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Evidence for correlation of electrical resistivity and seismic velocity in

heterogeneous near-surface materials

Max A. Meju and Luis A. Gallardo1

Department of Environmental Science, Lancaster University, Lancaster, UK

Adel K. Mohamed2

Department of Geology, University of Leicester, Leicester, UK

Received 4 August 2002; revised 24 October 2002; accepted 26 November 2002; published 4 April 2003.

[1] The electrical resistivity and seismic velocitydistributions over a buried hillside have been obtainedusing non-invasive controlled experiments on coincidentprofiles and 2D image reconstructions. The optimal imagesare in structural agreement and allow the deduction of twoopposite resistivity-velocity trends in the near-surface

materials. For both trends, the resistivity (r) and p-wavevelocity (Vp) are related in the form Log10 r = mLog10Vp + cwith the respective constants m and c having different signs inunconsolidated and consolidated materials. INDE XTERMS: 5102 Physical Properties of Rocks: Acoustic properties;

5109 Physical Properties of Rocks: Magnetic and electrical

properties; 5114 Physical Properties of Rocks: Permeability and

porosity. Citation: Meju, M. A., L. A. Gallardo, and A. K.

Mohamed, Evidence for correlation of electrical resistivity and

seismic velocity in heterogeneous near-surface materials, Geophys.

Res. Lett., 30(7), 1373, doi:10.1029/2002GL016048, 2003.

1. Introduction and Problem Definition

[2] Electrical and seismic relationship in the subsurface[Faust, 1953] is a subject of on-going debate as correlationbetween anomalous electrical conductivities and low veloc-ities are increasingly observed in non-invasive deep crustalstudies [see e.g., Marquis and Hyndman, 1992 and refer-ences therein]. In much of the attempts to reconcile elec-trical and seismic observations in deep wells, the commonthread is that resistivity and velocity are both functions ofporosity [see e.g., Rudman et al., 1975] which is also theunifying assumption in non-invasive experiments currentlyfocusing on correlating deep crustal data of variable qualityfrom approximately coincident regional studies [e.g., Mar-quis and Hyndman, 1992]. There is a need to study

heterogeneous near-surface materials for any such relation-ships especially as this may have implications for improvedstructural [cf. Eberhart-Phillips et al., 1995], petrophysicaland environmental characterizations and for the develop-ment of algorithms for effective joint multidimensionalinterpretation of electrical and seismic field data. If porosityis also the connecting factor in the near-surface, it is logicalto expect that additional insight may be gained fromcollocated studies of exposed fractured crystalline and

porous sedimentary materials. Portable audiofrequency mag-netotelluric (AMT), transient electromagnetic (TEM) and dcresistivity (herein collectively dubbed geoelectromagnetic orGEM) as well as seismic refraction methods can be adaptedto near-surface studies. Also, the available sophisticatedmulti-dimensional inverse modelling schemes for interpret-

ing traditional GEM and seismic field data [e.g., Mackie etal., 1997; Zelt and Barton, 1998] can be appropriately scaledto handle near-surface imaging problems. It is thus opportuneto collect high quality, spatially dense measurements alongthe same survey lines and invert them to determine anyresistivity-velocity relationships at shallow depths.

[3] In this letter, we present the results of coincident GEMand seismic experiments to investigate near-surface resistiv-ity-velocity relations at a selected area in Quorn in England(Figure 1). The Mountsorrel granodiorite (MG) forms thebedrock in Quorn and surrounding areas. This body wasunroofed, deeply weathered and eroded (resulting in a highlyirregular surface) during Permo-Triassic times and was sub-sequently overlain by the Mercian Mudstone (MM) deposits.Heterogeneous glacial drift deposits form a 13 m thicksurficial blanket in the area. MG outcrops in the southernmarginof thestudy site and is believed to descend northwardsunder sedimentary cover. It is heavily fractured at outcrop andpresumably at depth (based on field observations at the largesthardrock quarry in western Europe located ca. 400 m south of

Figure 1. Location map showing the geophysical survey

grid at Quorn in England. The lines run N-S and are 20 mapart.

GEOPHYSICAL RESEARCH LETTERS, VOL. 30, NO. 7, 1373, doi:10.1029/2002GL016048, 2003

1Also at CICESE, Mexico.2Now at Dept. of Geology, Mansoura University, Mansoura, Egypt.

Copyright 2003 by the American Geophysical Union.0094-8276/03/2002GL016048$05.00

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our survey grid). The Quorn site is thus an excellent naturallaboratory for testing the applicability of the hypothesis ofelectrical-seismic relations in heterogeneous porous and frac-tured materials. The questions we seek to answer using a 2D

data imaging approach are: (1) Are there any correlatabletrends in the vertical and lateral distribution of resistivity andvelocity within MG, MM and cover materials? (2) Do thenear-surface resistivity-velocity trends follow those predicted[e.g., Marquis and Hyndman, 1992] for deep crustal systemsand if not, what are the possible causes of the discrepancy?

2. Field Experiments and Model Correlations

2.1. Collocated High-Resolution Profiling

[4] TEM, dc resistivity, seismic refraction and AMTsurveying, in that order, have been conducted at the Quornsite. The site is a relatively flat grazing ground and topo-graphic heights were available from a previous differential

GPS survey using the Magellan 5000 PRO system. The

TEM profiling employed contiguous (20 m-sided) trans-mitter loops along six N-S survey lines (80E to 20W) shownin Figure 1 and served to pinpoint any spatial variability orsignificant fracture-zones in the bedrock and hence the bestlocation for the collocated 2D GEM and seismic experi-ments. Areal maps of the TEM voltage responses forselected time-windows (not presented here) showed spatialvariability with significant differences in amplitude betweennorth and south of position 180S.

[5] Line 20W was chosen for detailed 2D profilingexperiments based on TEM information. Bi-directional

Schlumberger dc soundings were made at selected positions

Figure 2. Example of TEM and bi-directional dc andAMT sounding curves from position 45S on line 20W.Shown are the north-south (xy) and east-west (yx) apparentresistivities.

Figure 3. 2D resistivity model for line 20W. Shown are the optimal model (top plot) and the fit of the model responses(ornamented solid line) to field data (round symbols) at six sounding locations (bottom plot).

Figure 4. Optimal 2D velocity model for line 20W. Themodel is shown in the bottom diagram. The fit to the fieldrecordings for different shot points (differentiated by

symbols) is shown in the top plot.

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(ca. 40 m apart) with N-S and E-W expanding electrodearrays (AB/2 of 1.5 to 90 m). Seismic travel-time data wererecorded along the line using a multi-channel seismographwith a sledgehammer as energy source and a geophonespacing of 2 m. The source was used at both ends of theprofile and at two intermediate points along the line togenerate continuous forward and reverse profiles of poten-

tial refractors. Finally, AMT data were simultaneouslyrecorded in two orthogonal directions in the frequencyrange 10 Hz to 100 KHz using a station spacing (andelectric dipole lengths) of 15 m. Sample dc, TEM andAMT apparent resistivity (ra) data from station 45S on line20W are presented in Figure 2 using a convenient common-scale [Meju, 2002, equations 1 and 2] in which AB/2 (or Lin metres) is converted to the equivalent transient time ( t inmsec) using the relation t = (pm0L

2)/2ra where ra is in mand m0 = 4p 10

7 H/m; t is then converted to anequivalent MT frequency. Notice the agreement betweenthe various ra sounding curves. The AMT data are relativelypoor in quality.

2.2. Model Comparability: Resistivity-VelocityRelations

[6] The inverse problem was to reconstruct the smoothest2D distribution of the relevant physical parameters in thesubsurface that explained the field observations to within apreset (1 rms) error. Only the in-line (N-S) measurements online 20W have been inverted to yield 2D images requiredfor the comparability analysis. The in-line AMT data weretaken as the TM-mode responses, corrected for static shift

using TEM data (cf. Figure 2) [e.g., Sternberg et al., 1988],and the noisy sections smoothed before inversion. Popular,finite-difference based, conjugate gradient inversionschemes [Mackie et al., 1997; Zelt and Barton, 1998] wereadapted to the task of imaging the Quorn AMT apparentresistivity and seismic travel-time data. A different 2Dinversion algorithm [Perez-Flores et al., 2001] was used

for imaging the dc resistivity data.[7] The optimal models from dc resistivity (Figure 3),

seismic refraction (Figure 4) and AMT (Figure 5) imagingshow similar subsurface structural features suggesting thatthere may be a geological basis for correlating these models.The configuration of the boundary between the bedrock andits cover materials can be discerned (approximated by the100 m and 3000 m/s contours) in these models.

[8] The dc and AMT resistivities are in good accord(Figures 3 and 5) and so either model can serve forcorrelation with seismic velocity. An interesting observationis that the resistivity (r in m) and p-wave velocity (Vp inm/s) distributions (sampled at coincident grid positions or

pixels in the 2D models) seem to be related in the form (seeFigures 6a and 6b)

Log10r mLog10VP c 1

where the constants m and c respectively have values of 3.88and 11 for the consolidated rocks (>3m deep) at this site(see trend B in Figure 6a). An inverse relation appears tohold for the unconsolidated soil/drift deposits (i.e., top 3 m)where m = 3.88 and c = 13 (see trend A in Figure 6a). Notethat Rudman et al. [1975, equation 10] interrelated ra andvelocity logs from 7001300 m deep wells (see Figure 6b)using an equation derived assuming raand Vp to be functionsof porosity. If we further assume that the transit time of the

elastic wave in the solid grains is very small compared to thatin the pore fluid, their equation simplifies to Log10 ra =(mLog10Vp mLog10B) where m and B are empiricalconstants. This is identical to our experimentally determinedrelation for the consolidated rocks at Quorn and wouldsuggest that porosity is also a connecting factor for resistivityand velocity in the near-surface.

[9] The Quorn AMT-seismic relation is compared inFigure 6b with the predicted resistivity-velocity trend for

Figure 5. Optimal AMT resistivity model for line 20W.The 13 sounding positions (15m apart) are indicated at thetop.

Figure 6. Relationships between logarithmic resistivity and velocity. Shown are: (a) Dc resistivity and (b) AMT resistivityversus seismic p-wave velocity on line 20W. The depth of sampling (in metres) is shown for selected points (pixels). Note theidentified trends A and B of inverse slope in (a). Trend B was constrained to pass through well estimated points thus giving

less emphasis to contributions (e.g. zone C in (a)) from unresolved deep features in our seismic model. In (b), trends D and Eare taken respectively from Marquis and Hyndman [1992, Figure 4] and Rudman et al. [1975, Figure 7] for comparison.

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a deep well [Rudman et al., 1975, Figure 7] and a lowporosity deep crustal system (aspect ratio of 0.01 andArchies law exponent of 1.2) [Marquis and Hyndman,1992, Figure 4]. Notice that the various curves (representingdifferent crustal depths) show the same basic trend. Furtherwork is required to fully understand the significance ofthese relationships or trends.

[10] Laboratory measurements on cores [Mazac et al.,1988] suggest that resistivity increases with decreasingsaturated permeability in the aerated zone of heterogeneoussoils over weathered granite. It is also known that Vpincreases with degree of grain packing in unconsolidatedmaterials while Vp increases as the natural logarithm ofpermeability in consolidated materials [Marion et al., 1992].It is thus probable that fracture or saturated permeabilitydecreases with depth in MM and MG with a correspondingrise in both resistivity and velocity. In the granular coversediments (top 3m), saturated permeability would appear toincrease (and hence r decreases) with depth. Accordingly,and because of probable air pockets in the shallower vadose

zone, Vp appears to increase with depth in these coversediments causing the observed reversed resistivity-velocitytrend (A in Figure 6a).

3. Conclusion

[11] Two-dimensional imaging of data from GEM andseismic profiling over porous sediments and fracturedgranodiorite at Quorn have yielded concordant images ofthe near-surface. Analysis of the 2D images suggests thepresence of correlatable trends in the near-surface resistivityand velocity distributions at this site and is interpreted aslending support to the hypothesis that porosity or fracture

permeability may be a key factor in understanding electri-cal-seismic relations in both consolidated and unconsoli-dated crustal materials. We suggest that joint 2D imaging ofGEM and seismic profile data may be a useful strategy for

improved resistivity-velocity correlations in near-surfacestudies.

[12] Acknowledgments. The authors are grateful to Doug Groom forproviding the STRATAGEM-EH4 system and Peter Fenning for providingthe TEM field system used in this study. We thank Nasir Ahmed for makingthe seismic refraction data available and Colin Zelt and M. Perez-Flores forpermis sion to use their inversi on codes. We thank two anonymous

reviewers for their very constructive comments.

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M. A. Meju and L. A. Gallardo, Department of Environmental Science,Lancaster University, Lancaster, LA1 4YQ, United Kingdom. ([email protected]; [email protected])

A. K. Mohamed, Department of Geology, Mansoura University,Mansoura, Egypt.

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