Subsurface resistivity measurements using square waveforms

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. REFERENCES [1] W. M. Tel o d, L. P. Gelda , and R. E. She i , Applied Geophysics, 2nd ed. Camb idge, U.K.: Camb idge Uni . P ess, 1990. [2] J. Milsom, Field Geophysics. New Yo k: Open Uni . P ess and Hal- s ed, 1988. [3] R. Pall´ as-A eny and O. Casas, “A no el synch onous demodula o o ac signals,” IEEE T ans. Ins um. Meas., ol. 45, pp. 413–416, Ap . 1996. [4] R. Pall´ as-A eny and J. A. B escol´ ı, “Elec ical impedance measu e- men s by synch onous sampling applied o squa e wa e o ms,” in IEE Colloq. Inno a ions in INs umen a ion o Elec ical Tomog aphy Dig., 1995/099. [5] O. Koe oed, Geosounding P inciples, 1—Resis i i y Sounding Measu e- men s. Ams e dam, The Ne he lands: Else ie , 1988. [6] M. Gasulla, J. Jo dana, R. Pall´as-A eny, and J. M. To en s, “The loa ing capaci o as a di e en ial building block,” in IEEE Ins umen a ion and Measu emen , Technology Con ., O awa, On ., Canada, May 19–21, 1997. Manel Gasulla-Fo ne (S’97), o a pho og aph and biog aphy, see his issue p. 29. Josep Jo dana-Ba nils (S’93), o a pho og aph and biog aphy, see his issue p. 29. Ram´ on Pall´ as-A eny (F’98), o a pho og aph and biog aphy, see his issue p. 29. Josep Ma ia To en s (M’90), o a pho og aph and biog aphy, see his issue p. 29.