Journal of Applied Geophysics 70 (2010) 93–102

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Journal of Applied Geophysics

j ourna l homepage: www.e lsev ie r.com/ locate / jappgeo

Lithological classification assisted by the joint inversion of electrical and seismic dataat a control site in northeast Mexico

Victor Infante a, Luis A. Gallardo b, Juan C. Montalvo-Arrieta a,⁎, Ignacio Navarro de León a

a Facultad de Ciencias de la Tierra, UANL, Mexicob School of Earth and Environment, The University of Western Australia, Australia

⁎ Corresponding author. Fax: +52 8212142020.E-mail address: montalvo@fct.uanl.mx (J.C. Montalv

0926-9851/$ – see front matter © 2009 Elsevier B.V. Aldoi:10.1016/j.jappgeo.2009.11.003

a b s t r a c t

a r t i c l e i n f o

Article history:Received 8 December 2008Accepted 6 November 2009

Keywords:Geospectral imagingGeophysical signaturesJoint inversionSeismic refraction tomographyElectrical tomographyNortheast Mexico

In this paper, evidence is presented that the combination of geospectral images and geophysical signatures(resistivity–velocity cross-plots) is a good tool to provide a natural visualization of the distribution and variationsof lithological features in a test site. This was confirmed by the correlation between the electrical resistivity andseismic velocity values obtained after cross-gradient joint inversion at two profiles and geotechnical informationprovided by shallow boreholes in a site located in the Earth Sciences School grounds in Linares, NortheasternMexico. The results obtained from this study show how the cross-gradient joint inversion facilitates the analysisof hydrological estimates and assists in lithological classification of subsurface materials.

o-Arrieta).

l rights reserved.

© 2009 Elsevier B.V. All rights reserved.

1. Introduction

The studies of the distribution of valuable subsurface resources andgroundwater processes commonly adopt two main strategies: i) toaccess limited regions of the subsurface aquifers by bench topmeasurements and borehole loggings, which might provide highdensity information and ii) to cover larger extensions by measuringphysical properties through geophysical fields on surface, cross-holeand airborne devices (Hubbard and Rubin, 2005). Both methodologiesare commonly used for lithology and aquifer characterization. However,while boreholes provide very precise information of the wells' vicinity(e.g. Walker et al., 2004), they require an appropriate and abundantsurface distribution to integrally describe an aquifer or rock formation.On the other hand, geophysical data covers larger extensions and mayrender a more integral description of the fluid and solid phases ofsubsurfacematerials. Unfortunately, they offer only physical values suchas electrical resistivity or permittivity. These individual values can rarelybe translated to hydraulic or petrophysical parameters directly (e.g.Huntley, 1986; Lesmes and Friedman, 2005; Purvance, 2003). From adifferent perspective, recent works have shown the high potential ofintegrating objectively geophysical and hydrologicalmeasurements as auseful strategy for an integral and detailed aquifer characterization(Bowling et al., 2006, 2007; Evett and Parkin, 2005; Guerin, 2005;Jorgensen et al., 2005; Linde et al., 2006;Metwaly et al., 2006; Rubin andHubbard, 2005; Strahser et al., 2007; Tronicke and Holliger, 2005;Vereecken et al., 2004; Vouillamoz et al., 2007).

The joint inversion of several types of geophysical and hydrologicaldata is emerging as a powerful tool for quantitative data integration(Chen et al., 2006; Day-Lewis et al., 2006; Gallardo and Meju, 2003,2004; Kowalsky et al., 2006; Linde et al., 2006; Paasche and Tronicke,2007; Tryggvason and Linde, 2006). Underlying the joint inversionstrategies is the assumption that the sought parameters areinfluenced by common subsurface physical and/or hydrologicalproperty fields. However, the lack of first hand evidence at controlledfield sites has hindered our understanding of the multiparametercorrelations that may result from such attributes (Bedrosian, 2007;Gallardo and Meju, 2003, 2004, 2007; Linde et al., 2006; Tryggvasonand Linde, 2006). Among the useful attributes that can be used forjoint inversion is the geological structure. Gallardo and Meju (2003,2004) quantified the geological structure by the image propertygradients and found a cross-gradient function that measuresstructural resemblance between two property images. Gallardo andMeju (2003, 2004, 2007), Linde et al. (2006), and Tryggvason andLinde (2006) have used this function to jointly invert pairedcombinations of geolectromagnetic and travel time data sets. Throughthis, they found useful resistivity–velocity correlations that might beassociated to underlying petrophysical or hydrological attributes. Weobserve that, despite its underlying structural assumptions, the cross-gradient constraint is independent of the magnitude of the physicalproperty contrasts and, implicitly, of the property values themselves.This is a methodology key feature, as it is expected that an intra-formation attribute –related to fluid and mineral phases– shouldinfluence differently electrical and elastic properties.

In this study we selected a near surface site located in the groundsof the Universidad Autónoma de Nuevo León, Earth Sciences School

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(ESS) in Linares, Mexico. The site is being prepared for constructionand basic geotechnical laboratory experiments weremade on selectedrock and sediment samples from shallow geotechnical boreholes,which include lithological descriptions as well as measurements ofmoisture and clay content at two boreholes. The measured geotech-nical values and lithological descriptions were correlated to jointlyestimated values of electrical resistivity and seismic velocity at theprecise geotechnical sites. This correlation provides a useful bench-mark to classify coupled resistivity–velocity values in terms of theirlithological association.

2. Field experimental design and joint seismic–resistivity datainversion

ESS field site is located near the city of Linares, in the northeast ofMexico (Fig. 1). The study site is situated in a wide transition zonebetween the Sierra Madre Oriental fold thrust belt and the Gulf

Fig. 1. Location of ESS field sit

Coastal Plain in northeast Mexico. The Sierra Madre Oriental is asequence of mainly carbonate and clastic marine sedimentary rocks ofLate Jurassic and Cretaceous ages, complexly folded and overthrustedduring the Laramide Orogeny (Gomberg et al., 1988; Dickinson andLawton, 2001; English and Johnston, 2004). The Gulf Coastal Plaincorresponds to a thick sequence of clastic sediments of Tertiary agecharacterized by an extensional deformation (Ortiz-Ubilla and Tolson,2004).

In the Linares area, the oldest outcrops are in the MendezFormation, located north and south of the region. This Formation iscomposed of shales of Upper Cretaceous age, with a thickness greaterthan 45 m and will be taken as bedrock. Younger rocks includeconglomerates (Tertiary age), Quaternary alluvium and recent soils,mostly silts. The maximum thickness of these Quaternary occurs inold stream beds which are mainly oriented in east–west direction(Montalvo-Arrieta et al., 2005). In ESS field site (Fig. 1) the thicknessof soft sediments is less than 5 m.

e in northeastern Mexico.

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2.1. The electrical and seismic data

To study the site we collected a set of in-line dc resistivity andseismic data along two perpendicular profiles (Fig. 2): Line 1, which isa 152 m long profile oriented 35° NW-SE, and Line 2, a 64 m longprofile oriented 74° NE-SW.

Line 1 was surveyed with 39 Schlumberger vertical electricalsoundings (VES) with array centers distributed every 4 m along theprofile usingmaximumAB/2 spreadings of 60 m. To attain appropriatedata sensitivity to the near surface target, the first AB/2 apertureswereincreased by 2 m steps for the first 30 m of the soundings as illustratedin Fig. 3a. Line 1 was also surveyed with a seismic refraction profilecomposed by ten 48 m-long direct and reversed profiles using asledgehammer as source at both ends of each profile and geophonesdistributed every 2 m. The refraction gathers were filtered and thetravel times of the first arrivals were selected for inversion (Fig. 3b).

Line 2 was also surveyed with 8 Schlumberger VES with AB/2ranging from 2 to 20 m and electrode spacing of 2 m. The center of

Fig. 2. Location of the two profiles in the ESS study area, and position of measurementpoints at Lines 1 and 2.

consecutive VES was equally displaced by 8 m to cover a total lengthof 64 m (Fig. 4a). In this line, we carried out 4 seismic refraction directand reversed profiles. The shot points were located at −8 m, −2 m,48 m and 54 m and the separation between geophones was 2 m tocover a 48 m long profile (Fig. 4b). For this second line, there werelithological, hydrologic, humidity percentage and thickness informa-tion available from two geotechnical boreholes which reached a depthof 6 m below the surface. The boreholes were positioned at 15 m and44 m along the profile. This borehole information constitutes ourgroundtruth and a basis to search for the possible correlations amongstructurally coupled electrical resistivity and seismic velocity proper-ties and their lithological attributes in the borehole vicinity.

2.2. Joint inversion of apparent electrical resistivity and seismic traveltimes

As widely studied in geophysical applications (e.g. Grand andWest, 1965; Kearey and Brooks, 1991; Burger, 1992), the electricalresistivity and seismic velocity values estimated independently, fromgeophysical surveys, are influenced by dispersive and attenuativephysical phenomena and data errors that are incoherently propagatedinto the models during the individual inversion of the geophysicaldata. The differences between geophysical models are noticeable inthe low correlation shown by the physical data attained for anexpected geological unit (e.g. Bedrosian et al., 2007; Slater, 2007). Ithas also been shown that such discrepancy can be largely improvedwhen common features of the geological target, which influence thedistribution or the values of geophysical parameters, are taken intoaccount in a joint inversion process (Gallardo and Meju, 2003; 2007;Tryggvason and Linde, 2006; Linde et al., 2008). For this work, weused the Gallardo and Meju (2003, 2004) 2D joint inversionalgorithm. This algorithm searches for electrical resistivity andseismic velocity images of the subsurface that structurally resembleeach other and attain satisfactory fit of their individual geophysicaldata. This is achieved by incorporating the 2D-cross-gradientsfunction (Gallardo and Meju, 2003), given by:

tðx; zÞ = ∇mrðx; zÞ × ∇msðx; zÞ; ð1Þ

as a measure of the structural resemblance of the electrical (mr) andseismic velocity (ms) images.

For inversion, the subsurface model was discretized into rectan-gular cells of variable sizes, optimized according to the naturalsensitivity of the collected data. In the best sampled area, the cells are4 m wide and their thicknesses vary from 0.5 m for cells up to 4 mbelow the surface, 1 m for cells up to 10 m depth, 2 m for cells up to20 m depth and 5 m for cells below 20 m depth. We started ourinversion process for both lines using the best-fitting layered seismicmodel that linearly increases its seismic velocity with depth from400 m/s at ground level to 3000 m/s at 10 m depth. These velocityvalues not only provide a good initial guess to ensure sufficient raycoverage since the first iterative step, but they also agree with thosefound by Montalvo-Arrieta et al. (2005) and are typical for theexpected lithological units. Similarly, the initial resistivity model washomogeneously set with a constant resistivity of 100 Ω-m, whichclosely matched the average values of the measured apparentresistivities. For the inversion experiments, we used the Gallardoand Meju (2004) algorithm of trying several damping factors tocontrol the smoothness within the models and the best models soobtained were chosen.

In order to compare, the inversion script was runwithout the cross-gradient constraint to determine separately estimated electrical andseismic models for Line 2. The models obtained after this separateinversionexperiment are shown in Fig. 5 and, as expected, the resistivityand seismic velocity models did not acquire a structurally compatible

Fig. 3. Resistivity (a) and travel time (b) data of profile 1.

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distribution. In this experiment, the normalized rms misfits obtainedwere 1.87 and 2.99 for resistivity and seismic, respectively.

After getting these results, we performed a series of full cross-gradient joint inversion experiments and obtained the velocity–resistivity model shown in Fig. 6. These models fit their data to anormalized rms misfit of 1.49 for resistivity and 1.95 for seismic data(Line 1). For Line 2 resistivity reached 1.05 and seismic velocity 1.4.

The models show the expected structural resemblance betweenthem, depicting a simple two layered model with some embeddedanomalous zones of very low resistivity. The stratigraphy correspondsto unconsolidated sediments at depth shallower than 5 m (see Fig. 6).

For larger depths (more than 5 m) the seismic velocity increasesshowing the presence of the Cretaceous bedrock (Mendez Formation).

3. Borehole lithology and geophysical signatures

To study the geological implications in the structural resemblanceof resistivity and seismic velocity models, we plot both geophysicalproperty values obtained for each cell in the search for theircorrelations to lithological–hydrological parameters. We found thegeophysical signatures shown in Fig. 7a and b. These signatures showcorrelated clusters that may be associated to the specific lithological

Fig. 4. Resistivity (a) and travel time (b) data of profile 2.

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units present in the area and intersected by borehole 1 (Fig. 7a) andborehole 2 (Fig. 7b) of Line 2.

The lithologic description of borehole 1 is shown in Fig. 8 alongwith the correlation between seismic and resistivity values in depthand the measured moisture content. Two main stratigraphic unitswere identified: soft sediments and bedrock. The first one includesthree sub-layers: (a) dark brown silty clay with organic material, withaverage resistivity and seismic velocity of 40 Ω-m and 850 m/s,respectively; (b) sandy claywith organicmaterial and caliche nodules,with a water content of 11%, and (c) sand, gravels and shale slabs thatreach depths of up to 3.0 m, finding depth-increasing resistivity andseismic velocity. For the sandy clay layer (sub-layer b) we found twodifferent resistivity and seismic values. Thefirst one (1–2.5 mdepth) ischaracterized by a lower resistivity (25 Ω-m) and P-wave velocity of750 m/s, that can be correlated to an increment in porosity within themixture of sandy clays. The second one has resistivities of 40 Ω-m and

P-wave velocities of 800 m/s. Stratigraphically this unit overlays theMendez Formation. The deepest unit (4 m below the surface) iscomposed of shale slabs and gray shale (Mendez Formation) withresistivity values of 63 Ω-m and P-wave velocities ranging from800 m/s to more than 1200 m/s.

To correlate the resistivity/velocity values shown in the cross-plotsof Fig. 7, we indicate the resistivity and seismic velocity values of theprecise inversion blocks that are crossed by the boreholes. We choselabels 1 to 4 according to the lithologies reported by the geotechnicalteam. The lithology for group 1 is described as dark brown silty clay withorganic material and attained resistivities that range from 10 to 16Ω-mand P-wave velocities of about 400 m/s. Similarly, the lithology forgroup 2 is described as sandy clay with organic material and calichenodules and their resistivity/velocity values fit within two characteristicclusters: groups 2a and 2b. Group 2a (shown in Fig. 7b) attainedresistivity values varyingbetween50 and 80Ω-m and P-wave velocities

Fig. 5. Optimal resistivity (a) and seismic velocity (b) models obtained by separate inversion of data for profile 2.

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ranging between 400 and 750 m/s. Group 2b (marked in Fig. 7a) hasresistivity values between 20 and 50Ω-mand the same range of seismicvelocities as group 2a. By observing the characteristic alignments ofclusters 2a and 2b, it is likely that a third subdivision of unit 2 may exist(with resistivities ranging from 22 to 40Ω-m and velocities from 400 to750 m/s), but none of the corresponding cells were crossed by thegeotechnical boreholes to provide a controlled lithological correlationand assign a proper new label. The third group is characterized byresistivity values that range between 50 and 60Ω-m and seismicvelocities varying from800 to 1000 m/s, corresponding to the transitionzone among soft soils and Mendez Formation (sand, gravels and shaleslabs). Group4 is described asgray shale and attained the largest seismicvelocity values (larger than1000 m/s) and resistivity values varyingfrom 60 to 80Ω-m. This last group corresponds to the presence ofbedrock (Mendez Formation). At this stage, it is important to remarkthat even though, the cross-gradient constraint does not impose any

Fig. 6. Optimal resistivity (a) and seismic velocity (b) models obtained after the joint inveobtained after the joint inversion of data for profile 2.

property/clustering restriction in the models, the structural resem-blance significantly reduces fuzzy-effects in the clusters and permits thedistinction of characteristic geophysical property correlations (cf. cross-plot of Fig. 7c). While this has been noted by previous works (see e.g.GallardoandMeju, 2003;2007; Tryggvasonand Linde, 2006; Lindeet al.,2008) none of them shows actual groundthruth lithological correlation.

4. Geospectral imaging and lithological correlation

To facilitate the joint analysis of the resistivity and velocityproperties found in the geophysical signature of Fig. 7 and theirdistribution within the geophysical section, we plotted an intregrativeGeospectral Image as introduced by Gallardo (2007). Similarly toconventional radiometric maps of U–K–Th isotopes extensively usedinmining exploration, a Geospectral image combines several propertyimages in one single colored display. In our particular case, we

rsion of data for profile 1, and optimal resistivity (c) and seismic velocity (d) models

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Fig. 7. Resistivity–velocity cross-plots for the optimalmodel for Line 2, the indicated numbers correspond to valueswhere lithological units are found for borehole 1 (a) and borehole 2(b). Values at depths larger than 10 mwere omitted from the cross-plots as no borehole information is available. The background color corresponds to that used to produce geospectralimages where lithological correlations are marked. (c) Resistivity–velocity cross-plots for the optimal separate inversion for Line 2.

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produced a colored RGB image of the electrical resistivity and seismicvelocity models shown in Figs. 9 and 10 for our profiles 1 and 2. Weassigned green tones for the mapped range of seismic velocities, redtones for the electrical resistivity, and no blue tones (resulting in thecombined color palette shown in the background of the geophysicalsignatures of Fig. 9). Note that these images bear no lithological orgeological preconception by themselves and no specific sharp or fuzzylithological boundaries are imposed by the interpreter beforehand (cf.Gallardo and Meju, 2003; Bedrosian, 2007; Bosch, 1999 amongothers). Instead, the post classification of possible lithological units

can be done by the user based on homogeneity, petrophysical orstatistical approaches that may be suitable for a particular study site.Note that, in our case, the final classification is largely based on thecombined resistivity–velocity values found at the precise boreholes,combination that is expressed in the geospectral image as a specificcolor.

Over the geospectral image for profile 1 (Fig. 2), we identified thefour groups (1, 2, 3 and 4) correlated to the borehole lithologicaldescriptions, which correspond to dark brown silty clay with organicmaterial (1a); brown sandy clays with gravels (2a); sand with clay,

Fig. 8. Lithological description and parameters reported for borehole 1. Indicated at the right are the velocity and resistivity values found for corresponding depths.

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gravels and shale slabs (3), and the bedrock unit composed of grayshale (4). At a distance of 110 to 140 m, and a depth between 4 and10 m, it was identified a low resistivity anomaly that is not correlatedwith any lithology found on the geotechnical boreholes. As indicatedin Fig. 2, there are two buildings and a paved sidewalk over thisparticular zone that may have laterally affected the electricalmeasurements for the largest offsets. At the end of this profile, thereis another low resistivity anomaly, located at distances between 200and 220 m, which corresponds to an artificial water channel thatcrosses the section.

The geospectral image for profile 2 (Fig. 10) depicts the seismicand resistivity variation values and its correlation with the fourgroups identified from the borehole data. For this image, we observe alow seismic and resistivity anomaly centered within profile positionsat 16 and 28 m. This anomaly directly correlates with group 2a. Asextra field evidence, we noted that at the time of the geophysical fieldwork, we found an increased water saturation of almost 15% at theinterface between units 2a and 3 at 4.0 m depth. On the other hand, atwell 2 no evidence of water was found. The resistivity values in thissite are increased and the water content is less than 6%. This well wasapparently dry during the field work. At depths beyond 5 m, theseismic velocities increased up to 2000 m/s, values that correlate toshales of the Mendez Formation. In general, we observed that theresistivity–velocity correlation groups depicted in the geophysicalsignatures and in the geospectral image of the profile 2, facilitated thedelineation of the geometrical distribution of the different unitsidentified from the geotechnical boreholes in both profiles as shownin Figs. 9 and 10. The variations in the water content across the profilewere characterized in the geophysical signatures and then identifiedin the geospectral images. The results obtained from this work show

Fig. 9. Geospectral image with correlat

that, for the studied ESS site, both geophysical parameters areinfluenced by common geological attributes such as water contentand geological structure. By means of structurally-constrained jointinversion, it is possible to identify multiparameter associationscorrelateable to geological attributes such as lithological compositionand moisture content, thus facilitating the search of lithological andgeophysical correlations.

5. Conclusions

In this work we correlated the electrical resistivity and seismicvelocity values of two-dimensional models obtained after cross-gradient joint inversion at two profiles, with geotechnical informationin a site located in the grounds of the Universidad Autónoma de NuevoLeon, Earth Sciences School (ESS) in Linares, Mexico. Two layers wereidentified: a unit of soft sediments (alluvial deposits) and the bedrockcomposed by shales of Mendez Formation. The analysis of thegeophysical signatures obtained from the joint inversion shows thatthe soft sediments are stratified on three lithological sub-units. Theintermediate sub-unit composed by sandy clay with organic materialand caliche nodules was subdivided in two facies due to the watercontent present in the medium. The third sub-unit represents atransition zone composed by sandy gravels and shale slabs. Weobserved that the combined analysis of the geophysical signaturesand the geospectral images obtained after joint inversion greatlyfacilitates the classification of the main lithological units at the studysite. The variation of the seismic and resistivity values so obtainedresulted highly correlateable to the lithological information providedby the geotechnical boreholes. The results obtained from this workshow that, for the studied ESS site, both geophysical parameters are

ed lithology marked for profile 1.

Fig. 10. Geospectral image with correlated lithology marked for profile 2. Note thecorrespondence between the geophysical values and the lithological boundaries of theboreholes indicated in Fig. 6.

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influenced by common geological attributes such as water content,lithological composition, and geological structure. The results alsoshow that, by means of structural joint inversion, it is possible toevidence hindered multiparameter correlations associated to relevantgeological attributes such as lithological composition and moisturecontent.

Acknowledgments

We are grateful to Max Meju and an anonymous reviewer for thecritical comments on the manuscript that helped improve it. Thanksto M. M. González-Ramos for the critical reading of the manuscriptand various useful remarks.

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