Geoph y sical Resear ch Letters
P resent-Da y Mars’ Seismicit y P redicted F r om 3-D Thermal
Ev olution Models of Interior D ynamics
A.-C. Plesa 1 , M. Knapmey er 1 , M. P . Golombek 2 , D . Br euer 1 , M. Grott 1 ,
T . Kaw amura 3,4 , P . Lognonné 3 , N. T osi 1,5 , and R. C. W eber 6
1 German Aerospace C enter (DLR), Berlin, Germany, 2 Jet Propulsion Laborat or y , California Institute of T echnology ,
P asadena, CA, USA, 3 Institut de Physique du Globe de P aris, Université P aris Diderot – Sorbonne P aris Cité, P aris, Fr ance,
4 National Astronomical Observator y of Japan, Oshu, Japan, 5 T echnische Universität Berlin, Berlin, German y, 6 NASA
Marshall Space Flight C enter , Huntsville , AL, USA
Abst rac t The Interior Exploration using Seismic I nvestigations , Geodesy and Heat T ranspor t mission,
to be launched in 2018, will per form a compr ehensive geoph ysical inv estigation of Mars in situ. The Seismic
Experiment for Interior Structure package aims to detect global and regional seismic events and in turn
offer c onstraints on core size , crustal thick ness, and core , mantle, and crustal composition. I n this study ,
we estimate the pr esent-day amount and distribution of seismicity using 3-D numerical thermal evolution
models of Mars, taking into account contributions fr om conv ective stresses as well as fr om stresses
associated with cooling and planetary contrac tion. Defining the seismogenic lithosphere by an isotherm
and assuming two end-member cases of 573 K and the 1073 K, we determine the seismogenic lithospher e
thickness. Assuming a seismic efficiency bet ween 0.025 and 1, this thickness is used to estimate the total
annual seismic moment budget, and our models show values between 5 . 7 × 10 16 and 3 . 9 × 10 19 Nm .
1. Introduction
The level of seismicity on Mars is usually believed to lie between that of the Earth and the Moon. Based on the
seismic events r ecorded between 1976 and 2013 and documented in the Harvard Centr oid Moment T ensor
catalog, the annual seismic moment r elease for the Earth is ∼ 3 × 10 23 N m. The values for the Moon are sig-
nificantly lower and range between 10 14 and 10 15 Nm only for the shallo w moonquakes (Oberst, 1987) and
below 10 14 Nm for deep moonquakes (Kawamura et al., 2017). F or Mars, only indirect estimates exist, which
are based on the analysis of surface faults and models of lithospheric cooling (e.g ., Golombek et al., 1992;
Knapmeyer et al., 2006; Phillips , 1991). The upcoming Disc overy class mission I nSight (Interior Exploration
using Seismic Investigations, Geodesy and Heat T ransport) to be launched in 2018 will employ a seismometer
(Seismic Experiment for Interior Structure) (Log nonné et al., 2015), a heat flow pr obe (Heat Flo w and Phy sical
Pr oper ties P ack age) (Spohn et al., 2014), and precision tracking system (Dehant et al ., 2011) to accurately mea-
sure the pr esent- day seismic activit y and the rate at which heat is lost from the planet (Baner dt et al., 2012,
2017). Such measurements will pr ovide an impor tant baseline to constrain the pr esent- day interior structure
and heat budget of the planet and, in turn, the thermal and chemical ev olution of its interior .
Pr evious seismic measurements on Mars wer e per formed in the mid-1970s by the V ik ing seismic experiment
(Anderson et al ., 1976). The Viking 1 seismometer failed to uncage , and no data were r ecorded . Howev er ,
the Viking 2 lander per formed seismic measurements with a short-period three- component seismometer in
Utopia Planitia and collected data between September 1976 and April 1978. The installation of the seismome-
ter on top of the lander instrument deck led to a high noise lev el produced by wind-induced mov ements of
the lander . During the 146 sols of operation of the V ik ing 2 seismometer , only one ev ent during sol 80 was
recor ded, which might be interpr eted as a local marsquake . Howev er , the absence of wind data during the
sol 80 signal makes it difficult to unambiguously catalog it as being of seismic origin. Never theless, a rec ent
study suggests that a wind gust can be excluded as a sour ce because of the low wind speeds r ecorded 20 min
befor e and 45 min after this event (Lor enz et al., 2017).
The nondetection of unambiguous marsquakes led to the conclusion that Mars’ seismicity is smaller than that
of the Ear th (Anderson et al., 1977). Indeed, the analysis of sur face faults suggests moment releases between
10 17 and 10 19 Nm/year (Golombek, 2002; Golombek et al., 1992), while studies taking into account global
RESEARCH LET TER
10.1002/2017GL076124
Key Poi nt s :
• We c ompute the cumulative
seismic moment due to conv ective
and cooling stresses fr om 3-D thermal
evolution models of Mars
• The annual seismic moment
budget calculated from our
models is between 5.7 × 10 16 and
3.9 × 10 19 Nm
• A new, self-consistent model for
the spatial distribution of seismicity
is derived from 3-D thermal
evolution models
Supporting Information:
• Suppor ting I nformation S1
•D a t a S e t S 1
•D a t a S e t S 2
•D a t a S e t S 3
•D a t a S e t S 4
•D a t a S e t S 5
•D a t a S e t S 6
•D a t a S e t S 7
•D a t a S e t S 8
•D a t a S e t S 9
•D a t a S e t S 1 0
•D a t a S e t S 1 1
•D a t a S e t S 1 2
Corr espondence to:
A.-C. Plesa,
ana.plesa@dlr .de
Citation:
Plesa, A.-C., K napmeyer , M.,
Golombek, M. P ., Breuer, D .,
Grott, M., Kawamura, T ., et al. (2018).
Pr esent- day Mars’ seismicity
predicted from 3-D thermal ev olution
models of interior dynamics.
Geophysical Resear ch Letters ,
45 , 2580–2589.
https://doi.org/10.1002/2017GL076124
Received 20 OCT 2017
Acc epted 19 FEB 2018
Acc epted article online 27 FEB 2018
Published online 30 M AR 2018
©2018. American Geophysical Union.
All Rights Reser ved.
PLESA ET AL. 2580

Geoph y sical Research L etters 10.1002/2017GL076124
cooling of the planet suggest values between 3 . 42 × 10 16 and 4 . 78 × 10 18 Nm/year (Knapmeyer et al., 2006;
Phillips, 1991). Along with assumptions about the lar gest marsquake and the moment-frequency relation, the
total moment release can be ascribed t o the frequency of individual marsquakes of different moment r elease.
Howev er , the spatial distribution of present-day seismicity on Mars is only indirectly constrained and previ-
ous work has f ocused on mapping the distribution of visible sur face tectonic faults, as these featur es may
hint at the internal str ess field distribution (e.g ., Banerdt et al ., 1992; Carr , 1974; Golombek & Phillips , 2009;
Wise et al ., 1979). Pr evious mapping campaigns have f ocused on not only local featur es (Anderson et al., 2004;
Hauber & Kronberg , 2001, 2005; T anaka, 1990; T anak a & Davis, 1988) but also prominent fault sy stems asso-
ciated with Tharsis (e .g., Anderson et al ., 2004; Banerdt et al ., 1992; T anaka et al., 1991). Using V iking Orbiter
imager y , Anderson et al. (2001) mapped the sur face faults on the entire west ern hemisphere, while Anderson
et al. (2008) compiled a paleot ectonic map of the eastern hemisphere to identify cent ers of tectonic activit y .
A study by Knapmeyer et al. (2006) deriv ed a global fault catalog using Mars Orbiting Laser Altimeter shaded
topographic r elief maps. Using this global catalog , Knapmeyer et al. (2006) suggested a distribution of epi-
centers b y associating individual event sizes with individual fault length, such that small ev ents may occur on
almost any fault, while lar ge events occur only on faults large enough t o produce them. Ho wever , it remains
uncertain which of the faults are currently active on Mars.
Of par ticular interest f or I nSight are the estimates of seismicity on Cerberus F ossae ( T aylor et al ., 2013), one of
the youngest tectonic f eatures on Mars that is only ∼ 1,500 k m to the east-nor theast from the InSight landing
site. Estimat es of moment release indicate r ecent marsquakes large enough to be r e corded b y the InSight
instruments ( T aylor et al ., 2013).
In this study , we use models of the thermal evolution of Mars in a 3-D spherical geometr y to assess the amount
and distribution of present-day seismicity . While previous studies have used str esses associated with cool-
ing and planetar y contraction to estimate the amount of seismicity of Mars, conv ective stresses hav e not
been considered so far but can r epresent an important contribution to the annual seismic moment budget.
In addition, 3-D thermal evolution models can be used to self-consistently derive the spatial distribution of
present-day seismicity on Mars. As the InSight lander will per form its measurements at a single designated
location in the Elysium Planitia r egion (Golombek et al., 2017), numerical simulations of planetar y interiors
can be used to interpr et the data in a global context.
2. Model
2.1. Thermal E volution Model
W e employ the thermal evolution models in 3-D spherical geometr y presented in P lesa et al. (2016). By extend-
ing the parameter space , we per form additional simulations to c ollect a number of cases for which we can
carr y out statistical analysis. In addition to solving the conservation equations of mass, linear momentum, and
thermal energy , our models account f or core c ooling and the decay of heat-producing elements (HPE). W e
consider adiabatic heating and cooling by using the extended Boussinesq appro ximation (K ing et al., 2010).
Our models use a crust whose thick ness does not change with time but varies laterally as inferr ed from gra v-
ity and topography data (Neumann et al ., 2004; Plesa et al., 2016). W e use the compositional model of Wänke
and Dreibus (1994) and partition the HPE bet ween the mantle and crust such that the present-day sur face
abundances match the a verage value inferr ed from gamma ra y measurements (Hahn et al., 2011; T aylor et al.,
2006). Because the crustal thickness shows larger variations than the sur face abundance of HPE, we neglect
spatial variations in crustal HPE and use an average c onc entration of 49 pW/kg at present da y (Hahn et al.,
2011). In addition, we consider the blanketing eff ect of the crust by using a lower thermal conductivity in the
crust compared t o the mantle. This leads to higher t emperatures in mantle reg ions cover ed by a thick crust
compared t o regions c over ed by a thin crust. A detailed model description is shown in section S1 of the sup -
por ting information (SI) and in Plesa et al. (2016). Input parameters f or each individual simulation are listed in
T able S3 of the SI.
Plesa et al. (2016) hav e shown that the struc ture and thickness of the crust play an impor tant role in the dis-
tribution and magnitude of the sur face heat flow and the elastic lithosphere thickness. F or the present study ,
we hav e selec ted three end-member crustal thickness models, which are consistent with curr ent gra vity and
topograph y data. W e note that a recently published crustal thickness model by Goossens et al. (2017), which
includes a spatially variable crustal density with an average value of only 2,582 ± 209 kg/m 3 , leads t o a differ-
ent crustal thickness pattern. This k ind of model will be addressed in future studies . The “ densit y dichotomy
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Geoph y sical Research L etters 10.1002/2017GL076124
crust” (DC) model, which uses a crustal density of 2,900 kg/m 3 for the southern highlands and 3,100 kg/m 3 for
the nor thern lowlands, sho ws a relativ ely uniform crustal thickness distribution apar t from the Tharsis r egion
(Plesa et al., 2016). The “high density crust” (HC) model, which uses a uniform crustal density of 3,200 kg/m 3 ,
exhibits the most pronounced variations in crustal thickness (Plesa et al., 2016). The model by Neumann et al .
(2004) (NC model), which assumes a lower unif orm crustal densit y of 2,900 kg/m 3 , is intermediate between
the previous two (F igure S1 of the SI).
2.2. Seismicity Model
W e use our thermal evolution models to compute the pr esent- day annual cumulative seismic moment budget
M cum follo wing Knapmeyer et al. (2006):
M cum = 𝜂 𝜀 V 𝜇 Δ t (1)
where 𝜂 is the seismic efficiency , a scale fac tor that determines how much of the actual deformation is r eleased
in the form of seismic ener gy (discussed below).  𝜀 is the strain rate computed fr om the thermal evolution
model, and V is the seismogenic v olume, which we calculat ed based on the depth of the 573 K or 1073 K
mantle isotherms. T he 573 K isotherm is often associated with the bottom of the seismogenic lay er since
this is the temperature abo ve which quartz, the most duc tile component of a granitic crust, shows a plastic
behavior (Scholz, 1998). Although the presence of quartzo-feldspathic material has been identified in the
lower units of V alles Marineris and in localized reg ions in the southern highlands (Bandfield et al., 2004), and
granodiorite-like r ocks hav e been analyzed in Gale crater (Sautter et al., 2016), the majority of the Mar tian
crust is considered t o be basaltic to andesitic in composition (e .g., Z uber , 2001). F or this t ype of materials,
the 1073 K isotherm marks the maximum depth of oceanic intraplate quakes on the Ear th (Bergman, 1986;
Wiens & St ein, 1983) and we will assume this to be the upper limit f or the seismogenic layer thickness on
Mars. W e varied the shear modulus 𝜇 between 30 and 70 GP a. The time interval Δ t is set here to 1 y ear to
obtain the annual seismic moment budget in the sense of the moment conservation principle. W e compute
the cumulative seismic moment on a 3 ∘ × 3 ∘ grid to filt er out small-scale structures that may be specific for
an individual simulation, given that w e are inter ested in f eatures associated with large geolog ic regions such
as the Tharsis and Elysium v olcanic provinc es, and large impact basins (e.g ., Hellas).
The seismic efficiency fac tor 𝜂 describes how much strain is r eleased in seismic events compar ed to aseismic
deformation (i.e ., folding and aseismic cr eep). F or the Ear th, W ard (1998a) and W ard (1998b) derived the seis-
mic efficiency f rom the ratio of seismic to geodetic moment r ates and found lar ge regional variations between
0.025 and 0.86, depending on location. While values abov e 0.7 are repr esentative f or Southern and Nor thern
Calif ornia regions located close t o the boundar y bet ween North American and Pacific plates , smaller values
of only a few per cent are r epresentative f or slow-straining reg ions, f or example, central USA and northwest
Europe . The small values, howev er , are attribut ed to lack of long-term observational data ( W ard , 1998a). In
this study , we varied the seismic efficiency bet ween 0.025 and 1.
In equation (1) the strain rate is computed either taking into account the con vective stresses or str esses pro-
duced by planetary contrac tion. If the former are used ,  𝜀 is calculated as the sec ond invariant of the strain
rate tensor:
 𝜀 = ( ∑
ij
 𝜀 ij  𝜀 ij ) 1 ∕ 2
(2)
where  𝜀 ij = 1
2 ( 𝜕 v i
𝜕 x j
+ 𝜕 v j
𝜕 x i ) and 𝜕 v i
𝜕 x j
is the spatial gradient of the v elocity vector . W e calculate equation (2)
throughout the seismogenic lay er . I n a stagnant lid planet con vective stresses bec ome smaller the shallower
the depth is. How ever , if the seismogenic layer is defined b y the 1073 K isotherm, it will reach depths where
strain rate values become nonnegligible (f or a t ypical strain rate profile , see F igure S4 of the SI).
When considering stresses pr oduced by mantle c ooling and planetar y contrac tion,  𝜀 is r elated to the planetary
radius change due to cor e and mantle heating or cooling:
 𝜀 = Δ R
R l ∕ 2
1
Δ t (3)
where R 1 ∕ 2 is the radius corr esponding to half the present-day seismogenic lay er volume and Δ t is the time
inter val ov er which the radius change ( Δ R ) is computed . The radius change is calculated column wise using
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Geoph y sical Research L etters 10.1002/2017GL076124
the temperature pr ofile beneath each sur face grid point. W e employ the same approach as Gr ott et al. (2011)
and T osi et al. (2013) but use the radius R l ∕ 2 instead of the planetar y radius:
Δ R = 𝛼 c ( T c ( t n )− T c ( t n − 1 )) R 3
c
3 R 2
l ∕ 2
+ 1
R 2
l ∕ 2 ∫ R l ∕ 2
R c
𝛼 m ( T m ( r , t n )− T m ( r , t n − 1 )) r 2 d r (4)
where 𝛼 c and 𝛼 m ar e the thermal expansion coefficients of the cor e and mantle, T c and T m ( r ) are the
core-mantle boundary (CMB) temperature and the mantle t emperature, and R c is the radius of the c ore. W e
choose R l ∕ 2 instead of the planetar y radius R p or the radius at the base of the seismogenic lay er , R l , because
we comput e an average radius change in the seismogenic la yer . T he radius change obtained when using R p
over estimates the actual Δ R that takes place in the seismogenic lay er , while the radius change calculated
using R l underestimates it. In contrast to the pr evious studies of Phillips (1991) and Knapmeyer et al. (2006)
who only computed the radius change within the seismogenic lay er , we take int o account the contraction of
the core and the entir e mantle up to the radius R l ∕ 2 . Our models use a time output r esolution of 10 Myr , and
since we ar e interest ed in the present-day seismic moment, we comput e the radius change based on the tem-
peratures at 4.49 Gyr and at present da y . Hence, T c ( t n ) and T m ( r , t n ) ref er to the present da y CMB and mantle
temperature , respectively , while T c ( t n − 1 ) and T m ( r , t n − 1 ) are the CMB and mantle temperatur e after 4.49 Gyr of
evolution, r espectively . Accor dingly , Δ t in equation (3) is set to 10 Myr .
3. Results
W e compute the seismic moment budget for each thermal ev olution simulation using the parameters listed
in T able S1 of the SI, and f or each crustal thick ness model we calculate the median of at least eight simulations
in every 3 ∘ × 3 ∘ grid region.
Our models show an annual seismic moment budget between 5 . 7 × 10 16 Nm and 3 . 9 × 10 19 Nm. The minimum
value is obtained by assuming the 573 K isotherm to define the seismogenic la yer v olume, a seismic efficiency
of 0.025, and a shear modulus of 30 GP a and using the median of simulations employing the NC model, which
shows the lo west seismic moment budget. The maximum value is comput ed by assuming the 1073 K isotherm
to define the seismogenic lay er volume , a seismic efficienc y of 1, and a shear modulus of 70 GPa and using
the median of simulations employing the HC model, which sho ws the highest seismic moment budget. In our
models, the annual seismic moment budget can r each values higher than 1 . 95 × 10 19 Nm only if the seismic
efficiency is larger than 0.5 and rather close to 1, while values below 10 17 Nm necessarily requir e 𝜂< 0 . 05
( T able S2 of the SI).
F igure 1 sho ws histograms of the seismogenic depth f or all models studied here using either the 573 K
(F igure 1a) or 1073 K (F igure 1b) isotherm to compute the seismogenic v olume. T he simulations employing
the NC and DC model show a similar distribution with a pronounc ed peak at around 50 km for the 573 K
isotherm and around 170 km for the 1073 K isotherm. The HC model exhibits the highest peak-to-peak crustal
thickness variations. This is also reflected in the highest peak-to-peak seismogenic depth variations . In fac t,
the crustal thickness and the crustal enrichment in HPE influence the temperature distribution in the shal-
low mantle and consequently r egions of thick crust overlie a hott er mantle compared to r egions cover ed by
a thinner crust. This eff ect is most significant for the HC model with a mean crustal thickness of 87 k m com-
pared to the other two crustal thickness models, f or which the average crustal thickness lies around 45 km.
Because the seismogenic depth has been computed based on an isotherm value of 573 and 1073 K, the his-
tograms sho w the depths at which these values have been attained . While f or the NC and the DC model the
seismogenic depth lies between 30 and 100 km for the 573 K isotherm, and between 50 km and 250 k m for
the 1073 K isotherm, the HC model exhibits a much wider range due to the lar ger variations in crustal thick-
ness and the overall thicker crust. F or this end-member crustal thick ness model, the seismogenic depth varies
between 30 and 170 km for the 573 K isotherm, and between 60 and 450 km for the 1073 K isotherm. In par-
ticular , the 1073 K isotherm suggests that, f or the HC model, marsquakes could orig inate at gr eater depths
than assumed in previous studies .
In Figur e 2 we illustrate the seismic moment contributions calculat ed from stresses associat ed with plane -
tar y cooling (F igure 2a) and con vec tive str esses (F igure 2b) as well as the sum of the two (F igure 2c) using the
1073 K isotherm and the HC model of Plesa et al. (2016) as an example (other crustal thickness models are
shown in the SI). If we consider str esses associated with cooling and planetary contrac tion, due to the less
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Fi gu r e 1 . Seismogenic lithosphere thick ness: Each line corresponds to a thermal evolution model. (a) The r esults
obtained using the 573 K isotherm. (b) The 1073 K isotherm. Results using the DC model are shown b y red lines,
simulations using the NC model are sho wn by black lines, while the DC model is sho wn by blue lines. The DC and NC
models indicate a similar range of seismogenic lithosphere thicknesses, while the HC model shows a much wider range
(blue lines). NC = Neumann crustal thickness model; DC = densit y dichotomy crust; HC = high density crust.
efficient insulation of the crust, the highest values for seismic moment budget ar e attained in regions of thin
crust (i.e., impact basins) and the nor thern hemisphere. In contrast, reg ions cov ered by a thick crust show
an inefficient cooling and thus the low est values of seismic moment budget. If, inst ead, the seismic moment
budget is computed b y tak ing into account c onvective str esses, the highest seismic moment values ar e
associated with reg ions where a thick crust is blanketing the underlying mantle. In such regions , higher t em-
perature in the mantle leads to mor e pronounced deformation and thus higher c onvective str esses. Hence ,
the two seismic moment contributions are spatially antic orrelated and their sum (F igure 2c) shows a r elatively
homogeneous distribution with relativ e highs in seismic moment from con vective stresses .
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Fi gu r e 2 . Spatial distribution of the annual seismic moment budget based on (a) the stresses produc ed by mantle cooling , (b) conv ective stresses, and
(c) the sum of the two contributions. Her e we use the HC model of Plesa et al. (2016) and define the seismogenic v olume using the depth of the 1073 K isotherm .
The seismic efficiency is set here to 1 and the shear modulus to 70 GP a.
Fi gu r e 3 . Geographic distribution of possibly seismically active areas based on the fault catalog of Knapmeyer et al. (2006). (a) all faults considered, (b) on ly faults
cutting areas with ages younger than the Noachian epoch (age < 3700 Myr), and (c) only faults on sur faces dated to early Amazonian epoch (age < 600 Myr).
White reg ions on the maps represent areas with z ero seismic moment. Spatial distribution of the annual seismic moment budget based on 3-D thermal evol ution
models that consider both stresses associated with planetary contraction an d convective stresses . The total annual seismic moment budget has been c alculated
using the (d – f ) 1073 K isotherm and (g – i) 573 K isotherm. Results based on the DC model are shown in F igures 3d and 3g, on the NC model in F igures 3e and 3h,
and on the HC model in Figur es 3f and 3i.
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W e compare our geographic seismic moment distribution with the seismicity distribution on the individual
faults mapped by Knapmeyer et al. (2006), discr etized on a 3 ∘ × 3 ∘ grid. F igures 3a – 3c show the geographic
distribution assuming that cer tain faults contained in the fault catalog of Knapmeyer et al. (2006) ar e seis-
mically active. F or all three cases, the pr esence or absence of faults cr eates an on-off pattern with aseismic
areas . The younger the age of the sur faces consider ed to be seismically active, the smaller the ar eas where a
nonzero seismic moment is a ttained. The distribution ranges fr om a nearly homogeneous map , if all faults are
considered seismically active (F igure 3a), to limited r egions in Tharsis , Elysium, and the nor thern latitudes if
only faults cutting Amazonian sur faces are used (F igure 3c). F igures 3a – 3c show that the distribution of sur-
face faults cannot constrain the spatial distribution of seismicity on Mars since it is not known which faults are
still active today .
In comparison, the seismic moment distribution predicted by the 3-D thermal ev olution models used in
this study shows a mor e homogeneous pattern with all reg ions being seismically ac tive (F igures 3d – 3i).
In par ticular , for the 1073 K isotherm the seismic moment show s a homogeneous distribution for the DC and
NC models (F igures 3d and 3e). F or the HC models, slightly larger seismic moment values ar e obtained in
regions c over ed by a thick crust (F igure 3f ). W hile conv ective stresses are similar in mag nitude but spatially
anticorrelat ed with the stresses associated with planetary cooling for the 1073 K isotherm, they are neglig i-
ble for the 573 K isotherm, because in a stagnant lid planet c onv ective stresses become smaller f or shallower
regions . Here the seismic moment distribution is dominat ed by the pattern obtained from mantle c ooling,
that is, r egions of thin crust experience a mor e pronounced cooling c ompared to r egions blanketed b y a thick
crust (F igures 3g – 3i).
4. Discussion
W e compare the moment release obtained in this study with pr evious estimates of Mars’ seismicity and with
the data obtained for the Moon and the Earth (F igure 4). Previous studies estimat ed the seismic moment
release either fr om differ ential cooling of the lithosphere using parametrized thermal evolution models and
employing various isotherms (i.e., 573, 873, and 1073 K) to calculate the seismogenic volume (Knapmeyer
et al., 2006; Phillips , 1991) or from total slip on surface faults (Golombek, 2002; G olombek et al., 1992). The
annual seismic moment release f or the Moon has been estimated from shallo w moonquakes (Oberst, 1987)
and from the r ecently published deep moonquake data for mor e than 100 events from thr ee deep moonquake
clusters (A01, A06, and A07) (Kawamura et al ., 2017). F or the Ear th, we used the Harvard Centroid Moment
T ensor catalog bet ween 1976 and 2013. T o compute the moment-frequency distribution for the values
obtained in this study , we choose a slope of 0.625, similar to the study of Knapmeyer et al. (2006). This value
lies in the inter val of [0.6, 0.65], which was obtained from the analy sis of quakes on Ear th when excluding deep
events close to olivine-bridg manite transition (i.e., 660 km depth on Ear th) and events close to mid-ocean
ridges (Kagan, 2002). We note that the value of 0.625 seems to fit the siz e-frequency distribution derived for
shallow moonquakes , while the deep moonquake distribution appears to be steeper . Ho wever , a larger num-
ber of events w ould be necessar y to accurately determine the slope in both cases . I n par ticular , the cur vature
shown by the shallo w moonquake distribution suggests that more small events oc curred than wer e identified
in the data recor ded by the Apollo network. In addition, rare large events occurring at longer time int er vals
than the duration of the Apollo seismic experiments may be absent fr om the catalog. T hus, the catalog might
underestimate the lunar seismic moment r elease.
The moment-frequency relation is sensitive t o the largest marsquake assumed and the number of events with
a moment larger than or equal to a g iven seismic moment M 0 increases if the maximum seismic moment is
decreased (F igure 4). W e adopt a value of 10 20 N m that was derived fr om the analysis of intraplate earthquakes
and well-documented normal faults, whose sizes ar e similar to large normal faults on the bor der of V alles
Marineris (Golombek, 1994). The moment-frequency distribution range calculated from our thermal evolution
models is in good agreement with pr evious estimates and confirms that the seismicity of Mars lies between
that of the Moon and the Ear th (Figur e 4).
In all our simulations we defined the seismogenic lithosphere by using either the 573 K or the 1073 K isotherm.
When using the 1073 K isotherm, the stresses pr oduced by mantle con vec tion are similar in magnitude but
anticorrelat ed to the stresses associated with c ooling and planetar y contraction. This leads to a homoge -
neous distribution of the annual seismic moment budget. In contrast, for the 573 K isotherm, the contribution
from con vec tive str esses is negligible and the distribution of the annual seismic moment budget follo ws
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Geoph y sical Research L etters 10.1002/2017GL076124
Fi gu r e 4 . Comparison of moment-frequency relation between previous studies , this work, and the annual seismic
moment release of the Earth (Har vard- CMT ) and the Moon from both shallow moonquakes and three deep moonquake
clusters (A01, A06, and A07). T o calculate the moment-frequency-relation, we use the total seismic moment budget,
which takes into account the c ontribution of both stresses from planetary contraction and convective stresses . The value
N ( M ≥ M 0 ) on the y axis shows the annual number of events with a moment larger than or equal to M 0 . The values
obtained in this study have been calculat ed using a slope of 0.625 and a maximum marsquake moment of 10 20 Nm.
the pattern of the seismic moment based only on planetary cooling, with a larger seismic moment in r egions
cov ered by a thin crust. Although the models f or which the annual seismic moment budget has been calcu-
lated using the 573 K isotherm might seem to contradict the association of faults in and around T harsis, these
faults are most likely due to str esses caused by lithospheric flexure due t o loading, which was not consider ed
in this study . Howev er , whether these faults are active toda y is not k nown. If indeed these faults are still active,
stresses pr oduced by lithospheric flexur e would repr esent an additional contribution to the amount of seis-
mic moment available in the Tharsis r egion. This c ontribution will need to be estimated by other studies using
flexural models.
The upcoming InSight measurements will help det ermine the amount and distribution of Mar tian seismicit y
by monitoring the seismic activity for one Mar tian year . Although the mission pr ovides only one seismic sta-
tion, the presence of depth phases and the r elative amplitude of sur face wav es with respect to body wav es
will provide c onstraints on the depth distribution of seismic sources . On Ear th, essentially all seismicity below
the Moho is connected to plate boundaries and subduction of cold lithosphere. Mars , on the other hand, is
a one-plate planet and so far deep seismicity was not expected to exist. This view , howev er , is challenged by
the HC models presented her e, which suggest that the seismogenic volume could extend to depths of about
400 km, if the base of the seismogenic layer is marked by the 1073 K isotherm. W e note that deep moonquakes,
occurring at 800 – 1,200 k m below the lunar sur face, repr esent one of the most numerous types of seismicit y
on the Moon (Nak amura, 2005). Why the deep moonquakes cluster at this depth is still enigmatic and a num-
ber of mechanisms, such as deh ydration embrittlement, and transformational faulting ha ve been suggested
to explain their occurr ence in what should be a ductile regime (F rohlich & Nak amura, 2009). Kawamura et al.
(2017) recently pr oposed that only mantle temperatur es of 1240 – 1275 K are consist ent with brittle failure
under loading by Earth tidal stresses. Nevertheless, on Mars such deep nucleation zone (800 – 1,200 k m) is
unlikely , because the interior temperature r apidly increases to values higher than 1500 K belo w 600 k m depth
even f or the most depleted mantle. T he depth of marsquake foci can be used to distinguish between diff er-
ent seismicity models presented in this study , that is, events orig inating at depths higher than 180 k m would
clearly indicate contributions fr om both cooling and con vective stresses while ev en deeper events (at depths
> 250 km) would suggest a cold, depleted mantle and a thick crust enriched in HPE. Moreover , the localization
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Geoph y sical Research L etters 10.1002/2017GL076124
of the seismic events , which can be obtained with the Seismic Experiment for Interior Structure instrument,
could also be used to distinguish between an incr eased seismicity in the nor thern hemisphere, indicating a
shallow seismogenic volume and only a c ontribution from cooling str esses, and a seismicity distribution that
is more homogeneous or slightly larger in the southern hemispher e, suggesting a large seismogenic volume
and contributions from both c ooling and conv ective stresses. In addition, the annual seismic moment bud-
get, which will be derived fr om InSight data, can be used to constrain the seismic efficienc y on Mars. If the
annual seismic moment budget of Mars lies below 10 17 Nm, our models indicate a seismic efficienc y smaller
than 0.05, while a value abov e 1 . 95 × 10 19 Nm would only be reached if the seismic efficiency is at least 0.5.
5. C onclusion
W e have used a series of numerical models of thermal ev olution of Mars in a 3-D spherical geometr y to assess
the magnitude and spatial distribution of present-day Mars’ seismicity . We ha ve comput ed the annual seismic
moment budget from 39 thermal ev olution simulations for which w e have identified thr ee categories of
models based on the assumed crustal thickness. W e have self-consistently deriv ed the amount and spatial
distribution of seismicity from the thermal evolution b y tak ing into account c ontributions from con vective
stresses as w ell as stresses caused by mantle cooling and planetary contrac tion. Our results predict an annual
moment budget between 5 . 7 × 10 16 and 3 . 9 × 10 19 Nm similar to the values presented pr eviously in Phillips
(1991); Golombek et al. (1992), Golombek (2002), and Knapmeyer et al . (2006).
The future seismic data t o be returned by InSight will better constrain the seismicity of Mars and greatly
improv e our understanding of the interior of the planet. In par ticular , the depth of marsquakes and the esti-
mate of the annual seismic moment budget would help distinguish between various models discussed her e.
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Ack n ow le dg m ent s
All the parameters used in the mod-
els and their outcomes are list ed
in the supporting information. W e
thank Mark Wieczor ek for pro viding
the crustal thickness models used
in this study . A.- C. Plesa acknowl-
edges suppor t from the Interuniversity
Attraction Poles P rogramme initi-
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Office through the Planet T OPERS
alliance. M. Golombek w as suppor ted
by the InSight Project, Jet Pr opulsion
Laboratory , California Institute
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N. T osi acknowledges support
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