estimation of hard rock aquifers hydraulic conductivity from geoelectrical measurements: a...

Journal of Hydrology (2008) 357, 218–227

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Estimation of hard rock aquifers hydraulicconductivity from geoelectrical measurements:A theoretical development with field application

Subash Chandra a,*, Shakeel Ahmed a, Avadh Ram b, Benoit Dewandel c

a Indo-French Center for Groundwater Research, National Geophysical Research Institute, Uppal Road,Hyderabad 500 007, Andhra Pradesh, Indiab Department of Geophysics, Banaras Hindu University, Varanasi 221 005, Indiac BRGM, Water Division, Hard Rock Aquifers Unit, 1039 Rue Pinville, 34000 Montpellier, France

Received 3 November 2006; received in revised form 11 April 2008; accepted 5 May 2008

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KEYWORDSGeoelectricalparameters;Hydraulic conductivity;Transmissivity;Longitudinalconductance;Hard rock

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* Corresponding author. Tel23434651.E-mail addresses: schand

s.in (S. Chandra).

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Summary Based on the analogy between Darcy’s law for groundwater flow and Ohm’slaw for electric current flow, a methodology has been developed to estimate the hydraulicconductivity and transmissivity of hard rock granite aquifer from geoelectrical parame-ters. The common parameter, aquifer thickness (t), has been used to combine the tworelations and form an analytical equation. Mathematical relation shows a negative corre-lation between hydraulic conductivity and aquifer resistivity, and a positive correlationbetween transmissivity and longitudinal conductance. The methodology has been cali-brated and validated in hard rock granite aquifers in India. The good agreement betweenaquifer hydraulic conductivity (K) and transmissivity (T) obtained from the resistivitysounding parameters and those obtained from pumping test analysis proves the potential-ity of the methodology. It has been applied to estimate the K and T from the surface elec-trical resistivity parameters and results were utilized to prepare the K and T maps ofMaheshwaram watershed in hard rock terrain in India.ª 2008 Elsevier B.V. All rights reserved.

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Introduction

The hydrogeological parameters, viz. hydraulic conductiv-ity, transmissivity, recharge, etc. are estimated by classicalhydrogeological techniques like pumping tests, tracerstudies, etc. which are sometimes destructive (e.g.borewell drilling). Geophysical techniques, viz. electrical,

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Estimation of hard rock aquifers hydraulic conductivity from geoelectrical measurements 219

electromagnetic, magnetic and seismic have been exten-sively used for groundwater studies especially in investigat-ing aquifer geometry, electrical conductivity of thesubsurface, mapping of the intrusive bodies, depth to base-ment, etc. The surface geophysical techniques are compar-atively simpler, cost effective and fast. Since 1951correlative studies between different geophysical proper-ties and hydrogeological parameters, e.g. electrical resis-tivity and hydraulic conductivity has taken initiation(Jones and Buford, 1951). Later several studies have beendiscussed on various aspects of correlation between hydro-geological and geophysical parameters (Pfannkuch, 1969;Kelley, 1977; Huntley, 1986; Mbonu et al., 1991; Frohlichet al., 1996; Singhal et al., 1998; Sri Niwas and Lima,2003; Chand et al., 2004; Singh, 2005, Chandra, 2006, etc.).

Kelley (1977) demonstrated a positive correlation be-tween aquifer resistivity obtained from geoelectrical mea-surements and hydraulic conductivity obtained frompumping tests in glacial outwash materials in southernRhode Island. Similarly he also found positive correlationbetween formation factor (i.e. the ratio between resistivityof the aquifer and resistivity of water) and the hydraulicconductivity. However, Heigold et al., 1979) showed a neg-ative relationship (K = 386.4q�0.93283) between hydraulicconductivity (K) and aquifer resistivity (q) in Niantic-Illiopo-lis aquifer, a Wisconsinan outwash deposit by melt waterfrom glacier in Central Illinois. Kelly and Frohlich (1985) re-jected the negative relationship established by Heigoldet al. (1979), with the reason that for correlation, onlythree data points were used that is not sufficient to gener-alize any relationship and showed again a positive correla-tion between them. They also warned that directcorrelation should not be expected in the clay free aquifermaterials. Similarly positive correlation between apparentformation factor from surface resistivity soundings andhydraulic conductivity from pumping tests in fresh watergranular aquifer was observed by Urish (1981).

Sri Niwas and Singhal (1981) estimated the aquifer trans-missivity from the Dar Zarrouk parameters in porous mediataking two fundamental laws: the Darcy’s law of fluid flowand the Ohm’s law of current flow. Analytical relationshipswere established between transverse resistance ‘R’ andtransmissivity ‘T’ (Eq. (1)) as well as longitudinal conduc-tance ‘C’ and transmissivity ‘T’ (Eq. (2))

T ¼ KrR ð1Þ

and

T ¼ K

rC ð2Þ

where ‘R’ is transverse resistance and ‘C’ longitudinal con-ductance and ‘r‘ electrical conductivity. It was also addedthat only one relation hold valid and can be applied for‘T’ estimation in a particular area depending upon the factthat whether product Kr remains constant or the ratio K/r.If Kr remains constant, Eq. (1) is applied otherwise Eq. (2).

Yadav (1995) studied the field data from north-easternpart of Singrauli Coal field in India. The area consists of Bar-akar sandstone with coarse grained, moderately to highlyweathered and poorly consolidated down to a depth of65 m covered by 3–10 m thick alluvial deposit. Normalizedaquifer resistivity has been found very well correlating pos-

itively with transmissivity. Yadav and Abolfazli (1998) alsoobserved similar positive relationships between normalizedaquifer resistivity and hydraulic conductivity, and normal-ized transverse resistance and aquifer transmissivity inweathered granite overlaid by sand dunes at Jalore, north-western India.

Ahmed et al. (1988) reviewed various relationships be-tween hydraulic and electrical parameters. However, theymade correlation between transverse resistance ‘R’ andtransmissivity ‘T’ using geo-statistical approach in estimat-ing the spatial variability of T. The advantage of the geo-statistical approach is that the estimation is based on themeasured values as well as their joint variability, and doesnot require the calculation of regression, and it also pro-vides the estimates of the required parameter at the points,where none of the parameters are known.

The previous studies were dealing with correlation ofgeophysical and hydraulic parameters mostly in alluvial/porous formation. The purpose of this paper is to establishrelationship between electrical properties and hydraulicparameters in hard rock aquifer. The Darcy’s law and Ohm’slaw have been applied over a theoretical cube of an aquiferand a mathematical relationship between hydraulic andgeoelectrical parameters has been formulated. The devel-oped formula has been calibrated, validated and appliedat hard rock granite aquifers in India (Fig. 1).

Hard rock granite aquifer

Hard rock granite aquifers generally occupy the first fewtens meters below the surface profile (Detay et al., 1989)and are usually assumed to consist of composite aquiferconstituted stratified layers (Molz et al., 1989; Dewandelet al., 2006) issued from the deep weathering of themother rock (Lachassagne et al., 2001). From top to bot-tom (i) saprolite derived from prolonged in situ decomposi-tion of bed rock with a thickness varying from negligiblewhere eroded to few tens of meter, (ii) fissured layer,and then (iii) unfissured bedrock, that may locally exhibittectonic fracturing. The fissured layer is generally charac-terized by two sets of sub-horizontal and sub-vertical fis-sures, where density decreases with depth (Houston andLewis, 1988; Howard et al., 1992; Dewandel et al., 2006)and assume the transmissive function of the compositeaquifer. As the density in fissuring rapidly decreases withdepth, the degree of interconnectivity of the fissures alsodecreases. Thus, when water level stays at shallow level,the aerial extent of the aquifer is found quite large, butwhen it recedes down lateral inhomogeneities divide theaquifer into small–small aquifer zones like compartments(Ahmed et al., 1995; Engerrand, 2002). Thus the hydrogeo-logical properties also can be quite variable in the horizon-tal plane.

Theoretical development

The flow rate of groundwater and electrical current mainlydepend on the hydraulic and electrical conductivities of theformation, respectively. The hydraulic and electric conduc-tivities of an aquifer depend on several factors; such aspore-size distribution, grain size distribution, void ratio,

Figure 1 Location map of study area.

220 S. Chandra et al.

roughness of mineral particles, fluid salinity or mineraliza-tion, degree of weathering, fissure density and interconnec-tivity, and water saturation, etc. But in case of hard rocksuch as in granite, the rock porosity saturated with wateris the dominant factor among all affecting the hydraulicand electrical conductivities. The current flow in the sub-surface is basically formed by two phenomena: electronicand electrolytic conductions (Keller and Frischknecht,1966). Electronic conduction (i.e. the current flow throughthe free electrons present in the minerals consisting therock) in the granite is insignificant due to high resistivityof the minerals and as a result the water in the fissures isthe main factor controlling the current flow (i.e. electro-lytic conduction). Thus the electrolytic conduction is thedominant phenomenon. Since ions flow through some ofthe same paths as water, the electrical resistivity andhydraulic conductivity of aquifer are expected to be af-fected by similar variables. Fluid (i.e. groundwater) andelectric currents flow from higher potential to lower poten-tial sites and their flow rates depend upon hydraulic andelectric potential gradients, respectively. The potential gra-dients occurrence could be natural as well as imposed whilecarrying out tests, for example hydraulic potential gradientis imposed while carrying out a pumping test and similarlyelectric potential gradient is imposed while carrying out ageoelectrical investigation. If the hydraulic potential gradi-ent exists (naturally), groundwater moves its own towards

low potential site. The movement of groundwater generatesself-potential current (electrokinetic or streaming poten-tial; Lowrie, 1997). While doing the pumping test groundwa-ter flows more or less horizontally towards the pumping wellfrom the surrounding region (Marechal et al., 2004). Simi-larly, the current flows more or less horizontally in the aqui-fer from source towards sink current electrodes whileperforming the vertical electrical sounding using Schlum-berger configuration. This is quite applicable in the caseof hard rock, where aquifer horizon is at quite deeper leveland requires enough inter-current electrode spacing (forSchlumberger configuration) to investigate it. Moreoverthe top layer is often dried saprolite having high resistivityand bottom layer is unfissured basement characterized byhigh resistivity too. Thus current flow lines in the aquifer(i.e. fissured layer saturated with water) get channelizedand flow horizontally. Thus, groundwater and current flowstake place in the same media (i.e. aquifer) and in the samedirection. This shows analogy between the two physicalproperties.

Either in the cases of Darcy’s law for groundwater flow orOhm’s law for current flow, processes are controlled by acommon factor, i.e. aquifer porosity saturated with water.Conceptually electrical resistivity method deals with theconservation of charge, i.e. Ohm’s law likewise hydrody-namics deals with the conservation of mass, i.e. Darcy’slaw.


Let us consider a cube of length ‘t’ where under steadystate condition water inflow and outflow rates are Q.According to the Darcy’s law, the specific discharge ‘q’is proportional to the hydraulic gradient developedbetween the opposite faces ABCD and MNOP, which canbe written as

A

B

C

D

M

P

t Q Q t

t

O

N

M t

q ¼ �K dh

tð3Þ

where Q, q, K, t, and dh are, respectively, inflow/outflowrate of water (m3/s), specific discharge in m/s (q = Q/t2),hydraulic conductivity (m/s), thickness (m) of medium anddifference of hydraulic heads between the opposite facesof the cube (m). The fluid flow takes place in the presenceof a hydraulic gradient.

Flow of water between opposite faces (i.e. ABCD andMNOP) of the cube means movement of ions present inthe water or in other words there is flow of electric current.According to the Ohm’s law, current flow in a medium isproportional to the potential gradient between two points.Mathematical expression can be written as

J ¼ �rdv

tð4Þ

where J, r, dv and t are, respectively, current density (A/m2), electrical conductivity (Siemens/m), potential differ-ence (volts) and thickness of medium (m).

Although these two fundamental laws (3) and (4) are dif-ferent but have analogy and are applied on a cube (seeAppendix A). The resistance–capacitance (R–C) analogmodel has been in practice for a long time, where ground-water system is simulated using the analogy betweenhydraulic parameters of groundwater flow and geoelectricalparameters of current flow (Rushton and Redshaw, 1979;Tod, 1980; Kresnic, 2007). To represent the aquifer proper-ties, the electrical model uses the assemblage network ofdiscrete electrical elements such as resistance–capaci-tance, resistance, etc. Therefore, Eqs. (3) and (4) can becombined together using common aquifer thickness param-eter as also dealt by Sri Niwas and Singhal (1981)

K ¼ q

dh

� � dv

J

� �r ð5Þ

where qdh

� �and dv

J

� �are nothing but ratios. The dependency

exists between q and dh and also between J and dv. Thustheir respective ratios remain constant and hence it canbe written as Aq and Aj. Now Eq. (5) can be written as

K ¼ AqAjr ð6Þ

The constant Aq (i.e. Aq = q/dh), characterizes the flow ofwater and hence it is dependent on the hydraulic conductiv-

ity of the formation/material, whereas, Aj (i.e. Aj = dv/J)characterizes the flow of current in the medium. Sincethere is electrolytic current conduction (dealing with theion, i.e. charge carrier) present in the subsurface fluid, Aj

could be considered to be dependent on the salinity of thewater. Consider a steady state horizontal flow in a homoge-neous medium, where groundwater quality remains fairlyconstant, the product of Aq and Aj will also be constant.Hence in Eq. (6) AqAj product can be replaced with constant‘A’

K ¼ Ar or K ¼ A1

qð7Þ

The above relation indicates that the hydraulic conductivity(K) is inversely proportional to the aquifer resistivity (q).This relation appears to be logical because of the fact thatlow resistive formation is an indication of highly fissured orporous water saturated material. In such conditions thehydraulic conductivity of the material is expected to behigh. Eq. (7) can be transformed by multiplying a factor‘t’ (i.e. aquifer thickness) on both sides. It leads

Kt ¼ At

qð8Þ

or

T ¼ AC ð9Þ

where T and C are transmissivity (m2/s) and longitudinalconductance (mho) of the aquifer respectively. These boththe properties carry the effect of the aquifer thickness.Although it is assumed here that the fissures are well con-nected, this may not always occur in reality. Robinson(1984), Charlaix (1985), Wilke et al. (1985), de Marsily(1985), and Sung-Hoon et al. (2004) studied the connectivityin fractured rock using the percolation theory. As the den-sity of fracture (i.e. number of fracture per unit volumeof fractured rock) reduces, the chance of intersection tothe neighbouring fractures reduces (Bear et al., 1993) andsame is true as the fracture area reduces. In hard rock, fis-sure density decreases with depth (Houston and Lewis,1988; Howard et al., 1992; Dewandel et al., 2006). Thusthe connectivity of fracture is function of depth as well assize of the domain. Since the proposed theory deals withthe flow of water and current, the developed relation(Eqs. ( 7) and (9)) will hold valid in the zone above the per-colation threshold i.e. the density of fracture above whichconnectivity of the fracture is sufficient to enable flowthrough network. However, Marechal et al. (2004) demon-strated that in hard rock aquifers the fissures network iswell connected and that sub-vertical fissures network en-sures the connection of sub-horizontal one, making thus avery good connectivity in all its aquifer thickness. In addi-tion to this, the methodology adopted for the estimationof the hydraulic conductivity and geoelectrical parametersshould be chosen in such a way that the estimated valuesare representative of sufficiently large volume ensuringthe good interconnectivity of the fractures. Or in otherword, hydraulic conductivity and aquifer resistivity mustbe estimated from long duration pumping test and from sur-face resistivity method, respectively, allowing an investi-gated area large enough to ensure that the interconnectedfractures are taken into account.

Table 1 Hydraulic conductivity and transmissivity from pumping test and estimated from surface resistivity measurementparameters from granite terrain at Hyderabad

S. No. Parameters from pumpingtest

Aquiferthickness ‘t’ (m)

EC of GWR(mho/m)

Parameters fromgeoelectricalmeasurement

Estimatedparametersusing Eqs. (7) and (9)

Hydraulicconductivity(Kp) in m/s

Transmissivity(Tp) in m2/s

Normalizedaquiferconductivity(mho/m)

Normalizedlongitudinalcondutance(mho)

Hydraulicconductivity(Kr) in m/s

Transmissivity(Tp) in m2/s

1 9.1E�07 1.9E�05 20.8 0.182 4.6E�03 9.5E�02 1.0E�05 2.1E�042 2.1E�06 2.7E�04 41.6 0.105 2.5E�03 1.0E�01 5.4E�06 2.3E�043 2.9E�06 9.3E�05 32.0 0.105 2.0E�03 6.4E�02 4.4E�06 1.4E�044 3.2E�06 1.6E�04 50.0 0.182 5.1E�03 2.5E�01 1.1E�05 5.6E�045 5.4E�06 2.1E�04 39.0 0.004 5.0E�03 2.0E�01 1.1E�05 4.2E�046 6.7E�06 1.7E�04 25.0 0.100 6.7E�03 1.7E�01 1.5E�05 3.6E�047 1.7E�05 6.2E�04 36.0 0.004 5.4E�03 2.0E�01 1.2E�05 4.2E�048 2.9E�05 2.0E�04 7.0 0.143 7.1E�03 5.0E�02 1.6E�05 1.1E�049 3.3E�05 6.7E�04 20.2 0.090 1.4E�02 2.8E�01 3.1E�05 6.2E�0410 4.6E�05 6.5E�04 14.1 0.095 1.7E�02 2.4E�01 3.6E�05 5.1E�0411 9.5E�05 1.8E�03 19.2 0.073 1.6E�02 3.1E�01 3.5E�05 6.6E�04


Correlation studies from the field data

The above theory has been applied to examine with the fielddata collected from hard rock (granite) terrain from Hyder-abad and its surroundings (Table 1). Vertical electricalsoundings were carried out using Schlumberger configura-tion with up to 200 m current electrode spacing. Data wereprocessed and interpreted for obtaining aquifer parameterslike aquifer resistivity, aquifer thickness, longitudinal con-ductance, transverse resistance, etc. Long duration (i.e.18–30 h) pumping tests were carried out in the tube wellslying in vicinity of VES points to get the hydraulic conductiv-ity and transmissivity of aquifer (Marechal et al., 2004). Aslong duration pumping tests and VES with considerable elec-trode spacing yield regional aquifer parameters, pumpingtests and VES results were taken for correlation studies.Since electrical conductivity of groundwater varies from695 to 2190 lS/cm due to agriculture and pollution from vil-lage in the area (Marechal et al., 2006), aquifer resistivitywas normalized, which is known as normalized resistivityqn (i.e. qn = qxqw/qw, where qw is average aquifer waterresistivity (i.e. 10 X m), q is bulk resistivity).

The field data belongs to granite aquifer. The thicknessbetween water level and depth to basement (investigatedfrom litholog and from VES studies) has been taken asthe aquifer thickness (t). It has been utilized to estimatenormalized longitudinal conductance ‘C’ (i.e. C = t/q). Nor-malized aquifer conductivity (mho/m) and hydraulic con-ductivity (m/s) of the corresponding location (11 datapoints) have been correlated (Fig. 2a). The correlationcoefficient (R2) obtained between these two parametersis 0.85. The correlation coefficient has been calculatedfor 11 data points falling in the granite. Normalized longi-tudinal conductance and transmissivity have been corre-lated on the same data points (Fig. 2b). The correlationcoefficient obtained between these two parameters is0.68.

Thus the correlation studies on the field data are in goodaccordance with the above discussed theory of correlationbetween hydraulic parameters and geophysical propertiesin hard rock terrain. Now, the Eqs. (7) and (9) can hereafterbe applied for estimation of hydraulic parameters, i.e.hydraulic conductivity and transmissivity from aquifer resis-tivity and longitudinal conductance.

Testing the methodology

Hydraulic conductivity estimation

A study has also been performed on the 11 data points dis-cussed above to compare the observed and computedhydraulic conductivity data. Value of constant factor ‘A’has been calculated first using relation ‘A = Kq’ at eachpoints for known values of hydraulic conductivity (Kp).Afterward average value of ‘A’ (i.e. 2.176E�03 in this area)has been used in Eq. (7) to estimate hydraulic conductivity(Kr) from normalized resistivity at 11 points (Table 1). Thehydraulic conductivity ‘Kr’ estimated from the surface resis-tivity was compared with the hydraulic conductivity ‘Kp’estimated from the pumping tests (Fig. 3a). A strong corre-lation (R2 = 0.85) was achieved, which is very encouraging.

The published data by Singh (2005) belongs to OsmaniaUniversity Campus (OUC), Hyderabad a hard rock graniteaquifer of Archean age. The data have been utilized to testthe methodology excluding two data points that representthe lowermost part of fissured zone (layer resistivity is morethan 3000 X m). Similar to previous case the value of ‘A’ hasbeen calculated with the known hydraulic conductivity (Kp)at 4 points and afterward average value of ‘A’ has been usedin Eq. (7) to calculate hydraulic conductivity (Kr) from aqui-fer resistivity. The correlation attempted between Kp and Kron the data obtained from the granite terrain of OUC,Hyderabad has shown correlation coefficient �0.18(Fig. 3b). Although, the number of values for comparison

Figure 2 Relationship of (a) normalized aquifer resistivity with hydraulic conductivity and (b) normalized longitudinalconductance with transmissivity.


is very less, however, an additional case to compare may beuseful. Out of 4 points, one point provides exceptionallylarge difference and hence the pair was omitted as obvi-ously either the experiment for Kp was not proper or thelocations of the two values may be considerably differentbringing out induced variability. After removing the ambig-uous data, correlation coefficient became 0.79. Thus astrong relationship exists between aquifer resistivity andhydraulic conductivity. The aquifer resistivity obtained fromthe surface resistivity methods can be used to estimate thehydraulic conductivity of the aquifer.

Transmissivity estimation

Exercise has also been made for the estimation of transmis-sivity from the surface resistivity data using Eq. (9). Though,the previous researchers have attempted correlating trans-missivity with aquifer resistivity, but does not look to belogical as it is mathematically shown in Eq. (9). Transmissiv-ity always carries the weight of aquifer thickness, whereasaquifer resistivity does not. Longitudinal conductance isthe parameter that includes aquifer thickness. Thereforeit’s always better to refer Eq. (9) for estimation of transmis-sivity from surface resistivity methods. The developedmethodology has been examined with the field data gener-ated at hard rock granite aquifer, Hyderabad. The average

value of constant ‘A’ (i.e. 2.176E�03 obtained from theknown value of Kp and q at 11 points) has been used in Eq.(9) to estimate transmissivity (Tr) from longitudinal conduc-tance (C). The transmissivity estimated by the pumping test(Tp) and the transmissivity estimated from the longitudinalconductance ‘Tr’ (Fig. 3c) have shown strong correlation(R2 = 0.68). Since the published data (such as OUC, Hydera-bad) do not have aquifer thickness parameter, transmissiv-ity could not be calculated.

Thus, the proposed methodologies are satisfactorilyapplicable in hard rock granite aquifer. The value of con-stant ‘A’ varies with formation and place because of changein the mineralogical composition, texture, weathering/frac-turing pattern and water association, etc. The constant ‘A’is needed to be obtained from the known values of hydraulicand geoelectric parameters at few points in any geologicalsettings and then average value of it can be utilized to cal-culate the hydraulic parameters from surface geophysicalmethods in the representative area.

Care should be taken in order to consider resistivity ofhard rock aquifer. For example, resistivity higher than acritical value (say �1500 X m in granite rock at Hyderabad)represents lower most part of the fissured zone, wherechances of fracture connectivity are less. In such casesthe proposed method may not be valid. In addition to this,the proposed methodologies are valid in the region, where

Figure 3 Comparative plots for (a) hydraulic conductivities (Kp & Kr)) of hard rock granite aquifer at Hyderabad, India, (b)hydraulic conductivities (Kp & Kr)) of granite aquifer at OUC, Hyderabad, India, and (c) transmissivity Tp & Tr at hard rock graniteaquifer at Hyderabad, India.


the clayey upper part of the aquifer is eroded and/or is notsaturated with water known from the adequate knowledgeof hydrogeology of the area (this is the case in the Hydera-bad region).

Application of the methodology

The developed methodologies have been applied at Mah-eshwaram watershed, which is bounded within latitudes17�06 0N and 17�11 0N and longitudes 78�24 0E and 78�29 0E.The geological setting of the watershed is comprised ofcrystalline rocks, i.e. leucocratic granites and biotite gran-ites of Archean age. The proposed method has been appliedover 69 VES points (carried out at watershed in 2000) to esti-mate the hydraulic conductivity (Kr). Although it is called assounding that gives lithological information vertically at thecentre of configuration, but electrical lines sound a volu-metric medium while injecting the current into the subsur-

face. Therefore, electrical parameter can be taken as aerialrepresentative in case of 1D sounding. The average value of‘A’ (i.e. A = 2.176E�03 obtained at Hyderabad) has beenused in Eq. (9) to calculate hydraulic conductivity (Kr) fromVES points in this watershed, which have been finally uti-lized to prepare hydraulic conductivity map of the area(Fig. 4a).

Since water quality varies significantly in the watershed,normalized aquifer resistivity has been calculated and con-verted into hydraulic conductivity map (Fig. 4b) using Eq.(7). Electrical conductivity (EC) of groundwater measuredin various wells, having good coverage in the entire wa-tershed, has been utilized to calculate the normalized resis-tivity as discussed above. This map (Fig. 4b) is more logicalcompared to the previous one. Some noticeable changescould be seen between these two maps. Few small patchesof high permeable zones have been disappeared and alsothe contour patterns have changed after the normalization.

0 km 1.1 km 2.2 km

78.41 78.42 78.43 78.44 78.45 78.46 78.47 78.4817.1

17.11

17.12

17.13

17.14

17.15

17.16

17.17

17.18

17.19

201

202

203

204

205

206

207

208

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211

212213

214

215

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222223

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229230

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235236

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248249

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259260

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262263

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270271

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279 280281

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288

Normalized Transmissivity Map

Maheshwaram Watershed

-6-5.9-5.8-5.7-5.6-5.5-5.4-5.3-5.2-5.1-5-4.9-4.8-4.7-4.6-4.5-4.4-4.3-4.2-4.1-4-3.9-3.8-3.7-3.6-3.5-3.4-3.3

+ VES

Log of Tr (m2/s)

Hydraulic Coonductivity (Kr) Map


78.4 78.41 78.42 78.43 78.44 78.45 78.46 78.47 78.4817.1

17.11

17.12

17.13

17.14

17.15

17.16

17.17

17.18

17.19

0 km 1.1 km 2.2 km

-5.65

-5.55

-5.45

-5.35

-5.25

-5.15

-5.05

-4.95

-4.85

-4.75

-4.65

-4.55

-4.45

-4.35

-4.25

Log of Kr (m/s)

Normalized Hydraulic Coonductivity (nKr) Map


0 km 1.1 km 2.2 km

78.4 78.41 78.42 78.43 78.44 78.45 78.46 78.47 78.4817.1

17.11

17.12

17.13

17.14

17.15

17.16

17.17

17.18

17.19

-5.7

-5.6

-5.5

-5.4

-5.3

-5.2

-5.1

-5

-4.9

-4.8

-4.7

-4.6

-4.5

-4.4

-4.3

-4.2

-4.1

Log of nKr (m/s)

-1.2

-1

-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

78.41 78.42 78.43 78.44 78.45 78.46 78.47 78.48

17.11

17.12

17.13

17.14

17.15

17.16

17.17

17.18

17.19

Wells

Log of P (m2/s)

Productivity Map MapMaheshwaram Watershed

a b

dc

e

Figure 4 (a) Hydraulic conductivity (Kr) map, (b) normalized hydraulic conductivity (nKr) map, (c) normalized transmissivity (nTr)map, (d) productivity maps of Maheshwaram watershed and (e) comparative plot for transmissivity (Tr) and productivity values atMaheshwaram watershed, Andhra Pradesh, India.


The derived formula (Eq. (9)) has been utilized to esti-mate the transmissivity (Tr) using the average value of A(i.e. A = 2.176E�03). Saturated thickness was known at 24

bore wells near the VES points. Saturated thicknesses werethus generated at remaining 45 points using range of varia-tion of the known values. Transmissivity (Tr) has then been


estimated at 69 VES points using Eq. (9) and transmissivitymap is prepared (Fig. 4c). This map is compared with thewater productivity map (Fig. 4d) of the watershed preparedby Dewandel (2003) that represents yield of the well dividedby its aquifer thickness having similar unit, m2/s as trans-missivity. Both the maps show almost similar highs and lowsat the corresponding places.

Point to point correlation has been attempted betweentransmissivity (Fig. 4c) and productivity map (Fig. 4d). Cor-responding productivity values for VES points have been ob-tained and correlated with transmissivity (Tr). A positivecorrelation (R2 = 0.62) has been obtained (Fig. 4e). Thus,it further validates the transmissivity map as well the meth-odology. The dissimilarity between these two maps mayprobably be due to reasons such as: (i) number and locationof observation points are different and (ii) as the year ofobservation for transmissivity map (prepared based on VESresults of the year 2000) and productivity map (preparedfor the year 2003) differs, over-exploitation of groundwaterresources changes the groundwater scenario with time. Theshallow aquifer active during the previous years may go dryas a consequence of over-exploitation.

In the virgin area, recommendation of the sites for dril-ling, basement depth essentially should also be taken intoconsideration. The deeper basement and high permeablezone qualifies the place for high yielding sustainable well,where the aquifer is saturated with water. This methodol-ogy will be very useful for groundwater modeling for flowas well as contaminant migration. Since the accuracy ofthe groundwater model depends on the accuracy of data in-put as well as data density, an optimally dense data is re-quired to represent the varying nature of hard rockhydrogeological parameters.

Conclusion

The above studies have shown a useful relationship betweenhydraulic parameters and geoelectrical properties in hardrock granite aquifers. A mathematical formulation has beendeveloped between hydraulic conductivity and aquifer resis-tivity, and between transmissivity and longitudinal conduc-tance. The developed methodologies have been validatedwith field data from hard rock granite aquifer at Hyderabad(India) followed by its testing with field data. Based on thedeveloped formula, hydraulic conductivity and transmissiv-ity have been calculated and mapped in granite aquifer. Po-sitive correlation between hydraulic conductivity (K) andaquifer conductivity (r), and also between transmissivity(T) and longitudinal conductance (C) in hard rock graniteaquifer have been achieved.

Estimated hydraulic conductivity and transmissivity frompumping tests (11) and geoelectrical measurements arefound very close to each other with a strong correlation fac-tor (R2 > 0.80) at hard rock granite aquifer at Hyderabad, In-dia. The methodologies have also been used for preparingthe K&T map of Maheshwaram watershed in granite aquiferfollowed by its validation.

The advantage of the methodology includes simplicity,cost effectiveness as well as fast, and hence dense K&T val-ues can be generated in an area to feed as input to thegroundwater model. The value of constant ‘A’ changes with

formation and need to be derived in the field from theknown values and afterward applied to estimate hydraulicproperties from surface resistivity using the developed rela-tionship in a close interval. As a result K&T maps can begenerated and allow to analyze the variations in suchparameters with hydrodynamic characteristics of the aqui-fer (e.g. K, T and aquifer geometry), in addition such resultscan be used in aquifer modeling, for bore well sitting, etc.In alluvium, the developed methodologies may not be muchuseful because of the presence of clay.

Acknowledgements

We are thankful to Dr. V.P. Dimri, Director, NGRI, Hydera-bad for according permission to publish this paper. We thankto Sri N.S. Krishnamurthy, Dr. V. Anand Rao, Dr. K. Subraha-mayam, Dr. Dewashish Kumar, and other members of IFCGRfor their cooperation and valuable suggestions. We alsothank the editor, reviewers especially Dr. P. Lachassagnefor the critical review and valuable suggestions that haveimproved the quality of the paper.

Appendix A. Water and electric current flow ina homogeneous earth

The Darcy’s law of water flow and Ohm’s law of current flowcan be written as

q ¼ �Krh ðiÞJ ¼ �rrv ðiiÞFor isotropic medium r and K are scalar functions. Forhomogeneous medium the divergence of specific dischargesand current density becomes zero, which can be written as

r:q ¼ 0 ðiiiÞr � J ¼ 0 ðivÞ

Now the Eqs. (i) and (ii) can be written as

$ � q ¼ �$K � $h� K$2h ¼ 0 ðvÞ$ � J ¼ �$r � $v� r$2v ¼ 0 ðviÞ

These are fundamental equations of, respectively, ground-water flow and electrical prospecting with direct current.If medium is homogeneous then the above equation become

$2h ¼ 0 ðviiÞ$2v ¼ 0 ðviiiÞ

These are Laplace’s equation and have clear analogy be-tween Darcy’s law of groundwater flow and Ohm’s law ofelectric current flow.

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