74 IEEE TRANSACTIONS ON INSTRUMENTATION AND MEASUREMENT, VOL. 47, NO. 1, FEBRUARY 1998
Subsu ace Resis i i y Measu emen s
Using Squa e Wa e o ms
Manel Gasulla-Fo ne , S uden Membe , IEEE, Josep Jo dana-Ba nils, S uden Membe , IEEE,
Ram´on Pall´as-A eny, Fellow, IEEE, and Josep Ma ia To en s, Membe , IEEE
Abs ac — This wo k analyzes he e ec o induc i e and
capaci i e coupling be ween he injec ing ci cui and he de ec ing
ci cui in esis i e ield su eys. Theo e ical and expe imen al
esul s demons a e ha i a squa e wa e o m is injec ed in o
he soil, and synch onous sampling is used o sample a he la
zone o he de ec ed ol age, hen he e ec o he in e e ence
is g ea ly educed. Fu he mo e, squa e wa e o ms a e easie o
gene a e han sinusoidal wa e o ms, so hey o e a new app oach
o subsu ace esis i i y measu emen s.
Index Te ms— Conduc i i y measu emen , da a acquisi ion,
elec omagne ic coupling, sampling me hods, soil measu emen s,
synch onous de ec ion.
I. INTRODUCTION
THE de ec ion o bu ied s uc u es om he su ace wi h-
ou d illing in o he soil is o in e es in a chaeology
and in o he applica ions such as de ec ion o wa e and
con aminan s om leaking unde g ound pipes. G ound pen-
e a ing ada and ime domain e lec ome y a e echniques
ha can be applied in hese cases. Ou wo k is conce ned wi h
geoelec ical p ospec ing me hods, which consis o injec ing
a cu en o he soil wi h a pai o elec odes and de ec ing he
d op in ol age wi h ano he pai o elec odes.
The pa ame e ha p o ides in o ma ion on he bu ied
s uc u e ( he anomaly) is he appa en esis i i y , which
is gi en by [1]. In his exp ession is
he de ec ed ol age, is he injec ed cu en , and is a
geome ic ac o , which depends on he con igu a ion o he
elec ode a ay. I is impo an o ecognize ha any possible
e o in he measu ed ol age will a ec and can hinde he
de ec ion o he anomaly. Some e o sou ces a e he posi ion
o he elec odes, ellu ic noise (which has i s main in luence
in dc measu emen s) and elec omagne ic coupling be ween
he injec ing and de ec ing ci cui s in ac measu emen s.
In elec ical su eys, elec omagne ic induc ion be ween
cu en and ol age cables mus be a oided. This is easily
achie ed by using dipole–dipole a ays [2], bu i is in e -
es ing o de ise a measu emen me hod able o educe his
in e e ence independen ly o elec ode con igu a ion.
II. PROBLEM STATEMENT
In elec ical impedance measu emen , we injec a cu en
( equency ) and de ec a d op in ol age whose ampli ude
Manusc ip ecei ed June 1, 1997; e ised Ap il 1, 1998. This wo k was
suppo ed by he Spanish DGICYT unde P ojec PB93-0961.
The au ho s a e wi h he Di isi´
o d’Ins umen aci´
o i Bioenginye ia, Depa -
amen d’Enginye ia Elec `
onica, Uni e si a Poli `
ecnica de Ca alunya, 08034
Ba celona, Spain.
Publishe I em Iden i ie S 0018-9456(98)05483-7.
Fig. 1. Impedance measu emen by homodyne de ec ion.
Fig. 2. Impedance measu emen by synch onous sampling.
is modula ed by he impedance sensed. Modula ion p oduces
an upwa d ansla ion o he in o ma ion spec um. Demodu-
la ion, he e o e, implies a downwa d equency ansla ion in
o de o eco e he in o ma ion om he modula ed wa e.
A common demodula ion echnique p o iding a good
signal- o-noise a io is homodyne de ec ion. This me hod can
be applied o impedance measu emen as shown in Fig. 1.
I we assume ha he signal de ec ed is
and he e e ence signal is
, hen he demodula ed signal a he ou pu o
he low pass il e , when ,is .In
a esis i e medium, , hen .
I he e is an in e e ing signal
, ha ing he same equency han he ca ie , ypically
capaci i ely o induc i ely coupled, hen he demodula ed
signal in a esis i e medium is .I
he phase angle o he in e e ence is 90 hen he signal
will be eco e ed wi hou any e o . Bu when
he e will be a measu emen e o . In p inciple, he la ge he
equency o he injec ed cu en , he la ge he in e e ence
will be, because bo h induc i e and capaci i e in e e ence
inc ease wi h equency. In ex eme cases he de ec o can
e en sa u a e because o he in e e ence.
Impedance measu emen by synch onous sampling (Fig. 2)
is ano he phase-sensi i e ampli ude demodula ion echnique
[3]. I is sampled a in ege , being
he pe iod o he signal, ha is, i he signal is
sampled a i s maximal alue, hen he de ec ed signal will
be . I can be seen ha
he measu emen e o also depends on he phase angle o
0018–9456/98$10.00 1998 IEEE
GASULLA-FORNER e al.: SUBSURFACE RESISTIVITY MEASUREMENTS USING SQUARE WAVEFORMS 75
Fig. 3. Linea a ay o cu en and po en ial elec odes.
he in e e ence. Bu he e his d awback can be a oided by
injec ing a squa e wa e o m o he soil ins ead o a sinusoidal
wa e o m [4]. In his case he de ec ed signal is sampled a
a ze o-slope poin , hus a oiding he s ay cu en coupling
om he injec ing ci cui o he measu ing ci cui (“ ans o me
e ec ”). The e o e, his allows us o measu e a a equency
high enough in o de o elec ode impedance o be ela i ely
low.
Elec omagne ic in e e ence is pa icula ly oublesome in
subsu ace esis i i y measu emen s because o he physical
dimensions and a angemen o ci cui s. Fig. 3 shows he
p inciple o his echnique [1]. A cu en o s eng h is
injec ed by elec odes and . The po en ial di e ence
be ween poin s and in a homogeneous medium is
(1)
whe e is he soil esis i i y, and o a e dis ances
be ween he elec odes. The appa en esis i i y is ob ained
by sol ing (1) o :
(2)
whe e is he geome ic ac o .
The appa en esis i i y p o ides in o ma ion abou he
p esence o an anomaly. The po en ial di e ence can be
a ec ed by he elec omagne ic coupling om he injec ing
ci cui o he de ec ing ci cui , which will al e he alue o
.
The e a e wo main coupling mechanisms: capaci i e cou-
pling and induc i e coupling [5]. Capaci i e coupling a ises
om he pa asi ic capaci ances be ween injec ing and de ec ing
wi es. Induc i e coupling appea s because he injec ing and
de ec ing ci cui s beha e like he p ima y and seconda y
winding o an o dina y ans o me .
I dc cu en s a e used, hen he e is nei he capaci i e no
induc i e coupling. Bu dc cu en s pose ano he impo an
p oblem: pola iza ion po en ials gene a ed a he con ac be-
ween a me allic conduc o ( he elec ode) and an elec oly ic
conduc o ( he mois g ound). These pola iza ion po en ials a e
dc ol ages ha mask he measu ed ol age di e ence.
In e e ence by capaci i e and induc i e coupling esul s
only when he e is a change in he ol age o cu en in he
injec ing ci cui . Fo a sinusoidal signal, his means he en i e
wa e o m excep a i s maximum and minimum. Fo a squa e
signal, howe e , in e e ence will esul only du ing ansi ion
Fig. 4. Synch onous sampling wi h squa e wa e o ms. F om
T
=
4
o
T=
2
he in e e ence is minimal.
Fig. 5. Induc i e and capaci i e coupling be ween injec ing and de ec ing
ci cui s.
imes. Hence, by sampling a o a bi la e he e ec o
he in e e ence should disappea (Fig. 4).
III. THEORETICAL ANALYSIS
Fig. 5 shows he ci cui model o a esis i i y measu emen .
and a e he injec ed and de ec ed ol ages, espec i ely,
is he capaci ance be ween he injec ing and de ec ing wi es,
and a e he sel and mu ual induc ance o cables, and
a e he con ac esis ances o he injec ing and de ec ing
elec odes, and is he esis ance be ween he elec odes
and . Fo simplici y, we s udy capaci i e and induc i e
in e e ences sepa a ely.
I no in e e ence is p esen , he ideal de ec ed ol age will
be
(3)
We de ine he ela i e e o in he measu ed ol age as
(4)
whe e is he de ec ed ol age con amina ed by he in e e -
ence. We conside an injec ed equency o up o 10 kHz,
abou 0.33 , and in he ange o 50 o 5 k ,
anging om 10–100 pF, and and be ween 10 and 100
H. Ei he o sinusoidal and squa e wa e o ms we sample
a , whe e is he pe iod o he signal and
is an in ege .
Fi s o all, we conside he e ec o s ay capaci ances.
When we injec a squa e ol age whose peak alue is he
76 IEEE TRANSACTIONS ON INSTRUMENTATION AND MEASUREMENT, VOL. 47, NO. 1, FEBRUARY 1998
de ec ed ol age is
(5)
and he ela i e e o o he assumed alue ange o he
di e en pa ame e s is
(6)
I he gene a o injec s a sinusoidal wa e o m, he ela i e
e o in he measu ed ol age o he in phase componen is
(7)
I can be seen ha he e o g ea ly inc eases as and
become la ge . Fo example, i he equency is 10 kHz,
pF, and he ela i e e o o
sinusoidal signals is only bu when pF and
k he ela i e e o inc eases o 30. I squa e
wa e o ms a e used he e o is negligible in bo h cases.
Secondly, we conside he e ec o induc i e coupling. The
ela i e e o o squa e signals in he same condi ions as abo e
is
(8)
and o sinusoidal signals is
(9)
I is in e es ing o poin ou ha i is educed he e o
inc eases in bo h cases. Fo sinusoidal signals he ela i e
e o a ies om when H and
, o 4.68 when H and
. This e o is minimized o when
using squa e wa e o ms.
Elec omagne ic coupling inc eases wi h equency. To
a oid he e ec o in e e ence in he measu ed ol age i
is ad isable he e o e o injec a squa e wa e o m in o he
soil ins ead o a sine wa e and o use a de ec o based on
synch onous sampling.
IV. MATERIALS AND METHODS
In o de o quan i y in e e ence in a ield su ey, we ca ied
ou some measu emen s in a ypical soil o ou campus. Fig. 6
shows he elec ode a angemen . The injec ing and de ec ing
cables we e a anged in a iangula geome y pa allel o he
g ound su ace. The ansmi e and he ecei e we e placed
in a e ex (TD) o his iangle, in on o he elec ode a ay.
The gene a o was an HP3245A and he de ec o was a ully
di e en ial synch onous demodula o , based on synch onous
sampling [6]. The ou elec odes we e made om s ainless
s eel, 20 cm in leng h and 1 cm in diame e . They we e inse ed
se e al cen ime e s in o he g ound o ensu e a good elec ical
con ac . Connec ing wi es we e 1 mm in diame e and had
Fig. 6. Field su ey: elec ode a ay and wi e a angemen .
plas ic insula ion, which a oided any possible di ec leakage
cu en o he g ound.
The HP3245 gene a es he sinusoidal/squa e signal o 20
Vand he signal e e ence o he sample . The sampling
equency was he same ha he inpu signal ( ) and i s
alues we e 100 Hz, 1 kHz, and 10 kHz. The de ec o had a
gain o 100. The du y cycle o he sampling signal was 10%.
The sampling ins an was a . The d op in ol age
moni o ed he injec ed cu en ac oss a esis o in se ies
wi h an injec ing wi e, by means o a po able oscilloscope
(Tek onix THS-710E).
V. EXPERIMENTAL RESULTS
In o de o quan i y elec omagne ic in e e ence, we mea-
su ed i s he capaci i e coupling, secondly he induc i e
in e e ence and inally hei combined e ec in he di e en ial
ol age measu ed be ween elec odes and .
Capaci i e in e e ence inc eases in alue i coupled o a
high-impedance ci cui . In o de o demons a e his e ec ,
a a iable esis o was connec ed o he end o wo wis ed
cables. The de ec ed po en ial inc eased wi h he esis o alue.
By placing a esis o o k , a 10 kHz and by sampling
a o he injec ed signal, 141 mV we e de ec ed a he
ou pu o a sinusoidal wa e o m and only 14 mV o a squa e
wa e o m. Capaci i e coupling inc eased wi h equency and
wi h cable leng h. Induc i e in e e ence was minimal because
he de ec ing wi es we e wis ed.
I he a ea o he de ec ing ci cui is inc eased and i s e mi-
nals sho -ci cui ed, capaci i e in e e ence is negligible (ze o
dependence) and induc i e coupling p edomina es. A 10 kHz
he de ec o ou pu was 23 mV when using sinusoidal signals
and only 2 mV by injec ing squa e wa e o ms. Induc i e
coupling inc eased wi h he a ea o he de ec ing wi es.
Table I shows he demodula ed dc ol age (once mul-
iplied by 100) and he injec ed cu en (peak o peak) wi h
sinusoidal and squa e wa e o ms a equencies 1 and 10 kHz.
The de ec o was connec ed o elec odes and . In his
case he e was, added o he ideal ol age, bo h capaci i e
and induc i e in e e ence and hey inc eased wi h equency.
Howe e , when using squa e wa e o ms he de ec ed ol age
was simila , which con i ms ou p edic ions ha sampling in
he la zone o he squa e wa e o m, minimizes he e ec o
in e e ence. When using sinusoidal wa e o ms, he ol age
GASULLA-FORNER e al.: SUBSURFACE RESISTIVITY MEASUREMENTS USING SQUARE WAVEFORMS 77
TABLE I
DETECTED VOLTAGE WHEN INTERFERENCE COUPLING IS MAXIMUM
TABLE II
DETECTED VOLTAGE WHEN DETECTING CABLES ARE TWISTED
de ec ed changed by 91%. The small change obse ed in he
squa e wa e is p incipally due o he dec easing alue in he
con ac esis ance wi h equency, which inc eases he
injec ed cu en .
I he de ec ing cables we e wis ed, in e e ence educed
because he dis ance be ween de ec ing wi es and injec ing
wi es inc eases and he a ea o he de ec ing ci cui was much
smalle . The esul s a e shown in Table II.
VI. CONCLUSIONS
We ha e p oposed a simple model o s udy he e ec s o
capaci i e and induc i e in e e ence in subsu ace esis i i y
measu emen s. Theo e ical analysis shows ha injec ing a
squa e wa e o m in o he soil ins ead o a sine wa e and using
synch onous sampling diminishes he e ec o he in e e ence.
Expe imen al esul s in a ypical soil o ou campus show
ha capaci i e in e e ence inc eases wi h he elec ode
impedance, cable leng h and equency. Then wa e ing he
elec odes educes he capaci i e in e e ence. Induc i e
coupling inc eased wi h he a ea o he de ec ing wi es and
wi h he equency. Twis ing he de ec ing cables educes he
in e e ence. Howe e , in any case he in e e ence e ec is
much smalle when using squa e wa e o ms. This is because
synch onous sampling allows aking samples in he in e al
– , when in e e ence e ec has disappea ed.
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