2. Electrical Resistivity Methods

2. Electrical resistivitymethods The resistivity method is used in the study ofhorizontal and vertical discontinuities in theelectrical properties of the ground.It utilizes direct currents or low frequencyalternating currents to investigate theelectrical properties (resistivity) of thesubsurface.A resistivity contrast between the target andthe background geology must exist.1

Possible applications ofresistivity surveyingFig. 1: Groundwaterexploration2

Possible applications ofresistivity surveyingFig. 2: Mineralexploration, detectionof cavities3

Possible applications ofresistivity surveyingFig. 3: Waste siteexploration4

Possible applications ofresistivity surveyingFig. 4: Oil exploration5

2.1 ResistivityA direct current withstrength I [A] flows througha conductor of a limitedsize.qV(2.1)I lFig. 5: Ohm's lawI:V:q:l: : 1 / :current strength [A]Voltage [V]cross section [m²]lengthresistivity m conductivity6

ResistivityThis can be written alternatively in terms of fieldstrength (E [V/m]) and current density (j [A/m²]). E/ j [ m ]Resistivity is one of the most variable physicalproperties. 8161.6 10 m 10 mnative silverpure sulfur7

Rock types and resistivityIgneous rocks highest resistivitiesSedimentary rocks tend to be the mostconductive due to their high fluid contentMetamorphic rocks have intermediate butoverlapping resistivitiesAge of the rock is also important for the resistivity.For example:Young volcanic rock (Quaternary) 10 200 mOld volcanic rock (Precambrian) 100 2000 m8

Rock types and resistivityMost rock forming minerals are insulators:81610 10 mHowever, measurement in situ:sedimentary rocks: 5 1000 m5100 10 mmetamorphic/crystalline rocks:Reason: Rocks are usually porous and pores are filledwith fluids, mainly water. As the result, rocks areelectrolytic conductors. Electrical current iscarried through a rock mainly by the passage ofions in pore waters. Most rocks conduct electricity by electrolytic9rather than ohmic processes.

Law of Archie2Observation: 1 / where : porosityEmpirical law of Archie m a nS w(2.2) : fractional pore volume (porosity)S : fraction of the pores containing water w: resistivity of watern 20.5 a 2.51.3 m 2.510

Example for the applicationof Archie's lawS 1 a 1.5 m 2 / w 1.5 104for 0.01 / w 150 for 0.14 / w 17 10 for 0.3 / w 6 for 0.511

Schematic current flow insoil sampleFig. 6An increase in the number of ions in soil water(groundwater contamination) linearly decreases thesoil resistivity.12

The approximate resistivityvalues of common rock typesFig. 7²13

Discussion: Resistivity values There is considerable overlap betweendifferent rock types.Identification of a rock type is not possiblesolely on the basis of resistivity data.Resistivity of rocks depends on porosity,saturation, content of clay and resistivity ofpore water (Archie's formula).14

2.2 Current flow in ahomogeneous earthFig. 8: Current flow fora single surface electrode²15

Current flow in ahomogeneous earth A single current electrode on the surface of amedium of uniform resistivity is considered.The voltage drop between any two points onthe surface can be described by the potentialgradient.dV/dr is negative because the potentialdecreases in the direction of current flow.16

Potential decay away fromthe point electrodeFig. 9¹ Current flows radially away from the electrodeso that the current distribution is uniform overhemispherical shells centered on the source.Lines of equal voltage (equipotentials)intersect the lines of equal current at rightangles.17

Potential of a pointelectrodeOhm's law I I V rq2 r2Thus, the potential Vr at distance r isobtained by integration. I IV r V r 22 r2 r(2.3)The circuit is completed by a current sink ata large distance from the electrode.18

2.3 Electrode configurationsand general case2.3.1 General CaseThe general case is considered, where thecurrent sink is a finite distance from the source.Fig. 10¹19

Fig. 11:Principle ofmeasurementand potentialfield for forgeoelectric DCsurveys³20

Potential for the generalcaseThe potential VM at the internal electrode M isthe sum of the potential contributions VA and VBfrom the current source at A and the sink at B.V M V A V BThe potentials at electrode M and N are[[]] I 11V M 2 AM MB I 11V N 2 AN NB .(2.4)(2.5)21

Potential for the generalcasePotential differences are measured I V M N V M V N 2 2 VM N I{[{[][1111 AM MBAN NB][1111 AM MBAN NB]}]}(2.6) 1.(2.7)Definition of the geometric factor{1111k 2 AM MB AN NB VM N k I.} 1(2.8)(2.9)22

Discussion True resistivity of the subsurface if it ishomogeneous.Where the ground is uniform, the resistivityshould be constant and independent of bothelectrode spacing and surface location.When subsurface inhomogeneities exist, theresistivity will vary with the relative positions ofelectrodes.23

Discussion The calculated value is called apparentresistivity a . VM N a kI (2.10)In general, all field data are apparentresistivity. They are interpreted to obtain thetrue resistivities of the layers in the ground.24

2.3.2 ElectrodeconfigurationsThe apparent resistivitydepends on thegeometry of the arrayused (Eq. 2.8 and 2.9).Fig. 12: Main types ofelectrode configurations ³25

Geometry factors fordifferent configurationsDerived geometric factors:. Wennerk 2 a k a[ ]2La 222. Schlumbergerk n n 1 n 2 a. Dipole Dipole26

2.3.4 Modes of deploymentFig. 13 There are two mainmodes of deploymentof electrode arrays.A) Geoelectric mapping:Determination of lateralvariation of resistivity indefined horizons.The current and potentialelectrodes are maintainedat a fixed separation andprogressively moved alonga profile.27

Applications of geoelectricmapping This method is employed in mineralprospecting to locate faults or shear zones orto determine localized bodies of anomalousconductivity.It is used in geotechnical surveys to determinevariations in bedrock depth and the presenceof steep discontinuities.28

Fig. 14: (a) The observed Wenner resistivity profileover a shale filled sink of known geometry inKansas, USA. (b) The theoretical profile for aburied hemisphere.²29

Fig. 15: A constant separation traverseusing a Wennerarray with 10melectrode spacingover a clay filledsolution feature(position arrowed)in limestone.¹30

Fig. 16: Observedapparentresistivity profileacross a resistivelandfill using theWenner array.¹31

Geoelectric SoundingB) Geoelectric sounding: determination of thevertical variation of the resistivity.The current and potential electrodes aremaintained at the same relative spacing andthe whole spread is progressively expandedabout a fixed central point.As the distance between the currentelectrodes is increased, so the depth to whichthe current penetrates is increased.32

Fig. 17: GeoelectricSounding33

Fig. 18: Realization of a geoelectric sounding,development of a sounding curve.434

Multielectrode systems Soundings and mappings are very timeconsuming.Therefore multielectrode systems aredeveloped. Typically 50 electrodes are laidout in two strings of 25 electrodes, withelectrodes connected by a multi core cableto a switching box and resistance meter. Thewhole data acquisition procedure is softwarecontrolled from a laptop computer.35

Fig. 19: Geoelectric mapping using a multi 4electrode device.36

Continuous geoelectricmappingA new and quick mapping system is the pulledarray continuous electrical profiling technique. Fig. 20 437

Continuous geoelectricmapping An array of heavy steel electrodes eachweighing 10–20 kg is towed behind a vehiclecontaining the measuring equipment.Measurement are made continuously. 10–15line kilometers of profiling can be achieved ina day.38

2.4 Interpretation ofgeoelectric dataAim of the interpretation: Determination of the resistivityand thickness of each layer from the observedresistivities.GeologicalInterpretaionFig. 21Vertical electrical soundings can be interpreted by using:a) graphical model curves (master curves) little usedb) computer modeling (inversion calculation)39

Master curvesMaster curves: The mastercurves are prepared ina dimensionless form fora number of reflectioncoefficientsk 2 1 / 2 1 or for 2 / 1 by dividing a / 1and by dividing a /z1 .z1 is the thickness of theupper layer (for twolayer case!).Fig. 22 540

Usage of the master curvesThe field curve to be interpreted is plotted ontransparent logarithmic paper with the samemodulus as the master curve. It is then shiftedover the master curve keeping the coordinateaxes parallel, until a reasonable match isobtained with one of the master curves orwith an interpolated curve.41

Fig. 23: The interpretation of a two layerapparent resistivity graph by comparison with aset of master curve. The upper layer resistivity 1 is68 m and its thickness z1 is 19.5 m. ²42

3 layer case3 layer case: Much larger sets of curves arerequired to represent the increased number ofpossible combinations of resistivities and layerthicknesses. a / 1 f 2, 3, k 1, z1, a Direct curve fitting is time consuming, better useauxiliary point techniques.43

Fig. 24: Example of curve fitting for three layers;experimental points are based upon actualmeasurements in the Arctic using a Schlumberger array.644

Fig. 24 (continued): 2 / 1 0.2, 3 / 1 3 . Number oncurves are values of z2 /z1 . To obtain the fieldparameters the axes (dashed lines) of the theoreticalcurves are extended to intersect the axes (full lines) ofthe field curve. The points of intersection give the fieldvalues of 1 and z1 . 2 and 3 follow from the ratiosgiven for this family of curves. z2 is found from the rationumber given on the best fitting curve. In this case anintepolation has been made between curves for 4 and6. Final results therefore give: 1 13 m , 2 1.6 m , 3 39 mz1 2.2 m , z2 11 m45

Computer modeling a L / 2 a L / 2 istivitiesINPUTOUTPUTINVERSIONstart model 1, h1 2, h2 3final model 1, h1 2, h2 346

Fig. 25: Inversion scheme in geoelectricsounding47

2.4.1 Possible interpretationerrorsa) Equivalent models Resistivities and thicknesses of each layer canbe derived from the apparent resistivity curveclearly.In the field measurement errors occur a a .The apparent resistivity curve can beinterpreted by different resistivity models.The principle of equivalence: The thickness andresistivity can not be derived independently.48

Fig. 2649

Fig. 27: Example ofa geoelectricsounding on agravel deposit.Depending on theassumed apparentresistivity of thetarget the thicknessof the depositvaries. 450

Fig. 28: Due to the principle of equivalencedifferent depth of the groundwater tablecan be derived from the data. 451

Model selection The geophysicist has to select the model, thatagrees best with the known geological andhydrogeological structures of the ground.Another selective criterion is the comparisonwith neighboring soundings.52

b) SupressionThis is particularly a problem when three ormore layers are present and their resistivitiesare ascending or descending with depth.The middle intermediate layer may not beevident on the field curve.53

Fig. 29: Example for supression. 754

c) The effect of anisotropyIn sediments such as clay or shale the resistivityperpendicular to the layering is usually greater thanparallel to the direction of layering.Anisotropy t / lcoefficientAveragedresistivity t lAnisotropy results in toolarge thicknesses beingassigned to layers.h ' hSand, gravelCoal 1.3 2Fig. 3055

d) Non horizontal layering1D interpretation is valid, if the dip of the layersis not greater than 15 .Fig. 3156

e) Interpretation errorscaused by faults Measurements perpendicular to the strikedirection of the fault.The location of the fault can be determined.Fig. 3257

Measurements parallel to the strike directionof the fault.No effect of the fault can be seen on theapparent resistivity curve.Fig. 33 Interpretation error. The curve can beinterpreted as a 2 layer case. However thereis only one layer!58

2.4.2 Methods for thedetermination of lateral variationsof resistivity in the earth Half Schlumberger measurementsFig. 3459