
Figure 7.8:
Cross sections A1-A1’ and B1-B1’ for the Vp model DWS distribution (Figure 7.7).
Darker shading indicates regions of higher ray density. Black crosses indicate the node positions.
7.4.2 Regularization
We performed a tradeoff test (Appendix 7.B) to select adequate damping values for a single
inversion grid (Eberhart-Phillips, 1990). Given the node spacing remained the same for all
228 inversion grids, we kept these damping factors fixed. Figure 7.11 shows the misfit value
changes with each progressive iteration for the 228 inversions. The misfits start at 0.2 s for all
models and progressively reduce to a mean value of
∼
0.102 s, which falls within the range of
the picking uncertainties, thus confirming the successful inversion of the models used with the
chosen regularization parameters.
7.4.3 Model quality and uncertainty
An adequate quality assessment of the solution is typically carried out to validate inversion
performance. The main objective is the identification of poorly resolved areas and unrealistic
model perturbations or artifacts that may have been introduced and affect interpretation.
Several parameters and procedures that analyze ray distribution and density include the
evaluation of the hit count, the diagonal element of the model resolution matrix (MRM), the
spread function (Michelini and McEvilly, 1991; Toomey and Foulger, 1989), the smearing
information of each node provided by the MRM, tests with synthetic data such as checkerboard
(Zelt, 1998) and recovery tests. In this study we calculate and display the results of a
77
7. Local earthquake tomography of a geothermal field
Figure 7.9: Nodes of the 228 inversion grids used to estimate the average velocities.
checkerboard test. Averaged spread values and diagonal elements of the MRM (RDE) are
shown in Appendix 7.C and 7.D, respectively.
We carried out a checkerboard test to determine what kind of anomalies can be retrieved
with the seismic network and catalog used. We perturbed the minimum 1D Vp model with
alternating
±
12%anomalies and the starting Vp/Vs model (constant value of 1.71) with
±
10%
perturbations. These anomalies are in agreement with the range of velocities obtained after the
3D inversion. Positive and negative anomalies are indicated in blue and red colors, respectively
(Figure 7.12 and Figure 7.13). They are comprise 4 nodes of the single grid (Figure 7.7) in
the horizontal directions (
∼
1.5 km x 1.5 km) and 2 nodes in the vertical direction (
∼
0.7-1
km). These perturbations have the approximate size of some of the main anomalies obtained
in the real data inversion. We computed synthetic traveltimes using the retrieved seismic
catalog and added Gaussian noise with
±
0.065 s standard deviation, which corresponds to the
standard deviation of the uncertainty distribution of the manual picks. Similar to the real
data inversion, we determined the damping parameters by performing a tradeoff test. Then,
we carried out inversions for the 228 grids of Figure 7.9 and averaged the results.
Figure 7.12 shows the recovered velocity anomalies for Vp and Vp/Vs across several depth
slices. Regions with higher ray density, particularly those closer to the identified seismic
clusters, appear to be best recovered. These areas coincide with those of lower spread and
high RDE values in Figure 7.21 and Figure 7.20, respectively. Depths between
∼
-2.10 km to
-1.6 km seem best resolved (Figure 7.12a, b, c, d), with errors of approximately
±
2-3 %in
the best cases for both Vp and Vp/Vs. At shallower and deeper levels (Figure 7.12e, f) the
polarity of the anomalies are recovered only towards the center and smeared towards the edges
78
7.4 3D seismic tomography
Vp/Vs modelVp model
Depth: -2.60 km Depth: -2.60 km
Depth: -1.10 km Depth: -1.10 km
DWS
a) b)
c) d)
Figure 7.10:
Averaged DWS distribution at different depth levels. Panels a) and c) show two
depth slices for the Vp model DWS distribution at -2.6 km and -1.10 km depth. Panels b) and
d) show the depth slices for the Vp/Vs model DWS distribution at -2.6 km and -1.10 km depth.
Darker shading indicates regions of higher ray density.
of Los Potreros caldera. Velocity uncertainties in these regions vary around
±
5-8 %. The
checkerboard is also well reproduced in some regions of the vertical sections (Figure 7.13). The
recovery looks best at the center of the cross sections A2-A2’, B2-B2’, and C2-C2’ to a depth
of -1 km, after which anomalies become smeared once more. The polarities of some velocity
anomalies, however, are reproduced to 0 to -0.2 km depth towards the center of section B2-B2’.
Overall, the uneven seismicity distribution (raypath configuration) marks a very limited area
(shallow north-central portion of Los Potreros caldera) of good recovery. This region coincides
with the area where spread values fall below a value of 1.5.
It is worth noting that a single inversion using the same grid configuration as the one used
to produce the synthetic model perturbations is able to retrieve these anomalies accurately.
However, when the parametrization is considerably different (e.g. a shifted or rotated grid),
the recontruction is worsened and significant smearing is introduced, distorting the anomalies.
79
7. Local earthquake tomography of a geothermal field
Iteration Number [-]
RMS misfit [s]
Final RMS misfit range: 0.10 – 0.11 [s]
Figure 7.11: RMS misfit variation for the 228 inverted models.
In reality it is complicated to know beforehand the location and direction of the perturbations.
By averaging several inversions using different model configurations, the dependence of the
results on a single model parametrization is reduced, therefore significantly enhancing the
accuracy of the final model.
80
7.4 3D seismic tomography
Figure 7.12:
Checkerboard recovery. Panels a), c), and e) show three depth slices for the recovered
Vp anomalies at -2.6 km, -2.10 km, and -1.10 km depth. Panels b), d), and f) show the recovered
Vp/Vs anomalies at -2.6 km, -2.10 km, and -1.10 km depth. The red and blue squares mark the
positions of the synthetic high and low velocity anomalies. Gray areas mark the regions where the
DWS is less than or equal to 5.
81
7. Local earthquake tomography of a geothermal field
Figure 7.13:
Cross sections A2-A2’, B2-B2’, C2-C2’, and D2-D2’ (Figure 7.12) for the retrieved
Vp and Vp/Vs model variations. Panels a), c), e), and g) show the recovered Vp anomalies, and
panels b), d), f), and h) show the recovered Vp/Vs anomalies of the checkerboard test. Gray areas
mark the regions where the DWS is less than or equal to 5.
82
7.5 Results and discussion
7.5 Results and discussion
The retrieved Vp (Figure 7.14 and Fine 7.15) and Vp/Vs (Figure 7.16 and Fine 7.17) models
together with the seismicity distribution provide new insights on the geometry of the different
geological units of LHVC, and the relation between some of the main structures and the
geothermal system. In this section, we describe and discuss the results of the 1D and 3D velocity
inversions in relation to existing geological and newly acquired petrophysical, geochemical,
and geophysical data at Los Humeros geothermal field.
7.5.1 1D velocity model
The selected minimum 1D velocity model (Figure 7.5) not only shows a good agreement with
alternative studies on the region (Lermo et al., 2008; Löer et al., 2020), it also shows one
possible geological boundary observed in retrieved well data (Norini et al., 2019). A prominent
discontinuity is seen at
∼
-1.2 km depth in Figure 7.5 for both Vp and Vs models. This
discontinuity could potentially mark an average transition between the pre-caldera group and
the sedimentary basement, as it is also seen in well data at
∼
-1.5 to -0.2 km depth (Norini
et al., 2019). Vp/Vs ratio values are fairly constant but rather low at different depth levels,
with the exception between -0.5 and 0 km depth, where most of the seismicity is concentrated
(hence the larger average value of 1.71). These unusually low values could be the consequence
of lateral averaging and the irregular distribution of sources and receivers. For this reason, we
consider that the minimum 1D velocity model should not be overinterpreted.
7.5.2 Seismicity distribution
Main results
The final earthquake catalog was obtained by averaging the coordinates and origin times of
the output catalogs of each inversion. The standard deviation of each component was used to
quantify the location uncertainties which were on average 131 m, 127 m, 214 m, and 0.027
s for x, y, z, and origin time, respectively. These values represent in some way the intrinsic
tradeoff between the errors of the model and hypocenter estimations.
Discussion
Similar to the catalog obtained after the initial relocation, the seismicity is grouped in three
clusters (Figure 7.3). The northernmost cluster (C1 in Figure 7.3) has already been evidenced
in Lermo et al. (2008) and is situated close to the main production area, where two out of
three neighboring injection wells are located (red stars in Figure 7.3). The southwestern cluster
(C2 in Figure 7.3) is located to the west of Los Humeros fault, close to a third injection well.
Finally, a deeper cluster (C3 in Figure 7.3) is located towards the east, between Las Papas
and Las Viboras faults. The remaining events are scattered within the geothermal field, with
some following major structures such as the Maztaloya fault.
Cluster C1 (Figure 7.15a and Figure 7.17a) has a narrow sub-vertical distribution relating to
Los Humeros Fault Zone at the surface. We define Los Humeros Fault Zone as the combination
of very closely spaced (
∼
100-250 m) N-S fault strands (Loma Blanca fault, Los Humeros
83
7. Local earthquake tomography of a geothermal field
fault, and Los Conejos fault). In a similar manner, cluster C2 (Figure 7.15c and Figure 7.17c)
reflects the position of Los Humeros fault further south. Given their vicinity to injection
wells (see green vertical lines in Figure 7.15 and Figure 7.17), most of them could probably
be induced/triggered events. The third cluster (C3) is located at a deeper level towards
the east (Figure 7.15b, c and Figure 7.17b, c). At the surface, this region coincides with
the area between the E-W trending Las Papas and Las Viboras faults, but does not seem
directly associated with any geothermal wells. However, the proximity of this cluster to C2
could potentially indicate a deeper fluid pathway towards the east. These two faults show
no hydrothermal alteration along their strike at the surface (Norini et al., 2019). However,
the presence of this cluster could hint to an increase of permeability of these faults at greater
depths.
7.5.3 Vp structure
Main results
Our results provide new detailed insights into the 3D P-velocity structure of Los Humeros
geothermal field. We present our results in a series of horizontal depth slices (Figure 7.14)
followed by E-W vertical sections (Figure 7.15) across Los Potreros caldera. Average P-wave
velocities range from
∼
2-4.1 km/s, with standard deviations in the order of
±
0.06 km/s
(Figure 7.22 in Appendix 7.E). We show velocity perturbations relative to the minimum 1D
Vp model, as it is easier to observe the physical properties of rocks (e.g. presence of fluids and
temperature) in this form. Nevertheless, we show absolute velocity values with contour lines
in the cross sections to ease interpretation.
Close to the surface (Figure 7.14a), a large low velocity anomaly (
∼
-8 to -12%) marked as
a(Figure 7.14a) is located at a highly faulted region towards the center of Los Potreros caldera.
This anomaly is surrounded by high velocity anomalies (
∼
+6 to +10%) to the northeast,
south, and west (marked as b). Further in depth (Figure 7.14b), a clear division between
high (
∼
+10%) and low (
∼
-5%) velocity anomalies (cand d) is separated by the main Los
Humeros fault. This velocity contrast remains at depth, although the low velocity anomaly
to the east appears attenuated (
∼
-3%) at deeper levels. One large high (
∼
+10 to +13%)
velocity anomaly (h) appears at -1.60 km depth (Figure 7.14c) almost following Los Humeros
and Maztaloya faults, which extends in a much narrower corridor at -1.10 km depth (jin
Figure 7.14d).
If we observe the Vp variations in cross sections (Figure 7.15a, b, and c), the high velocity
anomaly is located mostly towards the east of Los Humeros normal fault. At larger depths,
a second minor high (
∼
+3%) velocity anomaly (mainly visible in sections B-B’ and C-C’)
appears further to the east where cluster C3 is located. This feature barely reaches the limits
of the imaging capabilities of our dataset, and must therefore be interpreted with caution.
A smaller low (
∼
-5 to -3%) velocity anomaly appears west of the northern portion of Los
Humeros Fault and is traceable at depth (f,g, and iin Figure 7.14). This anomaly is also seen
in the cross sections (Figure 7.15a, b, and c), mostly west of the buried La Antigua fault. The
low velocity region visible to the east in cross sections B-B’ and C-C’ is associated to din
Figure 7.14b.
84
7.5 Results and discussion
Discussion
Some of the velocity anomalies at -2.6 km depth (Figure 7.14a) accurately follow the surface
geology (See Figure 7.1). The low velocity anomaly marked as ais located where undefined
pyroclastics belonging to the post-caldera stage are deposited (Figure 7.1). In a similar manner,
the high velocity anomalies marked as b, are related to regions with rhyodacitic, andesitic, and
basaltic volcanic rocks.
The high velocity anomalies observed at depth correspond to intrusive-like bodies in the
absolute velocity contour lines. Similar structures have been indicated by the combined
interpretation of structural field analysis, and analog modelling at Los Potreros caldera and
interpreted by Norini et al. (2019) and Urbani et al. (2020) as discontinuous resurgence
associated with the intrusion of multiple magma bodies rather than a single magma chamber.
The shallow low velocity anomalies in cross sections B-B’ and C-C’ indicate the increased
thickness of the post-caldera unit in these areas and reveal the variable deposition of volcanic
materials during the complex volcanic history of the caldera.
To determine possible unit boundaries, we marked the positions of several neighboring
interpreted wells (Carrasco-Núñez et al., 2017b) in the cross sections shown in Figure 7.15.
We compared the depth ranges of the units seen in the interpreted wells with ultrasonic pulse
velocity measurements of collected core and outcrop rock samples (Table 7.1) and our retrieved
velocities. Then, we marked approximate unit boundaries with solid gray lines in Figure 7.15.
We deduced the post-caldera stage (pyroclastics) with Vp around
∼
2.2-2.4 km/s at shallow
depths. This velocity range is well within the range of laboratory measurements of collected
rock samples (2.0-3.7 km/s). The caldera stage (mainly ignimbrites) lower boundary was
interpreted at around -2.0 km depth with average Vp of 2.8 km/s. Laboratory measurements
range between
∼
1.8-3.5 km/s for rocks found in this unit. Below, we interpreted the pre-
caldera unit (andesites) with Vp up to
∼
3.8-3.9 km/s. After that the marbles and limestones
belonging to the basement start in our sections with Vp
≥
3.9 km/s. The basement boundary
is shallower close to Los Humeros fault zone.
7.5.4 Vp/Vs structure
Main results
Average Vp/Vs values varied between 1.50 and 1.77 throughout the studied region (Figure 7.16
and Figure 7.17), with standard deviations in the order of
±
0.02 (Figure 7.22 in Appendix
7.E).
At shallow depth (Figure 7.16a), a prominent low Vp/Vs anomaly (
≤
1.60) is located at
the northern portion of Los Humeros fault system with the lowest values concentated between
Los Humeros, La Cuesta, and Cueva Ahumada faults (k). This anomaly extends at depth
towards the southeast (land nin Figure 7.16). This behavior is also seen in the cross sections
of Figure 7.17, where in many cases the anomaly extends at depth mostly towards the east of
Los Humeros fault.
On the other hand, two higher Vp/Vs anomalies (
≥
1.71) are observed at the northern
portion of Los Potreros caldera (oin Figure 7.16) at -1.10 km depth. These anomalies are
85
7. Local earthquake tomography of a geothermal field
Table 7.1:
Approximate mean P- velocities obtained from laboratory measurements of different core and outcrop rock samples. Modified from Bär and Weydt
(2019)
.
Stage Lithology P-wave
velocity (km/s) Stage Lithology P-wave
velocity (km/s) Stage Lithology P-wave
velocity (km/s) Stage Lithology P-wave
velocity (km/s)
Basement
Limestone J 4.5
Pre-caldera unit
Andesite
(core) dry/
saturated
4.1
Caldera unit
Xaltipan
Ignimbrite
(outcrop)
altered
3.0
Post-caldera unit
Ash fall
(outcrop) 2.0
Limestone K 4.7
Teziutlan Andesite
(outcrop)
porous
3.0
Xaltipan
Ignimbrite
(outcrop)
1.8 Basalt
(core) 2.5
Skarn (outcrop) 4.3 Teziutlan Andesite
(outcrop) 4.8 Ignimbrite
(core) 3.5 Basalt
(outcrop) 3.7
Marble (core)
dry 3.0 Alseca andesite 2.8 Ignimbrite
(outcrop) dry 2.3
Inner
caldera
ignimbrite
(outcrop)
2.2
Marble (core) 4.1 Cuyoaco andesite 3.0
86
7.5 Results and discussion
particularly evident in Figure 7.17a and Figure 7.17b. In Figure 7.17a the high Vp/Vs anomalies
are divided by the Los Humeros fault and the anomaly towards the east is higher.
Discussion
Although Vp/Vs values appear low in Los Humeros (minimum
∼
1.5), they are not uncommon
in volcanic and geothermal regions (e.g. Husen et al. (2004) (minimum
∼
1.57), Muksin
et al. (2013) (minimum
∼
1.47)). The shallow low Vp/Vs anomaly coincides in shape and
position with a conductive body (
≤
10 Ωm) imaged by a new MT survey at Los Humeros
geothermal field (Benediktsdóttir et al., 2019), hinting at the location of the cap rock composed
of ignimbrites. If we consider porous media (and low Vp), this region of low Vp/Vs values can
be inferred as a gas bearing chamber (Gassmann, 1951). Such interpretation is supported by
the modelling of low Vp and low Vp/Vs anomalies in porous volcanic rocks in Husen et al.
(2004). This hypothesis is confirmed by a new survey of CO
2
emissions at the surface (Jentsch
et al., 2020), where higher flux regions coincide with kin Figure 7.16a.
Further in depth, the high Vp/Vs anomalies could hint at regions with increased liquid
content (Gassmann, 1951). The anomaly to the east of Los Humeros fault zone (Figure 7.17a)
coincides with a region close to the bottom of a neighboring injection well. West of Los
Humeros fault zone, the second high Vp/Vs anomaly coincides with generally lower Vp values
(3.2-3.4 km/s), which could be an indication of rocks, namely the andesites, influenced by the
presence of liquid. These areas could potentially be considered for further exploration and
exploitation of the geothermal field.
A local heat source could be assumed as located at greater depths transporting heat along
permeable faults especially in the region close to Los Humeros Fault zone. Such a hypothesis
would be in correlation with the analog and structural work by Urbani et al. (2020) that
suggests recent shallow magma emplacement in the region close to the Loma Blanca fault.
Given the limited imaging capabilities of the dataset used, this hypothesis would need to
be confirmed with other geophysical and seismic imaging techniques such as ambient noise
tomography.
87
7. Local earthquake tomography of a geothermal field
Figure 7.14:
Vp model variations with respect to the minimum 1D velocity model at different
depth levels. Panels a), b), c), and d) show depth slices for the resulting Vp model variations at
-2.60 km, -2.10 km, -1.60 km, and -1.10 km depth, respectively. Green circles mark the location of
earthquakes +/- 150 m away from slice. Dashed red lines indicate the boundary at which spread
values are less than or equal to 1.5. Gray areas mark the regions where the DWS is less than or
equal to 5.
88
7.5 Results and discussion
Figure 7.15:
Cross sections for the Vp model variations (Figure 7.14). Green circles mark the
locations of earthquakes +/- 200 m away from the slice. Dashed red lines indicate the boundary at
which spread values are less than or equal to 1.5. Gray areas mark the regions where the DWS is
less than or equal to 5. Dashed gray lines indicate different absolute velocity levels, and solid gray
lines mark approximate unit boundaries. Approximate locations of main structures are indicated
in black. Vertical green lines indicate the positions of neighboring injection wells.
89
7. Local earthquake tomography of a geothermal field
Figure 7.16:
Vp/Vs structure at different depth levels. Panels a), b), c), and d) show depth slices
for the resulting Vp/Vs model at -2.60 km, -2.10 km, -1.60 km, and -1.10 km depth, respectively.
Green circles mark the locations of earthquakes +/- 150 m away from the slice. Dashed red lines
indicate the boundary at which spread values are less than or equal to 1.5. Gray areas mark the
regions where the DWS is less than or equal to 5.
90
7.5 Results and discussion
Figure 7.17:
Cross sections for the Vp/Vs model (Figure 7.16). Green circles mark the locations
of earthquakes +/- 200 m away from the slice. Dashed red lines indicate the boundary at which
spread values are less than or equal to 1.5. Gray areas mark the regions where the DWS is less
than or equal to 5. Approximate locations of main structures are indicated in black. Vertical green
lines indicate the positions of neighboring injection wells.
91
7. Local earthquake tomography of a geothermal field
7.6 Conclusions
A new seismological analysis using a dense temporary seismic network was undertaken at Los
Humeros geothermal field. We collected high quality earthquake data to image the Vp and
Vp/Vs models for the first time in this region. These models were obtained by extending the
classical local earthquake tomography using a post-processing statistical approach. Several
models were inverted and averaged to reduce the potential bias introduced by the choice of
model parametrization and enhance the final spatial resolution. The results were then carefully
integrated with new geophysical, geological, and petrophysical data for interpretation.
The statistical approach reduces the potential smearing resulting from selecting model
parametrizations that do not align with anomaly location and orientations, which are in many
cases unknown prior to computing a tomography. The consideration of different initial grids
allows for a much finer solution and helps overcome the code restriction of using a fixed coarse
grid. It also allows assesing and reducing the error bars of the final solution.
From this analysis, we identified three seismogenic areas within Los Potreros caldera, one
of which does not appear in direct relation to any geothermal wells. A deep earthquake
cluster was located between Las Papas and Las Viboras faults. Although these faults show no
hydrothermal alteration at the surface (Norini et al., 2019), the presence of this seismic cluster
suggests that these faults may increase permeability at depth. The vicinity of this new cluster
to another one close to an injection well could potentially highlight a deeper fluid pathway
towards the east.
The main geological boundaries found from well and new petrophysical data were also
found in our Vp model. The presence of two instrusive bodies supports the idea of resurgence
at Los Potreros caldera (Norini et al., 2019; Urbani et al., 2020). Urbani et al. (2020) suggest
that intrusions in the region are the result of the inflation of the magma chamber at depth,
and may represent locations of local heat source(s).
The Vp/Vs model also supports the resurgence or uplift due to the intrusion of new magma
at Los Potreros caldera. High Vp/Vs ratio anomalies are located to each side of Los Humeros
Fault zone, where the hypocenters in between have a sub-vertical configuration. This could
hint at a deeper heat source transporting hot fluids upwards along permeable faults. A new
petrological study (Lucci et al., 2020) also suggests such a system, with several (ephemeral)
magma pockets in the crust being fed by multiple magma transport and storage layers. The
high Vp/Vs values in this region could potentially indicate higher fluid content. Therefore,
this area could be further studied.
Above this anomaly, a low Vp/Vs region coincides with the conductive clay cap seen in a
new MT study (Benediktsdóttir et al., 2019). The low Vp/Vs in combination with low Vp values
could indicate gas bearing regions (Gassmann, 1951; Husen et al., 2004). This hypothesis
is also supported by a new CO
2
emissions survey at the surface (Jentsch et al., 2020). The
shallower portions with the lowest Vp/Vs value coincide with regions of higher CO2fluxes.
Further steps to be considered for better understanding of the geothermal system include
an attenuation tomography and the imaging of deeper structures with techniques such as
ambient noise tomography. In addition, a more quantitative approach such as a cluster analysis
92
7.6 Conclusions
of different physical properties will be performed to improve the accuracy of the interpretation
and to build a conceptual model.
93
7. Local earthquake tomography of a geothermal field
Appendix 7.A Station corrections associated with the 1D ve-
locity model
Station corrections are defined as scalar terms accounting for near-surface velocity variations
below each seismic station. In other words, they are potential indicators of surface geology
and/or site conditions. Figure 7.18 shows the a) P-wave and b) S-wave station corrections
associated with the minimum 1D velocity model. There are slightly higher P- delays at stations
located towards the southeast of Los Potreros caldera. This is a region characterized by
several fault outcrops and undefined pyroclastic deposits. The delays decrease towards the
north-western edge of Los Humeros caldera. This area is characterized by basalts and andesites
at the surface (Figure 7.1). Station delays for stations further away from Los Humeros caldera
show higher values than those within the dense array, which could be associated with larger
picking uncertainties. S-delays (Figure 7.18b) are also relatively balanced within Los Potreros
caldera.
Table 7.2 shows the retrieved station correction values. Locations, elevations, and sensor
types are available as the seismic network associated metadata in Toledo et al. (2019).
Figure 7.18:
a) P-wave and b) S-wave station corrections associated with the 1D velocity models.
Topographic lines are indicated in gray and main structures are shown in black.
94
7.A Station corrections associated with the 1D velocity model
Table 7.2: Station corrections associated to the minimum 1D velocity model
Station network Station code
P-delay [s] S-delay [s]
6G DB01
0.01 -0.02
6G DB02
0.08 -0.06
6G DS03
0.03 -0.15
6G DS04
-0.01 0.03
6G DB05
0.01 -0.02
6G DS06
0.05 -0.06
6G DB07
0.02 -0.06
6G DS08
0.0 -0.14
6G DS09
-0.02 -0.16
6G DS10
0.05 0.06
6G DB11
-0.16 -0.12
6G DB12
0.0 0.01
6G DB13
- -0.11
6G DB14
0.04 -0.09
6G DB15
0.06 -0.02
6G DB16
0.06 -0.01
6G SS17
0.07 0.32
6G SS18
-0.27 -0.36
6G SB19
0.82 2.41
6G DS20
0.04 -0.15
6G SB21
- -
6G SB22
- -
6G SS23
0.26 0.26
6G SB24
-0.34 -0.39
6G DB25
0.04 0.04
6G SB26
- -
6G DB27
0.09 0.04
6G DB28
0.02 0.09
6G DB29
0.07 -0.08
6G SB30
-0.26 0.9
6G DB31
-0.05 -0.11
6G SS32
-0.36 -0.73
6G DS33
-0.09 -0.07
6G DS34
0.1 -0.06
6G SS35
-0.41 -0.64
6G SS36
-0.24 -0.46
6G SS37
- -
6G SS38
- -
6G SS39
- -
6G SB40
-0.1 -0.37
6G SS41
- -
6G DB42
-0.07 -0.05
6G DB43
0.07 0.08
6G SB44
- -
6G DS45
- -
95
7. Local earthquake tomography of a geothermal field
Appendix 7.B Tradeoff test sample for a single model
parametrization
Damping parameters for an inversion using a single model parametrization are chosen such that
the data variance is minimized at a moderate model variance. We first determine the damping
factor for Vp by testing several values while fixing the damping factor for Vp/Vs. In a similar
manner we select a damping factor for Vp/Vs by testing a range of values in combination with
the selected Vp damping factor. Through this approach, the damping parameters chosen for
this experiment were 7 and 10 for Vp and Vp/Vs models, respectively (Figure 7.19). Given the
node spacing did not vary when inverting for the different inversion grids, damping factors
remained the same throughout all inversions perfomed.
a) b)
Vp model Vp/Vs model
Model variance [km2/s2]
Data variance [s2]
Model variance [-]
Data variance [s2]
Figure 7.19:
Tradeoff curves for a) Vp and b) Vp/Vs to select the optimal damping values. The
parameters selected were 7 and 10 for Vp and Vp/Vs models, respectively.
Appendix 7.C Diagonal elements of the MRM (RDE)
Diagonal elements are representative of the inversion resolution, with values closer to 1
indicating better resolved areas. Figure 7.20 depicts the averaged RDE distribution for Vp and
Vp/Vs at different depth levels. Higher RDE values (>0.3) are found in the topmost layers,
especially in the region neighboring the northermost seismic cluster (C1 in Figure 7.3) for
both Vp and Vp/Vs models. Surrounding this area, RDE values then decrease to 0.1-0.3 for
both models, and are reduced at deeper levels due to decreased ray coverage. Overall good
resolution is restricted to Los Potreros caldera, and is best towards the north.
Appendix 7.D Spread values
Off diagonal elements of the MRM contain information on the dependency of the solution of
each node with respect to neighboring nodes. Smaller values indicate that the solution for a
96
7.E Model statistics
particular node is more independent, hence less smearing is associated with it. Figure 7.21
shows the averaged spread distribution for the Vp and Vp/Vs models for different depth slices.
Smaller spread values (<1-2) coincide roughly with regions of RDE of 0.1-0.9 (7.C). As in the
case of higher DWS values, the areas of lower spread values are for the most part concentrated
within Los Potreros caldera.
Spread and RDE values are closely related to model parametrization and regularization.
Therefore in a strict mathematical sense, these parameters may not be directly interpolated
and averaged. We opted to recover this information for a rough estimate of resolvable areas.
However, these final values should be treated with caution.
Appendix 7.E Model statistics
We computed and displayed the associated standard deviation of the final models in Figure 7.22.
Variations of the standard deviation for the Vp model have a fairly homogeneous distribution
across the areas of greater sensitivity (regions within dashed red lines in Figure 7.22), with
some locations reaching a maximum value of around
±
0.10 km/s. Standard deviation values
are lower and more evenly distributed at -2.10 km depth, which coincides with the depth slice
with the highest ray density. Similarly, maximum variations for the obtained Vp/Vs model are
in the order of
±
0.026. As in the case of the Vp model, variations appear more homogeneous
at -2.10 km depth.
Acknowledgements
The GEMex project is supported by the European Union’s Horizon 2020 programme
for Research and Innovation under grant agreement No 727550 and the Mexican Energy
Sustainability Fund CONACYT-SENER, project 2015-04-68074. The authors thank the
Geophysical Instrument Pool Potsdam (GIPP) for facilitating the seismic equipment used in
this project (GIPP-Grant number GIPP201719), and the Comisión Federal de Electricidad
(CFE) of Mexico for granting access to the geothermal concession area.
Waveform data and associated metadata are archived at the GEOFON seismological
archive, FDSN code 6G (2017-2018) (Toledo et al., 2019), and are embargoed until January
2023.
The authors thank Dr. James Mechie, the editor, and two anonymous reviewers for their
comments and observations which vastly improved this manuscript.
97
7. Local earthquake tomography of a geothermal field
a) b)
c) d)
e) f)
Vp model Vp/Vs model
Depth: -2.60 km Depth: -2.60 km
Depth: -2.10 km Depth: -2.10 km
Depth: -1.10 km Depth: -1.10 km
RDE
Figure 7.20:
Average RDE distribution at different depth levels. Panels a), c), and e) show three
depth slices for the Vp model RDE distribution at -2.6 km, -2.10 km, and -1.10 km depth. Panels
b), d), and f) show the depth slices for the Vp/Vs model RDE distribution at -2.6 km, -2.10 km,
and -1.10 km depth. Darker shading indicates higher resolution values.
98
7.E Model statistics
Figure 7.21:
Averaged spread distribution at different depth levels. Panels a), c), and e) show
three depth slices for the Vp model spread distribution at -2.6 km, -2.10 km, and -1.10 km depth.
Panels b), d), and f) show the depth slices for the Vp/Vs model spread distribution at -2.6 km,
-2.10 km, and -1.10 km depth. Darker shading indicates regions with less smearing.
99
7. Local earthquake tomography of a geothermal field
Figure 7.22:
Standard deviation distribution at different depth levels associated with the
averaged models. Panels a), c), and e) show three depth slices for the Vp model standard deviation
distribution at -2.60 km, -2.10 km, and -1.10 km depth. Panels b), d), and f) show the depth slices
for the Vp/Vs model standard deviation distribution at -2.60 km, -2.10 km, and -1.10 km depth.
Pink circles mark the locations of earthquakes +/- 150 m away from the slice. Dashed blue lines
indicate the boundary at which spread values are less than or equal to 1.5. Gray areas mark the
regions where the DWS is less than or equal to 5.
100
8
Seismic interferometry for imaging and
monitoring a geothermal field
This chapter consists in the application of seismic interferometry techniques to image and
monitor a producing geothermal in NE Iceland.
Ambient seismic noise monitoring and imaging at the Theistareykir geothermal
field (Iceland)
Tania Toledo, Anne Obermann, Philippe Jousset, Arie Verdel, Joana Martins, Kemal Erbas,
Anette Mortensen, Charlotte Krawczyk
Article in preparation 2021.
From autumn 2017 to the present date, a network of 14 broadband seismic
stations was deployed to improve the monitoring (previously with 7 short
period sensors) of the high temperature Theistareykir geothermal field (NE
Iceland). This experiment is conducted as part of the current efforts to
characterize the main structures, and short and long term variations in the
geothermal field due to the ongoing operations which started in autumn
2017/spring 2018. In this work, we use two years seismic records to compute
the ambient noise tomography and to detect possible stress changes related
to the injection and production activities. Cross correlations and auto
correlations were computed from the vertical component of continuous noise
records using a phase cross correlation approach. We measure the Rayleigh
wave group velocity dispersion curves from the cross correlation functions
to obtain 2D group velocity maps between 1 and 5 s. Subsequently, we use
a neighborhood algorithm to retrieve the 3D shear wave velocity model of
Theistareykir. Mainly, two sets of high and low elongated velocity anomalies
are oriented in a NW/WNW direction, parallel to the lineaments of the
active Tjörnes fracture zone. The velocity reductions west of Ketilfjall
and at Baerjafjall could indicate the location of a magmatic reservoir or
101
8. Seismic interferometry for imaging and monitoring a geothermal field
hydrothermal system. This hypothesis is supported by existing and newly
acquired geological and geophysical data. We compute the temporal velocity
changes of autocorrelations using coda wave interferometry and observe their
behavior in relation to the geothermal field operations. We detect two possible
velocity changes associated to drops in the injection rates. Additionally, we
notice a small seismic velocity decrease of 0.05%/year in the reservoir compared
to the outer regions (0.04%/year).
8.1 Introduction
Theistareykir is a high temperature geothermal field located in NE Iceland (Figure 8.1a). It is
situated atop the Mid-Atlantic Ridge, at the divergent boundary between the North American
and the Eurasian plates, a region rich in recent volcanism, seismicity, and geothermal activity.
Presently, 17 deep wells (up to
∼
2 km depth) have been drilled in the region with the hottest
well registering temperatures exceeding 300
◦
C at 1.1 km depth (Khodayar et al., 2018). Since
spring 2018, the geothermal power plant at Theistareykir generates 90 MW electric power
and is administered by the national power company of Iceland (Landsvirkjun) (Landsvirkjun,
2016).
Several exploration and monitoring studies have been conducted since the late 70s to
assess the geothermal field’s energy production capabilities (Ármannsson, 2014; Gautason
et al., 2000). First gravity and aeromagnetic maps were reported by Gíslason et al. (1984).
Karlsdóttir et al. (2012) performed a 3D inversion of MT and TEM data to obtain the field’s
resistivity structure and better locate the heat source. Khodayar and Björnsson (2013) used
aerial photos to identify main fracture patterns. Khodayar et al. (2015, 2018) combined these
results with geological mapping, surface alteration, gas geochemistry, and water geochemistry
in a multidisciplinary analysis that defined the basis for the choice of drilling targets at
Theistareykir (Kristinsson et al., 2013a,b; Óskarsson, 2011; Saemundsson, 2007). Finally,
Blanck et al. (2017a,b, 2018a) recorded and analyzed the local seismicity at Theistareykir
using a seismic network of four stations.
The start of electric production at Theistareykir triggered new studies to improve its
characterization and monitoring prior and during production. In the framework of the
Microgravimotis project, a multiparameter network was installed to monitor the geothermal
field starting in autumn 2017. A set of 27 time-lapse micro-gravity stations were measured
at different time periods in 2017, 2018, and 2019 to analyze the field’s mass distribution
changes (Portier et al., 2020). This data was complemented with 4 permanent superconducting
gravity meter stations deployed at the injection and production areas (Erbas et al., 2020). The
permanent stations are equipped with GPS receivers, tiltmeters, and meteorological stations.
Vertical displacements were obtained through an INSAR analysis by Drouin (2020). Finally, a
set of 14 seismic broadband stations was deployed to support the permanent monitoring and to
provide detailed insights on the seismicity, underground structure, and stress and deformation
changes of the geothermal field. The present study expands on the seismicity study of Naranjo
(2020) and Ágústsson et al. (2020) to investigate the seismic structure and temporal velocity
changes at Theistareykir.
102
8.2 Geologic setting and seismic network
Local earthquake tomography (LET) is a technique commonly used to investigate deep
structures in seismically active geothermal settings (e.g. Calò and Dorbath, 2013; De Matteis
et al., 2008; Jousset et al., 2011; Karastathis et al., 2011; Muksin et al., 2013; Toledo et al.,
2020a). 3D compressional P- (Vp) and shear S- (Vs) wave velocity models are obtained using
P- and S-wave arrival times from local earthquakes (Kissling, 1988; Thurber, 1983). Although
LET provides reliable information of the subsurface, high resolution is limited to regions
characterized by high seismicity rates and adequate ray coverage (homogeneous distribution of
local earthquakes and seismic stations). This is a major limitation at Theistareykir, where the
seismicity is mostly clustered at the producing geothermal field (Blanck et al., 2018a; Naranjo,
2020).
Ambient noise tomography (ANT) is an alternative method that has rapidly gained
popularity in geothermal exploration due to its increased resolution achieved by turning
receivers into (virtual) sources (e.g. Granados et al., 2020; Lehujeur et al., 2017; Martins et al.,
2020a,b; Planès et al., 2020). ANT is based on the reconstruction of Green’s functions between
different receiver pairs retrieved from the cross correlation of long duration ambient noise
records (Campillo and Paul, 2003; Wapenaar, 2004; Wapenaar and Fokkema, 2006).
Noise-based methods have also been applied for monitoring geothermal systems. Small
elastic and structural changes in the medium are detected by measuring the distortions of so
called "coda" waves (Sens-Schönfelder and Wegler, 2006; Snieder, 2002). This technique is
commonly known as coda wave interferometry (CWI). Obermann et al. (2015) used CWI to
detect a likely gas infiltration in the St. Gallen geothermal site (Switzerland). Similarly, Hillers
et al. (2015) detected structural changes due to a reservoir stimulation in Basel (Switzerland).
Taira et al. (2018) measured the response of the Salton Sea geothermal field (California) to
earthquakes and fluid extraction. Finally, Sánchez-Pastor et al. (2019) reported on short
and long-term variations of the Reykjanes geothermal field (Iceland), due to injection and
production activities.
In this study, we image the 3D Vs structure and assess the temporal velocity variations
at the Theistareykir geothermal field using seismic interferometry. First, we report on the
geological setting and the seismic network deployed at Theistareykir. We describe the data
processing steps to retrieve the surface Rayleigh waves in part 2. Part 3 addresses the 3D
ambient seismic noise Rayleigh wave tomography. We assess the time-lapse changes in velocity
using CWI in part 4. Finally, part 5 discusses the obtained results in relation to existing and
newly acquired geophysical and geological data.
8.2 Geologic setting and seismic network
8.2.1 Geologic and tectonic setting
The Mid-Atlantic Ridge (MAR) spreads at an average rate of 2 cm/year (Einarsson, 2008).
In Iceland, the MAR consists of a series of active rift and transform segments that bring
forth numerous high temperature areas with the potential for geothermal energy exploitation.
Theistareykir is located at the intersection between the active Northern Rift Zone (NRZ) and
the active Tjörnes Fracture Zone (TFZ) (Figure 8.1a).
103
8. Seismic interferometry for imaging and monitoring a geothermal field
SKI
TH01
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BOND
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Th
Má
Figure 8.1:
a) Map of Iceland and location of the Theistareykir geothermal field. The rift
fissure swarms GOR (Grímsey Oblique-Rift), HFF (Húsavík-Flatey Fault), and DL (Dalvík
Lineament) of the TFZ (Tjörnes Fracture Zone) are shown with blue lines. The fissure swarm Th
(Theistareykir)/Má (Mánáreyjar) of the NRZ (Northern Rift Zone) is shown with a yellow line. b)
Main exploitation area. The location of injection and production wells are marked with yellow and
white circles, respectively. Approximate well deviations are shown as black lines. c ) Temporary
(red triangles) and permanent (blue and green triangles) seismic networks at the Theistareykir
geothermal field. The location of panel b) is shown with white dashed lines. The yellow dashed
lines indicate the region shown in Figure 8.7.
The NRZ comprises five N-S fissure swarms. Theistareykir/Mánáreyjar is the westernmost
of them, with a roughly 9 km wide area and N-S extensional fractures that extend towards the
sea (Khodayar et al., 2018; Saemundsson et al., 2012; Thoroddsen, 1983). The TFZ consists of
three main WNW lineaments: the Grímsey Oblique Rift (GOR), the Húsavík-Flatey Fault
(HFF), and the Dalvík Lineament (DL). It is characterized by dextral and dip slip-motions, and
high seismicity rates (Stefánsson et al., 2008). More specifically, our study area lies between
the Theistareykir/Mánáreyjar Fissure Swarm, and the HFF and DL lineaments.
At the surface, Theistareykir is mostly covered by lava flows originated in the last stages
of the Ice Age (Saemundsson, 2007). The bedrock is composed by hyaloclastites produced
by sub-glacial eruptions, and basaltic interglacial and recent lava flows (younger than 10,000
years) (Ármannsson et al., 1986). Neighboring the geothermal field, Ketilfjall is the oldest
hyaloclastite formation (Figure 8.1b) and was formed during the eruption of a 4 km long fissure
below the Quaternary ice-sheet. Further south, two younger table mountains (Baejarfjall and
Kvíhólafjöll in Figure 8.1b) were formed by either eruptions on short fissures or single volcanic
104
8.3 Data processing
events. The surface geothermal activity is most intense to the north and northwestern slopes
of Baejarfjall and from there northwards to the western part of Ketilfjall (Ármannsson et al.,
2000). A resistivity survey (Karlsdóttir et al., 2012) suggests that the heat source and upflow
zones of geothermal fluids are located below Ketilfjall, Bæjarfjall and north of Stórihver.
8.2.2 Seismic network
From September 2017 to the present date, a temporary seismic network comprising 14 three-
component broadband (Trillium Compact 120s) sensors records continuous seismic data at
a sampling rate of 200 Hz (red triangles in Figure 8.1b and Figure 8.1c). This network was
primarily designed to monitor the local microseismicity associated with the exploitation of
the geothermal field (Toledo et al., 2020b). Two permanent seismic networks within the
region bring an additional 4 three-component short period 3DLite MkII (1s) sensors (blue
triangles in Figure 8.1b and Figure 8.1c) and 3 three component short period LE-3D 5s
sensors (green triangles in Figure 8.1b and Figure 8.1c). These networks are operated by the
Icelandic Geosurvey (ISOR) and Landsvirkjun, and the Icelandic Meteorological Office (IMO),
respectively.
8.3 Data processing
In this study we analyze the continuous seismic records between September 2017 and October
2019 of the stations belonging to the temporary network (120s sensors) and to the ISOR/IMO
permanent network (5s sensors). We cut the seismic traces of the vertical components into 2
hour long segments. Then, we downsample the traces to 5 Hz, apply a band-pass filter between
0.1-2.0 Hz, and remove the instrumental response using the MSNoise Python package (Lecocq
et al., 2014).
We compute the cross correlations and auto correlations using a phase cross correlation
approach (PCC; Schimmel, 1999). The PCC functional is based on the coherence of
instantaneous phases of analytical traces. Its main advantage over the classical cross-correlation
scheme (Bensen et al., 2007) is that it is amplitude unbiased and therefore does not require
any preprocessing that could inflict waveform distortion (Schimmel et al., 2011, 2018). This
technique has successfully been used in other noise-based studies for imaging and monitoring
(e.g. D’Hour et al., 2015; Sánchez-Pastor et al., 2018, 2019).
Finally, we stack the correlations linearly over a 2, 5, and 10 day sliding data window for
monitoring structural changes in the media, and over their full recording period to compute the
ambient noise tomography. In the latter case, we additionally average positive and negative
lag-times to enhance the symmetric part of the signal and to increase the signal-to-noise ratio
(SNR) (e.g. Obermann et al., 2016).
8.4 Ambient noise tomography
8.4.1 Group velocity dispersion analysis
We perform a Frequency Time Analysis (FTAN, Levshin et al., 1989) to extract the group
velocity dispersion curves from the retrieved cross-correlation functions (CCFs). Then, we
105
8. Seismic interferometry for imaging and monitoring a geothermal field
manually revise and pick the fundamental mode of the dispersion curves with inter-station
distances larger than 1.5 wavelengths and SNR
≥
10 (e.g. Mordret et al., 2015; Obermann
et al., 2016; Planès et al., 2020). Figure 8.2a shows the complete set of extracted group velocity
dispersion curves. Notice the increment in group velocities with increasing periods for most
dispersion curves. Based on the number of measurements per period (Figure 8.2b), we restrict
our analysis to the range between 1 and 5 s.
a) b)
Figure 8.2:
a) Full set of picked Rayleigh wave dispersion curves. b) Number of measurements
per period. The vertical red lines indicate the limits of the measurements used in this study.
To assess the dataset distribution we display the raypath maps at two different periods
(Figure 8.3a and Figure 8.3b). Note the increase in velocities with increasing period, especially
to the west and to the south east of the geothermal field. We then discretize the study area into
cells of
∼
3.5 x 3.5 km. This value was chosen after exhaustive testing taking into account the
raypath distribution and the resulting spatial resolution. Figure 8.3b and Figure 8.3d shows
the ray path density (number of rays per cell) associated with the chosen grid discretization
for 2 and 5 s. Notice the inhomogeneous ray density distribution for both periods due to
the irregular seismic network configuration, originally deployed for recovering local seismicity.
A higher ray density is observed towards the center of the geothermal field, where a higher
number of closely spaced stations are located.
8.4.2 2D group velocity tomography
We perform 40 tomographic inversions for periods between 1 and 5 s (with 0.1 s step) following
the methodology proposed by Barmin et al. (2001) and Mordret et al. (2013). The inversions
are based on ray theory coupled with a damping constraint and a Gaussian-shaped lateral
smoothing term. Group times for each period are calculated by integrating the group slowness
along each ray path. We ignore the effects of the topography, assuming they are negligible on
the retrieved traveltimes (e.g. Mordret et al., 2015). A first inversion is computed for each
period using the mean group velocity as the initial model. The aim is to reject measurements
with time residuals larger than 0.01 standard deviations. The remaining travel times are then
used in a second inversion using the obtained velocities of the previous step as the initial
model. These results correspond to the final group velocities for each period.
106
8.4 Ambient noise tomography
Figure 8.3:
Raypath (a, c) and ray density (b, d) maps for periods of 2 and 5 s. Raypaths in a)
and c) are colored with their associated measured group velocity. The chosen cell size is
∼
3.5 x
3.5 km. Black triangles indicate the seismic stations positions and the gray lines correspond to
topographic contours.
Figure 8.4a-d illustrate the obtained group velocities at periods of 2, 3, 4, and 5 s,
respectively. Following the inversions, the variance is reduced
∼
80 %for all periods. The
group velocities increase with greater periods and range between 1.62 and 2.74 km/s. Two
large elongated velocity anomalies stretch with a NW-SE direction. The high velocity anomaly
107
8. Seismic interferometry for imaging and monitoring a geothermal field
is located to the west and to the southeast, and is discontinuous below the Baejarfjall table
mountain. North to this anomaly, a low velocity anomaly crosses the Ketilfjal formation.
Figure 8.4:
Rayleigh wave group velocity maps at a) 2, b) 3, c) 4, and d) 5 s. Initial velocities
used in each inversion are shown in the upper right corner. Black triangles indicate the seismic
stations positions and the gray lines correspond to topographic contours.
108
8.4 Ambient noise tomography
8.4.3 Model quality
To identify the location of poorly resolved areas we analyze the inversions associated model
resolution matrices (MRM). The diagonal elements of the MRM provide an estimate of the
inversion resolution. Off-diagonal elements contain information on the dependency of the
solution of each cell with respect to neighboring cells.
As in Mordret et al. (2015), we define the spatial resolution as the equivalent diameter of a
fitted ellipse to the contour level at 40 %of each row of the MRM. The minimal resolution
value is estimated as twice the distance between two cells, in this case
∼
7 km. Then the
resolution shift is defined as the distance between the center of each ellipse and the target
cell coordinate. The latter is an indicator of smearing. Figure 8.5a and Figure 8.5c show the
calculated spatial resolution at 1.0 s and 5.0 s, respectively. The values range between 7 and
≥
13 km, and is lower towards the main exploitation area, where the seismic array is denser.
Similarly, Figure 8.5b and Figure 8.5d show the resolution shift for 1 and 5 s, respectively.
Shift values are, once more, lower towards the center of the geothermal field. We display the
contour level at 80 %(red lines in Figure 8.5a-d) for three rows of the MRM to observe the
direction of the smearing associated to three cells (red crosses in Figure 8.5a-d). Seemingly,
the contours at the center indicate a more focused solution, whereas the contours to the west
indicate strong EW smearing product of a single ray direction (Figure 8.3a and Figure 8.3c).
For the interpretation, we thus restrict our analysis to the center of the geothermal field.
109
8. Seismic interferometry for imaging and monitoring a geothermal field
Figure 8.5:
Spatial resolution (a, c) and resolution shift (b, d) at 2 and 5 s. The red lines indicate
the 80 %contour levels of the MRM associated to three cells points (red crosses). Black triangles
indicate the seismic stations positions and the gray lines correspond to topographic contours.
110
8.5 Determination of time-lapse changes
8.4.4 Retrieval of 3-D Vs model
We perform a second series of inversions to associate the 2D Rayleigh group velocity results to
a precise depth. First, we construct local group velocity dispersion curves at all cell points by
combining the tomographic inversions at different periods. Each of these dispersion curves are
then inverted to obtain single 1D local layered velocity models which are later assembled into
the final 3D S-wave velocity (Vs) model.
The 1D velocity profiles are obtained following a Monte Carlo inversion approach called
the Neighborhood Algorithm (NA, Sambridge, 1999). For each cell, we first generate a large
set (N
ini
) of random continuous Vs functions that are later discretized into layered models of
constant thicknesses and velocities. We define these functions as power law velocity profiles
overlaid by three splines to reduce the number of inverting parameters (otherwise 2n
l
, where
n
l
is the number of layers) (Mordret et al., 2014, 2015). The associated dispersion curves are
then calculated using the Computer Programs in Seismology package (Herrmann, 2013). We
evaluate the misfit between these synthetic models and the data dispersion curves. Later, we
select the N
b
best fitting models and randomly resample N
r
new models in their neighborhood.
This procedure is carried for N
iter
iterations or until the misfit is reduced at a given threshold.
In this work, we select N
ini
= 1000, N
b
= 750, N
r
= 2, and N
iter
= 20, giving a total of 31,000
probed models. Figure 8.6a and Figure 8.6b display an example of the synthetic dispersion
curves and the associated 1D Vs models, respectively, for the 1D inversion of a single grid
point. The lines in these figures are colored according to the logarithm of their misfit. Figure
8.6c shows the recovered 1D Vs models for all the locations in the 2D plane. Up to
∼
2 km
depth, the models show a good agreement with the 1D Vs model used in Iceland for earthquake
locations (South Iceland Lowland -SIL- model, Stefánsson et al., 1993).
In Figure 8.7a-f we present several depth slices of the retrieved 3D Vs model for the central
part of the geothermal field (best resolution). Similar to the 2D group velocity maps, two
main trends of anomalies are oriented in NW-SE direction. Two high velocity anomalies (
∼
+10 %) are located to the west and to the south of the Baejarfjall mountain, and become
weaker at shallow and deeper levels (
∼
+6 %). An elongated low velocity anomaly is located
to the northeast of Baejarfjall, and is slightly discontinuous at the Ketilfjal formation. The
low velocity anomaly to the west of Ketilfjal becomes stronger with depth (
∼
-9 %at
≥
2 km
b.s.l.). North to this anomaly, another high velocity anomaly with smaller amplitude (
∼
+4
%) is visible mostly at shallow levels (≤2 km b.s.l.).
8.5 Determination of time-lapse changes
Seismic monitoring using CWI has been successfully implemented in various applications
using techniques like the moving-window cross-spectra analysis (MWCS, Ratdomopurbo and
Poupinet, 1995), the observation of waveform similarity evolution (D’Hour et al., 2015), and
the stretching technique (Lobkis and Weaver, 2003; Sens-Schönfelder and Wegler, 2006).
A thorough comparison between the MWCS and the stretching method was performed by
Hadziioannou et al. (2009) showing more stable results for the latter. In this work, we compute
and analyze the velocity variations using the stretching technique on the auto correlations (AC)
111
8. Seismic interferometry for imaging and monitoring a geothermal field
Figure 8.6:
a) Example of synthetic local dispersion curves and b) their associated 1D Vs models.
The local (data) dispersion curve is represented as a thick black line. Lines are colored according
to their corresponding misfit. c) Best fitting 1D Vs profiles for each grid cell (gray lines). The
1D model that is routinely used for earthquake locations in Iceland (SIL model, Stefánsson et al.,
1993) is shown with a red line.
for a period of 2 years (October 2017 - October 2019). ACs are known to be more sensitive to
local changes and to probe larger depths (D’Hour et al., 2015; Sánchez-Pastor et al., 2018).
8.5.1 Waveform stretching
To quantify the temporal evolution of seismic velocities, we analyze the waveform changes
of "current" CCFs (
φcurr
) with respect to a reference CCF (
φref
). We define the
φref
as the
stacked daily CCFs over the entire recording period, and
φcurr
as the daily stacked CCFs
over a 2, 5, and 10 day sliding window. Each
φcurr
is then stretched or compressed in time
112
8.5 Determination of time-lapse changes
Figure 8.7:
Vs depth slices. Resistivity contour lines are taken from Karlsdóttir et al. (2012).
Black triangles indicate the seismic stations positions and the gray lines correspond to topographic
contours. White circles represent the location of injection and production wells, and the approximate
well deviations are shown with black lines. The location of these maps are shown with yellow
dashed lines in Figure 8.1c.
by a factor
t
(1 +
ϵ
)and compared to
φref
. The stretching factor
ϵ
by which the correlation
coefficient (CC) between
φref
and
φcurr
is maximized corresponds to the apparent velocity
change (ϵapp =−∆v
v) (Nakata et al., 2019; Sens-Schönfelder and Wegler, 2006).
113
8. Seismic interferometry for imaging and monitoring a geothermal field
Figure 8.8 displays the velocity variations computed on two ACs between 1 and 21 s lag
time. The ACs are associated to a station close (SKI) and a station further away (TH05)
from the injection/production site. Except for a few points, most CCs are
∼
0.9, and the
peak-to-peak velocity variations are
∼
0.3 %. The most prominent feature in both cases is a
sinusoid with period of
∼
365 days, maxima in January 2018 and January 2019, and minima
in August 2018 and August 2019. Additionally, similar short-term fluctuations at various lag
times are visible in both curves which could be associated to a range of factors like weather
and seismicity. Although both curves have similar shapes, the velocity changes for SKI-SKI
has occasionally lower values than TH05-TH05.
We group the stretching results from ACs of stations inside (blue lines in Figure 8.9a-c)
and outside (orange lines in Figure 8.9a-c) the region within Figure 8.1b to evaluate whether
local changes exist due to the exploitation activities. We single out the results of the station
closest to the injection site with red lines. Notice how the results are very stable for all ACs.
Both the sinusoidal behavior and several short term fluctuations are similar in the three curves.
However, it is evident that
∆v
v
of locations within the exploitation area are, in many instances,
lower than for those outside it. In fact, when fitting the average velocity changes of both
groups to a linear function, we observe larger decreases in velocity for the curve associated to
the producing geothermal field (Figure 8.9d).
We highlight three local perturbations (labeled as I, II, and III in Figure 8.9) accompanying
two prominent changes in injection/production rates and one change in local seismicity rate
(Figure 8.9e). Region I and III show a window where the injection was abruptly shut down
for a few days. In III, the velocity variation curves show larger differences in amplitudes
between the stations inside and outside the exploitation zone (mostly in Figure 8.9c). Region
II indicates a time window leading to an increase of recorded seismicity below Baejarfjall (see
change of slope of the pink line in Figure 8.9d).
In Figure 8.10, we remove the sinusoidal trend of the average velocity variations of the two
station groups and compare their spectrograms. To remove the sinusoid feature, we first fit
one of curves to a sine function f(t) of the form:
f(t) = A∗sin(ω∗t+ϕ) + c(8.1)
where A,
ω
,
ϕ
, and ccorrespond to the amplitude, angular frequency, phase, and offset,
respectively. In this case we assume
ω
= 2
∗π/T
, where the period (T) is 365 days. The
corrected curves then correspond to difference between the original and the fitted f(t).
Although the corrected curves (Figure 8.10b and Figure 8.10d) exhibit similar waveforms,
their spectra (Figure 8.10a and Figure 8.10c) reveal several differences. In many instances, the
spectrogram associated to the production site presents slightly higher amplitudes than the one
associated to distant stations. Region III, for example, shows somewhat higher amplitudes for
frequencies ≥10−1days−1for the curve neighboring the exploitation zone.
1
1Production rates are not complete and I am waiting for this data
114
8.6 Interpretation and discussion
8.6 Interpretation and discussion
8.6.1 Ambient noise tomography
The ambient noise tomography in Section 8.4 (Figure 8.7) shows a clear separation between high
(N and NE) and low (S and SW) velocity anomalies trending with a NW/WNW orientation.
This direction is almost parallel to the HFF lineament (Figure 8.1a), and follows the location
of a series of fractures (narrow weak zones) with WNW and NW dextral oblique-slip mapped
at the surface (Khodayar et al., 2018). The boundary of the velocity anomaly separation is
located a few kilometers to the north of the Baejarfjall mountain, where the injection and
several production wells are located. This pattern is consistent at all depth levels, and matches
the direction of several MT resistivity anomalies (colored line contours in Figure 8.7, taken
from Karlsdóttir et al. (2012)) .
The low velocity anomalies (
∼
-7 %) to the N and NE coincide with the location of various
low resistive bodies Karlsdóttir et al. (2012). One major low velocity anomaly to the north of
Baejarfjall and west of Ketilfjall becomes stronger (
∼
-10 %) starting from
∼
2 km b.s.l. (Figure
8.7d-f). Studies have shown that rocks saturated with hydrothermal fluids have typically
lower shear wave velocities than those same unaltered rocks (De Matteis et al., 2008; Vanorio
et al., 2005). In a lithologically homogenous subsurface, the decrease of Vs in this region
could point to the location of either magmatic material or an upflow zone. Such a hypothesis
is consistent with the MT survey, which highlights the heat source(s) beneath Ketilfjall,
Bæjarfjall, and north of Stórihver below a shallow cap rock composed of zeolite/ smectite
alterations (Karlsdóttir et al., 2012). This region the north of Baejarfjall and west of Ketilfjall
is also known to experience high decreases in microgravity variations (Portier et al., 2020) and
negative vertical displacements (Drouin, 2020) with time. In addition, surface geothermal
manifestations (Kristinsson et al., 2015) and emanating gases (Gíslason et al., 1984) have been
reported mostly at the northern and northwestern flank of Bæjarfjall.
The high velocity anomalies (
∼
+10 %) to the west and south/southwest of Bæjarfjall
coincide with medium to high resistivity bodies (
≥
100 Ωm) at depths between 0.5-3 km b.s.l.
Between these two anomalies, a lower high velocity anomaly (
∼
+5 %) sits below Bæjarfjall,
which reduces its amplitude mostly at depths
≥
3 km b.s.l. (
∼
+1 %). This reduction could,
once more, hint to the presence of hot fluids at Bæjarfjall. Another weaker high velocity
anomaly is located further to the north following, once more, some resistive bodies.
8.6.2 Time-lapse changes
To analyze possible structural changes we monitor the differences between the ACs at different
times with respect to a reference. In a geothermal context, some of these velocity variations
have been successfully linked to the operation activities (Obermann et al., 2015; Sánchez-Pastor
et al., 2019). Figure 8.9a-c shows the velocity variations associated to the ACs of all stations
computed with the stretching technique. The results are colored according to their distance
with respect to the injection and production wells (red and blue lines for stations close to the
geothermal field, and orange lines for distant stations). Several short term fluctuations are
consistent among all the curves, however, most of them are difficult to directly associate to
natural or man-made processes.
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8. Seismic interferometry for imaging and monitoring a geothermal field
We distinguish two regions (I and III) where there is an abrupt change of injection volume
in Figure 8.9a-c. Region I shows a large
∆v
v
fluctuation for both station groups which coincides
with a significant injection drop and rise. The curves in region III not only show changes in
∆v
v
, they reveal some clear differences between the two station groups. We average the velocity
changes of both station groups, remove their sinusoid trend, and display their spectrogram in
Figure 8.10. Higher amplitudes at frequencies
≥
10
−1
days
−1
are visible for the curve associated
to the operations site. This confirms the likelihood of this fluctuation to be associated to the
field’s operations. For the remaining time period, the injection and production changes are
too low for their effect to be seen in the ∆v
vshort term fluctuations.
A third region (marked as II), is a special case where we observe distinct velocity variations
(drop then rise) prior to the increase of local seismicity. During this period, the injection rates
were doubled for the first time, leading to the increase of induced seismicity (abrupt change in
the earthquake frequency slope in Figure 8.9d) to the northwest of Baejarfjall (Naranjo, 2020).
Such short precursor behavior is observed in similar studies (Obermann et al., 2013, 2015).
Long term noise studies typically exhibit seasonal variations (e.g. Sánchez-Pastor et al.,
2019; Sens-Schönfelder and Wegler, 2006) which are evident in the distortion of the ballistic
waves (e.g. Hadziioannou et al., 2011). These variations are mostly the consequence of changes
in the oceans noise sources at different seasons (Stutzmann et al., 2009). In this study, the
seasonal variation appears as a sinusoidal trend which is evident for the
∆v
v
curves of all station
positions (Figure 8.9a-c). We average the velocity variation curves for the two station groups
and compute their linear regression to distinguish the difference between their long term
variations (Figure 8.9d). There is a slow velocity decrease for both station groups. However
this reduction is stronger for the production area (0.05%/year vs 0.04%/year). Such a local
decrease in velocities is consistent with the negative microgravity variations reported in the
production zone (Portier et al., 2020). Additionally, (Drouin, 2020) reports a subsidence in
this region of ∼7 mm/year since the start of the operations in 2017.
8.7 Conclusions
Upon the deployment of a temporary seismic network at the Theistareykir geothermal field,
we collected and analyze the ambient noise records for the period of 2 years. We compute a 3D
ambient noise Rayleigh wave tomography and compare the results with available geophysical,
geochemical, and geological data. We could identify velocity anomalies oriented in a NW/WNW
direction almost following the orientation of the HFF lineament. This observation is consistent
with the direction of reported resistivity anomalies at Theistareykir (Karlsdóttir et al., 2012).
A clear division between high and low velocity anomalies follows the location of weak
active fractures with dextral oblique-slip (Khodayar et al., 2018). We observe a velocity
reduction in two anomalies: one to the west of Ketilfjall (depths
≥
2 km b.s.l.) and one at
Baejarfjall (depths
≥
3 km b.s.l.). We interpret these regions as locations of possible magmatic
or hydrothermal bodies. Such hypothesis is consistent with geophysical and geochemical data
(Gíslason et al., 1984; Karlsdóttir et al., 2012; Kristinsson et al., 2015). In addition, the low
velocity anomaly to the west of Ketilfjall roughly coincides with the region of high decreases
116
8.7 Conclusions
in residual micro-gravity variations (Portier et al., 2020) and negative vertical displacement
(Drouin, 2020).
We compute the temporal velocity changes for the 2 year period using CWI and compare
the results associated to the stations close and far from the geothermal field. Several short
term fluctuations are inconsistent with the injection and production variations, and could
be associated with several other medium instabilities. Alternatively, various injection and
production changes may be too low for their effect to be seen in the
∆v
v
short term fluctuations.
Furthermore, we report on a slow velocity decrease (0.05%) within the geothermal system,
possibly associated to a deficit of water in this region.
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8. Seismic interferometry for imaging and monitoring a geothermal field
Figure 8.8:
Velocity changes computed with the stretching technique for the ACs of stations a ) SKI and b) TH05. The color scale represents the associated CC.
Results for 2, 5, and 10 day stacks are shown in the upper, middle, and lower panels, respectively.
118
8.7 Conclusions
Outer station
Injection area
Production area
a)
b)
c)
d)
e)
Slope: -0.05 %/year
Slope: -0.04 %/year
III III
Figure 8.9:
Velocity changes computed for all available ACs. Results for a) 2, b) 5, and c) 10 day stacks times. Line colors represent three station groups:
station neighboring the injection site (red), stations close to the production sites (blue, located within 8.1c), stations far from the exploitation zone (orange).
We discarded
∆v
v
values with CC
≤
0.35. d) Linear regressions of the velocity variation averages for stations inside and outside the exploitation area. e) Total
production (red) and injection (blue) rates at the geothermal field, and local seismicity rates (pink) from the 1 January 2018 to 15 July 2018 (taken from Naranjo
(2020)). The gray boxes highlight the fluctuations I, II, and III. See main text for more details.
119
8. Seismic interferometry for imaging and monitoring a geothermal field
Figure 8.10:
(a, c) Spectrograms and (b, d) velocity variation averages (2-day stack window) for stations inside and outside the exploitation area (within 8.1c).
The sinusoidal trend has been removed for both curves. e) Total production (red) and injection (blue) rates at the geothermal field, and local seismicity rates
(pink) from 1 January 2018 to 15 July 2018 (taken from Naranjo (2020)). The gray boxes highlight the fluctuations I, II, and III. See main text for more details.
120
Part III
Discussions and Conclusions
121
9
Discussions of results
This thesis evaluates, extends, and applies survey design theory for microseismic monitoring,
passive seismic imaging, and coda wave interferometry for the exploration and monitoring
of three geothermal fields: Los Humeros (Mexico), Theistareykir (Iceland), and Reykjanes
(Iceland). Although specific to these fields, the results are discussed in this chapter in
consideration to future geothermal studies. Furthermore, a comprehensive analysis of the
advantages and disadvantages of the methods is presented, as well as a comparison with other
similar studies.
9.1 Optimized experimental network design for microseismic-
ity location and monitoring
The exploitation of geothermal resources often results in stress changes that give way to
induced/triggered seismicity (Evans et al., 2012). When the magnitudes are large enough,
this seismicity can pose risks for the continuation of the exploitation activities (e.g. Basel,
Switzerland; St. Gallen, Switzerland; Pohang, South Korea in Deichmann and Giardini, 2009;
Diehl et al., 2017; Grigoli et al., 2018, respectively), hence the need for permanent seismic
monitoring.
High quality microseismic event retrieval and locations can be achieved with optimal
seismic network geometries. In some cases, these geometries are fixed depending on the seismic
tool choice. More often, however, the design follows a heuristic strategy with few azimuthal
and/or distance guidelines (e.g. azimuthal GAP
≤
180
◦
and average inter-station distances
in the order of expected hypocentral depths). The first approach is limited by field and/or
instrumentation restrictions. The second strategy can lead to difficulties in evaluating prior
error estimates and risks missing necessary data to resolve a target parameter. Although one
could argue the use of a large number of sensors, in practice, geothermal experiments are
highly constrained by budget.
In Chapter 6 (Toledo et al., 2020b) a destructive sequential survey design (DSSD) algorithm
(with quality measure based on the D-criterion) was developed for constructing new optimized
123
9. Discussions of results
networks and for qualifying existing ones. The studied scheme was based on well-established
survey design concepts, that although have been applied for a broad range of applications (e.g.
Coles and Curtis, 2011a; Kraft et al., 2013; Maurer and Boerner, 1998; Nuber et al., 2017),
they had yet to be applied in a geothermal exploration context. The selected algorithm was
simple and fast to compute and was successfully used to extend (Theistareykir) and to qualify
(Reykjanes) two seismic networks.
9.1.1 Survey design experiments at Reykjanes and Theistareykir (Iceland)
After defining candidate station locations and building a synthetic earthquake catalog that
takes into account the region’s seismic history, the Theistareykir network was augmented from
12 to 23 sensors. We estimated that for earthquakes located within the network and with
mean picking errors of
tp
=0.2 s and
ts
=0.4 s, there was an improvement of
∼
0.2 km for
all estimated hypocentral components using the augmented array. The picking errors were
overestimated in the computations, therefore, better results should be expected in practice.
The algorithm was later applied to the deployed Reykjanes network, this time using the
existing station positions as candidate station locations. Doing so, we obtained an order of
station importance. By analyzing both the station order and the resulting benefit/cost curve,
we observed that, although the placement of OBS stations around the Reykjanes peninsula
was necessary for the experiment, approximately 18 stations could be spared and still obtain
earthquake location estimates with comparable errors. Such observations are essential for
project budget management hinting the importance of survey design experiments prior to
deployment. In addition, these experiments can be used to identify stations that could be
removed or relocated if necessary during a project.
9.1.2 General considerations for survey design experiments
Several considerations are necessary prior to a survey design experiment. These include the
selection of a quality measure and an optimization scheme. The selected choices are discussed
in the following sections, where their advantages and disadvantages are addressed. In addition,
the aspect of detectability is discussed to improve the definition of candidate station positions.
Finally, a few outlooks for future studies are outlined.
9.1.2.1 Quality measure choice
In the previous case studies we used a quality measure (Θ) based on the D-criterion. One
main advantage of the selected measure (Eq. 3.5) is its sensitivity to the entire eingenvalue
spectrum of matrix
GTG
. In addition by minimizing function Θ, one would in some sense
also minimize the confidence volumes of all the studies seismic events. Another advantage is
its weighting factor term. This term can be modified to favor more interesting event targets at
a geothermal field (e.g. events close to injection and production wells).
One main drawback of the selected quality metric is station clustering. This effect is the
result of Θignoring model error correlations. In our work we interpreted station clustering
as regions of higher importance, however, this clustering can be alleviated by introducing an
interstation weight (Hardt and Scherbaum, 1994).
124
9.2 Passive seismic imaging for the exploration of geothermal fields
Eq. 3.5 is a linearized quality metric. Another approach for a more robust assessment
is the application of fully nonlinearized quality measures such as the one used in Guest and
Curtis (2009). However, the latter would be more costly to compute.
9.1.2.2 Optimization choice
One main advantage of sequential optimizations is the analysis of benefit/cost curves, which is
important for geothermal exploration planning. In addition, these schemes are flexible and
relatively fast to compute. They can be quickly modified to take into account possible changes
of station positions due to field constraints.
A major disadvantage of sequential optimizations is it does not guarantee global optimality.
However, they do provide good solutions to design temporal networks. A better approach is
the use of global search algorithms and/or non-linear experimental design. Although, they
require higher computational costs, they are strongly recommended especially for permanent
networks.
9.1.2.3 Detectability
An important aspect to be considered prior to a survey design experiment is the analysis of
the varying noise conditions throughout a target field (SNR studies). Such exercise allows a
better constraint on the candidate station location areas, and avoids placing stations in noisy
sites (where the target microseismic signals are masked in the background noise).
We considered the noise levels to be homogeneous throughout the analyzed geothermal
fields. A better approach, however, is proposed by Kraft et al. (2013) where they estimated
noise levels by correlating them with land use to expand the permanent seismic network in
Switzerland.
9.1.2.4 Outlooks
The applications for survey design techniques are multifold. A possible new exercise is the
extension of the algorithm to build networks dedicated for local earthquake tomographies
(assuming there is an adequate earthquake distribution at a region), or better yet for an
ambient noise tomography (where the seismicity distribution is not necessary). These exercises
will depend, however, on the research objectives of the network.
9.2 Passive seismic imaging for the exploration of geothermal
fields
A vital aspect for geothermal exploration is seismic imaging. This can be achieved, among
others, by means of a local earthquake tomography (LET) or an ambient noise tomography
(ANT). These are the techniques applied at Los Humeros geothermal field in Mexico (Chapter
7) and at Theistareykir in Iceland (Chapter 8), respectively.
125
9. Discussions of results
9.2.1 Local earthquake tomography at Los Humeros geothermal field
A passive seismic network comprising 45 stations was deployed and maintained at Los Humeros
for the period of one year (Toledo et al., 2019). We collected high quality earthquake data
(488 events) to compute the 3D Vp and Vp/Vs models (333 events) for the first time at this
field (Toledo et al., 2020a).
Aside from the classical earthquake tomography approach (Chapter 4), we applied a
post-processing scheme where 228 models were inverted and averaged to enhance the spatial
resolution of the final models. This approach has the advantage of obtaining a much finer
final resolution, thus overcoming the limits of a coarse grid used by the SIMUL2000 code. In
addition, the post-processing approach reduces the potential smearing that can be introduced
by model parametrization choices that favor preferential velocity anomaly and/or ray directions
(Calò, 2009). A similar post-processing approach in a geothermal context was performed at
Soultz-sous-Fôrets in France (Calò and Dorbath, 2013), where instead of a simple averaging
they computed a weighted average of several models with respect to the ray density values
(DWS).
The quality of the 3D final models was assessed by analyzing the model resolution matrix
(diagonal elements and spread function) and by computing a checkerboard test (Section 7.4.3).
Nodes with high diagonal elements and low spread values are considered to be well resolved
(Section 2.4.3). With this information and the computed synthetic tests we defined as well
resolved the region within the inner Los Potreros Caldera and up to
∼
2.5 km depth for Vp
and up to
∼
2.0 km depth for Vp/Vs. Tomography quality assessments are important to define
regions where meaningful interpretations can be obtained.
9.2.2 Joint interpretation at Los Humeros geothermal field
Seismicity distribution
Retrieved seismic events are excellent tools to potentially delineate structures, reservoir
boundaries, and preferential fluid pathways (e.g. Muksin et al., 2013; Philips et al., 2002).
From the recorded seismicity at Los Humeros we identified three seismogenic areas, two of
which are possibly associated to the exploitation activities. A third deeper cluster was located
between Las Papas and Las Viboras faults. These faults showed no hydrothermal alterations
at the surface (Norini et al., 2019), however, the presence of the seismicity could indicate a
permeability enhancement at deeper levels in this region. Such observations are important for
future drilling and development of a geothermal field.
Vp model
We combined the retrieved Vp model with well log interpretations (Norini et al., 2019) and
new petrophysical data (ultrasonic pulse measurements of collected rock samples in Bär and
Weydt, 2019) to estimate possible geological unit boundaries. This exercise is important for
defining the geometry of, for example, the reservoir unit which is necessary for the future
development of a geothermal field.
126
9.2 Passive seismic imaging for the exploration of geothermal fields
Vp/Vs model
We used our Vp/Vs model in combination with a newly acquired resistivity model (Benedik-
tsdóttir et al., 2019) to identify the location and geometry of the conductive clay cap above
the reservoir (Vp/Vs
≤
1.65 and resistivities
≤
10 Ωm). In addition, we interpreted the areas
with lowest Vp/Vs values (Vp/Vs
≤
1.55 and Vp reduction) as gas bearing regions. This
interpretation was supported by the high CO
2
emissions at the surface in these areas (Jentsch
et al., 2020).
Finally we interpreted the zones with high Vp/Vs values (
≥
1.71), Vp reduction, and
resistivities between
∼
10-60 Ωm as possible fluid bearing zones. These areas can potentially
be considered for further exploration and exploitation of the geothermal field.
General remarks on Los Humeros geothermal field
We could identify an important intrusion in the Vp model located at the main production
site. We combined this intrusion, the neighboring subvertically aligned earthquakes, and the
high Vp/Vs anomalies (higher fluid content) on both sides of the seismicity to interpret hot
fluids being transported upwards along deep reaching permeable faults. Such behavior is called
resurgence, and consists of shallow magma emplacements (several local heat source(s)) from
a deeper magma chamber. Such hypothesis is consistent with new analog, structural, and
petrological studies in the area (Lucci et al., 2020; Norini et al., 2019; Urbani et al., 2020).
9.2.3 Ambient noise tomography at the Theistareykir geothermal field
In seismically quiet areas or in regions with uneven ray path distributions (from the earthquake-
station geometries), a LET may not be feasible to retrieve the seismic structure of a geothermal
field. In these cases, the use of ambient noise techniques are powerful to image the subsurface.
In Chapter 8, we successfully computed the 3D ambient noise Rayleigh wave tomography of
Theistareykir following the methodology described in Part I (Section 5.3.2).
The quality of the retrieved velocity maps was assessed by analyzing their associated model
resolution matrices. We defined the spatial resolution as the equivalent diameter of a fitted
ellipse to the 40 %contour level of each row in the matrix, and the resolution shift as the
distance between the center of this ellipse with its associated cell coordinate (to indicate
smearing). We defined as well resolved the region at the center of the geothermal field, where
the seismic array is denser (resolution 7-9 km).
Resolution values are directly related to the network geometry (inter-station rays) and
can be improved by adding more sensors to the field. However, it is advisable to perform
synthetic or survey design experiments beforehand to estimate optimal locations for improving
the tomography.
9.2.4 Joint interpretation at the Theistareykir geothermal field
From the derived 3D Vs model we observed a division between high and low velocity anomalies
following the orientation of the HFF lineament (belonging to the Tjörnes Fracture Zone). This
geometry was consistent with the direction of the region’s resistivity anomalies as shown in
127
9. Discussions of results
Karlsdóttir et al. (2012) and with a series of fractures (WNW and NW dextral oblique-slip)
mapped at the surface in Khodayar et al. (2018).
Slight Vs reductions were visible in two anomalies starting at
∼
2 km b.s.l. and
∼
3
km b.s.l.: one west of Ketilfjall and the other below Baejarfjall, respectively, indicating the
location of rocks possibly saturated with fluids. In a lithologically homogeneous subsurface,
these regions could correspond to locations of magmatic and/or hydrothermal bodies. Such
interpretation is consistent with resistivity and geochemical data of the region (Gíslason et al.,
1984; Karlsdóttir et al., 2012; Kristinsson et al., 2015).
In addition, the locations of these velocity anomalies coincide with the main production
area and with regions of higher decreases in micro-gravity variations (Portier et al., 2020) and
negative vertical displacement (Drouin, 2020). The latter properties could imply a depletion
in these zones.
9.2.5 Advantages and disadvantages of the methods
LET and ANT are powerful tools for geothermal exploration. Both methods provide the
seismic structure and, to some extent, information of additional rock properties such as fluid
content.
One advantage of LET is the additional structural information derived from the seismicity
distribution. Furthermore, the study of the focal mechanisms can help understand the stress
field of a geothermal reservoir, which is important for drilling, resource assessment, and
resource management. Another follow-up study of LET is the computation of an attenuation
tomography. Seismic attenuation is more sensitive to rock properties such as pore, crack,
fracture, and fluid content than solely the Vp and Vp/Vs structures. Therefore, its computation
is highly recommended in geothermal contexts.
One main advantage of ANT over LET is the increased extensions of the obtained models,
which can be managed to a certain extent with the network geometry. In addition, ANT is
independent of the earthquake distribution of a target zone and does not require the extended
recording periods needed for LET. Given that these two techniques work at different frequency
ranges, their recovered information is highly complementary. Therefore, whenever possible, it
is strongly recommended the computation and analysis of both.
One interesting ongoing field of research is the computation of body wave tomographies
using the ambient noise field retrieved from very dense seismic arrays. This technique does
not require extended recording periods and have not yet been tested in a geothermal context.
9.2.6 Multi-parameter interpretations
We performed a joint interpretation at both Los Humeros and Theistareykir geothermal fields
by combining their seismic parameters with additional geophysical, geological, and geochemical
data. We observed that such approach avoids ambiguities, provides robust interpretations
regarding the structure and dynamics of a geothermal field, and helps building their conceptual
models.
A more quantitative approach, however, is the cluster analysis of the different physical
parameters. A pattern recognition technique was, for example, employed by Muksin et al.
(2013) to quantitatively delineate fluid and gas bearing regions from the computed Vp and
128
9.3 Coda wave interferometry for monitoring geothermal fields
Vp/Vs models at the Tarutung geothermal area (Indonesia). Similarly, a k-means cluster
analysis technique was applied to three geophysical parameters (resistivity, Vp, and density)
at the geothermally active Solfatara-Pisciarelli area of the Campi Flegrei caldera (Italy) to
identify differences in local rock rheologies and locate the brittle-to-ductile transition (Di
Giuseppe et al., 2018).
9.3 Coda wave interferometry for monitoring geothermal
fields
9.3.1 The Theistareykir case study
Changes in the coda waves (obtained from the auto- or cross-correlations of ambient noise
records) are the result of structural changes in the medium. We computed the temporal
velocity changes with the stretching technique (CWI) using two years ambient noise records at
Theistareykir (Chapter 8). We compared the obtained ∆
v/v
with injection and production
rates to evaluate the effects of the exploitation activities on the geothermal reservoir.
Although we could identify slight variations in the short term ∆
v/v
fluctuations after two
injection cuts, typically the injection/production variations were too small for their effect to
be seen in the ∆
v/v
curves. We could, however, observe a slightly higher long term velocity
decrease within the production area (-0.05 %/year), as opposed to the surrounding regions
(-0.04 %/year). This observation was consistent with decreases in micro-gravity variations
(Portier et al., 2020) and negative vertical displacement (Drouin, 2020) reported at the
production zone and could therefore indicate a slow mass depletion in this area (subsidence).
Overall, the small effects of the exploitation activities in the medium changes could favor
an open system behavior. Fluids may migrate from and out the system without over or under
pressuring it significantly (large ∆
v/v
changes) at the present injection and production rates.
This information is important for safe long-term continuation of operations at a geothermal
field.
9.3.2 Importance of coda wave interferometry for monitoring geothermal
operations
From the Theistareykir case study we observed no significant velocity changes due to variations
in injection and production rates. Other geothermal studies, however, had different experiences.
Obermann et al. (2015), for example, reported significant losses in the waveform coherence of
coda waves obtained in St. Gallen (Switzerland) 4 days prior to a gas kick which also resulted
in large earthquake (M
L
3.5). Another CWI study at Reykjanes (Sánchez-Pastor et al., 2019)
showed prominent medium changes due to sharp variations of water injection volume and
energy production. With their observations they could estimate a production rate threshold
above which the elastic properties of the medium change significantly.
Overall, monitoring the changes of coda waves can be useful for observing aseismic processes
prior to potentially large triggered/induced seismic events and would be complementary to
microseismic monitoring. In addition, this technique helps to better understand the reservoir
dynamics and mitigate the associated risks of geothermal operations.
129
10
Conclusions
From the gained experience, this chapter gathers a set of conclusions and recommendations
for the exploration and monitoring of future geothermal targets.
First, the application of survey design algorithms are useful for designing, extending, and
qualifying seismic arrays. Heuristic approaches (e.g. designs with few azimuthal and/or
distance guidelines) can become costly to a seismic experiment while resulting in no meaningful
reduction of hypocentral errors. Using survey design techniques like the one we apply in this
work (destructive sequential suvery design with quality measure based on the D-criterion) can
ultimately help optimize the expenses (number of seismic stations) dedicated for a geothermal
project and obtain comparable results (location errors of target events) at the same time.
Two powerful techniques for characterizing geothermal reservoirs are local earthquake
tomography and ambient noise tomography. The first technique relies on high seismicity rates
and a good earthquake/station distribution, while the second depends only on a good and
sufficiently dense station distribution.
While seismicity locations help identify structures and permeability enhancements of
faults, Vp models in combination with well and petrophysical data can indicate geologic unit
boundaries. Using a Vp/Vs model together with resistivity and geochemical data, for instance,
can enable the geometry identification of conductive clay caps (low Vp/Vs and low resistivity).
Changes of Vp/Vs (or Vs) can potentially hint to variations in the fluid content of rocks to
detect fluid-rich areas (Vp reduction, high Vp/Vs, and intermediate resistivity; or Vs reduction
and intermediate resistivity) and gas filled regions (very low Vp/Vs and high surface CO
2
concentrations). Ultimately, joint interpretations will help avoid ambiguities and to better
understand the structures and behavior of a geothermal system. This approach is, therefore,
highly recommended for future exploration studies.
Changes in the coda waves are the result of structural changes in a medium. Velocity
decreases in combination with decreases in micro-gravity variations and negative vertical
displacements will help point at regions of subsidence due to slow mass depletion (from the
extracted water). Short-term velocity changes due to variations in injection and production
rates are useful for the safe exploitation of a geothermal field. Although not yet a standard
practice, it is strongly advisable to continuously monitor the changes in the coda waves along
131
10. Conclusions
with the seismicity monitoring. This practice allows for the observation and control of aseismic
processes prior to stress drops that could result in large earthquake generation and helps to
understand better the reservoir dynamics.
132
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A
Contributions to the publications
This is a cumulative thesis based on articles that are published or in preparation status. It is
submitted to the Faculty VI of the Technical University of Berlin and follows its guideline for
cumulative dissertations. The results in Chapter 6 and Chapter 7 are published in Elsevier’s
Journal of Volcanology and Geothermal Research and AGU’s Journal of Geophysical Research:
Solid Earth, respectively. In addition, the data publication associated to Chapter 7 is available
at the GFZ’s GEOFON Data Center. Finally, the results of Chapter 8 correspond to a
manuscript in preparation. In the following I outline the contribution of each author to each
publication.
Chapter 6
Optimized experimental network design for earthquake location problems: Appli-
cations to geothermal and volcanic field seismic networks
,Journal of Volcanology and
Geothermal Research, 2020, (391) by Tania Toledo
1
, Philippe Jousset
2
, Hansruedi Maurer
3
,
Charlotte Krawczyk4
As a first author I programmed the sequential survey design algorithm described in the
publication. I subsequently computed the test cases and applied the algorithm to the two
case studies showcased therein. Then, I prepared the manuscript and figures, and discussed
the final results. Authors 2 and 3 guided me through the principles and ideas behind survey
design and vastly contributed in reshaping the methodology used. Finally, authors 2, 3, and 4
corrected and improved the submitted manuscript and greatly supported me with the received
journal’s revisions and modifications of the techniques used.
Chapter 7
Local Earthquake Tomography at Los Humeros Geothermal Field (Mexico)
,
Journal of Geophysical Research: Solid Earth, 2020, 125, by Tania Toledo
1
, Emmanuel
151
A. Contributions to the publications
Gaucher
2
, Philippe Jousset
3
, Anna Jentsch
4
, Christian Haberland
5
, Hansruedi Maurer
6
,
Charlotte Krawczyk7, Marco Calò8, Ángel Figueroa9
Authors 1, 8, and 9 contributed with the seismic data acquisition. The set up and tunning
of the earthquake detection algorithm was performed by authors 1 and 2, and the phase
picking by authors 1, 2, and 3. The seismic processing (1D and 3D inversions) was computed
by me with close guidance of authors 2, 3, 5, and 6. Authors 5 and 8 contributed with
post-processing suggestions. Authors 2 and 4 assisted me with the integration of available
geological and geophysical data collected at Los Humeros and with the results interpretation.
I prepared the submitted manuscript, tables, and images therein. However, Figures 7.1, 7.15,
and 7.17 and Table 7.1 were prepared in close collaboration with author 4. Then all co-authors
critically revised and corrected the complete manuscript, contributed to the results discussion,
and assisted me with the responses to the journal’s revisions (especially authors 2, 5, and
7). My colleague James Mechie improved the writing as a native English speaker during the
article resubmission.
Dataset of the 6G seismic network at Los Humeros, 2017-2018
.GFZ Data Services.
Other/Seismic Network, 2019, by Tania Toledo
1
, Emmanuel Gaucher
2
, Malte Metz
3
, Marco
Calò4, Angel Figueroa5, Joel Angulo6, Philippe Jousset7, Katrin Kieling8, Erik Saenger9
Several tasks were required for the data acquisition, preparation, and quality control of the
seismic database. The contributions to each of these tasks are listed as follows:
•Network design
Authors 1, 2, 4, 5, 7, 9
•Equipment preparation
Authors 1, 4, 5, 6, 7, 8, 9 in collaboration with Geophysical Instrument Pool
Potsdam (GIPP), Universidad Nacional Autónoma de México (UNAM), and Universidad
Michoacana de San Nicolás de Hidalgo (UMSNH) members.
•Station position scouting and installation
Authors 1, 4, 5, 6 in collaboration with UNAM and UMSNH members.
•Data collection
Authors 4, 5, 6 in collaboration with UNAM and UMSNH members.
•Seismic database construction and QC
Authors 1, 2, 3
•Metadata assembly
Authors 1, 2, 3
Chapter 8
Ambient seismic noise monitoring and imaging at the Theistareykir geothermal
field (Iceland)
,in preparation, 2021, by Tania Toledo
1
, Anne Obermann
2
, Philippe Jousset
3
,
Arie Verdel4, Joana Martins5, Kemal Erbas6, Anette Mortensen7, Charlotte Krawczyk8
152
As a first author I carried out the seismic processing, wrote the manuscript, and prepared
all the figures therein. Author 2 supported me with codes for obtaining the dispersion curves
and for performing ANSWT workflow. Then authors 2, 3, 4, and 5 closely guided me through
the theoretical principles of ANSWT and CWI, and vastly contributed in redirecting and
reshaping the processing that I carried out. Authors 6 and 7 were responsible for the data
collection and revision of the interpretation in relation to the available and new geophysical and
geological data. Finally, all co-authors critically revised and corrected the complete manuscript
which is currently in preparation.
153
B
Statutory declaration
I declare that I have authored this thesis independently, that I have not used any other than
the declared sources, and that I have explicitly marked all the material which has been quoted
either literally or by content from the used sources.
.....................................
Date and signature
155
B. Statutory declaration
156
