time-lapse electrical resistivity anomalies due … time-lapse electrical resistivity anomalies due...

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ANNALS OF GEOPHYSICS, VOL. 50, N. 3, June 2007

Key words landfill – hydrogeological modeling –salinity – resistivity – geophysical forward and in-verse modeling

1. Introduction

Characterizing and monitoring the under-ground conditions of landfills and the locationof subsurface contaminants has always been achallenge. Conventional environmental moni-

toring used to determine the spread and fate ofgroundwater contamination is performed by theexpensive and labour intensive task of drillingclosely spaced boreholes for point sampling(Granato and Smith, 1999). More advanced,non-invasive geophysical techniques, less cost-ly and more environmentally friendly, were de-veloped as tools for interpreting the under-ground structures without disturbing them.Contaminant plumes usually have a sufficientlyhigh contrast in physical properties against thehost media due to an increase in dissolved saltsin the groundwater and a resulting decrease inpore water resistivity; therefore, they may bedetected by geo-electrical techniques.

Early studies have shown that the electricalresistivity method is one of the most efficient

Time-lapse electrical resistivity anomaliesdue to contaminant transport

around landfills

Monica Radulescu (1), Chifu Valerian (2) and Jianwen Yang (3)(1) Conestoga Rovers and Associates, Waterloo, Ontario, Canada

(2) Avalanche Mobile Development, Bucharest, Romania(3) Department of Earth and Environmental Sciences, University of Windsor, Windsor, Ontario, Canada

AbstractThe extent of landfill leachate can be delineated by geo-electrical imaging as a response to the varying electri-cal resistivity in the contaminated area. This research was based on a combination of hydrogeological numeri-cal simulation followed by geophysical forward and inversion modeling performed to evaluate the migration ofa contaminant plume from a landfill. As a first step, groundwater flow and contaminant transport was simulatedusing the finite elements numerical modeling software FEFLOW. The extent of the contaminant plume was ac-quired through a hydrogeological model depicting the distributions of leachate concentration in the system.Next, based on the empirical relationship between the concentration and electrical conductivity of the leachatein the porous media, the corresponding geo-electrical structure was derived from the hydrogeological model. Fi-nally, forward and inversion computations of geo-electrical anomalies were performed using the finite differencenumerical modeling software DCIP2D/DCIP3D. The image obtained by geophysical inversion of the electric da-ta was expected to be consistent with the initial hydrogeological model, as described by the distribution ofleachate concentration. Numerical case studies were conducted for various geological conditions, hydraulic pa-rameters and electrode arrays, from which conclusions were drawn regarding the suitability of the methodologyto assess simple to more complex geo-electrical models. Thus, optimal mapping and monitoring configurationswere determined.

Mailing address: Dr. Monica Radulescu, ConestogaRovers and Associates, Waterloo, Ontario, N2V 1C2, Cana-da; e-mail: [email protected]

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Monica Radulescu, Chifu Valerian and Jianwen Yang

geophysical tools in detecting, delineating andmonitoring groundwater contamination (Ben-son et al, 1983; Greenhouse and Slaine, 1983).More recently, Khair and Skokan (1998) inves-tigated the early detection of salt water intru-sion through systematic observation of electri-cal resistivity in selected positions with fixedelectrode arrays. Geo-electrical techniqueswere also used in the detection of gasoline andsaline leaks (Bevc and Morrison, 1991; Rami-rez et al., 1996a), characterization of hazardouswaste disposal sites (Ogilvy et al., 1999; Sim-mons et al., 2002), and the mapping and moni-toring of contaminant plumes in groundwatersystems (Ramirez, 1996b,c; Tekzan, 1999; Nau-det et al., 2003). Electrical resistivity tomogra-phy was used to determine the spreading patternof a saline tracer into groundwater (Singha andGorelick, 2005).

However, field geo-electrical experimentsare very expensive. In addition, characterizinglandfills and location of subsurface contami-nants is problematical as the extent and locationof contaminant plumes are largely unknownduring real site investigation. In order to mini-mize site characterization costs, it is advanta-geous to investigate theoretical responses ofplanned experiments before field programs areinitiated. In addition, geophysical forward stud-ies followed by inversion are essential to the fi-nal interpretation of observed geophysical data.

Electrical conductivity governing the elec-trical field is the key physical parameter used ingeo-electrical exploration. As the dissolvedcontaminant travels with groundwater flow, ad-vection and hydrodynamic dispersion cause thespreading of the contaminant plumes in direc-tions transverse and longitudinal to the flowpath. Consequently, the electrical conductivityof the targets varies not only with space but al-so with time. Thus it is essential to include thetime-dependent feature of electrical conductivi-ty in the forward and inversion studies per-formed during geo-electrical exploration.

The present research used the hydrogeolog-ical modeling of a groundwater contaminantflow path and the resulting distribution of resis-tivity/conductivity as a basis for the geophysi-cal modeling of the geo-electrical structure. Im-ages of the resistivity/conductivity distribution

acquired through forward geophysical compu-tations followed by inversion were expected topredict the initial distribution of concentrationsin the hydrogeological model. The presentedmodels and scenarios were designed to concep-tualize a diverse range of hydrogeological envi-ronments, from simple to more complex, withvarious types of deposits and shapes of theplume.

2. Methodology

The methodology used in the paper hasbeen developed by Yang (2005) for the theoret-ical investigation of geo-electrical responses as-sociated with hydrothermal fluid circulation ina mid ocean ridge environment. The study pres-ents the hypothetical, highly conceptualizedscenario of a landfill, designed to assess thesuitability of geo-electrical methods in describ-ing the spreading of leachate plumes into thegeologic environment. Several hypotheticalscenarios of the leachate spreading into differ-ent geological structures were investigated.

The hydrogeological model simulated ground-water flow and contaminant transport by usingFEFLOW 5.1, a 3D finite element code developedby WASY (WASY, 2005) capable of performingnumerical modeling of density-dependent fluidflow and mass transport based on the hydrogeo-logical components included in the conceptualmodel.

Once the spatial-temporal pattern of contam-ination was obtained by hydrogeological model-ing as a distribution of concentrations, the con-centration data was converted into resistivities/conductivities, depicting the geo-electrical mod-el. The conversion was based on the empiricalArchie’s law, describing the relation betweenconcentration of contaminant and resistivity ofgroundwater.

The resulting electrical anomalies werecomputed by geophysical electrical modeling,using a finite difference software DCIP2D/DCIP3D (2004), with different electrode con-figurations.

Electrical resistivity profiles and pseudosec-tions corresponding to various electrode config-urations were obtained by forward computation

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Time-lapse electrical resistivity anomalies due to contaminant transport around landfills

of the geo-electrical model. The direct conver-sion of salinity data acquired over a finely dis-cretized mesh into electrical response offeredthe possibility of simulating the use of verylarge numbers of locations for the electrodes.Based on the results obtained at this stage, theconfigurations of electrodes which describedmost accurately the transient and space depend-ent image of the geo-electrical structure associ-ated with the contaminant were selected. Geo-physical inversion of the electrical data wasthen performed in order to recover the initialgeo-electrical models. The inverted geo-electri-cal models were compared with the electricalmodels obtained previously by hydrogeologicalsimulation.

Further analysis was conducted to evaluatethe most suitable electrode configurations ableto describe the spatial and temporal evolution ofthe contaminating plume originating from thelandfill and consequently, the viability of theproposed methodology.

3. Hydrogeological modeling

Flow modeling is based on Darcy’s law inporous media. As a density-dependent transportphenomena is simulated, FEFLOW uses the ex-tended Oberbeck – Boussinesq approximation(Nield and Bejan, 1999). The solution of thegoverning equations is achieved using an im-plicit adaptive time stepping scheme. FEFLOWperforms calculations in discrete time steps, im-posed by the stability criteria required duringthe numerical simulation. Numerical stabiliza-tion is achieved with Petrov-Galerkin least-square upwinding, an alternative numericalscheme used to solve advective dominant flowand transport (Nguyen and Reynen, 1984).

A two-dimensional transient ground-waterflow model was developed, describing variousgeological settings, according to different hy-draulic conditions. The hydrogeological modelsare displayed in fig. 1a-c. The hydrostratigraph-ical conceptualization of the models was cho-sen to depict gradually more complex geologi-cal and hydraulic settings in order to assess theviability of the proposed methodology on awide range of conditions.

Triangle, a specialized code for creating two-dimensional finite element meshes (Shewchuk,1996, 2002), was used to build Delaunay trian-gulations during mesh generation. A minimumangle of 20 degrees was used for each triangle,aiming to obtain a more uniform structure of themesh while supporting the structure of the mod-

Fig. 1a-c. a) Model 1, one intervening layer of low-er hydraulic conductivity; b) Model 2, discontinuouslayer; c) Model 3, layer displaced by fault.

a

b

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el. A triangular finite elements mesh with dimen-sions of 600 m by 50 m, consisting of 5000 ele-ments, was designed. The mesh was further re-fined in critical areas of contacts between differ-ent hydrostratigraphic units, to account for thenumerical oscillations which could occur as a re-sult of the increased hydraulic conductivity con-trast.

The model simulates a transient evolution ofthe system over a period of 10000 days for allthe presented models, steady state being usual-ly reached after 2000-4000 days, depending oneach model. The postprocessing of simulateddata within FEFLOW was used as an evaluationtool for mass distribution and as a graphicaloutput for fluid flow and mass transport.

The simulations were run under saturatedconditions. The flow and the mass transport bo-undary conditions are presented in table I. Theinitial fluid velocity and contaminant concentra-

tion throughout the model have been assumed tobe equal to zero. A leachate concentration of20400 mg/l was assigned over the interval BC onthe upper boundary (fig. 1a-c). The concentrationof the leachate release was estimated as a conser-vative value based on the average composition ofa waste landfill, consisting of specific chemicalsubstances (McBean et al., 1994; Timur et al.,2000). The Total Dissolved Solid (TDS) valuesare converted to a common unit, NaCl and theunit expressed in terms of concentration (mg/l).At this stage of the study, focussing on finding thebest electrical configurations which describe ac-curately the leachate spreading into the geologi-cal environment, the authors did not account forthe chemistry of the plume, as it was not crucialfor the purpose of the simulation. However, giventhe high concentration of the contaminant mass,simulations were run accounting for the densityeffect of the spreading plume.

Table I. Flow and the mass transport boundary conditions.

Section Flow boundary Contaminant mass transport boundaryType Value Comment Type Value Comment

A-B - - Impermeable - - ImpermeableB-C Neumann −0.0125 m/day Influx Dirichlet 20400 mg/l Predefined concentrationC-D - - Impermeable - - ImpermeableD-E Dirichlet 50 m Permeable - - ImpermeableE-F - - Impermeable - - ImpermeableA-F Neumann −0.1 m/day Influx Dirichlet 0 mg/l Predefined concentration

(fresh water)

Table II. Hydraulic parameters.

Model Hydrostratigraphic unit Hydraulic conductivity (10-4 m/s) Porosity (%)

Model 1 Layer 0.00042 10Host 0.125 20

Model 2, Scenario 1 Layer 0.125 20Host 0.00042 10

Model 2, Scenario 2 Layer 0.00042 10Host 0.125 20

Model 3 Layer 0.00042 10Host 0.125 20Fault 1.36 30

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Klayer denotes the hydraulic conductivity ofthe intervening layers and Khost the hydraulicconductivity of the host rock. Porosities are re-garded as φlayer, φhost and φfault.

Table II presents a summary of the hy-draulic parameters used for the simulations.

Model 1 (fig. 1a) presents the simple case ofone intervening layer of lower hydraulic con-ductivity.

Model 2 (fig. 1b) represents a discontinuouslayer into the porous media and two scenarios:Scenario 1, where Klayer > Khost and Scenario 2,where Klayer < Khost.

Model 3 describes more complex geologicalsettings, with the presence of a layer displaced bya dip slip, normal fault, dipping in the ground-water flow direction (fig. 1c).

Porosities and hydraulic conductivities havebeen assigned for the various conceptual scenar-ios according to the type of rocks and values tak-en from literature (Domenico and Schwartz,1990). Less permeable layers were assigned low-er hydraulic conductivities of 10-6m/s to 10-8 m/s,characteristic to sandstones, while more porouslayers were assigned higher conductivities of10-5 m/s, typical of gravel aquifers.

Over the simulated models and scenarios,representative contaminant plume distributionscorresponding to specific time steps were select-ed to be converted into electrical data. The fol-lowing time steps were selected for further geo-physical forward and inversion computation:2000 days for Model 1 (one intervening layer oflower hydraulic conductivity), 700 days for Mod-el 2, Scenario 1 (discontinuous layer of higherhydraulic conductivity), 700 days for Model 2,Scenario 2 (discontinuous layer of lower hy-draulic conductivity) and 300 days for Model 3,the faulted system.

4. Changes in bulk resistivity caused by contaminant plume infiltration

The mechanism generating the variations inresistivity is the change in fluid concentrationcreated by the highly conducting contaminantfluid. Archie’s law formula (4.1) was used toestimate the bulk resistivity of the rock as afunction of the pore fluid’s resistivity.

(4.1)

where ρf resistivity of the pore fluid, φ porosi-ty, a and m empirical parameters set up formoderately well cemented sandstones, a=0.62and cementing factor m=1.72.

According to various authors (Keller andFrischknecht, 1966; Levannier and Delhomme,2003; Hwang et al., 2004), different formulashave been found in the literature, relating fluidconcentration to bulk resistivity. The equationused in this study (4.2) (Morrison and Becker,2004) has been derived from the resistivity-concentration plots (Keller and Frischknecht,1966)

(4.2)

where c= concentration of the fluid [mg/l].The resistivity – concentration relationship

was tested against various data sets obtained bydirect resistivity measurements performed on awide variety of saline solutes. Further verifica-tion showed that eq. (4.2) works the best at con-centrations exceeding 3000 mg/l, which is thecase for the landfill leachate in the present re-search.

The plume spreading pattern as concentra-tion was converted directly into a model of re-sistivity/conductivity as a means of comparisonwith the resistivity model generated later duringthe geophysical forward/inversion procedure.According to the relationship between resistivi-ty and concentration (eq. (4.2)), the distributionpattern of resistivities was similar to the con-centration model.

5. Building up the input files for the DCIPF2D software

The concentration data corresponding to thenodal values of the hydrogeological model builton a finite triangular elements mesh was dis-cretized into rectangular distribution and, con-sequently, converted to time-dependent resistiv-ity/conductivity models. The F2D convertersoftware was used to build up the input files forthe forward geophysical modeling based on theelectrical resistivity data.

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6. Geo-electrical modeling

6.1. Forward modeling

Various arrays with different electrode con-figurations were used to derive potentials fromthe resistivity data, as follows: pole-pole (pp),pole-dipole array with the potential electrodes onthe left (pdL), pole-dipole array with the potentialelectrodes on the right (pdR), dipole-dipole (dd).

The forward modeling of the direct currentDC potentials computed time-lapse apparent re-sistivity anomalies based on a finite differencetechnique used by the DCIPF2D code (DCIP2D,2004). The anomalies consisted of synthetic datathat would be acquired over the 2D resistivitystructures obtained previously from the concen-trations acquired through hydrogeological mod-eling.

Initially, the two dimensional, vertical crosssectional domain was set 600 m wide and 50 mdeep, corresponding to 60 cells on the horizontaldimension and 10 cells on the vertical. The mod-el was extended according to the mesh genera-tion algorithm (Li et al., 1995) to 620 cells in thex-direction (x=−2042 ... +2642 m) and 54 cellsin the z-direction (z=0 ... −170 m). For each con-figuration, surface electrodes were spaced grad-ually in incremental steps of 1 to 5 m in the in-terval x=(0 ... +600) m, until reaching the rightside of the model. The initial data was contam-inated with independent Gaus-sian noise whosestandard deviation was equal to 5% of each ac-curate datum.

The resulting observations of forward mod-eling consisted of images of apparent resistivi-ty distribution as pseudosections acquired withdifferent configurations of electrodes over theinitial geo-electrical model.

Additional information was provided by plotsof the apparent resistivity variation over the sur-face of the model.

6.2. Inversion of the DC data

The DC potentials as apparent resistivitieswere inverted to recover the geo-electrical mod-el by using the computing program DCINV2D(DCINV2D, 2004; Oldenburg et al., 1993).

The same mesh from the forward simulationwas kept for the inverse problem, such that theinversion generated resistivities for all the 620horizontal cells until the observations were ad-equately fit.

The inversion program estimates a referencemodel and an initial model, assigns estimatederror standard deviations to the data, and con-structs a smooth model that best fits the data byreproducing the initial electrical model to theexpected value.

7. Results and discussions

The figures show the results of the researchby describing the evolution of the contaminantplume for various geological models, as follows:the evolution in space and time of the solutetransport, in terms of concentration, as acquiredduring the hydrogeological numerical modelinggenerated with FEFLOW (figs. 2 to 5); the asso-ciated geo-electrical response, based on the geo-physical forward modeling performed with theDCIPF2D code. The geo-electrical response isdescribed in terms of pseudosections (figs. 7a-dto 10a-d) and apparent resistivity profiles (onlyfor Model 2, Scenario 1, fig. 6). Figures 11a-c to14a-c present the result of the geophysical inver-sion through the DCINV2D code, as a summaryof observed data, predicted data and differencebetween observed and predicted data normalizedby standard deviation. Figures 15 to 18 show therecovered resistivity models.

Finally, the computed resistivity models werecompared with the models describing the hydro-geological mass distribution.

7.1. Hydrogeological modeling

For Model 1, the plume was constrained bya layer with a hydraulic conductivity two ordersof magnitude lower than the host rock. As a re-sult, the contaminant is mainly contained abovethe lower hydraulic conductivity layer (fig. 2).

The presence of intervening layers and afault, with different hydraulic parameters and anincreased contrast of hydraulic conductivities be-tween different formations enables a more com-

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Fig. 2. Evolution in space and time of the solute transport, in terms of concentration, Model 1.

Fig. 3. Evolution in space and time of the solute transport, in terms of concentration, Model 2, Scenario 1.

Fig. 4. Evolution in space and time of the solute transport, in terms of concentration, Model 2, Scenario 2.

Fig. 5. Evolution in space and time of the solute transport, in terms of concentration, Model 3.

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plex pattern of the plume (Freeze and Wither-spoon, 1967). As a result, the next conceptualmodels relied on a higher contrast of hydraulicproperties between intervening layers, host rockand fault. A higher conductivity of the host rockenables a more diffuse spreading of the contam-inant, at lower concentrations (fig. 4) comparedto a lower hydraulic conductivity of the hostrock, which favours the development of a moresharply delineated plume, at higher concentra-tions (fig. 3).

For Model 2, Scenario 1, discontinuous lay-er, two orders of magnitude contrast betweenthe higher conductivity layer and the medium(Klayer= 0.125∗10−4m/s, Khost= 0.00042∗10−4m/s)can be regarded as a physical shield, causing re-fraction of the flow line such that flow in thehigher conductivity layer is mainly horizontal,meanwhile flow in the lower conductivity medi-um in essentially vertical (Freeze and Wither-spoon, 1967, Neuman and Whiterspoon, 1969).As a result of this phenomenon, the contaminantplume spreads at higher concentrations mainlyabove and below the higher conductivity layer(fig. 3).

Figure 4, Model 2, Scenario 2, describes thesame discontinuous layer model, except its hy-draulic conductivity is two orders of magnitudelower than the hydraulic conductivity of the hostrock (Klayer = 0.00042∗10−4m/s, Khost = 0.125**10−4m/s). The layer acts as a barrier to theplume development. Significant flow occursmainly within the higher conductivity rock, en-abling diffuse transport of the plume in the sys-tem, at lower concentrations (fig. 4).

A comparison between Scenario 1 and Sce-nario 2 shows that the presence of a lower con-ductivity layer (Scenario 2) (fig. 4) favouredthe retention of high concentrations of contam-inant in a small area, meanwhile the overallspreading of the contaminant in the host rock atlower concentrations was significantly en-hanced compared to the case of the higher hy-draulic conductivity layers (Scenario 1) wherethe contaminant spread as a more sharply delin-eated, elongated plume of higher concentra-tions (fig. 3).

Model 3 describes a dip slip, normal fault,dipping in the same direction as the fluid flow.The hydraulic conductivities were 1.36∗10−4m/s

Fig. 6. Forward modeling, apparent resistivity pro-file at 700 days, Model 2, Scenario 1.

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for the fault, 0.125∗10−4m/s for the host rock and0.00042∗10−4m/s for the layer. The fault acted asa pathway facilitating the spread of the contam-inant along it and into the host rock (fig. 5).

Overall, the density effect due to high con-centration of the pollutant generated a decreasein fluid flow velocities. A higher hydraulic con-ductivity layer associated with reduced fluid ve-locity enabled the accumulation of the contami-nant within the layer. The phenomena can be re-garded as a vertical restriction of the plume de-velopment.

7.2. Forward geophysical modeling

For each array, the electrodes spacing wasgradually increased incrementally until reachingthe right limit of the model on the surface. Theincremental spacing was varied from steps of 1to 10 m at a time. As a preliminary observation,a lower incremental spacing between electrodesalong the entire length of the model enableshigher resolution of the apparent resistivity pseu-dosections. A major outcome of the proposedmethodology resulted from the versatility of us-

Fig. 11a-c. Result of geophysical inversion, pdL con-figuration, Model 1, at 2000 days: a) observed data; b)predicted data; c) difference between observed andpredicted data.

Fig. 12a-c. Result of geophysical inversion, pdL con-figuration, Model 2, Scenario 1, at 700 days: a) ob-served data, b) predicted data, c) difference betweenobserved and predicted data.

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ing a wide range of steps for electrode spacing,where field and technical constraints can be dis-regarded and consequently, detailed informationabout the subsurface can be depicted. It is a cru-cial aspect, as the proposed methodology is atheoretical exercise intended to offer the bestpreparatory knowledge before the investigativework in the field. In this case, the only con-straints referred to the computing procedures,where significant running times restricted the useof very small incremental steps. The electrodes

spacing which most accurately describes thehorizon where the plume is moving within a rea-sonable computing time was selected. Withoutprevious hydrogeological information, the deci-sion of which electrode spacing is most appro-priate is quite difficult to reach.

The electrical resistivity figures in the nextsections present the case of an increment of 5 min electrodes spacing.

Based on the concentration values trans-formed into resistivities, the geophysical for-

Fig. 13a-c. Result of geophysical inversion, pdL con-figuration, Model 2, Scenario 2, at 700 days: a) ob-served data; b) predicted data; c) difference betweenobserved and predicted data.

Fig. 14a-c. Result of geophysical inversion, pdL con-figuration, Model 3, at 300 days: a) observed data; b)predicted data; c) difference between observed andpredicted data.

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ward modeling pseudosections offered a pre-liminary image of the contaminant plume. Val-ues of resistivity were within the range of 20-190 Ω-m, corresponding to variations of con-centrations between 0 to 20400 mg/l.

7.2.1. Apparent resistivity profiling

The following observations were drawnbased on the apparent resistivity profiling usingvarious electrode configurations for each of the

Fig. 15. Result of geophysical inversion, pdL configuration, Model 1, at 2000 days: recovered resistivity.

Fig. 16. Result of geophysical inversion, pdL configuration, Model 2, Scenario 1, at 700 days: recovered resis-tivity.

Fig. 17. Result of geophysical inversion, pdL configuration, Model 2, Scenario 2 at 700 days: recovered resis-tivity.

Fig. 18. Result of geophysical inversion, pdL configuration, Model 3, at 300 days: recovered resistivity.

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hydrogeological scenarios. Figure 6 presents theapparent resistivity profiling for Model 2, Sce-nario 1, at 700 days. Apparent resistivities profil-ing cannot offer relevant information about thedistribution of the resistivities with depth. How-ever, the profiles can be regarded as useful to de-lineate the contact between the noncontaminat-ed/contaminated area at the surface, along the in-vestigation line.

The profiles showed decreased values of re-sistivity in the leaching area, increasing with timeand space according to the spreading and dilutionof the plume, until eventually reaching again thebase line of the noncontaminated area. The initialflat trend of the apparent resistivity, correspon-ding to the presence of the noncontaminated areaat designated intervals of time, can be used as abaseline for characterizing clean conditions.

However, there were certain resolution dif-ferences which made some configurations moresuitable to delineate the leachate spread at thesurface, as follows:

– In the case of dd configuration, the initialincreasing peak on the profile distinctivelymarked the contrasting properties between thenoncontaminated and contaminated area, offer-ing accurate information about where theleachate spill originated at the surface. Figure6-a, for example, showed a sharp delineation ofthe initiation of the plume. According to it, thelength of the noncontaminated area at the sur-face is of approximately 170 m, in fair agree-ment with fig. 3-c, snapshot of concentrationsdistribution over the model.

– For the pdL configuration, the sharply in-creasing peak on the profile before the cleanbaseline, as a result of the contrasting proper-ties between the noncontaminated/contaminat-ed surface, indicated the end of the contaminat-ed area and could be used as marker as long asthe contamination does not extend outside thehorizontal boundaries of the initial geo-electricmodel, which is the case in fig. 6-b.

– For the pdR configuration, the initial in-creasing peak on the profile marked sharply thebeginning of the contamination area, providingreliable information about the leachate spread-ing at the surface (fig. 6-c).

– In the case of pp configuration, the peakpresent for other electrodes configurations was

absent at both ends of the contaminate area (fig.6-d).

As a first conclusion, the apparent resistivi-ty profiles can be used as a rougher interpreta-tion tool to delineate the contaminant plumespreading through time at the surface. dd andpdR are the optimal configurations which delin-eate the initiation of the leachate spill at the sur-face.

7.2.2. Apparent resistivity pseudosections

Pseudosections of apparent resistivities gen-erated by the leachate spreading were investigat-ed with various electrode configurations (dd,pdL, pdR, pp), respectively figs. 7a-d, 8a-d, 9a-dand 10a-d.

For Model 1, of a uniform environment andconsequently sharp delineation of plume, allelectrode configurations described quite accu-rately the extension of the contaminant in timeand space (fig. 7a-d).

In the case of Model 2, Scenario 1 (fig. 8a-d), where the plume becomes more diffuse atlower depths, accurate information was ob-tained for the dd and pdL configurations.

For Model 2, Scenario 2 (fig. 9a-d) andModel 3 (fig. 10a-d) and a diffuse pattern of thecontaminant, relatively accurate informationwas provided by the pdL configuration.

Dispersion along the flow lines in theporous media creates dilution of concentration,where the resistivity contrast between theleachate and the clean groundwater decreasesand consequently the geo-electrical image ofthe model is less accurate. As first order esti-mates, not all the dipole electrode configura-tions were equally suitable to offer reliable in-formation about the spreading of the contami-nant.

All the electrical imaging pseudosectionsdepicted accurately the patterns of contaminantfor sharply delineated plumes, with concentra-tions ranging between 10000 to 12000 mg/l, re-gardless of the electrodes configuration.

Where the plume spreads diffusely into thegroundwater, at lower gradients of concentra-tion, between 2000-4000 mg/l, the resistivitiescontrasts have not been sufficiently sharp to

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create an accurate forward electrical image(figs. 7a-d and 8a-d). The pseudosections whichhave best revealed the time-space transient fea-ture of the contaminant plume given complexgeological and hydraulic settings were acquiredwith the pdL configuration.

Prior to inversion, results plotted as conven-tional pseudosections enabled preliminary in-terpretations, as first order estimates of dataquality, anticipating the spreading of the plumein terms of structural features of the geo-electri-cal model.

Based on the ability of the pdL configura-tion to profile the extent of the plume at the sur-face and to offer an acceptable pseudo image ofthe distribution of apparent resistivities indepth, the pdL was chosen to perform the in-verse problem of the geo-electrical model.

7.3. Inversion of the DC data

The inversion was carried out for the select-ed configuration by supplying to the programthe DC data observation file from the forwardmodeling and the same user-designed mesh.The inversion program estimated a referencemodel and an initial model, assigned estimatederror standard deviations to the data, and con-structed a smooth model that best fits the ob-served data to the expected value. Figures 11a-c to 14a-c present for each inverted model theinitial resistivity model, the observed data fromthe forward modeling, the predicted data, andthe difference between the observed-predicteddata normalized by standard deviation. As canbe observed from figs. 15 to 18, the essentialfeatures of the resistivity were all recovered.

8. Conclusions and further investigations

The hydrogeological numerical simulationof contaminants spreading in the groundwaterwas used as a support for the geophysical mod-eling of the associated geo-electrical models.Four electrode configurations, pole-pole array(pp), pole-dipole with the potential electrodeson the left (pdL), pole-dipole with the potentialelectrodes on the right (pdR), dipole-dipole

(dd), were used for the numerical modeling ofthe electrical anomalies. The results were ini-tially computed through forward modeling asapparent resistivity profiles and pseudosec-tions, followed by inversion.

Reliable and accurate data from 1D profilesof electrical resistivity, delineating the initiationof the contaminating plume at the surface alongthe investigation line, can be acquired regard-less the complexity of the model by the use ofeither dd or pdR configurations. The pdL appar-ent resistivity profiles have proven suitable todelineate the end of the contaminated area atthe surface as long as the contamination did notextend beyond the limits of the investigationline.

The pseudosections, as preliminary inter-pretations prior to inversion, have revealed ac-curately the time-space transient feature of thecontaminant plume for all the electrodes con-figurations, as long as the hydrogeological en-vironment is fairly uniform and there is a sharpcontrast of concentrations between the leachateand the fresh groundwater. For complex andmore diffuse distributions of concentrations,with lower gradients between the resistivityfeatures in the models, the pseudosections pro-duced the best results for the pdL configuration.

However, the optimal contrast between re-sistivities cannot be quantified and generalizedfrom one case study to another. The level ofcontamination detected by forward modeling ofresistivity in different aquifers can be differenteven when using the same electrodes configura-tions and spacing, due to diverse geo-electricalstructures and resistivity contrasts.

The inversion of the observed data recoveredthe essential resistivity features for all the scenar-ios. Consequently, there was a good time-spacecorrelation between the recovered resistivitiesprofiles and the plume as described by the hydro-geological model, for all the electrode configura-tions in case of the uniform model and for pdLconfiguration for more complex distribution ofthe plume. The inverted electrical structures alsooffered a matching distribution of the contami-nant concentrations, as initially described in thehydrogeological model.

As reemphasized by the present research, agood knowledge of the contamination patterns

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in the area before planning field work in realsituation is an essential asset. Based on thecomplexity of the geological and hydraulic set-tings, an educated decision can be made regard-ing the further use of certain array configura-tions, aiming to acquire the best results and op-timization of costs. Within the selected array,the proposed methodology allows the theoreti-cal use of a wide range of electrodes spacings,directly related to depth of investigation, fromwhich the configuration offering the best infor-mation about the contamination horizon can beselected.

Furthermore, there is no limitation to thescale of the model, as runs can be performed forany dimensions of the finite elements and,therefore, finite difference meshes.

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(received September 12, 2007;accepted October 15, 2007)

time-lapse electrical resistivity anomalies due … time-lapse electrical resistivity anomalies due...

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