AC Resistivity

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AC resistivity soundingNiels Beie Christensen 1

IntroduetionElectrical and electromagnetic geophysical methodshave been among the most imporant ones for investi-gating the uppermost 100 me tres of the solid earth. Fordecades traditional resistivity methods using directcurrent (DC) have been in widespread use in Denmarkas in most other parts of the world. Resistivity profilesand soundings have been used for gathering geologicalinformation in general, in prospecting for raw materiaIs,for hydrogeological surveys, and to solve foundationproblems in engineering.DC resistivity sounding is a galvanic method, and the

type of information obtained from application of th atmethod is determined by the behaviour of galvanic cur-rents in the ground. This behaviour imposes inherentlimitations on the scope for determination of earthparameters from the measurements. Among these limi-tations the equivalences of high-resistivity layers andlow-resistivity layers are weil known. The high-resistiv-ity equivalence, where neither the thickness nor theresistivity of a highly resistive layer embedded in betterconducting surroundings may be determined but onlythe product of the two, is annoying in the context ofmany practical applications. In many cases highly resist-ive layers of dry sand and gravel are underlain by eitherwet and better conducting layers of sand and gravel or bylow-resistivity c1ays. In these cases it becomes impos-sible to determine the amount of dry sand and gravelfrom DC resistivity soundings alone when prospectingfor raw materiaIs, and in hydrogeological applicationsthe depth to the water table is of ten undetermined. Fur-thermore, DC resistivity measurements do not all ow adetermination of the anisotropy of the ground.Besides the galvanic method of DC resistivity sound-

ing, there are a number of electromagnetic or inductivemethods such as SLINGRAM and AMT (audiomag-netotelluric) with or without controlled source. Theinformation gained from these methods is determinedby the behaviour of induced currents in the ground anddiffers from the galvan ie information. Measurementswith the inductive methods are strongly influenced bythe presence of good conductors, while poor conductorsare more or Ie ss invisible. The depth to a good conductoris usually accurately determined from inductivemethods.'Laboratory of Geophysics, Geological Institute, University ofAarhus, Finlandsgade 6, DK-8200 Aarhus N, Denmark.

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Though the galvanic and inductive methods are of tenapplied in different prospecting situations, they mayalsobe combined in the same survey. In some instances thecombined interpretation of galvanic and inductive meas-urements enables the high-resistivity equivalence of theDC resistivity sounding method to be resolved (Jupp &Vozoff 1975). The DC resistivity sounding method maybe used to determine the thickness of the overburdenoverlying a high-resistivity layer, while an inductivemethod may be used todetermine the depth to the goodconductor underlying the high-resistivity layer. Thus thethickness-and thereby also the resistivity-of the high-resistivity layer may be determined from a combined useof galvanic and inductive measurements.The AC resistivity sounding methodIn the AC resistivity sounding method an alternatingcurrent (AC) souree is applied to a grounded e1ectricaldipole of finite length at a number of different frequen-cies, and the amplitude of the potential difference, tl.V,between the endpoints of the receiver dipole is meas-ured. The method is thus a combined one. Galvaniccurrent is put into the ground by the current electrodesand the use of AC gives an inductive contribution to thefields (Serensen et al. 1979, Serensen 1979, 1981, Christ-ensen 1983, 1985).Analogous to DC resistivity sounding, the apparent

resistivity is defined bypaCJ) =K(Y) I tl.~(f) I (1)

where K(Y) is the same geometrical factor as would beused in the DC case, Iis the amplitude of the galvaniccurrent introduced at the electrodes, fi s the frequencyused, and Y is the transmitter-receiver separation. Thephase of the potential difference is not measured.Response curves for electromagnetic methods over ahomogeneous halfspace are normalized with respect tothe induction parameter oxry2 (w is the angular fre-quency and 0" the conductivity). The above definition ofapparent resistivity has the implication that for lowvalues of the induction parameter the apparent resistiv-ity curve coincides with the DC curve, while for highvalues of the induction parameter the curves will be dif-ferent. Thus the behaviour of the apparent resistivitycurves for large values of Ywill differ from the DC case.In analysing the data, we assume the earth model of

Fig. 1 showing a horizontally stratified earth with


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4481FIRST BREAK VOL 7. NO 11. NOVEMBER I"R"

r;;~--..IABI = 20

z~- - - - ~- - - - - - - - - - ~- - - - - - - - h1=0d1~- - - - - - - - - - - - - - - - ~ - - - - - - - - h 2

~- - - - - - - - - L- - - - - - h31----------y------h-1

P~-1 P~-1~- - - - - - - - ~- - - - - - ~- - - - - - - - hNFig. I.The souree and model contiguration. p 7 , p: and d, are the hori-zontal resistivity, the vertical resistivity. and tbc layer tbickncss of theith layer. respectively.

homogcneous, transversely isotropie layers. The solu-tion to the theoretieal problem of ea\culating eleetrie andmagnetie fields from a grounded eleetrie dipale earryingalternating current has been given previously by severalauthors (Riordan and Sunde 1933, Dcy and Morrison1973, Wynn and Zonge 1975, Kauahikaua 1978). In ourapproach to the numerical problem a modified digitalfilter theory has been developcd, whieh eliminates theneed for integration of the response of thc infinitessimaleleetrie dipale (Serensen 1979, Christensen 1983). Themet had is as fast and accurate as the digital filter met hadfor ealeulation of Hankel transfarms (Ghosh 1971,Johansen and Serertsen 1979, Christensen 1979).The field equipment consists of a transmitter unit and

a receiver unit completely isolated from one another.The transmitter yields AC eurrent at a number of dif-

ferent frequeneies stepping up by factors of 2 in therange 1-40 kHz. The sinusoidal signal is governed by anoscillating erystal. Maximum voltage is 180 V rrns andmaximum current is 1 A rms. The transmitter is oper-ated in a constant current mode with an output currentnormally between 30 and 200 mA into a souree dipalewith a length typieally equal to 10 m. Three standardfrequencies are used: 76,2441 and 9765 Hz. The lawestfrequency of 76 Hz is chosen suffieiently high to avoidinduced polarization effects and sufficiently low to becomparabIe to DC in most instances. This frequencycontains almost exclusively galvanic information. Thefrequency 9765 Hz is about the highest which is practi-

cally realizable in the field and thus contributes most ofthe inductive part of the sou ree field. Analyses show thatthree frequencies give a better determination of theearth parameters than two, while less is gained byincreasing the number offrequeneies beyoud three. Thefrequency 2441 Hz is a convenient intermcdiate value atwhich the inductive effect is approximately one quarterof that at 9765 Hz, and experiencc shows that there isusually a good signal-to-noise ratio at this frequency.The receiver box uses a phasc-Iocked teehnique of

detection by referring the measured signal to an oscillat-ing crystal matching the one in the transmitter box. Amicroprocessor controls the measurements and calcu-lates the mcan value and standard deviation of theapparent resistivity over a specified time window toprovide automatic quality con trol of the measurements.Data are stored on digital cassette tapes.In principle any conventional De electrode layout can

be used for AC soundings, but in praetice electtornag-netic coupling between the transmitter and receiver.which is a geometrieal effect independent of carthparameters, makes the popular Schlumberger and Wen-ner configurations unattractive. Dipole-dipole con-figurations with transmitter and receiver dipole lengtbsof approximately 10 m solve these problems but sufferfrom the well-known effects of near surface inhomo-geneities , resulting in 'jumpy' apparent resistivitycurves. Af t er numerous experiments we have found thehalf-Sehlumberger array to be the best anc. In th is eon-figuration a eurrent dipale with a length of 10m remainsfixed during the sounding, while one potenrial electrodeis placed 'infinitely far away (in practiee 250-400 m) andthe inner potential electrode is moved (Fig. 2). Measure-ments are made with a density of 10 pcr decade in theinterval 1.26-199.53 m (or more) and computationsmake exact account of the finite distance to the outer-most potential electrode.

10 n(10 co

A o B M N.. y -Fig. 2. The half-Schlumberger electrode configuration. A and B arecurrent electrodes, Mand Nare potential electredes. DistanceOM =Y is taken as the abscissa of the following model responses anddata.

Interpretation of the data is done by rneans of a com-puter program based on the well-known iterative least-squares procedure. The inherent non-linearity of theproblem is somewhat reduced by werking with thelogarithm of the data values and the logarithm of themodel parameters. Coefficicnts of anisotropy areincluded in the model parameter space and a priori data


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AC SOUNDI NG CURVES o HZ

2

10 ' 100 2 5 10' 2 5 102 2 5 103Y ( M I

AC SOUNDI NG CURVES 2441 HZ103

2 30

5 '00 "0 .00

"001000 rsro

2 500 20re:>: 25:>:I 30910 " ro


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may be treated in the inversion scheme thus making pos-sible so-called 'elastic bounds' on the parameters(Jackson 1978, 1979, Jacobsen 1982). The covariancematrix of the least-squares problem is used for esti-mating the uncertainty of the model parameters when acertain data error is assumed.The ability of the AC resistivity sounding method to

resolve the high resistivity equivalence problem may beshown in different ways. Figure 3 shows apparent re s is-tivity curves for the three equivalent mode Is for the DCcase (a) and for a freq uency of 2441 Hz (b). I t is seen thatthe DC curves do not differ appreciably from oneanother while the 2441 Hz curves separate nicely forlarge electrode spacings.The linear analysis of variances may be used to

demonstrate what is al ready indicated by the apparentresistivity curves. The varianee of the model parametersof one of the three-Iayer mode Is in Fig. 3 with a highresistivity equivalent second layer is shown in Table 1forth r ee different cases: a DC sounding, a combination of aDC sounding and one higher frequency of 2441 Hz, anda full AC sounding using three standard frequencies. Anordinary DC sounding leaves the parameters of the sec-ond layer totally undetermined while the addition of justone higher frequency resolves the parameters of the sec-ond layer. The use of all three standard frequencies givesa very good determination of the model parameters.ExampleThe following example is from Sperring, 17 km N ofAarhus, where AC soundings were made in prospectingfor sand and gravel. The measured data with the modelcurves and the physical model resulting from theinterpretation are shown in Fig. 4 (a) together with ananalysis of the uncertainty of the model parameters (b).The three-Iayer model shown is in good agreement withthe measurements, though there are discrepancies incertain parts of the curves. However, models with morethan three layers do not make a better fit to the data andare not geologically relevant. The discrepancies must beattributed to near-surface inhomogeneities. The toplayer is interpreted as cIayey till, which covers most ofthe area. The second layer is dry sand and gravel, whilethe bottom layer is also interpreted as cIayey till.The coefficients of anisotropy of the first and second

layer are unity, but a value of 1.11 is found for the bot-tom layer. This may be due to thin layers of sand andgravel embedded in the till, which do not show up in-dependently in the apparent resistivity curve but whichmake the third layer macro-anisotropic. Since the sec-ond layer is of the same thickness as the top layer, thereis a very cIear high-resistivity equivalence. Figure 4 alsoshows an analysis on the basis of the 76 Hz frequencyalone. This low frequency, which is comparable to DC,exhibits very cIearly the expected high-resistivity

equivalence. The parameters of the second layer aretotally undetermined as is the depth to the bottom layer.However, on the basis of all three frequencies all modelparameters are resolved. This sounding demonstratesthe ability of the AC sounding method to resolve thehigh-resistivity equivalence of dry sand and gravellayersand to determine their depth extent.

Table 1.An analysis of the uncertainty of the model parameters of oneof the three layer models of Figure 3 in three different cases: a DCsounding, a DC sounding with one higher frequency of 2441 Hz, anda full AC sounding with the three standard frequencies. Ithas beenassumed that measurements were made in the interval from 6.31 to199.53 m with a density of 10 per decade and with a data error of 3%.The outer potential electrode is398.11 m away. Coefficients of aniso-tropy have been fixed at a value of 1.00 with an uncertainty factor of1.001, i.e. they are excluded from the analysis.

76 Hzoe 2441 Hz

oe 2441 Hz 9765 Hz

r hol ~ 100 ohm m I. OS 1. 02 \ . 02r ho2 ~1000 ohm m 00 1.29 1. 10r ho3 ~ 10 ohm m \ . 20 1. 11 1.09

th ick1 ~ 10 m 1. 51 1. 04 1. 03th ick2 ~ 10 m 00 1. 29 1.10

depthl ~ 10 m 1. 51 1. 04 1. 03depth2 ~ 20 m 00 1. 12 1. 04

ConclusionThe AC resistivity sounding method is an efficient newprospecting method for general geological investigationof the topmost 100 metres of the earth. In prospectingfor raw materials the method will be weil suited forfinding and estimating the volume of dry sand and graveldeposits, which in Denmark are of ten overlain andunderlain by cIays of high conductivity. For hydro-geologicaI surveys the method will be effective in thelocation and depth estimation of salt-water fronts.The main asset of the method is that it is a combined

one which in the same measuring procedure gives bothgalvanic and inductive information. The inductive con-tribution to the measurements of the AC resistivitysounding method makes it possible to find the depth to agood conductor, thus resolving the well-known high-resistivity equivalence of the DC soundings.


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DEY, A. and MORRISON, H.F. 1973. Electromagnetic coupling in fre-quency and time-domain induced polarization surveys over amultilayered earth. Geophysics 38.380-405.

GHOSH, D.P. 1971. The application of linear filter theory to the directinterpretat ion of geoelectr ical resist ivity sounding measurements.Geophysical Prospecting 19,192-217.

JACKSON,D.D. 1978. Linear inverse theory with a priori data. AppliedInverse Problems. P.C. Sabatier (ed. ), pp. 83-102. Springer-Ver-lag, Berlin.

JACKSON.D .D. 1979. The use of a priori data to resolve non-unique-ness in l inear inversion. Geophysical Journal ofthe Royal Astro-nomica/ Society 57,137-157.

JACOBSEN,B.H. 1982. A priori data. Why, which, and how? ProtokollElektromagnetischen Tienfenforschung. V. Haak and J. Homelius(eds). Freie Universitt Berlin.

JOHANSEN, H.K. and S0RENSEN, K. 1979. Fast Hankel Transforms.Geophysica/ Prospecting 27,876-901.JuPP. D.L.B. and VOZOFF. K. 1975. Joint inversion of geophysical

data. Geophysical Journal of the Royal Astronomica/ Society 42,977-991.

KAUAHIKAUA,J. 1978. Electromagnetic fields about a horizontal elec-tric wire souree of arbitrary length. Geophysics 43, 1019-1022.

RroRDAN. J. and SUNDE. E.D. 1933. Mutual impedance of groundedwires for horizontally stratified two-Iayer earth. BeU SystemsTechnical Journa/12, 162.

S0RENSEN. K. 1979. Schlumberger sounding using alternating cur-rents. Lic. scient. thesis, Laboratory of Geophysics, University ofAarhus.

S0RENSEN, K. , CHRISTENSEN,N.B. and JEPSEN, J.B. 1979. AC-DC-geoelektrik. Et pilotstudium (AC-DC-geoelectrics. A pilot study.In Danish). Fredningsstyrelsen, Copenhagen.

S0RENSEN. K. 1981. Midtvejsrapport (Interim Report. In Danish).Rapport t il Fredningsstyrelsen, Copenhagen.

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AC Resistivity