zohdy, eaton & mabey - application of surface geophysics to ground-water investigations - usgs

8/7/2019 Zohdy, Eaton & Mabey - Application of Surface Geophysics to Ground-water Investigations - USGS

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Techniques of Water-Resources Investigationsof the United States Geological Survey

CHAPTER DlAPPLICATION OF SURFACE GEOPHYSICS

TO GROUND-WATER INVESTIGATIONS By A. A. R. Zohdy, G. P. Eaton,

and D. R. Mabey

BOOK 2COLLECTION OF ENVIRONMENTAL DATA

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Electrical MethodsBy A. A. R. Zohdy

The electrical properties of most rocks inthe upper part of the Earths crust are de-pendent primarily upon the amount of waterin the rock, the salinity of the water, andthe distribution of the water in the rock.Saturated rocks have lower resistivities thanunsaturated and dry rocks. The higher theporosity of the saturated rock, the lower itsresistivity, and the higher the salinity ofthe saturating fluids, the lower the resistivity. The presence of clays and conductiveminera ls also reduces the resistivity of therock.Two properties a re of primary concern inthe application of electrical methods : (1) theability of rocks to conduct an electric cur-rent, and (2) the polarization which occurswhen an electrical current is passed throughthem (induced polarization). The electricalconductivity of Earth materials can be studied by measuring the electrioal potential distribution produced at the Earths surface byan electric curren.t that is passed through the

Earth or by detecting the electromagneticfield produced by an alternating electric cur-rent that is introduced into the Earth. Themeasurement of natural electric potentials(spontaneous polarization, telluric currents,and streaming potentials) has also found ap plication in geologic investigations. The principal methods using natural energy sourcesare (1) telluric current, (2) magnetotelluric, (3) spontaneous polarization, and(4) streaming potential.

Telluric Current MethodTelluric currents (Cagniard, 1956 ; Berdichevskii, 1960; Kunetz; 1957) are naturalelectric currents that flow in the Earths

crust in the form of large sheets, and thatconstantly change in intensity and in direction. Their presence is detected easily byplacing two electrodes in the ground separated by a distance of about 300 meters(984 feet) or more and measuring the potential difference between them. The originof these telluric currents is believed to bein the ionosphere and is related to ionospherictidal effects and to the continuous flow ofcharged particles from the Sun which be -come trapped by the lines of force o f theEarths magnetic field.If the ground in a given area is horizontally stratified and the surface of the basement rocks is also horizontal, then, at anygiven moment, the density of the telluric cur-rent is uniform over the entire area. In thepresence of geologic structures, however,such as anticlines, synclines, and faults, thedistribution of current density is not uniform over the area. Furthermore, currentdensity is a vector quantity, and the vector

is larger when the telluric current flows atright angles to the axis of an anticline thanwhen the current flows parallel to the axis(fig. 1). By plotting these vectors we obtainellipses over anticlines and synclines andcircles where the basement rocks are horizontal: The longer axis of the ellipse is oriented at right angles to the axis of thegeologic structure.The measurement of telluric field intensityis relatively simple. Four electrodes, M, N,M/, and N are placti on the surface of the

ground at the ends of two intersecting perpendicular lines (fig. 2), and the potentialdifferences are recorded on a potentiometricchart recorder or on an z-g plotter (Yungul,1968). From these measurements two cornponen ts E,, and Ey of the telluric field can5


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TECHNIQUES OF WATER-RESOURCES INVESTIGATIONS

c3

t +

Figure I.--Flow of telluric current over on onticline. Ellipse and circles indicate te lluric field intensity asa function of direction with respect to axis of anticline.MM-I-- N

M.M N. I NFigure 2.- Examples of electrode arrays for measuring x

and y components of telluric field. M, M, N, and Nare potential electrodes.

be computed, and the total field obtained byadding E, and Ey vectorially.The intensity and direction of the telluriccurrent field vary with time; thereforemeasurements must be recorded simultaneously at two different stations to take intoaccount this variation, One station is keptstatronary (base station), and the other ismoved to a new location in the field (fieldstation) after each set of measurements.The ratio of the area of the ellipse at thefield station to the area of a unit circle(Keller and Frischknecht, 1966) at the basestation is calculated mathematically. Whena contour map of equal elliptical areas isprepared (Migaux, 1946, 1948 ; Migaux andothers, 1962 ; Migaux and Kunetz, 1955 ; Schlumberger, 1939) it reflects the major geologic structures of the basement rocks in

very much the same manner as a gravitymap or magnetic map. However., a telluricmap (fig. 3) delineates rock structure baaedon differences in electrical resistivity ratherthan on differences in density o:r magneticsusceptibility.

Magneto-Telluric MethodThe magneto-telluric method (Berdichevskii, 1960; Cagniard, 1953) of measuring resistivity is similar to the telluric currentmethod but has the advantage of providingan estimate of the true resistivity of thelayers. Measurements of amplitude variationsin the telluric field E, and the associatedmagnetic field H, determine earth resistivity.

Magnet&&uric measurementi at severalfrequencies provide information on the variation of resistivity with depth because thedepth of penetration of electromagneticwaves is a function of frequency.. A limitation of the method is the instrumenta l difficulty of measuring rapid fluctuations of themagnetic field. Interpretation techniquesusually involve comparisons of observed datawith theoretical curves. The method is usefulin exploration to depths greater tlhan can be


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APPLICATION OF SURFACE GEOPHYSICS


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8 TECHNIQUES OF WATER-RESOURCES INVESTIGATIONSreached effectively by methods using artificially induced currents.To the authors knowledge the telluric andmagneto-t&uric methods have not been usedextensively in the Western Hemisphere ;however, the methods have been used extensively in the Eastern Hemisphere by Frenchand Russian geophysicists in petroleum exploration. The use of the methods in ground-water exploration is recommended at presentonly for reconnaissance of large basins.

Spontaneous Polarization andStreaming PotentialsSpontaneous polarization or self-potentialmethods involve measurement of electric potentials developed locally in the Earth by

electro-chemical activity, electrofiltration activity, or both. The most common use of self-potential surveys has been in the search forore bodies in contact with solutions of different compositions. The result of this con-tact is a potential difference and current flowwhich may be detected at the ground surface.Of more interest to ground-water investigations are the potentials generated by watermoving through a porous medium (streaming potentiala). Measurements of these potentials have been used to locate leaks inreservoirs and canals (Ogilvy and others,1969).Spontaneous potentials generally are nolarger than a few tens of millivolts but insome placee may reach a few hundred millivolts. Relatively simple equipment can beused to measure the potentials, but spurioussources of potentials often obscure thesenatural potentials. Interpretation is usuallyqualitative although some quantitative interpretations have been attempted.

Direct Current-ResistivityMethodIn the period from 1912 to 1914 (Dobrin,1960) Conrad Schlumberger began his pie-

neering studies which lead to an understanding of the merits of utilizing electrical resistivity methods for exploring the subsurface (Compagnie GBnerale de Gbphysique,1963). According to Breusse (1963)) the realprogress in applying electrical methods toground-water exploration began duringWorld War II. French, Russian,and Germangeophysicists are mainly responsible for thedevelopment of the theory and practice of dire&current electrical prospecting methods.

Definition and Units of ResistivityIt is well known that the resistance R, inohms, of a wire is directly proportional to itslength L and is inversely proportional to itscross-sectional area A. That is:

R = L/-A,or R=,,-, A (1)where p, the constan t of proportionality, isknown as the electrical res iativit,y or electrical specific resistance , a characteristic ofthe material which is independent of itsshape or size. According to Ohms law, the resistance is given by

R = AV/I, (2)where AV is the potential difference acrossthe resistance and Z is the electric currentthrough the resistance.Substituting equation 1 in equation 2 andrearranging we get

AAVP=t7 (3)

Equation 3 may be used to determine theresistivity p of homogeneous and isotropicmaterials in the form of regular geometricshapes, such as cylinders, parallelepipeds,and cubes. In a semi-infinite material the resistivity at every point m,uat be dlefined. Ifthe cross-sectional area and length of anelement within the semi-infinite material areshrunk to infinitesimal size then the resistivity p may be defined as


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APPLICATION OF SURFACE GEOPHYSICS 9

20 (AV/L)0=r

;To U/A)or

ELp=Jwhere EL is the electric field and J is the cur-rent densi,ty. TQ generalize, we writeEp = -.JEquation 5 is known as Ohms law in its diff erential vectorial form.The resistivity of a materia l is defined asbeing numerically equal to the resistance ofa specimen of the material of unit dimensions.The unit of resistivity in the mks (meterkilogramaond) system is the ohm-meter.

In other systems it may be expressed in ohm-centimeter , ohm-foot, or other similar units.Rock Resistivities

The resistivity p of rocks and minera ls displays a wide range. For example, g,raphitehas a resistivity of the order of lOasohm-m,whereas some dry quartsite rocks have res;istivitiee of more than 1O l2ohm-m (Parasnis, 1962). No other physical property ofnakura.lly occurring rocks or soils displayssuch a wide range of values.In most rocks, electricity is conductedelectrolytically by the interstitial fluid, andresistivity is controlled more by porosity,water content, and water quality than by theresistivities of the rock matrix. Clay minerals, however, are capable of conducting electricity electronically, and the flow of currentin a clay layer is both electronic and electrolytic. Resistivity values for unconsolidatedsediments commonly range from less thlan 1ohm-m for certain clays or sands saturatedwith saline water, to several thousand ohm-m for dry basalt flows, dry sand, ,and gravel.The resistivity of sand and gravel saturatedwith fresh water ranges from about 15 to600 ohm-m. Field experience indicates thatvalues ranging from 15 to 20 ohm-m a recharacteristic of aquifers in the southwest-

ern United States, whereas in certain areasin California the resistivity of fresh-waterbearing sands generally ranges from 100 to250 ohm-m. In parts of Maryland resistivities have been found to range Ibetween about300 and 600 ohm-m, which is about the samerange as that for ,basaltic aquifers in south-ern 1 ,daho. These figures indicate that thegeophysicists should be familiar with theresistivity spectrum in the survey area be-fore he draws conclusions about the distribution of freshwater aquifers.Principles of Resistivity Method

In mak,ing resistivity surveys a commut,ated direct current or very low frequency(


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--

---

---

--

10 TECHNIQUES OF WATER-RESOURCES INVESTIGATIONSFor a semi-infinite medium, which is thesimplest Earth model, and with both currentand potential point-electrodes placed at theEarth surface (z = 0), equation 6 reduces to

v= pr =- ds w + Y2 2&i@ (7)

where AM is the distance on the Earthsurface between the positive current electrode A and the potential electrode M. Whentwo current electrodes, A and B, are usedand the potential difference, AV, is measuredbetween two measuring electrodes M and N,we getv&i!2 = potential at M due to positive2n AMelectrode A,Vii d!t = potential at N due to positive2n ANelectrode A,v;=p = potential at M due to negative2rrBMehwtrode B,v~=pI1 = potential at N due to negative2wBNelectrode B,VIYB=$(&-k) = total potential atMduetoAandB,V~*B~~~&-3) = tptalpotentialatINduetoAandB,and,therefore, the net potential difference is :AV& v, - v; =

1 1 1 (81Rearranging equation 8, we express the resistivity p by:

2* AV=P 1 1 1 (9)Equation 9 is a fundamental equation in direct-curren t (d-c) electrical prospecting.

2rrThe factor 1 1 1 i----m + .-AM BM AN BNis called the geometric factor of the electrodearrangement and generally is designated bythe letter K. Therefore,

P =K?!. ZIf the measurement of p is made over a semi-infinite space of homogeneous and isotropicmaterial, then the value of p computed fromequation 9 will be the true resistivity ofthat material. However, if the medium is in-homogeneous and (or) anisotropic then theresistivity computed from eqaation 9 iscalled an apparent resistivity jzThe value of the apparent resistivity is afunction of several variables: the electrodespacings AM, AN, BM, and BN, the geometryof the electrode array, and the true resistivities and other characteristics of the sub-surface materials, such as layer thicknesses,angles of dip, and anisotropic properties. Theapparent resistivity, depending on the electrode configuration and on the geology, maybe a crude average of the true resistivitiesin the section, may be larger or smaller thanany of the true resistivities, or may even benegative (Alpin, 1950 ; Zohdy, 1969b).

Electrode ConfigurationsThe value of ,C(eq. 9) depends on the four

distance-variables AM, AN, BM, and BN. Ifp is made to depend on only one distance-variable the number of theoretical curves canbe greatly reduced. Several electrode arrayshave been invented to fulfill this goal.

Wenner ArrayThis well-known array was first proposedfor geophysical prospecting by Wenner(1916). The four electrodes A, M, N, and Bare placed at the surface of the ground- alonga straight line (fig. 5) so that AM = MN =

NB = a.


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APPLICATION OF SURFACE GEOPHYSICS 11A M N B;-a-~.:.-;

WENNER ELECTRODE ARRAY

A M 0 N B

LEE-PARTITIONING ELECTRODE ARRAY

A MN B;n,2.*.m-;

SCHLUMBERGER ELECTRODE ARRAYFigure 5.-Wenner, Lee-partitioning, and Schlumb e+

ger electrode arrays. A and B are current electm&es ,M, N, and 0 are potential electrodes; a and AB/2are electrode spacings.

For the Wenner array, equation 9 reduoesto:

Thus the resistivity iiw s a function of thesingle distance-variable, a. The Wenner array is widely used in the Western Hemisphere.Lee-Partitioning Array

This array is the same as the Wenner array, except that an additional potential electrode 0 is placed at the center of the arraybetween the potential electrodes M and N.Measurements of the potential difference aremade between 0 and M and between 0 andN. The formula for computing the Lee-par

titioning apparent resistivity is given byFL.P. =4.&V Zwhere AV is the potential difference between0 and M or 0 and N. This array has Ibeenused extensively in the past (Van Nostrandand Cook, 1966).

Schlumberger ArrayThis array is the most widely used in eletrical prospecting. Four electrodes are placedalong a straight line on the Earth surface(fig. 5) in the same order, AMNB, as in theWenner array, but with ABSMN. For anylinear, symmetric array AMNB of electrodes,equation 9 can be written in the form:

P =(D/2)2 - (MN/W z, (12)-= m zbut if MN+O, then equation 12 can be writtenas E5 = P (AB/2)a r

Avwhere E = lim - = electric field.MN+0mConrad Schlumlberger defined the resistivity in terms of the electric field E ratherthan the potential difference AV (as in theWenner array), It can lbeseen from equation13 .that the Schhmberger apparent resistivity 78 is a function of a single distance-variable (m/2). In practice it is possible tomeasure 78 according to equation 13, butonly in an approximate manner. Tlhe apparent resistivity pa usually is calculated byusing equation 12 provided that AB 1 5cm(Dappermann, 1954).

Dipole-Dipole ArraysThe use of dipole-dipole arrays in elec

trical prospecting has ,becomecommon sincethe 1959s, particularly in Russia, whereAlpin (1950) developed the necessary)theory.In a dipole-dipole array, &hedistafice betweenthe current electrodes A and B (current dipole) and the distance between the potential


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12 TECHNIQUES OF WATER-RESOURCES INVESTIGATIONS

(4

AZIMUTHAL

(c)

PARALLEL

EQUATORIALFigure 6.-Dipale-dipo le arrays. The equatorial

electrcdes M and N (Imeasuring dipole)aresignificantly smaller than the distance T, be-tween the centers of the two dipoles. Figure6 (a, b, c, and d) shows the four basic dipole-dipole arrays t.hat are recognized : azimuthal,radial, parallel, and ,perpendioular. When theazimuth angle 0 formed by the line T and thecurrent dipole AB equals z, the azimuthal2

(b)

RADIAL@>PERPENDICULAR

AXIAL OR POLARis a bipole-dipole array because A6 is large.lel and radial arrays reduce to the polar (oraxial) array. It can be Bhown (AYpin, 1960;Bhattacharya and ..Patra, 1968; Keller andFrischknecht, 1966) that the el&ric fielddue to a dipole at a given point is inverselyproportional to the cube of the distance Tand that for a given azimuth angle 8the valueof the apparent resistivity T;is a function ofthe single distance-variable r.array and the parallel array reduce to the Of the various dipoledipole arrays, theequatorial array, and when B = 0 the paral- equatorial array in iti,bipoledipole form (AB


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0 APPLICATION OF SURFACE GEOPHYSICS 13is large and MN is small) has been used moreoften than the other dipole-dipole-arrays. Byenlar,ging the length o f the current dipole,that is, by making it a bipole, the electric cur-rent required to generate a given potentialdifference AV at a given distance T from thecenter of the array, is reduced. Furthermorethe apparent resistivity remains a functionof the single distance variable,E = d(AB/2)2 + r2, (Berdichevskii andPetrovskii, 1956). The equatorial array hasbeen used extensively ,by Russian geophysicists in petroleum exp loration (Berdichevskiiand Zagarmistr, 1958). Recently it has beenused in ground-water investigations in theUnited States (Zohdy and Jackson, 1968 and1969 ; Zohdy, 1969a).

Electrical Soundingand Horizontal ProfilingElectrical sounding ,is the process by whichdepth investigations are made, and horizontal profiling ,is the process by which lateralvariations in resistivity are detected. How-ever, the resulrte of electrical sounding and ofhorizontal profiling often are affected by bothvertical and horizontal variations in the electrical properties of the ground.If the ground is comprised of horizontal,homogeneous, and isotropic layers, electricalsounding data represent only the variationof xesistivity with depth. In practice, how-ever, the electrical sounding data are influenced by both vertical and horizontalheterogeneities. Therefore, the execution, interpretation, and presentation of soundingdata should be such that horizontal variationsin resistivity can be distinguished easilyfrom vertical ones.The basis for making an electrical sounding, irrespective of the electrode array used,is that the farther away from a current

source the measurement of the potential, orthe potential difference, or the electric fieldis made, the deeper the probing will be. Ithas been stated in many references on geophysical prospecting that the depth of probing depends on how far apart two current

electrodes are placed, but this condition isnot necessary for sounding with a dipole-dipole array. Furthermore, when soundingwith a Wenner or Sohlumberger array, whenthe distance ,between the current electrodesis increased, the distance between the cur-rent and the potential electrodes, at the center of the array, is increased also. It is thislatter increase that a.ct+y matters.

In electrical sounding with the Wenner,Schlumberger, or dipole-dipole arrays, theABrespective electrode spacing a, -, or r, is

increased at successive logarithmic intervals and the value of the appropriate apparen t resistivity, &, -ir,, or po, is plotted asa function of the electrode spacing on logarithmicardinate paper. The curve ofAB-P = f (a, -, or r) is called an electrical

sounding curve.In horizontal profiling, a fixed electrodespacing is chosen (preferably on the basisof studying the results of electrical soundings), and the whole electrode array is movedalong a profile after each measurement ismade. The value of apparent resistivity isplotted, generally, at the geometric center 0of the electrode array. Maximum apparentresistivity anomalies are obtained by orienting the lprofiles at right angles to the strikeof the geologic structure. The results are presented as apparent resistivity profiles (fig.7) or apparent resistivity maps (fig. 8), orboth. In making horizontal profiles it is recommended that at least two different electrode spacings rbe used, in order to aid indistinguishing the effects of shallow geologicstructures from the effects of deeper ones(fig. 9). In figure 9, the effect of shallowgeologic features is suppressed on the profileinade with the larger spacing, whereas the

effect of deeper features is retained.In certain surveys, the two current electrodes m ay be placed a large distance apart(1-6 km) and the potential electrodesmoved along the middle third of the line AB.This method of horizontal profiling has been


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14 TEXHNIQUES OF WATER-RESOURCES INVESTIGATIONSHORIZONTAL DISTANCE, IN METERS

0 100 200 300 400 500

Gravelly Clay Gravel Clay Gravel Clay (GravelI I I I I I I I

0 200 400 600 800 1000 1200 1400 1600WEST HORIZONTAL DISTANCE, IN FEET EAST

Figure 7.Uorizontal profile and interpretotions over a shallow grovel deposit in California (fohdy, unpub. data,1964; Zohdy, 1964) using Wenner

called the Schl,umberger AB profile (Kunetz,1966 ; Lasfargues, 1957) ; in Canada and inparts of the United lStates it is referred tosometimes as the Brant array (fig. lOa).A modification of this procedure where thepotential electrodes are moved not only alongthe middle third of the line AB but alsoalon,g hnes lateral,ly displaced from andparalle l to AB (fig. lob) i,s called the Rectangle of Resistivity Method (Breusse andAstier, 1961; Eunetz, 1966). T,he lateral displacement of the profdes from the line AB

ABmay be as much as -. 4Another horizontal profiling technique,used by many mining geophysicists, has beengiveq, the name dipoledilpole method, although it does not approximate a true dipole-dipole. The lengths of the current and potential dipoles are large in comparison to the

array at o = 9.15 meters.

distance between their centers. This arrangement introduces an extra variable in the calculation of theoretical curves :and makesquanti~tative interpretation of lthe resultsdifficult.

Practically all types of the common eloctrade arrays have been used in horizontalprofiling, including poledipole (Hedtkrome,1932 ; Logn, 1964) and dipoledipole array8(Blokh, 1957 and 1962).The interpretation of horizontsJ pro6lingdata is generally qualit&ive,and the primaryvalue of the data is to locate g&logic structures such as buried stream channels, veins,

and dikes. Quantitative interpretation can beobtained by making a sufficient number ofprofiles with different eJectrode spacings andalong sets of traverses of different azimuths.Best interpretative results are obtained ,generally from a com,bination of horizontal pifiling and electrical sou.nd.ing data.


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Figure 8.-Appare nt-resistivity map near Campbell, Calif. Unpublished data obtained by Zohdy (1964) usingWenner array. Crosshatched areas are buried stream channels containing thick gravel deposits. Stippled areasare gravelly clay deposits.


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16 TIXXINIQUES OF WATER-RE,SOURCES INVESTIGATIONS

100 -90 - 0 a = 30 Feet+-+Y) A a = 60 FeetEE 80 -ZL;F

Z$70-&O:'60-$ IQ?

50 -HORIZONTAL SCALE

4fl - VES 4

.:.::San* :.+ .:.;::. . .. d

Figure 9.-Horizontal profiles over a buried stream channel using two electrode spacings : o = 9.l!j meten (30feet) and CI = 18.3 meters (60 feet) (after Zohdy, 1964). V ES 4 marks the location of an electrical scunding used to aid in the interpretotion of the profiles.

Comparison of Wenner,Schlumberger, and Dipole-DipoleMeasurementsThe Schlumberger and the Wetier electrode arrays are the two most widely usedarrays in resistivity prospecting. There aretwo essential differences Ibetween these ar

rays : (1) In the Schlumlberger array the distance between the potential elect 3des MN issmall and is always kept equal to, or smallerthan, one-fifth the distance *betweenthe cur-rent electrodes AB ; that is, AB L 5MN. Inthe Wenner array mis always equal to 3MN.

(2) In a Schlumberger sounding, the p&ential electrodes are moved only otx.aeionally,whereas in a Wenner sounding they and thecurrent electrodes are movti after eachmeasurement.As a direct consequenceof these two differences the following facta are realized:1. Schlumberger sounding curves portray a

slightly grea,ter probing depth and resolving power than Wenner sounding curvesfor equal AB electrode spacing. The maxi-mum and the minimum values of apparentresistivity on a theoretical Schlumibergercurve (MN+O) appear on the sounding


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ELECTRODE SPACING, s/Z, IN FEET10 20 50 100 200 500 1000 2000 5000 10,000

100. 1, / I lI,,,,I1 , I 1 I I,,,z

1 I I f-1 Y1l 1 I_Fr

50 -I6 20-z-

IQ:- lo-

5I=v)z 5-:2z2 2-[L PI or Pz < ,+ and on the ellectrode cowgguration used. At electrode spacings muchlarger than the thickness of thle first layer,the sounding curve asymptotically approaches a horizontal line whose ordinate isequal to pz. The electrode spacin,g at whichthe apparent resistivity p asymptotically approaches the va lue P2depends on three factors: the thickness of the first layer h,, thevalue of the ratio p2/p,, and the type of electrode array used in making the soundingmeasurements.

The dependenceof the electrode spacing onthe thickness of the first layer is fai,rly obvious. The larger the thickness of the firstlayer, the larger the spacing required forthe apparent res istivity to be approximatelyequal to the resistivity of the second layer.This is true for any given electrode arrayand for any given resistivity ratio. However,for m,ostelectrode arrays, including the conventional Schlumberger, Wenner, dipoleequatorial and dipole polar arrays, whenp2/pl > 1, larger electrode spacings are re-Oquired for jito be approximately equal to p2than when P2/Pl< 1. Figure 16 shows a corn-,parison between two Schlumberger soundingcurves obtained over two-Iayer Earth modelsin which h, = 1 meter (3.28 feet), &p, =:10,and Pz/pl = 0.1. Figure 17 shows the dif-


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APPLICATION OF SURFACE GEOPHYSICS 25ELECTRODE SPACING, K8/2, IN FEET

1 2 5 10 20 50 100 200 500 10001 I I ItI1 I I 1111 I 1 1111 I I IlfI I I 1 I

0.2 -

0.1^ . I I, I,,,, I I I IllI, I I, IIll I , I IIIC LU.1 0.2 0.5 1 ELECTRODE 5 10 20 50 100 200 500 1000SPACING, m/S, IN METERSFigure 16.--Compar ison between two-layer Schlurnberger curves for p/p, = 10 and 0.1; hl = 1 meter (3.28 feet)

for both curves.ference in the form of sounding curves, andthe asynrptotic approach of p to pl and to pzas a function of electrode array for h, = 1meter, pz/pl = 9, and pz/pl - 0.2. The comparison is made between equatorial andpolar-dipole sounding ourves.

Three-layer medium .-If the ground iscomposedof three layers of ,resistivities pl,p2,and p3,and thicknesses h,, h2, and hs = 00,the geoelectric section is described accordingto the relation between the values of pl, pi,and p3. There are four possible combinationsbetween the values of pl, p2, and pa. Theseare: Pl > p2 < pa - __-H-type eection,

p1 < p2 < ps __-A-type section,PI < p2 > ps ----K-type section,Pl > pa > ps ----Q-type section.

The use of the letters H, A, K, and Q to de-scribe the relation between pl, p2,and p3in thegeoelectric section is very convenient and alsois used to describe the corresponding sounding curves. For examgle, we talk about anH-type electrical sounding curve to indicatethat it is obtained over a geoelectric sectionin which p l > pz < P3.H-, A-, K-, and Q-typeSchlumlberger sounding curves are shown infigure 18.Multilayer-medium.- If the ground iscomposed of more than three horizontallayers of reaistivities pl, p2, ps, . . . p,, andthicknesses A,, hz, h, . . . h, = 00, the geoelectric section is described in terms of relationship between the reeistivities of thelayers, and the letters H, A, K, and Q are


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26 TECHNIQUES OF WATER-RESOURCES INVESTIGATIONSused, in combination, to indicate the variation of resistivity with depth. In four-layergeoelectric sections, there are eight possiblerelations between pl, pZ,p3,and p,:

pi > pz C pa < p4 __,-HA-type section,pl > pz< p3 > p4 ----HK-type section,pl < pz< p3< p4 _---AA-type sectionpl < pz< pS> ,o~----AK-type section,PI < PZ > P3-c p4 ----KH-type section,Pl < PZ > p3 > p4 ___-KQ-type section,pl > p2> p3< p4 ----&H-type section,pl > p2 > p3> p4 -QQ-type section.Examples of Schlumberger electrical sounding curves for three of these eight types offour-layer models are shown in figure 19.For a five-layer geoelectric section thereare 16 possible relationships (between pl, p2,p3, p4, and pS,and, therefore, there are 16types of five-layer electrical sounding curves.

Each of these 16 geoelectric sections may bedescribed by a combination of three letters.For example, an HKH section is one in which(pl > p2< p3 > p4 < pd. In general, ian n-layer section (where n&3) is described by(n-2) letters.

Electrical Sounding Over Laterallylnhomogenek Media Lateral inhomogeneities in the groundaffect resistivity measurements in differentways. The effect depends on (1) the size ofthe inhomogeneity with respect to its depthof burial, (2) the size of the inhomogeneitywith respect to the size of the electrode array, (3) the resistivity contrast between theinhomogeneity and the surrouading media,(4) the type of electrode array used, (5) thegeometric form of the inhomogeneity, and(6) the orientation of the electrode arraywith respect to the strike of the inhomogeneity.The simplest type of a lateral inhomogeneity, from the geometric and mathematicalpoi,nts of view, is that of a vertical plane

boundary separating two homogeneous andisotropic media d resistivities p1and pZ,Although this Earth model is ideal and doesnot exi,st commonly in nature,. its studyserves to illustrate the general form of theresistivity anomaly to be expected over aDIPOLE-DIPOLE ELECTRODE SPACING, re, r,. IN FEET

2 5 10 20 50 100 200 500 1000

a5g 0.1 I I L ,111 I I I IllI 1 1 IllIll I I 111111;; 0.1L 0.2 0.5 1 2 5 10 20 50 100 200 500 1000

DIPOLE-DIPOLE ELECTROD E SPACING re, rr, IN METERSFigure 17.-Compa rison between two-layer azimuthal br equaturiol) and radial (or polar) sounding curves h = 1

meter (3.28 feet), PI /PI = 9 or 0.2).


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APPLICATION OF SURFACE GEOPHYSICS 27ELECTRODESPACING,n/S, IN FEET

IO 20 50 100 200 500 1000 2000 5000 10,000

/0 A-ty _pe

Pz=2.5 I ,AI L2.0 - /ul

z 0.5 - P, q0.4

c P,=I2 1.0

i \ Q-WeI AA4 1 P,=O.l1 I II1111 I I I -LJ11 I 1 1 I11110.1; I I 1, IO 20 50 100 200 500 1000 2000 sootl 10,000 ElECfRODE SPACING, n/2, IN METERS

Figure 18 .-Examp les of the four types of three-layer Schlumberge r sounding curves for three-layer Earth models.large variety of more complicated lateral in-homogeneities.

The electrical sounding curves obtainedwith an ideal Schlumberger array (m-0)oriented at different angles to the surfacetrace of a vertical contact (Zohdy, 1970) areshown in figure 20. The most im,portant feature on the sounding curves that indicatesthe presence of the lateral inhomogeneity isthe formation of a cusp which is well developed whenever the sounding line makes anazimuth angle close to 90 with the surfacetrace of the vertical plane boundary. TheWenner sounding curves for azimuth anglesof 0 to 90 are shown in figure 21. The Wenner curves are more complicated than the

Schlumberger curves because a potentialelectrode crosses the contact. The effects ofsuch things as dipping, vertical and horizontal contacts, and pipe lines have been de-scribed in the literature for different ehxtrode arrays (Kunetz, 1966; Albin andothers, 1966).Limitations of the ResistivityMethod

The interpretation of a multilayer sounding curve generally is not unique. This meansthat a given electrical sounding curve cancorrespond to a variety of subsurface distributions of layer thicknesses and resistivities. Furthermore, several other limitations


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28 TECHNIQUES OF WATER-RESOURCES INVESTIGATIONSare inherent in the conventional methods ofelectrical sounding and these are consideredin the following sections.Equivakace of K-type curves .--Considertwo three-layer sections of the K type(p1pd. If p1 in one section equals p;in the other section, p3= p;, and T, 5 pzhz=T: = p$hi, then the sounding curves for bothsections wih be practically identical (fig. 22,curves a and b) .This type of equivalence is known asequivalenceby T and it also applies approximately to Q-type curves.Equivalence of H-type curves.- Considertwo three-layer asections of the H type(pl > p2C ps). If pl in one section equals pi

in the other section, p3 = pi and S2 = h2/p2= S: = hz/pi, then the sounding curves forboth sections (fig. 22, curves c and d) will bepractically identical (equivalence by S) . Theequivalence by S also applies to soundingcurves of the A type (pl < p2< pa).For both equivalence by T and equivalenceby S, there is a certain range, depending onthe ratios pz/pl and hz/h,, where the twosounding curves coincide very closely. Specialnomograms published by Pilayev ((1948) de-fine this range, which is referred to as thedomain of the principle of equivalence. Thesecharts were published in the books ofBhattacharya and Patra (1968)) Dakhnov(1953)) Golovtsin (1963)) Kalenav (1957))

ELECT RODESPAC ING,E/2, IN FEETIO 20 so 100 200 500 1000 2000 5000 10,000

10.0 , , I,,; 1 ,, , ;,,; 1 ,I, , /,, 1 ,, , ,,,u

i-

2 . \.0.01 I I I III I I I Ill I I\ I I I!11112 5 IO 20 50 100 200 500 1000 2000 50Q0 10.000ELECT RODESPACIN G,n/2, II METERS

Figure 19 .-Examples of three of the eight possible types of Schlumberger sounding curves for four-layer Earth models.


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APPLICATION OF SURFACE GEOPHYSICS 29 I I

P =co

-+t

P =o

J O1 \ I7 II IO 100 1000 HALF THE DISTANCE BETWEEN CURRENTELECTRODES PERPENDICULARDISTANCE FROM CENTER ARRAY TO VERTICAL CONTACT

Figuie 20 .-Examples of the voriation of Schlumb erger sounding cur ves across a vertical contact ot various az imuths.m/2, electrode spacing; d, perpendicula r distance from center of array 0 to surface trace of vertical contact;P; apparent resistivity ; p, true resistivity ; 7, azimuth angle (after Zohdy , 1970).


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30 TECHNIQUES OF WATER-RESOURCES INVESTIGATIONSand Keller and Frischknecht (1966).Approximate equivalence of soundingcurves of sections with horizontal or verticalcontacts, or both, to sounding curves of sections with horizontal boundaries only .- Theform of sounding curves. obtained over sections with horizontal and (or) vertical orinclined contacts can be quite similar tocurves obtained over sections with horizontalcontacts only. This is true when the sounding line is parallel to the strike of the vertical (or inclined) contact. Depending on theratio d/h of the perpendicular distance fromthe center of the sounding line to the surfacetrace of the vertical contact d to the thickness of the top layer h, one may obtainsounding curves that are equivalent to curvesobtained over a three, or more, horizontally-layered Earth model (fig. 22, curves e andf) . This type of equivalence is resolved easilyby making crossed soundings (soundingshaving the same center but expanded at right

angles to one another). The forms of the twosounding curves are so different from oneanother that it is easy to realize the presenceof a lateral heterogeneity in the ground (seecurve e, fig. 22). The expansion of the Lee-partitioning array parallel to the strike ofa vertical or inc lined contact does not yielddata that are indicative of the presence ofthe lateral heterogeneity, and thle making ofa crossed sounding is required.Approximate equivalence between twomultilayer sections .-A ,sounding curve obtained over a four- or five-layer section maybe nearly equivalent to one obtained over athree-layer section. Generally this is attributed to the so-called principle of suppression (Maihet, 1947). The error, causedby theeffect, in interpreting the depth of contactsis sometimes referred to as pseudoanisotropy(Genslay and Rouget, 1967; Flathe, 1955,1963). An example of this type of equivalenceis shown in figure 22, curves g and h.

Figure 21 .-Examples of thevkiation of Wenni?r sounding curves across a vertical contact ot various azimuths. Unpublished data calculated by Zohdy, 1970. a, Wenner spacing; d, perpendicular distance from center of arrayto surface trace of vertical conitoct; 7, apparent resistivity; p, true resistivity.


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I-::In N - .e N -0d 0 S8313W-WHONISU313W-WHO d AlIAIlSIS3ti lN38VddV ti39139WlllHlSN;i

d AlIAIISIS3N IN3lVddV ti39139WfllHX

2 P VI N - OQSJ313W-WHONISY313WWHO NI d A lIAIlSIS3U lN3UVddV H39ti3tlWfllHjS cj AlIAIlSIS3N lN3IVddV #39#38WfIlHX


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32 TECHNIQUES OF WATER-RESOURCES INVESTIGATIONSEquivalence between isotropic and anisotropic media .-The equivalence between anisotropic layer and an anisotropic layer isexact when the equivalent layer has micro-anisotropic properties. In practice, depthsare generally overestimated ,bya factor equal

to the coefficient of anisotropy A = 5 ,PIIwhere p. and p,,are the (resistivities I/perpendicular to, and parallel to, the bedding, respectively (dg. 22, curves i and j). Valuesof A genera lly range from 1.1 to 1.3 and rarely exceed2.Monotonic change in resistivity .-Whenthe resistivity of Ithe subsurface layers increasesor decreasesmonotonically (A-, AA-,Q-, or &Q-type sections), the sounding curvemay resemble a curve of a simple two-layer

Earth model (principle of suppression), unless the thicknesses of the layers increasesignificantly with depth. Recently, two newmethods for making so-called differentialsoundings have lbeenintroduced (Rabinovich,1965; Zohdy, 1969) whereby the resolvingpower of the sounding curve is greatly improved for A- and Q-type sections.Relative thickness of a Zuger.-The detect-ability of a layer of given resistivity dependson its relative thickness, which is defined asthe ratio of the bed thickness to its depth of

burial. The smaller the relative thickness ofa given layer, the smaller the chance of itsdetectability on a soundSingcurve. In four-layer (or more) Earth models the so-calledeffective relative thickness of a layer(Flathe, 1963)) which is defined as the ratioof the layer thickness to the product of thepseudoanisotropy, and the total thickness ofthe layers above it must be considered. Forexample, ,a layer 50 meters (164 feet) thickat a depth of 10 meters (32.8 feet) has arelative thickness of 5, which is qui,te favor-able for its detection on a sounding curve.However, if the top 10 meters (32.8 feet) arecomposed of ,two layers of thicknesees of 2meters (6.56 feet) and 8 meters (26.2 feet)and resistivities of 10 ohm-m and 1,000 ohm-

m, respectively, then the pseudoanisotropy Aof the top two layere is 4.1. Tlhereflore,the effective relative thickness is 50/ (4..1>(10) =1.22,which is considerably smaller than therelative thickness of 5 previously calculated.The resistivity of the 50 meter (164 feet)third layer and of the underlying layers alsopl,ay an important role in the detectability ofthe layer on the sounding curve.The limitations to interpretation mentioned above should not be discouraging tothe geophysicist nor should they persuadethe reader to consider the interpretation ofsounding data as an entirely hopeless endeavor. All geophysical methods that arebased on potential theory (electrical,gravity, and magnetic methods) lack unique solutions. In practice, it is by correlation of several sounding curves, by makingcrossed soundings, by sounding with different arrays, by traversing the area withhorizontal resistivity profiles, by knowledgeof its general geology, and by recognition ofthe electrical properties of the rocks in thestudied area that correct interpretations areachieved. When drilling information is avail-able it is advisable to make parametric electrical soundings near the wells i.n order todetermine the resistivity parabmeters ofthe layers using accurately determined layerthicknesses. Then using these known resistivity parameters, we can determine thelayer thicknesses in areas where drilling in-formation is lacking.

Analysis of Electrica I SoundingCurvesWhen an area is investigated, the sounding curves generally are not all of the sametype (H, A, K, Q, and HA, for example).Furthermore, all the curves may not be interpretable in terms of horizontally stratified media. In this section we shall describesome of the qualitative and quantitativemethods of interpretation of electrical sounding data.


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Oualitative lntemretation 1 2. Preparation of apparent-resistivity maps.Each map is prepared by Blotting theThe qualitative interpretation of sound\ apparent resistivity value, as regising data involves the following : tered on the sounding curve, at a given1. Study of the types of the sounding curves 1 electrode spacing (common to allobtained and notation of the area1 dis soundings) and contouring the resultstribution of these types on a map of (fig. 23).the survey area. 3. Preparation of apparent-resistivity sec-

ADrill hole

20 30 75 ohm-meters

Figure 23.-Map of apparent resistivity neor Rome, ltoly (after Breusse, 196 la).


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Sounding statlon andnumber of statlon

34 TECHNIQUES OF WATER-RESOURCES INVESTIGATIONSC 12 13,14 15.16 10 9 8 4 5 1

z 3000z< 4000-1%"tiE 5000z2g 6000 EXPLANATION0E 10vz 7000'I Sounding statlon andnumber of statlon

8000.9000'

10,000

N2la-1500 gGa%z- 2000 &5UJ

- 2500:~30Figure 24.-Section of apparent re sistivity near Minidoko, Idoho. Values on contour lines designate apparent re

sistivities in ohm-meters. Snake Rivertions. These sections are constructed byplotting the apparent resistivities, asobserved, along vertical lines locatedbeneath the sounding stations on thechosen profile. The apparent resistivityvalues ,are then contoured (fig. 24).Generally a linear vertical scale isused to suppress the effect of near-surface l,ayers.4. Preparation of profilas of apparent-resistivity values for a given electrodespacing, profiles of the ordinate or abscissa of the values of the minimumpoint F~, for H-type sections, profilesof the ordinate or absicissa of the maxi-mum point pmmsXor K-type sections, pro-files of pL values, and profiles of S andT values.These m,aps,sections, and profiles constitute the basis of the qualitative interpretation which should precede quantitative interpretation of the electrical sounding data. I

basalt thickens toword the north.It should be noted, however, that an apparent resistivity map for a given electrodespacing (fig. 23) does not represent theareal vari,ation of resistivity at a depth equalto that electrode spacing, it merely indicatesthe general lateral variation in electricalproperties in the area. For example, an areaon the map having high apparent resistivityvalues may correspond to a shallow high resistivity bedrock, it may indicate th ickeningin a clean sand and gravel aquifer saturatedwith fresh water, or it may indicate thepresenceof high resistivity gypsu:mor anhy-Idrite layers in the section.

Determination and Use of Total TransverseResistance, T. from Sounding CurvesIn three-layer sections of the Ii: type, theJalue of transverse resistance of the secondIayer can be determined approximately from

aL Schlumberger sounding curve (ng. 25) bynnultipIying the ordinate value of the maxi-


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APPLICATION OF SURFACE GEOPHYSICS 85)um point (E max by the correspondingabscissa value of m/2 (Kunetz, 1966). Thevalue of Tz thus determined generally is underestimated (fig. 26)) especially when thereal value T, is large and is ~approximatelyequal to the total transverse resistance of the

upper two layers T = T, + Tz z Tzr (with,T, 4 10% T,).The total transverse 8resistance of theupper two layers T = T, + Tz = & + pzhzis determined approximately by anothergraphical technique (Dzhavarof and Biramova, 1965). The intercept of a straightline tangent to the Schlulmberger soundingcurve and inclined to the abscissa axis atan angle of 136 (or 45) with the horizontal line for ~;=l ohm-m is approximatelyequal to T (fig. 25). The value of T e T bythis graphical method generally is overestimated. Therefore, for large values of T andwhere Tt z T, the average of the values ofT, and T is closeto the true value of T (fig.25). This is especially true when ,Jpl < < 1.Where the value of T increases from onesounding station to the next, this generally

means that the thickness of the resistivelayer in the section (gravel, ~basalt,etc.) alsoincreases. However the increase in T mightbe caused also by an ,increase in the resietivity va lues. A north-south profile of graphically determined values of total transverse resistance east of Minidoka , Idaho, (fig. 26) isan excellent qualitative indication that theSnake River basalt increases in thickness appreciably from south to north.

Determination of Total LongitudinalConductance, S, From Sounding CurvesIn H, A, KH, HA, and ,similar type set+Cons the terminal branch on the sonndingcurve often rises at an angle of 45. Thisusually indicates igneous or metamorphicrocks of very high resistivity (> i,OOOohmm). However, in the presence of conductive

sedimentary rocks saturated with salt water(p< 5 ohm-m) the so-called electric basement of high resistivity rocks may correspond to sandstones or limestones having resistivities of only 200-500 ohm-m. The totallongitudinal conductance S is determinedELECTRODE SPACING, z/2, IN FEET

IO 20 50 100 200 500 1000 2000 5000 10,000

EXPLANATION10 m 40 nm 60 m1) Real T1=40x50=2000m

4) T'FY2300 m

4am 10m

ELECTROD E SPACING, n/2, IN METERS

Figure 25.--Grophico l determination of totol transverse resistance from o K-WE Schlumbe rger sounding curve. PI= 4 ohm-meters, pn = 40 ohm-meters, ps = 0 ohm-meters, hl = IO meters (32.8 feet), h, = 5 0 meters (I 64feet), ha = ao.


33/63

36 TECHNIQUES OF WATER-RE,SOURCES INVESTIGATIONSEXPLANATION

:Electrml soundlhg

Figure 26.- Profile of total transverse resistance values,T,indicate thickening of basalt layers.

from the slope of the terminal branch of aSchlumberger curve, rising at an angle of46 (here called the S-line). It should be re-membered that the slope of a rectilinearbranch inclined to the abscissa at 45 is notnecessarily equal to unity when the curve isplotted on logarithmic paper. The value ofS is numerically equal to the inverse of theslope of this line (Kalenov, 1957 ; Keller andFrischknecht, 1966), and it is usually deter-mined, very quickly, by the intercept of theextension of the S-line with the horizontalline, pd = 1 ohm-m (fig. 27). The determination of S by this method is as accurate as agraphical procedure can be, and is valid irrespective of the number of layers that over-lie the high resistivity layer provided the terminal branch rises at an angle of 45. Whenthe resistivity of the *bottom layer is not sufficiently high to make the terminal branchrise at an angle of 45, other methods areused for the graphical determination of S(Berdichevskii, 1957 ; Orellana, 1966 ; Orellana and Mooney, 1966; Zohdy, 1968). In-creases in the value of S from one soundingstation to the next indicate an increase inthe total thickness of the sedimentary section, a decrease in average longitudinal resistivity (pt) , or both.

in ohm-meters squared, neor Minidoka, Idaho. High valuesDota obtained by Zohdy (1969).

Determination of Average LongitudinalResistivity, pL, from a Sounding CurveAs the value of longitudinal conductanceS can be determined easily from a Schlumberger sounding curve, graphical ,methods forthe evaluation of average longitudinal resistivity (& from the sounding curve weresought so that the total depth H to the highresistivity bedrock could be calculated fromthe simple relation H = Sp,. It was found(Zagarmistr, 1957) that for three-layer eections of the H type, the value of the apparentresistivity at the minimu,m point (~,,,,,,,)on a polar dipoledipole curve is approximately equal to pL, provided that the thicknessof the middle low resistivity layer is atleast 3 times as large as the thickness of thefirst layer (h, % 3h,). This was found to be

valid for all valaes of p = E- (Zagarmistr,1957; Berdichevskii and Za&rmistr, 1968).Using formulas developed by Alpin and byTsekov (A lpin, 1958 ; Zagarmistr, 1957 ;Zohdy, 1969a), Schlumberger and equatorialsounding curves can be transformed intopolar dipole sounding curves (fig. 28). Theaverage longitudinal resistivity then can bedetermined and the thickness of the sectioncan be calculated.


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APPLICATION OF SURFACE GEOPHYSICS 97ELECTRODE SPACING, n/2, IN FEET

ID 20 SD 100 200 500 1000

I I I I 1 I I I I II I I I I I III1 2 5 IO 20 50 100 200 500 1000ELECTRODE SPACING, m/2, IN METERS

Figure 27.-Grophicol determination of total longitudinal conductance S from an H-type Schlumbe rger sound ingcurve.

Average longitudinal resistivity also maybe determined -from borehole induction logsof wells in the area,Distortion of Sounding Curves by ExtraneousInfluencesElectrical sounding curves may ,be distorted by lateral inhomogeneities in theground, by errors in measurements, or byequipment failure. It is important to realizethe cause of various com mon distortions onsounding curves.Formation of cusps.-The formation of acusp on a Schlumberger sounding curve gen

erally is causedby a lateral heterogeniety, bycurrent leakage from poorly insulated cables,by electrode spacing errors, or by errore incalculation (Zohdy, 1968b). When plottingdata in the field, it is advimble to check forcurrent leakage whenever a cusp is formed

on the sounding curve. A resistive lateralinhomogeneity, in the form of a sand lens ora near-surface oaliche layer, produces a cusplike the one shown in curve A, figure 29;and a conductive inhomogeneity, in the formof a buried pi,pe or a clay pocke t, producesa cusp as the one shown in curve B, figure29.Sharp maximum.-The maximum or peakvalue on a K-type sounding curve is3alwaysgentle and broad, and should never have asharp curvature where the ground is horizontally homogeneous. The formation of asharp peak (fig. 30) generally is indicativeof the limited lateral extent of the buried(middle) resistive layer (Alfano, 1969).Curve diecontinuities.-Two types of discontinuities are observed on Schlumbergersounding curves. The first type is observedwhen the spacing MN is enlarged (with AB


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r, IN METERS3 10 50 100 500 1000 5000 10,000

I I I IllI I I I III1 I II1000 I , , I1 I 1 I I16 300 330036 1 330, I 3.37 1 00

36 1 330 3.0 1 a316 300 3000

t Observed P; curve A

50s Transformed ii, curvez-IQ! tIQ?

VES II

m,D =4=3.7 ohm-meters -

50 100 500 1000 5000 10,000 50,000 100,000ni2, r, IN FEET

Figure 28.-T ronsformation of a Schlumberger KH-type curve into a polor dipole-dipole curve to evaluate j5.m,n= PL and H = SpL(after Zohdy, 196901. Reproduced with permission of Geophysics.

constant) aandthe value of the apparent sesistivity, for the larger MN spacing, does notconform to the theoretical magnitude forsuch a change in MN (Deppermann, 1954).The repetition of such a discontinuity whenMN is changed to a larger spacing for thesecond time indicates a lateral inhomogeneityof large dimensions. This type of discontinuity also may indicate current leakage, electrade spacing errors (Zohdy, 1968b), orthat the input impedance of the potential-difference measuring device is not sufficiently high. Examples of the discontinuities thatare not in conformity with the assumption of

a horizontally homogenous Earth a re shownin figure 31. When the discontinuitiees are notsevere, the curve can ,be corrected easily byshifting the distorted segment of the curvevertically to where it should be.The second ty,pe of discontinuity is leascommon ,and occurs during the expansion of thecurrent electrode spacing i% when soundingwith a Schlumberger array. In general, thecurve is displaced downward, that is, thevalue of the apparent resistivity at the largerAB is much less than the previous reading(fig. 32). This type of discontinuity generally is caused by a narrow, shallow, dike-like structure which is more resistant than

5


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APPLICATION OF SURFACE GEOPHYSICS 39the surrounding media and whose width issmall in comparison to the electrode spacing(Kunetz, 1955, 1966; Zohdy, 1969a). Theabscissa value at which the discontinuity onthe sounding curve occurs is equal to the distance from the sounding center to the dike-like structure.

Quantitative InterpretationSeveral methods are used in the quantitstive interpretation of electrical soundingcurves. These methods are class ified {asanalytical methods, semiempirical methods, andempirical methods.

Analytical Methods of InterpretationThe analytical methods are based on thecalculation of theoretical sounding curvesthat match the observed curves. There areseveral catalogues of theoretical master

curves calculated for a variety of Earthstruotures, most of which represent horizon-tally stratified media. Mooney and Wetzel(1956) published an extensive catalogue ofmaster curves for Wenner soundings overtwo-, three-, and four-layer Earth models.The Mooney-Wetzel album, now out of print,has several shortcomings that limit its usefulness (Zohdy, 1964).

Two problems are encountered in the calculation of theoretical sounding curves andin their application for the interpretation offield data. First, the calculation of the apparent resistivity value at each electrode spacinginvolves the evaluation of a difficul,t integral (Stefanesoo and others, 1930) or thesummation of an infinite series (Hummel,1929). Thus the use of a high speed digitalcomputer is almost always necessary for thecalculation of theoretical curves.oundingI

ELECTRODE SPACING, n/2, IN FEET 10 20 50 100 200 500 1000 2000 5000 10,000

later ,al inhomogeneity (pipeline)

'2 5 IO 20 50 100 200 500 1000ELECTRODE SPACING, K8/2, IN METERSFigure 29 .-Distortion of sounding curves by cusps caused by laterol inhomogeneites.


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40 TECHNIQUES OF WATER-RESOURCES INVESTIGATIONSSCHLUMBERG ER ELECTRODE SPACING, z/2, IN FEET

10 20 50 100 200 500 1000 2000 5000 10,000I 1 I III11 1 I I Illll I 1 I I I III I 1 I II I I I 1 III I I I Ill I I _

vP, =25

--Epggiyy--Ps q25

Normal curve

1x IO 1 I I1111 I I I I I II I I I I1111 I-l2 5 IO 20 SD 100 200 500 1000 2000 4000SCHLUMBER GER ELECTRODE SPACING, n/2, IN METERS

Figure 30.-Exomple of a narrow peak on a K-type curve,dle layer (after Alfano, 1959). R eproduced withRecently, however, the calculation of VES(vertical electrical sounding) curves of theSchlumberger type for horizontally stratifiesmedia was simplified and greatly acceleratedthrough the use of the method of convolution (Ghosh, 1971).The second difficulty in the calculation oftheoretical curves is that in multilayer Earthmodels, the possible combinations of resistivity contrasts and layer thicknesses are infinite. Even in a simple two-layer Earth model,there are three variable parameters, pl, p2,and h,. With pl, pz,and h, as variables thereare an infinite number of possible soundingcurves for the two-layer. geoelectric section.However, by considering the reeistivity andthickness of the first layer as unity and byplotting the theoretical sounding curves ona set of logarithmic coordinates with thedimensionless variables AB/2 h, (Schlumberger), a/h1 (Wenner), or r/h, (dipole-dipole), on the abscissa; and 7dp1, idpI, or

caused by the limited loteral extent of a resistive mid-permission of Geophysical Prospecting.

pa/p1 on the ordinate, a simple family ofcurves is obtained. These two-layer curvesvary in shape, in a unique manner, and inaccordance with the infinite number of valuesthat the ratio pJpl may attain. A set of two-layer master curves for the Schlumbergerarray is shown in figure 33 ; two-layer mastersets of other arays may be different in shape.

In three-layer Earth models, there are fivevariable parameters : pl, p2,ps,h,, and hr. Byusing the dimensionless variablesIisCl - jdpu pa - pa/p19 vi - ;r

1and by plotting the theoretical soundingcurves on logarithmic coordinates, the resultis still an infinite number of curves (Cagniard, 1962).

T*helimitations on the calculation and application of theoretical sounding curvesshould not discourage their use. Several


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APPLICATION OF SURFACE GEOPHYSICS 41graphical methods have been devised for theconstruction of electrical sounding curvesof p1= P2/Pl, pi? = p3/pl, and u1= b/h, thathave not been thoretically calculated (Kalenov, 1957; Matveev, 1964). The graphicalconstruction of a given sounding curve isdone by using the available theoretically calculated curves in conjunction with specialnomograms. The graphical interpretation ofsounding curves often is checked by calculating the exact sounding curve for the derivedmodel on a digital computer.Before interpretation is made with themaster sets for horizontal layers, the interpreter Imust ~besatisf ied with the form of thesounding curve, in that it is sufficientlysmooth and not severely distorted by sharpcusps or discontinuities. A certain amountof smoothing generally is required. The typeof curve (such as H, A, K, Q, HA, HK)and the minimum number of layers it seemsto represent can be determined by visual

inspection. Because of the principles of suppression and equivalence, certain three-layercurves may resemble two-layer ones andfour-layer curves may resemble threlayercurves. The estimated number of layers is,generally considered to be the minimumnumber.

Two-layer InterpretationIf the field curve, which is plotted on logarithmic transparent paper of the samemodule as the ma&r curves, seems to represent a two-layer Earth model, we superposethe transparent sheet with the field curveover the two-layer master set, and move thetransparent paper up, down, right, or left(maintaining the coordinate axes of the twosheets parallel) until a $bestfit of the fieldcurve against one of the theoretical curves isobtained. Occasionally the field curve mayhave to be matched #byinterpolation


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42 TECHNIQUES OF WATERRESOURCES INVESTIGATIONSTIT IN METERS

1 5 10 50 100 500 1000l

/-

IL 1 1 I ,111 1 1 1 ,111 ,

A,J&y+y i;fl , I,,,,J1 5 10 50 100 500 1000 ( 5000 10,000w-?-, IN FEET Distance from soundingstation to dikeiike structure

Not toscaleI INTERPRETED MODEL

Figure 32.- Exomples of tares (discontinuities) on Schlumberger curves caused by a neor vertical dikelike structure.(after Zahdy, 1969a). Reproduced with permission of Geaph ysics.

Determine the position of the cross, whichis the origin of coordmates of the theoreticalcurve, and trace it on the sheet of the fieldcurve. Also determine the resistivity of thesecond layer (Pz) by tracing the asymptoteto the theoretical two-layer curve.The abscissa value (AB/2, a, or r) of thecross equals the thickness of the first layerand the ordinate value (JJ) of the crossequals the true res istivity, pl, Qf the first

layer. The trace of the asymptote to p2on thefield sheet equals the true resistivity, p2, ofthe second layer (fig. 34).Three-layer Interpretation

Determine the type of three-layer curve(H, A, K, Q) by inspection and aelect the

applicable set of theoretical master curves.Although one of the values of p1= p2/p1ina set of theoretical curves may correspond tothe real value of p1 = p2/pl of thle field curve(or although a value of P1= ,J~/P~in thealbum fits the observed curve through theprinciple of equivalence by T or by S), thevalue of p2 = p3/pl for the field curve maynot ,be among those for which the theoreticalcurves were computed. Therefore, the firstclosest fit of the field curve should not berelied on. Better interpretations generallyare obtained lby enveloping the field curvebetween two three-layer curves having thesame value of p, = p2/Pl amI the same valueof v= hi/h, but different values of p2=P3/Pl (fig. 35). If thevaluesof Pz = pS/pxfor


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II

!0.2 --+-

III0.1 --f

!II0.05 --A-

SOUNDINGSTATIONV

h,=m

Figure 3X-Two-layer master set of sounding curves for the Schlumberger orroy (adopted from Orellonaand Mooney, 1966).


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44 TECHNIQUES OF WATER-RESOURCES INVESTIGATTONSthe field curve and the theoretical curve areequal, then complete curve matching may beattained.

Maintaining parallelism #betweenthe axesof the field curve and the theoretical curve,determine the position of the cross on thefield curve, note the value of u1= h&z, designating the theoretical curve, and note thevalues of pI = p2/pl and p2= p2/pl.

Knowing h, and p1 from the abscissa andordinate of the cross, the values of p2,hO,andp3 can be calculated from the val,ues of pl =&PI, w = hdh,, and p2= p3/pl, respectively.The determined values of hz and pz may notbe equal to the real values in the geologicsection because of the principle of equivalence. Consequently the Pylaeve equivalencydiagram (Dakhnov, 1953 ; Kalenov, 1957;Keller and Frisschknecht, 1966 ; Bhattaeharyaand Patra, 1968) should be consulted for thesection (H, A, K, or Q) under consideration,and the minimum and maximum values of hzand pzdetermined.

If a satisfactory match be tween the fieldcurve and a theoretical three-layer curve isimpos&ble, then eikher the curve representi

more than three layers, or it is a.three-layercurve with a large value of v := h2/h, andvalues of 1, = pz/p, or 1~~= p3/p l that are notin the album. The interpretation then is madeusing the two-layer curves in conjunctionwith auxiliary point diagrams (Orellanaand Mooney, 1966; Zohdy, 1965) or bygraphically constructing (Bhattacharya andPatra, 1968 ; Matveev, 1964 ; Kallenov, 1957)or numerically calculating (Ghosh, 1971)sets of three-layer master curves for the required values of W, ,A~,and p2.

Four-layer (or more) InterpretoRionIn practice, especially with large spacings,four or more layers may ,be distinctly reflected on the curve. The maximum numberof layers detected by the curve with the elec

trode spacing AB/2 of as much as 10,600 m(32,899 feet) generally does not exceed eightlayers. Four- and five-layer curves are oftenencountered. The graphical interpretation(fig. 36) of multilayer sounding curves ismade by using the three-layer curvrvesand theauxiliary point diagrams (Bhattacharya andPatra, 1968 ; Kalenov, 1957; Orellana andELECTRODE SPACING, E/Z, IN FEET

10 20 50 100 200 500 1000g 200 I I~ I I I I I II I Ill I I I I I III2 I 1 Illrz

asymptote

theoretical

z2 h,=14 ma I I ,,1111~2 IO I I lllll I 1 I llllla 2 5 IO 20 50 100 200 500 1000

ELECTRODE SPACING, a/2, IN METERSFigure 34.-Interpretation of a two-layer Schlumberg er curve (pa/p = 5).

_--


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SCHLUMBERGER ELECTRODE SPACING, n/2, IN FEET10 20 50 100 200 SD0 1000 2000 5000 lD,ODO

three-layertheoretical curve

= ID- h,=25 mz4w h2=2h,=50 mz Pz =5nm H=hl+h2=75 m= s-g I- 2

I I I115 IO

1 I I I III I I20 50 100 200

I 11 II500 1000

I I I5000

SCHLUMBERGER ELECTRODE SPACING, E/2, IN METERSFigure 35.4nterpretotion of o three-layer Schlumberger H -type curve.

Mooney, 1966; Zohdy, 1966). The accuracy ofthe interpretation depends on the effectiverelative thickness of the layers and the experience of the interpreter. It is suggestedthat the interpreted model be checked by (1)reconstructing the curve graphically usingthe method described lby Matveev (1964))(2) reconstructing the first part of thecurve *by #graphical methods and calculatingthe second part of the curve using themethods of Flathe (1956), Van Dam (1964,1965), or Tsekov (1957), or (3) calculatingthe entire curve on a high-speed digital computer.

Empirical and Semiempirical Methods 9fInterpretation of Sounding CurvesSeveral empirical methods were inventedbecauseof the lack of calculated sets of master curves and these methods are still asedby some investigators.

bores Cumulative Resistivity MathodMoore (1945,196l) developed the so-calledY?umulative resistivity method, which is an

empirical method for determining the depth(but not the resistivity) to horizontal layersfrom Wenner soundings. The method haabeen the subject of ,much discussion and hasreceived both praise and condemnation (M,uskat, 1945; Wantland, 1951).The cumulative resistivity curve is constructed by plotting

as a function of the Wenner electrode spacinga. The points on the curve will have the~ordhh3 (ii&J, 4) ; bdad + F&AeJ ; Mad + g&f.d + idad,~) ; . q . ;h&-h) + dad + . . . + fdan), G),where a, - a, = a3 - & = a, - G., = contant. This curve consis ts of straight linesegments intersecting at points where theabscissa values, according to Moore areequal to the depths of horizontal boundaries. The method can be tested easilyby using the theoretical data published inthe Orellana-Mooney tables (Orellana and


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46 TECHNIQUES OF WATER-RESOURCES INVESTIGATIONSMooney, 1966) for Wenner curves. However,interpolation between the values given inthe tables is necessary because the tablesare based on electrode spacing vahxs thatincrease at a logarithmic rate (1, 1.2, 1.4,1.6, 2, 2.6, 3, 4, . . .), whereas Mooresmethod assumes a constant linear increase(1, 1.1, 1.2, 1.3, 1.4, 1.5, 1.6, 1.7, . . .).It is found that for horizontal two-layerEarth models the method gives reasormblyaccurate results provided the contrast in resietivity is modera& If the contrast is large(pz/pl)+ * or 0, the depth to the interfaceis underestimated by aa much as 50 percent,whereas if the &ntrast is small, (pz/pl) = 1,the depth is overestimated by XUJmuch as 50percent. This explains why Moores methodseems to work in certain areas and ,fails inother ear-. T,he use of the method to interpret three-, or more, layer curves is highly

questionable. Furthermore, the method doeanot give an estimate of the resistivities of thelayers.Born& Lqer M&,od

Barnes (1962, 1954) developed.an empirical method for the interpretation of electricalsounding data. The method, now known aaBarnes layer method, is baeedon the erroneous assumption that the electrode spacingin the Wenner array is equal to the layerthickness. The layer resistivity as definedby Barnes, however, has interesting possibilities, especially if the Sohlumberger array isused in lieu of the Wenner array, and provided curve-matching interpretation is usedin lieu of Barnes empirical approach (Keller,1968).

All empirical methods either are rejectedor improved by testing them with theoreti-ELECTRODESPACING, z/2, IN FEETIO 20 50 100 200 500 1000

three-layer curve

I .- 1 I

58 m 19Yrn I LLuLLLll- I I lllll 13 m I I I I111142 5 10 20 50 100 200ELECTRODE SPACING, n/2, IN METERS

Figure 36.4nterpretation of a four-layer Schlumberger curve by the auxiliary point method using two three-layer CUTVBS. Thanumeral 2 on the upper curve indicates that the thickness of the third layer is twice es great as the abscissa of the auxiliary Kpoint. (For details of method, sea Bhattacharya and Patra, 1966; Zohdy, 1965.)


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0 APPLICATION OF SURFACE GEOPHYSICS 47tally exact calculations. By testingempiricalmethods against tested. theoretical curves,semiempirical methods are evolved. The conditions for which such semiempirical relations are valid generally ,are well defined,and for many of these relations rigorousmathematical formulations proving their approxi,mate validity can (bederived. Examplesof these methods are: the determination ofthe value of T from K-type Schlumbergersounding curves, and the evaluation of ,,&from polar dipole-dipole sounding curves.The Russian literature is richly endowedwithsuch methods (Abdullaev and Dzhafarov,1964; Kalenov, 1957). Many of these methodsresulted in the development of useful nomograms. The general goal of all such methodsis to avoid complete curve-matching procedures ; consequently,only a part of the information contained in a sounding curve isutilized in interpretation, and large errorssometimes occur. Semiempirical methods,however, are useful in preliminary intcrpretations and in supplementing the ftnal interpretation.The empirical and semiempirical methodsof interpretation are not ~recommendedexcept in the preliminary examination ofsounding curves. Considerable work hasbeen done using these methods and some ofit has ,beeneffective in ground-water studies.However, in almost every survey where theinterpretation has ,beenIbasedon empiricaland semiempirical methods only, more complete and accurate information could havebeen obtained using analytical methods.Applications of Resistivity Surveysin Ground-Water Studies

In ground-water studies, the resistivitymethod can furnish information on su)bsurface geology which might be unattainable byother geophysical methods. For example,electrical met,hods are unique in furnishinginformation concerning the depth of thefresh-salt water interface, whereas neithergravity, magnetic, nor seismic methods cansupply such information. A thick clay layer

separating two aquifers usually can be detected easily on a sounding curve but thesame clay bed may #bea low ve locity layer inseismic refraction surveys and cause erroneous depth estimates.Mapping Buried Stream ChannelsBuried stream channels, which often canbe mapped accurately


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-\-A.

. PENITENCIA

i \ SANTA CLARA COUNT*\ \ \

5 0 5 10 Milesl Geophysical Surve:Figure 37.--Map of San Jase area, California, showing areas studied.


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.QE


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------- --APPLICATION OF SURFACE GEOPHYSICS 61

0 25 50 METERS

EXPLANATION0

.- -Horizontol reristivity profile (o q 30 fret)

lElectrical sounding

-5o-lsoresisfivity contour, in ohm-meters

aBorehole following surveybJ50 100 150 ohm-meters

Figure 40.--Map of opporent resistivity near Campbell, Calif., obtained with Wenner array at a = 9.15 m(30 feet) and showing location of section AA. (Unpub. data obtained by Zohdy, 1964.)


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62 TECHNIQUES OF WATER-RESOURCES INVESTIGATIONS8

160

EXPLANATION i, Id0 260 360 FEET

40-6octlU-METERS 300-4200-120HM-YETERSWY-METERSSILT AN0 CLAY GRAVELLY CLAY SAH) AND GRAVELt --u

LECTRICAL SOUNDING TEST WELLAND NUMBERFigure 41.--Geoelectric section and drillitq results near Campbell, Colif. Numbers in layers designate interpreted

true resistivities. (Unpub. data obtained by Zohdy, 1964.)

by making horizontal profiling using theSchlumberger AB profile technique ( seefig.10a). In this survey the AB line was 4,090m (13,120 feet) long. Eleven parallel pro-files spaced 100 m (323 feet) apart weremade, each of which consisted of 111 measurements spaced at 100 m (326 feet) intervals. The apparent - resistivity map obtained from this survey (fig. 44) was usedto delineate the traces of the faults.In New Zealand, Banwell and MacDonald(1965) and Hatherton and others (1966) re-ported on the successful use of Wenner sounding and horizontal profiling for delineatinggeothermal areas. Figure 45 shows an apparent-resistivity map prvred from Wenner horizontal profiling data using an electrade spacing of a = 549 m (1,800 feet). Thetwo low-resistivity areas outlined by the 5ohm-meter contour are .believed to delineatethe hottest ground. The northern area atthe Wairakei Geyser Valley was already

noted for its geothermal power production,but the large low-resistivity area southeastof Wairakei and northeast of Taupe was discovered by resistivity measurements. A teatwell (well 225) was drilled in tlhat area,anda temperature of 220C was recorded at adepth of 256.2 m (840 feet) where a well-marked structural discontinuity is encountered between relatively impermeable m ud-stones and a ~permeablepumice breccia. Thegeothermal power potential in this newly discovered area is probably considerable.Other studies of geothermal areas weremade in Italy by Alfano (19160) and byBreusse and Mathiez (1956).Mapping Fresh-Salt Water Interfaces

From 1965 to 1969, the US. GeologicalSurvey made several resistivity surveys inthe southwestern United States where fresh-salt water interfaces wore mapped successful-


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APPLICATION OF SURFACE GEOPHYSICS 53ly with Schlumberger and equatorial electrical sound,ings. The apparent-resistivity map(fig. 46) wae obtaisned with m/2 = 306 m(1,000 feet) in the W,hite Sands Missile Rangearea (Zohdy and others, 1969). The apparent-resistivity contour of 10 ohm-m delineates,qualitatively, the area where mineralizedgroundwater is to be expected at shallowdepth. Quantiatative interpretation of the electrical sound ing curves, using a digital computer for calculation of multilayer curves,resulted in the map shown in figure 47. Theisobath lines on the map indicate depths at

2000 1

HORIZONTAL RESISTIVITYPROFILE

(7?=400 FEETm=80 FEET)

Vertical exaggeration 5x0 100 200m

which the true resistivity of the rocks isless than 10 ohm-m (saline ground water)or more than 500 ohm-m (crystalline basement). Examples of electrical soundings obtained in the White Sands Missile R ange areaare shown in figure 48.The literature is rich with case historiesof areas in many parts of the world where theresistivity method was successfully used formapping the fresh-salt water interface(Breusse, 1950 ; Flathe, 1967, 1968 ; Flatheand Pfeiffer, 1964; Van Dam and Meulen-1 kamp, 1967; Zohdy, 1969a).

om of channelrom drilling data

0-

e igure 42 .-Apporent -resistivity profile and geologic interpretation over buried channel, near Solisbury, Md. Dotoobtained by Zohdy ond Jockson in 1966.

1


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....................................................................................................................54 TECHNIQUES OF WATER-RESOURCES INVESTIGATIONS

........I/EXPLANATION

350samFigure 43.-Buried skeom channel near Bremerhoven, West Germany, mopped from electrical sounding (after Hallenbach, 1953). Resistivities of more than- 200 ohm-m were

interpreted to be within the buried channel. Reproduced with permission of GeophysicalProspecting.

Mapping the Water TableUnlike the mapping of the fresh-salt waterinterface, the determination of the depth tothe water table is generally a more difficultproblem. Deppermann and Homilius (1965)investigated the geoel&tric conditions where

the water table can be detected on an electrical sounding curve. Wherever the watertable is overlain and underlain by severallayers of different resistivities, its detectionon a sounding curve may be virtually impossible. Under favorable conditions the wa

ter table can (bedetect4 on a sounding curveaa a conductive layer.,On the island of Hawaii, Zohdy and Jack-son (1969 ) made several deep electricalsoundings to determine the depth to low-resistivity layers that may relpresent basalticlava saturated wih water. !Phey concluded

that the minimum depth to such a layer isof the order of 900 m (3,000 feet) (the survey was made at an average elevation ofabout 1,900 m (6,200 feet) above sea level)..A block diagram based on the interpretationof electrical soundings in the Pohakuloa


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APPLICATION OF SURFACE GEOPHY SICS 66

EXPLANATIONFault

-solsoreslstwbty contour,in ohm-meters

ElectrIcal proflle lmes andpoints of measurementsOd 500 1000 1500 ft

Figure 44.-b&p of opporent re sistivity in the Bad-Krozingen geothermal Oreo, Germany. AB = 4,000 m(13,120 feet) (after Breusse and Astier, 196 1).

Humuula area is shown in figure 49. The topof the layer with resistivity of less than 1,000omh-m presumably may represent the watertable. The ground water in this part of theisland probably is partly impounded by dikes.Mapping Clay Layers

Near Bowie, Ariz., a blue-clay layer separates two aquifers. The lower aquifer isartesian. The resistivity of this clay wasfound to be in the range of 0.5-7.0 ohm-m.The cross section shown in figure 50 is basedon the interpretation of electrical soundingsin th& area. In places near VES 7 (fig. 51)0

where the clay is covered by less than 9 m(30 feet) of soil, and where it has very lowresistivity (


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68 TECHNIQUES OF WATER-RESOURCES INVEISTIGATIONSa few hundred feet of the surface, but hasfound only limited use in ground-water investigations. Ihe technique has been usedeffectively in mapping buried channels wherethe channel-filling material has a resistivitycontrast with the enclosing medium (Collett,1967).In recent years several powerful radiotransmitters have begun broadcasting at frequencies of a few tens of kilo-Hertz. Radiowaves at these frequencies penetrate the;Karthto suffcient depths to be of use in geophysical exploration. Both ground and air-borne detection systems have been developed.The measurements consist of one or morecomponents of the electrical and magneticfields. This method, which is undergoingrapid development, has proved e ffective indete&ing near-surface highly conductive de-posits, but quantitative interpretation techniques are not yet available.

.

A description of inductive methods is con-tamed in Keller and Frischknecht (1966).

Induced Polarization MethodThe induced electrical polarization methodis widely used in exploration for ore bodies,principally of disseminated sulfideA. Its usein ground-water exploration has been limited.The origin of induced electrical polarizationis complex and is not well understood. Thisis primarily becauseseveral physico-chemicalphenomena and conditions are reeponsible foris occurrence.Conrad Schlumberger (Dobrin, 1960) probably was first to report on the induced polarization phenomenon, which he called provoked polarization. While making conventional resistivity measurements, he notedthat the potential difference, Imeasured be-

EXPLANATION-SO-/

Apparent resirtivity contourin ohm-metersl Drill hole

r//d Geothermal field

1 Mile

Figure 45.--Map of apparent resistivity in geathermol oreas in New Zeolond. Wenner spacing o = 549 m (1,800 feet).After Banw ell and MacDonald (1965). Reproduced with permission of Commonwealth Mining and MetollutgicalCongress.


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APPLICATION OF SURFACE GEOPHYSICS 57106375 IO630 106O225 15/

32a30

32225EXPLANATION

Electricalrounding

5 IO 20 50 150 Ohm -meteIY Paleozoic rocks

0 5 MILESt IFigure 46 .-Mop of apporent resistivity in White Sands area, New Mexico, far electrode spacing E/2 = 305 m

(1,000 feet) (afier Zohdy and others, 1969 ).

tween the potential electrodes, often did notdrop instantaneously to zero when the cur-rent was turned off. Instead, the potentialdifference dropped sharply at first, thengradually decayed to zero after a given interval of time. Certain layers in the groundbecame electrically polarized, forming a battery when energized with an electric current;

upon turning off the polarizing current, theground gradually discharged and returned toequilibrium.The study of the decaying potential difference as a function of time is now known asthe study of IP (induced polarization) in thetime domain. This type of study requiresheavy and generally bulky equipment in the


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68 TECHNIQUES OF WATER-RESOURCES INVESTIGATIONSfield; to avoid this limitation, mining geophysicists began to study the effect of alternating currents on the measured value ofresistivity. This is known as IP in the frequency-domain.Ground-water studies generally have beenmade with time-domain IP. In the time-domain IP, several indices have been used todefine the polarizability of the medium.Seigel (1959) defined the chargeability (in

106 37 5 106 30 .

32 30

32 22 5

32O 15

~ second,s)as the ratio of the area under thedecay curve (in millivolt-seconds) to the potential difference (in millivolts) measuredbefore switching the current off. Komarovand others (1966) define the polarizabilityas the ratio of the potential difference aftera given time from switching the current offto the potential difference before switchingthe current off. The polarizability is ex-1 pressed as a ,percentage.

106 22 5 15I

Jl- EXPLANATION.. Elec+ricol*sounding

0Test wellFault

Axis of rno&num fresh-water thickness!ZJ Paleozoic rocks

0 1 2 3 4 5 6 KILOME TERS01 4 MILES

-

Figure 47.-Map of White Sands area, New Mexico , sho wing isobaths of the lower surface of fresh-water aquifer.Dotum is land surface (after Zohdy and others, 1969).


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59PPLICATION OF SURFACE GEOPHYSICSw-T, IN METERS

1 2 5 10 20 50 100 200 500 1000I I I ,111 1 I 1 I I ,111 1, I000. 1 11 IlO I ,111 I ,111 I Ill11 I,, I1

500 -VES IO

200 - VES 69VES 8

g loo?ii VES 94 50 -zzti 20-

10 -

5-

2-

1 1 I, I,,, I I ,I,,,, 1 I I ,111 I lllll1 2 5 10 20 50 100 200 500 1000 2000 5000iTI-T, IN FEET

Figure 48 .-Examples of Schlumberger sounding curves obtained in ,the White Sands area, New Mexico (afierZohdy and others, 1969).

zohdy, eaton & mabey - application of surface geophysics to ground-water investigations - usgs

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