Advances in interpretation of subsurface processes with ...€¦ · 1 p. An ERI, TDIP, or CR survey is acquired by collecting many measurements on different current and potential

HYDROLOGICAL PROCESSESHydrol. Process. (2014)Published online in Wiley Online Library(wileyonlinelibrary.com) DOI: 10.1002/hyp.10280

Advances in interpretation of subsurface processes withtime-lapse electrical imaging

K. Singha,1* F. D. Day-Lewis,2 T. Johnson3 and L. D. Slater41 Hydrologic Sciences and Engineering Program, Colorado School of Mines, Golden, CO 80401, USA

2 Office of Groundwater, Branch of Geophysics, U.S. Geological Survey, 11 Sherman Place Unit 5015, Storrs, CT 06269, USA3 Pacific Northwest National Laboratory, 902 Battelle Blvd., Richland, WA 99352, USA

4 Department of Earth and Environmental Sciences, Rutgers University - Newark, 101 Warren St., Newark, NJ 07102, USA

*CingE-m

Co

Abstract:

Electrical geophysical methods, including electrical resistivity, time-domain induced polarization, and complex resistivity, havebecome commonly used to image the near subsurface. Here, we outline their utility for time-lapse imaging of hydrological,geochemical, and biogeochemical processes, focusing on new instrumentation, processing, and analysis techniques specific tomonitoring. We review data collection procedures, parameters measured, and petrophysical relationships and then outline thestate of the science with respect to inversion methodologies, including coupled inversion. We conclude by highlighting recentresearch focused on innovative applications of time-lapse imaging in hydrology, biology, ecology, and geochemistry, amongother areas of interest. Copyright © 2014 John Wiley & Sons, Ltd.

KEY WORDS electrical resistivity; induced polarization; complex resistivity; imaging; petrophysics; inversion

Received 18 November 2013; Accepted 30 June 2014

INTRODUCTION

Geophysical data have long been used to characterizeEarth systems for mineral and energy exploration,geotechnical investigations, and water resources. Thedevelopment of time-lapse technologies, in particularthose with applications in near-surface processes,however, is more recent. Electrical methods, defined hereas direct-current (DC) electrical resistivity imaging (ERI),time-domain induced polarization (TDIP), and complexresistivity imaging (CRI), have become increasinglyapplied to monitor dynamic systems over the last decade.These technologies, sensitive to pore fluid conductivity,pore space, geometry and the electrochemical interactionat grain interfaces, are important to hydrogeologistsattempting to characterize flow and transport processes.Time-lapse electrical images and even simple time seriesof electrical measurements readily provide qualitativeinformation to help infer changes associatedwith unsaturated flow (e.g. Daily et al., 1992; Park,1998; Binley et al., 2002), solute transport (Slater et al.,2000; Kemna et al., 2002; Singha and Gorelick, 2005;Muller et al., 2010), contaminant remediation operations(e.g. Ramirez et al., 1993; Daily et al., 1995; Truex et al.,

orrespondence to: Kamini Singha, Hydrologic Sciences and Engineer-Program, Colorado School of Mines, Golden, CO 80401, USA.ail: [email protected]

pyright © 2014 John Wiley & Sons, Ltd.

2013), aquifer/surface-water interaction (e.g. Hendersonet al., 2010; Coscia et al., 2012), biogeochemical processes(Atekwana and Slater, 2009), and other hydrologicprocesses of interest (e.g. Kemna et al., 2006). In mostwork, the goal is to translate the time-lapse electrical resultsinto information on variations in moisture content orsalinity, although information on other time-varyingparameters (temperature, mineral exploration, or dissolu-tion) also has been demonstrated. Early demonstrations oftime-lapse studies were of ERI in soil cores and experi-mental tanks (e.g. Binley et al., 1996; Slater et al., 2002) aswell as field-scale studies (Ramirez et al., 1993). Time-lapseCR and TDIP may provide additional information beyondwhat is measured with ERI (Slater and Binley, 2006; FloresOrozco et al., 2011).Extraction of quantitative hydrologic information from

geophysical data or images remains an importantchallenge in hydrogeophysical research, as evidenced bya burgeoning literature focused on translation ofgeophysical information into hydrologic information. Inthis paper, we discuss more recent developments in thisarea and, in contrast to previous reviews (e.g. Rubin andHubbard, 2005; Linde et al., 2006; Singha et al., 2007;Loke et al., 2013), we focus specifically on time-lapseelectrical imaging. We outline the state of the science intime-lapse ERI, TDIP, and CR measurements, includingdata collection and analysis, inversion, and petrophysical

K. SINGHA ET AL.

relations. We follow this section with an outline of capabilityadvances both in data collection and inversion as well asemerging applications specific to time-lapse studies.

DATA COLLECTION AND PETROPHYSICSBACKGROUND

ERI, TDIP, and CR measurements

The nomenclature describing electrical measurementsand electrical properties can be unclear in meaning to thenon-expert. Common terminology used to describe theinstrument or method includes DC resistivity, electricalresistivity (ER), electrical impedance (EI), complexresistivity (CR), induced polarization (IP), spectralinduced polarization (SIP), and time-domain inducedpolarization (TDIP). ER is the same as DC resistivity,where measurements are made using a DC (or low-frequency alternating current) and the system is assumedto be in steady state during the measurement. In this case,only charge transport by electromigration is measured. Inall other methods (EI, CR, IP, and SIP), an additionalmeasurement is made to quantify temporary chargestorage (via electrochemical mechanisms) in addition toelectromigration. EI is commonly used in the literature forprocess and medical tomography, where frequencieshigher than those in ER are used, and will not bediscussed here. In the geophysical literature, CR, IP, andSIP are the most common terms used to describethese frequency-dependent measurements. The terms IP,SIP and TDIP originate from the development of

Figure 1. (A) Example electrode configuration for surface electrical measuremennegative (V�) electrodes. (B) Diagram of frequency-domain measurement includand corresponding potential waveform observed between potential electrodes. Aphaseϕ. (C)Diagramof a time-domainmeasurement including transmitted curre

waveform measured include the total potential ϕT, and th

Copyright © 2014 John Wiley & Sons, Ltd.

geophysical instruments in mineral exploration, whereasthe term CR has been adopted for environmental applica-tions (e.g. Olhoeft, 1985). In most papers, CR, IP, and TDIPmean probing frequency-independent impedance proper-ties. SIP, on the other hand, includes measurements atmultiple frequencies to probe frequency-dependentimpedance properties, typically from a few mHz up to1 kHz (e.g. Kemna et al., 2012). However, some authorsalso refer to CR as meaning a frequency-dependentmeasurement. Here, we use ER (or ERI, when discussingimaging specifically) to describe all approximately DCmeasurements, TDIP to describe polarizationmeasurementsmade in the time domain, and CR to describe polarizationmeasurements made in the frequency domain.Measurements of ERI, TDIP, and CR are collected using

two current injection electrodes (source and sink), and twopotential measurement electrodes (positive and negative).Both current and potential electrodes may be deployed on thesurface or beneath the surface (e.g. in boreholes), or somecombination of these. The key criterion is that there is anelectrical contact between the electrode and the earth. For agiven measurement, a current waveform is injected betweenthe current electrodes, and attributes describing thecorresponding potential waveform are measured acrossthe potential electrodes. Figure 1 shows a schematic offrequency-domain measurements, which are collected duringCR experiments, and time-domain measurements, which arecollected during ERI and TDIP experiments. Figure 2 showsa schematic for the workflow of time-lapse geophysicalexperiments and subsequent translation to hydrologicparameters and is referred to throughout this paper.

t including current source (I+) and sink (I�) electrodes, and positive (V+) anding transmitted current source waveform injected between current electrodes,ttributes of the potential waveform measured include the amplitude |φ| and

nt waveform and corresponding potentialwaveform.Attributes of the potentiale apparent chargeability Ma (see Equations (1) and (2))

Hydrol. Process. (2014)

Figure 2. Schematic diagram depicting the workflow for electrical imaging of a subsurface manipulation (e.g. tracer experiment or biostimulation) andtranslation to hydrologic parameters of interest

TIME-LAPSE ELECTRICAL IMAGING

During ERI, CR, and TDIP experiments, an alternatingsquare current waveform (or in the case of CR, sometimes asinusoidalwaveform) is injected across the current electrodes.The resulting voltage difference developed across thepotential electrodes is measured in terms of the magnitudeφT for the ERI experiment, and both φT and apparentchargeability (Ma) for the TDIP experiment, as described inthe succeeding section. The corresponding attributes mea-sured in the frequency domain, for CR for example, are thefrequency-dependent magnitude |φ| and phase lag ϕ relativeto the current waveform, or the real or in-phase component ofthe potential response φ ′ and the complex or quadraturecomponent of the potential response φ ″. Both the phase lagand the apparent chargeability develop due to chargepolarization mechanisms in the subsurface, or the ability ofthe subsurface to store charge, as reviewed in the next section.The potential waveform can equivalently be represented

by the complex potential given by

φ� ¼ φ′ þ iφ″ (1)

where

φ′ ¼ φj j cos ϕð Þ (2)

and

φ″ ¼ φj j sin ϕð Þ (3)

Here, i ¼ ffiffiffiffiffiffiffi�1p

.


An ERI, TDIP, or CR survey is acquired by collectingmany measurements on different current and potentialelectrode pairs strategically chosen to provide adequateimaging resolution. Time-domain electrical measurementsare attractive for electrical monitoring as they are generallyquicker to acquire than multi-frequency, frequency-domainmeasurements. The time-domain measurement of thecharge storage is Ma, defined as (Siegel, 1959; Oldenburgand Li, 1994)

Ma ¼ φMφT

(4)

where φM is the part of the total potential (φT) arising due tocharge polarization mechanisms (Figure 1). In practice, φMis difficult to measure precisely, and Ma is typicallyapproximated by

Ma≈1Δt

1φT∫t2

t1φ tð Þdt (5)

where Δt= t2� t1 is the length of the sampling window andφ(t) is the voltage at time t (Figure 1). According toEquations (4) and (5), φM is approximated as the averagepotential recorded during the IP time window. Note thatMa

is partly a function of the settings of the TDIP instrumentand thus not an intrinsic property of the Earth, requiringquantitative data-processing algorithms to decouple theinstrument response given some assumptions about thephase angle (e.g. Kemna et al., 1997). Some IP instrumentsmeasure a property known as percentage frequency effect


K. SINGHA ET AL.

(PFE) that quantifies the decrease of impedance magnitudewith frequency associated with polarization. PFE is nottypically used in time-lapse imaging but is a traditional IPmeasure used in mining exploration.Although Ma depends on the configuration of the TDIP

instrument settings, a linear proportionality between Ma andϕ can be both theoretically shown (Slater and Lesmes, 2002)and experimentally demonstrated (Lesmes and Frye, 2001;Slater and Lesmes, 2002; Mwakanyamale et al., 2012). Alinear proportionality between PFE, Ma, and ϕ can also beexpected (Slater and Lesmes, 2002). To be clear, a summaryof the measurement types provided by ERI, TDIP, and CRmeasurements is given in Table I.

Low-frequency electrical properties

Electrical methods operate at low frequencies wheredisplacement currents, which are time-varying andassociated with magnetic fields, are insignificant incomparison with galvanic, or direct, currents ( f< 1 kHz).At these frequencies, the relationship between current,potential, and electrical properties of the Earth is definedby the Poisson equation. Here, we consider a complexelectrical conductivity (σ*) that contains information onboth electromigration and polarization, such that thePoisson equation is given as

∇�σ� r;ωð Þ∇φ� r;ωð Þ ¼ I r0;ωð Þ (6)

where I is the sinusoidal point current source injected atposition r0 and frequency ω, and φ* is the correspondingcomplex potential field at position r and frequency ω.Note that for ER, the equivalent conductivity andpotential terms appearing in Equation (6) are the realterms |σ| and φT, respectively.The measured complex conductivity describing the

properties of the Earth can equally be defined as acomplex electrical conductivity (σ*), a complex resistivity(ρ*), or a complex permittivity (ε*),

σ� ¼ 1ρ�

¼ iωε� (7)

as each of these parameters contains an energy storage(polarization) part and an electromigration (conduction)

Table I. Electrical technologies and measured properties

Method

TotalpotentialφT (V)

ApparentchargeabilityMa (V/V)

Frequency-dependentpotentialmagnitude|φ|(ω) (V)

Frequency-dependentphase shiftϕ(ω) (rad)

ERI XTDIP X XCR X X


part. Here, we use σ* for convenience when describingmeasurements in terms of the parallel conduction modelcommonly used to relate electrical properties to physico-chemical properties of the subsurface, as described later. Interms of σ*, the in-phase (real, σ′) conductivity componentis the property defining the ability of the Earth to transportcharge via electromigration, whereas the out-of-phase(imaginary or quadrature) conductivity (σ″) is a propertydefining the strength of the polarization associated with alocalized redistribution of charge,

σ* ¼ σ′ þ iσ″ (8)

At the low excitation frequencies employed for electricalmonitoring (typically less than 1000Hz), electromigrationdominates over polarization, i.e. σ″<<σ′. The phase angle,

ϕ ¼ tan�1 σ″=σ′� �

≅ σ″=σ′� �

(9)

determines the rotation of the resultant conductivity vectoraway from the real conductivity axis and is small (typically,ϕ< 100 mrad); the approximation shown in Equation (9) istherefore often valid.While real and imaginary conductivitiesand phase angles are measured with CR, ERI only estimatesthe magnitude of σ*,

σj j ¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiσ′ð Þ2 þ σ″ð Þ2

q≅ σ′ (10)

where the approximation shown again holds for small phaseangles. In non-metallic soils, this low-phase assumption isgenerally valid, but it can be violated over metal-rich soilswhere phase angles of a few hundredmrad are possible due tothe strong polarization properties of disseminated metallicminerals. As with the complex potential, the real andimaginary conductivities are related to the conductivitymagnitude and phase by

σ′ ¼ σj j cosϕσ″ ¼ σj j sinϕ (11)

Early formulations related the current and potentialto the electrical properties using the concept of anintrinsic chargeability (M), which relates the conduc-tivity (at DC) of a polarizable material (|σ|) to adecreased conductivity of a non-polarizable material(σnp) (Siegel, 1959),

σnp ¼ σj j 1�Mð Þ (12)

based on measurement of Ma using TDIP instrumenta-tion. The chargeability (M) is then related to the totalpotential and the current by

∇� σj j 1�Mð Þ∇φT ¼ I (13)



Electrical petrophysics

The electrical properties sensed with ER, TDIP, and CRmeasurements depend on the pore fluids and pore architecture.The additional properties sensed with CR and TDIP are alsomodified by mineral dissolution and precipitation, biominer-alization, reactive contaminant transport, and biodegradationof hydrocarbon contaminants. In other words, time-lapseinverse estimates of polarization properties (i.e. ϕ or M inaddition to |σ|) provide an opportunity to monitor processesthat modify the physicochemical properties of the grain–fluidinterface. These processes may not be detectable using inverseestimates of |σ| alone.Wedemonstrate the basic relations usingthe real and imaginary parts of the complex conductivitydefined earlier (e.g. Lesmes and Friedman, 2005).Most models for σ* of a porous material devoid of metals

at low frequencies (e.g. less than 100Hz) are based on aparallel addition of two conduction terms representing (1) anelectrolytic contribution via electromigration through theinterconnected pore space (σel) and (2) a complex mineralsurface conduction contribution (σ*

surf) (e.g. Vinegar andWaxman, 1984),

σ� ¼ σel þ σ�surf (14)

Here, σ*surf arises due to both electromigration and

polarization of ions in the electrical double layer (EDL)that forms at mineral–fluid interfaces. In aquifers containingpotable water, the EDL is most commonly considered alayer of net negative ions adsorbed on colloidal particles thatattracts a layer of net positive ions in the surroundingelectrolytic solution (Grahame, 1947; Davis et al., 1978).Other polarization mechanisms, such as the Maxwell–Wagner mechanism that results from charge accumulationat contrasts in electrical conductivity (dominant in the kHzrange) and molecular polarization (dominant in the GHzrange), are assumed to be insignificant at low frequencies.For a fully saturated medium,

σ′ ¼ 1Fσw þ σ′

surf (15)

and

σ″ ¼ σ″surf (16)

where F is the electrical formation factor and σw is thefluid conductivity. The true formation factor F is relatedto the interconnected porosity (n) of a fully saturated soilvia Archie’s law (Archie, 1942),

F ¼ n�m (17)

where m is the cementation exponent ranging from 1.3 forclean sand to 4.4 for Mexican Altered Tuff (a clay-richmineral) (Lesmes and Friedman, 2005).


Equation (16) states that the measured σ″ is exclusivelycontrolled by the surface conductivity, whereas themeasured σ′ is controlled by both electrolytic and surfaceconductivity terms (Equation (15)). For simplicity,surface conduction is often considered to be negligibleat high fluid salinities. Weller et al. (2013) show that thisassumption is typically only valid above 1000 mS/m andthat unreliable estimates of F and σw will result fromsingle salinity measurements if surface conduction isignored below these salinities (i.e. in the range of potableaquifers). In such a situation, only an apparent formationfactor is determined; measurements at multiple highsalinities are needed to reliably compute the trueformation factor (e.g. Weller et al., 2013).The effect of partial saturation on σel is most commonly

accounted for using a second power law such that

σel ¼ σwnmSn (18)

where S is the saturation (from 0 to 1) and n is the saturationexponent that typically ranges between 1.3 to 2.7 (Schön,1996) and is approximately 2 for unconsolidated sediments.From consideration of the electrolytic conductivity alone, awell-founded interpretational framework therefore exists to useelectrical monitoring to track changes in σw, n, and moisturecontent, θ, (θ =nS) in the subsurface. This opportunity in largepart explains the growing popularity of electrical monitoringwithin the hydrogeophysical community.Empirical and mechanistic formulations for the surface

conductivity now exist (e.g. Revil et al., 2012) but are notas well established as for σel via Archie’s classic law.Such formulations describe the surface conductivity interms of (1) a volume-normalized surface area of thematerial or the cation exchange capacity and (2) thesurface charge density and surface charge mobility withinthe EDL (Waxman and Smits, 1968; Rink and Schopper,1974; Vinegar and Waxman, 1984). In a study based on114 samples from 10 independent datasets, Weller et al.(2010) defined the following simple linear relation,

σ″ ¼ cpSpor (19)

where Spor is the pore volume-normalized specific surfacearea (typically determined from a Brunauer–Emmett–Teller(BET) nitrogen adsorption and porosity measurement) andcp is the specific polarizability invoked to describe the roleof EDL chemistry on surface polarization. Weller et al.(2010) suggested that Equation (19) represents the equiv-alent of Archie’s law for the surface conductivity. Theconcept of specific polarizability accounts for the fact thatsome minerals are more polarizable than others. Forexample, metallic minerals have a much higher polarizabil-ity per unit Spor than non-metallic minerals due to thetendency of the metal to engage in redox reactions with ionsin the pore fluid. When the full complex conductivity is


K. SINGHA ET AL.

measured, the opportunity therefore exists to use electricalmonitoring to track changes in mineral surface area, as wellas changes in the chemistry of the EDL. Numerousbiogeochemical processes associated with contaminanttransformations, mineral–fluid chemistry, and microbialactivity have the potential to impact the electrical propertiesof mineral–fluid interfaces. This fact in large part explainsthe recent surge of interest in CR monitoring forhydrogeophysical and biogeophysical applications(Atekwana and Slater, 2009; Williams et al., 2009).Given the opportunities to sense geochemical and

biogeochemical processes that cannot be captured with ameasurement of |σ| alone, interest in CR imaging is likely togrow. When measured, the frequency dependence of thecomplex surface conductivity can provide further informa-tion on the physical properties of the subsurface.Polarization only occurs when charge cannot move freelyby electromigration such that a local accumulation of chargeresults from application of an electrical field. For anyparticular length scale where electromigration is discontin-uous, a critical frequency will exist where this polarizationresponse is maximized. A relationship between this lengthscale (dl) and the time constant (τ) describing thispolarization response is often formulated in terms of thediffusion coefficient (D) for the ions in the EDL,

dl2 ¼ τ�D (20)

This length scale is usually equated to a grain diameter ora pore length. The shape of the polarization spectrum cantherefore be related to the distribution of polarization lengthscales within the porous medium, e.g. a distribution of grainsizes (e.g. Lesmes andMorgan, 2001; Leroy et al., 2008) orpore sizes (Titov et al., 2002; Tong et al., 2006). Assumingthat spectral measurements can be reliably obtained, CRmonitoring therefore also has the potential to track changesin the distribution of grain or pore sizes (e.g. due tocementation or dissolution) with time.

NUMERICAL MODELLING BACKGROUND

Analysis of electrical geophysical data commonly entailssolution of the forward problem (i.e. simulation ofmeasurements given physical parameters) and solutionof the inverse problem (i.e. estimation of physicalparameters given measurements). The forward problemis commonly solved numerically using, for example thefinite-difference or finite-element method to identifysolutions to the governing partial differential equation(e.g. Equation (6)). The inverse problem is commonlysolved using optimization methods to identify the 2-D or3-D cross section or volume of electrical parameters thatprovide the best fit to the measurements. In this section


we review approaches to the forward and inverseproblems in time-lapse electrical geophysics.

ERI/TDIP/CR forward problem

The relationship between subsurface complex conductiv-ity, potential, and current in the frequency domain is definedby the Poisson equation given in Equation (6). The objectiveof the forward solution is to simulate the potential fieldgenerated by the current source and extract the simulatedvoltages. The solution is typically produced by solving the setof matrix equations arising from the discretization ofEquation (6) according to an appropriate numerical scheme(e.g. Dey and Morrison, 1979a; Dey and Morrison, 1979b;Rucker et al., 2006). The particular simulatedmeasurement isthen produced by subtracting the simulated potential at thenegative potential electrode from the simulated potential atthe positive electrode. In cases where every electrode is usedas a source during a survey, it is more efficient to computethe pole solution for each electrode than it is to computethe dipole solution for each measurement. The pole solutions(i.e. the solution for a current injection source with a currentsink at infinite distance) may be used to form the dipolesolutions arising from any source electrode pair bysuperposition, thereby requiring only ne forward simulationsas opposed to nm, where ne is the number of electrodes andnm is the number of measurements.Although efficient algorithms for solving Equation (6)

have been available for some time (e.g. Saad and Schultz,1986; Van der Vorst, 1992), recent developments inmeshing algorithms (Si, 2006) have facilitated greateraccuracy in forward solutions through explicit modellingof known conductivity boundaries into the numericalmesh. Accurate forward solutions are critical foroptimizing ERI/TDIP/CR resolution because they enablemisfits between observed and simulated data to bereduced in the inversion process, and they enable accurateJacobian matrix calculations as discussed in the nextsection, ultimately improving imaging resolution. Forexample, Rucker et al. (2006) and Gunther et al. (2006)presented a 3-D finite-element algorithm using meshesgenerated by advanced unstructured tetrahedral meshgeneration software (Si, 2006) to accurately modelsurface topography. To ease the computational demandsof 3-D inversion, they used the same meshing software toproduce a finely discretized forward mesh within aconcurrent coarsely discretized inversion mesh. Doetschet al. (2010) used the same algorithm to explicitlyincorporate fluid-filled borehole boundaries into theforward and inversion mesh, which enabled smoothingconstraints, described in detail in the succeedingparagraphs, to be relaxed between the inside and outsideof the borehole, which effectively reduced the boreholeartefacts that otherwise were evident in ERI images.



Using synthetic models, Robinson et al. (2013a) used asimilar approach to demonstrate how explicitly incorpo-rating wells and dominant fractures into the meshsubstantially improved characterization and time-lapseimaging of tracer movement within a fracture. Theyinvestigated the potential of the approach on field data tomonitor groundwater movement within a dominantfracture during pumping at a carboniferous limestonequarry (Robinson et al., 2013a). Wallin et al. (2013) useda mesh with finely divided unstructured triangularelements to relax smoothing constraints across thetransient, but known, water-table boundary during anexperiment to image stage-driven river water intrusioninto a contaminated aquifer using 2-D time-lapse ERI.The meshing that enabled the inversion to place a sharpconductivity boundary across the moving water tablesubstantially improved the accuracy of the images.

ERI/TDIP/CR optimization problem

In the context of this paper, inversion is the numericalprocess whereby a discretized estimate of subsurfaceelectrical conductivity (real or complex), called atomogram, is generated that (1) honours the data acquiredduring a survey to a degree consistent with data noise and(2) accurately represents the subsurface electrical con-ductivity at the spatial scale that the data can resolve(Figure 2, step 2). This estimate is referred to herein as theinverse solution. Because the inverse problem is generallynon-unique, there are an infinite number of solutions thatsatisfy the first condition (Backus and Gilbert, 1968), andthe second condition is not automatically satisfied by thefirst. To find a solution that satisfies both conditions, twotypes of constraints are placed on the inversion: dataconstraints that force condition 1, and solution constraintsthat force condition 2. The solution constraints are oftenreferred to as regularization constraints (Tikhonov, 1963)and, following Occam’s principle (Constable et al., 1987;LaBrecque et al., 1996), enforce parsimonious solutionsthat only resolve the conductivity structure that isrequired to honour the data.In time-lapse imaging, a chronological sequence of

inverse solutions is generated, with the objective that eachsolution honour conditions 1, 2, and a third condition (3)that the inverted sequence provides an accurate represen-tation of subsurface conductivity at the temporal scaleresolvable by the data, which is determined primarily bythe time required to conduct a single survey. As with thespatial dimensions, it is typically assumed that conduc-tivity varies smoothly in the time dimension. Althoughexplicit solution constraints to enforce this condition arenot required, many practitioners have found it difficult toproduce smoothly varying conductivity in the timedimension without some form of transient solution


smoothing constraint (Cassiani et al., 2006). Hence,many of the original and recent advancements intime-lapse inversion have focused on methods ofimposing transient solution constraints through analysisof difference data (e.g. Daily et al., 1992; LaBrecque andYang, 2001), differencing of multiple inversions usingimages from previous time steps to define constraints orprior information (e.g. Miller et al., 2008), or temporalregularization constraints (e.g. Day-Lewis et al., 2003;Kim et al., 2009; Karaoulis et al., 2011b).The objective of the inversion is to minimize a function

of the general form (Farquharson and Oldenburg, 1998)

Φ ¼ Φd udð Þ þ Φs usð Þ (21)

where Φd and Φs represent the data and solution norms ofthe inverse solution(s). These norms are, respectively, ascalar measure of the misfit between the observed andpredicted data, and a scalar measure of the misfit betweenthe inverse solution structure and the structure imposed bythe solution constraints in both space and time. The vectorsud and us represent the data and solution constraint residual(or misfit) vectors, respectively. The specific form of usdepends on how the spatial and temporal constraints areimplemented, and generally defines the time-lapse inversionapproach. The cascaded time-lapse inversion approach(Miller et al., 2008), for example, which is a slightmodification of a common implementation for staticinversions, and the starting point for the succeedingdiscussion, has the objective function

Φ ¼ Wd dtobs � dtsim� �� 2þβ Ws mt

est �mt�1est

� �� 2 (22)

Here Φd =Φs = ‖‖2 represents the L2-norm operator,

ud ¼ Wd diobs � dtsim� �

is the data misfit term, andus ¼ βWs mi

est �mi�1est

� �is the model misfit term where

β is known as a trade-off parameter that determines therelative weight on the misfit terms. Here, dtobs is the vectorof observed data at time t, dtsim is the correspondingsimulated data which are produced as described in theforward modelling section, and Wd is the data errorcovariance matrix or data weighting matrix, discussed inthe following paragraphs. The vectors mt

est and mt�1est are

the inverse solutions at times t and t � 1, respectively.The regularization or solution constraint matrix Ws isused to impose constraints on the inverse solution. Forexample, Miller et al. (2008) used Ws to imposesmoothness constraints onmt

est �mt�1est , thereby imposing

a smooth temporal transition from mt�1est to mt

est . In thiscase, mt�1

est is provided from a previous time-lapseinversion, or from a static inversion ifmt�1

est is the baselinesolution. Constraints also can be used to restrict time-lapse changes to regions in space where data indicate that


K. SINGHA ET AL.

changes are occurring (e.g. Day-Lewis et al., 2003;Karaoulis et al., 2011b).Continuing with this example, the objective of the

inversion is to find a solution, mtest , that minimizes

Equation (22), subject to appropriately fitting the data (seethe Section on Data Weighting). The standard nonlinearleast squares solution for model updates is given by

JTWTdWdJþ βWT

sWs� �

δmtest

¼ JTWTdWd dtobs � dtsim

� �þβWT

sWs mtest �mt�1

est

� �

where J is the Jacobian matrix with elements Jij being thesensitivity of measurement i with respect to thediscretized conductivity j (

∂dtsim;i

∂mtj). The vector δmt

est is asolution update vector which, when added to mt

est ,decreases the value of the objective function. Equation(23) forms a series of matrix equations that are typicallysolved using a Gauss–Newton iteration algorithm.Although the details vary for other time-lapse inversionimplementations, the general objective function formula-tion and solution strategy are similar to that presentedearlier. For example, Kim et al. (2009), Karaoulis et al.(2011a), and Hayley et al. (2011) all presented differentvariants of time-lapse inversion methods that simulta-neously invert for mt�1

est and mtest (or in theory for any

number of time steps) using augmented and slightlymodified versions of Equation (23). Each time-lapseinversion approach presented in the literature hasadvantages and disadvantages, such that the optimumapproach often depends on the application. For example,the simultaneous inversion approaches mentioned earlierare flexible and theoretically appealing but computation-ally demanding and impractical for large inverseproblems. The difference inversion method presented byLaBrecque and Yang (2001) is computationally efficientbut requires that changes in conductivity with time aresmall enough that the same Jacobian matrix can be usedfor each time-lapse inversion.As a note, inverse estimation of |σ| from ER measure-

ments is relatively straightforward in comparison with CRmonitoring. The signal-to-noise ratio of the polarizationmeasurements (ϕ or Ma), made via CR, is typically 2–3orders of magnitude smaller than for the correspondingmeasurement of potential magnitude. Electromagnetic andcapacitive coupling between input and output channels, andbetween these channels and the earth, can render themeasurements unusable. A rigorous assessment of mea-surement errors in CR is necessary to prevent noisy datafrom generating image artefacts (Flores Orozco et al., 2012;Mwakanyamale et al., 2012). Furthermore, the additionalinformation comes at the cost of longer data acquisitiontimes. Despite these limitations, inversion algorithms forinterpretation of time-lapse CR data have recently become

(23)


available beyond the individual developer (Karaoulis et al.,2011a; Karaoulis et al., 2013).

Data weighting

Data weighting refers to the scaling factors applied toobserved and simulated measurements in order to giveeach the appropriate influence within the objectivefunction. For example, noisy measurements have greateruncertainty and therefore should not have the requirementof being closely fit by the simulated data. Data weightsare applied with the data covariance matrix Wd.Measurement errors are typically assumed to be randomand uncorrelated such that Wd is a diagonal matrix witheach diagonal element being the reciprocal of the standarddeviation for the corresponding measurement. Errors aregenerally quantified one of two ways: via stacking –collecting the same measurement more than once, or byreciprocal measurements – which are a measurement ofvoltage with the current and voltage electrodes swapped.In either case, the duplicate or reciprocal measurementshould provide the same data as the original in theabsence of noise, and any difference can be used as anestimate of error. Given these errors, the first term of theobjective function in Equation (22) becomes the root-mean-square (RMS) error given by

RMS ¼ Wd dobs � dsimð Þk k2

¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiXnmi¼1

dobs;i � dsim;i

� �2sd2i

vuut (24)

where sdi is the standard deviation for measurement i andnm is the number of measurements. Note that the quantitywithin the radical is the χ2 value. Both the RMS and χ2

values are commonly used to determine convergence.Assuming (1) data noise has zero mean and is normally

distributed, (2) measurement standard deviationsaccurately represent the true error for each measurement,and (3) the forward model simulation error is insignificantwith respect to the measurement error, the χ2 value shouldbe equal to nm when the data are appropriately fit. Withnormalization by nm, both the χ2 and RMS values shouldbe equal to 1 when the data are appropriately fit. Inpractice, estimates of measurement standard deviationproduced by repeat measurements and/or reciprocalmeasurements often produce values which, when appliedto derive an appropriate convergence criteria by Equation(24), are too small to be of use. Either the inversioncannot fit the data to the degree suggested by theestimated deviations, or if it can, the solution at RMS = nmis obviously over fit. Assuming standard deviationestimates are accurate and condition 1 above holds, thissuggests condition 3 is violated; the forward model isunable to model the data to the precision consistent with



noise in the field. Indeed, forward modelling errors areoften assumed to be adequately small if they are less than2% of transfer resistance magnitude. Data errors estimat-ed through repeat and reciprocal measurements can besmaller than the modelling errors. This suggests that, toachieve optimal imaging resolution by adequately fittingthe data, forward modelling errors should be reduced asmuch as possible. Forward model accuracy can beimproved by, for example, appropriately refining forwardmeshes, accurately modelling surface topography andother known conductivity interfaces, appropriately han-dling boundary conditions – for example, using theknown no-flux boundaries in tank experiments, and usingsolution improvement techniques such as singularityremoval when possible (Lowry et al., 1998). In addition,the conductivity discretization must be adequately fine forthe inversion to make smaller-scale changes that might berequired to honour the data. This has implications forapproaches where forward modelling is executed on a finemesh, and the inversion solution is done on a coarsermesh to reduce computational demands. That is, if theinversion mesh is too coarse, a conductivity distributionthat enables an adequate data fit is not possible, and theresolving potential of the data is not fully realized.

TRANSLATING GEOPHYSICAL IMAGES INTOHYDROLOGIC INFORMATION

Strategies for the translation from time-lapse electricaltomograms to quantitative hydrologic information can bedivided into five general categories: (1) conversion bypetrophysical transformation, (2) correlation in time, (3)condensing to summary information, (4) calibration ofprocess models, and (5) coupled inversion; these categoriesare represented by step 3 in Figure 2. We note that othercategorizations are possible but suggest that this schemecapturesmost of the ongoingwork to capitalize on time-lapsegeophysical imaging. These five general strategies providedifferent levels of information and require varying degrees ofdifferent limiting assumptions and approximations.

Conversion by petrophysical transformation

The most straightforward approach to translategeophysical information to hydrologic information isthrough simple application of a petrophysical relation,such as those listed previously (e.g. Equations 15–18), orsome empirical relation derived from laboratory or fieldexperimental data (e.g. by linear or nonlinear regression)(e.g. Purvance and Andricevic, 2000; Bowling et al.,2006). This approach falls under ‘direct mapping’ in theclassification proposed by Linde et al. (2006). Thepetrophysical transformation is applied to convert eachtime-lapse image in turn, producing a time-lapse 2-D


cross section or 3-D volume of the hydrologic parameterof interest. The strength of conversion-based approacheslies in their simplicity, but the weaknesses of theseapproaches are severe.In past work monitoring flow and transport with ERI,

the limitations of conversion-based approaches manifest-ed as poor recovery of spatial and temporal moments oftracer plumes. For example, Binley et al. (2002) noted a50% mass-balance error in their effort to monitor a fluidtracer with ERI. Singha and Gorelick, (2005) and Mulleret al. (2010) observed similar or larger mass-balanceerrors in their effort to monitor tracer experiments withERI. Singha and Gorelick (2005) offered three explana-tions for these problems. First, unresolved lithologic/soilheterogeneity can result in a petrophysical relation withparameters that vary spatially in a manner that is difficultor impossible to map; consequently, the conversion is non-unique. Second, there commonly is a discrepancy betweenthe support volumes of hydrologic and geophysicalparameters; i.e. the two are averaged over differentvolumes of rock or soil, and this averaging complicatesconversion. Third, geophysical image resolution can varyin space and time, resulting in spatially and time-varyingloss in correlation between the estimated geophysicalparameter and hydrologic parameter of interest (e.g. Cassianiet al., 1998; Day-Lewis and Lane, 2004; Day-Lewis et al.,2005). The second and third issues are linked through thephysics underlying hydrologic and geophysicalmeasurements. The third issue, furthermore, is a functionof choices made in the inversion of both data types.Assumptions that are necessary to constrain the inversesolution (e.g. regularization, inversion constraints, and priorinformation) can provide results that degrade the correlationbetween estimated geophysical parameters and the hydro-logic parameter of interest. In the last decade, considerableeffort has been devoted to understanding and addressingthese issues to develop more effective strategies to converttomograms to hydrologic parameter estimates.Geophysical measurement support volume, sensitivity,

and tomographic resolution are longstanding topics ofresearch and well-established issues in the interpretationof geophysical images (Menke, 1989; Ramirez et al.,1993; Oldenburg and Li, 1999; Alumbaugh and Newman,2000; Friedel, 2003; Dahlen, 2004). Geostatisticalapproaches, such as co-kriging and conditional simulation(e.g. McKenna and Poeter, 1995; Cassiani et al., 1998),and Bayesian frameworks (Hubbard and Rubin, 2000)can convert geophysical images to hydrologic estimateswhile accounting for uncertainty in the parameters ofpetrophysical relations, but the petrophysical relation maynot hold at the field scale or be appropriate for an invertedimage. For time-lapse imaging, identifying an effectivefield-scale petrophysical relation is especially problema-tic, as measurement sensitivity and measurement error,


K. SINGHA ET AL.

and thus image resolution, may vary in time as well asspace; moreover, temporal smearing and aliasing canoccur as a result of the non-negligible time required tocollect a geophysical imaging dataset and the timeinterval between datasets.Several statistical approaches have been devised to

develop field-scale calibrations to convert geophysicaltomograms to estimates of hydrologic parameters. Day-Lewis and Lane (2004) used random field averaging(RFA) to predict the field-scale correlation between twoproperties (i.e. geophysical and hydrologic) correlated atthe point scale, when one property is found by inversionand thus resolution-limited. Day-Lewis et al. (2005)applied this approach to ERI, providing insight into thepattern of correlation loss for ERI (Figure 3). Moyseyet al. (2005) developed an approach, Full InverseStatistical (FISt) calibration, to convert geophysicaltomograms to estimates of hydrologic parametersaccounting for the imperfect resolution of geophysicaltomograms. Their conversion strategy entails MonteCarlo simulation of numerical analogues of the geophys-ical experiment, generating an ensemble of tomogramsfrom which a field-scale petrophysical relation isdeveloped. Singha and Gorelick (2006) applied theapproach to a field-scale ERI problem. The concept of‘apparent petrophysical relations’, outlined in thesepapers, provides a means to upscale point-scale relations,as derived in the laboratory, to the field scale whileaccounting for survey geometry, measurement physics,regularization, and measurement error. Singha et al.(2007) developed apparent petrophysical relations usingRFA and FISt and found that the two approachesproduced similar results for linear problems; however,the RFA approach likely breaks down where assumptionsof second-order stationarity, Gaussian errors, and a linearforward model are violated. Although FISt relaxes theseassumptions, the approach still requires some knowledgeof the spatial models of geophysical and hydrologicvariability, an underlying petrophysical model linking thegeophysical and hydrologic properties, and quantificationof measurement errors. Such information is commonlynot available a priori.

Correlation in time

Simple comparison of inverted images between timesteps is no longer the state of the science. Such qualitativeinterpretation of time-lapse tomograms can providevaluable insight into subsurface properties and changesassociated with diverse hydrologic processes and engi-neering practices; however, the objectives of time-lapsegeophysical surveys are increasingly quantitative innature. Time-lapse geophysical tomograms provide richdatasets amenable to analysis using classical time series


and spectral frameworks. However, such analysis hasonly recently been reported. Johnson et al. (2012) andWallin et al. (2013) examined cross-correlation betweentime series of 3-D and 2-D conductivity tomograms andColumbia River stage proximal to the Hanford 300 Areanear Richland, Washington, to infer aquifer/streaminteraction. Correlation coefficient, time lag, and coeffi-cient of variation between river stage and conductivity allrevealed preferential pathways (Figure 4) connecting theaquifer and river. This work required no assumption of apetrophysical model yet provided quantitative informa-tion for the timing of aquifer/river interaction. Time-frequency analysis using the S-transform providedadditional insight into non-stationary behaviour (Johnsonet al., 2012).

Condensing to summary statistics

Given direct sampling of tracer concentration ormoisture associated with an injection experiment orinfiltration experiment, it is common practice to condensethe sampled data to temporal or spatial moments, fromwhich plume morphology and evolution are inferred. Inthe case of solute concentration, spatial and temporalmoments provide valuable insight into controllingprocesses such as advection, dispersion, and rate-limitedmass transfer (e.g. Freyberg, 1986; Goltz and Roberts,1987; Garabedian et al., 1991; Harvey and Gorelick,1995b). The 3-D spatial moments at time t and the 1-Dtemporal geometric moments at location (x,y,z) ofconcentration C are given, respectively, by

mspatiali; j;k ¼ ∫∫∫xiy jzkC x; y; z; tð Þdx dy dz; and (25)

mtemporall ¼ ∫tlC x; y; z; tð Þdt (26)

where i, j, k, and l, are the moment orders for x, y, z, and t,respectively.Time-lapse images comprise valuable spatially distrib-

uted time series relevant to hydrologic processes and canbe summarized similarly to solute concentration ormoisture, as spatial or temporal moments of electricalconductivity; these geophysical moments have been takenas surrogates for moments of injected tracer (Singha andGorelick, 2005; Ward et al., 2010a) and moisture content(Binley et al., 2002; Haarder et al., 2012). Time-lapseERI results for tracer injection experiments also havebeen condensed to effective velocity and dispersivityvalues, termed effective convection–dispersion equation(CDE) parameters (Kemna et al., 2002; Vanderborghtet al., 2005; Koestel et al., 2008; Muller et al., 2010). In anumerical study, Vanderborght et al. (2005) demonstratedthat with high-resolution ERI, the effective velocitiesderived from ERI are strongly correlated with hydraulic



conductivity. In controlled laboratory experiments,Koestel et al. (2008) found good agreement betweenapparent CDE parameters from ERI and effectiveparameters calculated from breakthrough curves.The same issues impeding conversion between

geophysical and hydrologic estimates manifest to varyingdegrees in calculation of moments, CDE parameters, orother summary statistics. Day-Lewis et al. (2007)evaluated the recovery of plume moments by tomograph-

Figure 3. Syntheticmodels fromDay-Lewis et al. (2005) demonstrating howspatiathis case, water content based on cross-well data collection, hence the longer z-axis tlog10 diagonal of the model resolutionmatrix, (d) the inverted tomogram of ln(resis

(resistivity). In the bottom are a series of assumed (white line) and e


ic imaging as a function of survey geometry, measure-ment error, and regularization. Although their examplesfocused on linear ray-based tomography (i.e. not ERI,TDIP, or CR), Day-Lewis et al. (2007) found that theconventional pixel-based parameterization and Tikhonovregularization (Tikhonov and Arsenin, 1977) commonlyused for electrical inversion can produce images fromwhich inferred moments only poorly approximate trueplume moments. In addition to issues of incomplete or

lly variable resolution inERI images impact estimated hydrologic parameters (inhan x-axis). Cross sections of (a) truewater content and (b) true resistivity, (c) thetivity), and (e) the predicted correlation coefficient between true and estimated lnstimated (surface plot) petrophysical relations from this example


K. SINGHA ET AL.

limited survey coverage, regularization, and imperfectresolution, another issue in time-lapse electrical data istemporal smearing. Commonly, time-lapse electricaldata are inverted with the assumption that changesin resistivity structure during data collection arenegligible, i.e. data acquisition for a single image issubstantially faster than any changes occurring as aresult of tracer migration, infiltration, or other processes

Figure 4. Summary statisticswere extracted from time-lapse ERI byWallin et alHanford 300 Area near Richland,Washington, USA. (Top) Time-lapse ERI imag(Bottom) (A) Normalized river stage and conductivity time series at the five exariver stage and conductivity time series in each image pixel, indicatingwhere rivertomaximumcorrelation between river stage and conductivity in each pixel, whichtime series in each pixel, indicating most active zones of groundwater/river wate

series, which is indicative of flow velocity. Red electrode p


under study. Koestel et al. (2008) suggest thatcalculation of effective CDE velocity and dispersivityis more robust than calculation of moments fromimages, but the resolving power of tomographicimaging still limits the quality of results.Recently, the ERI inverse problem has been reformulated

to invert directly for plume geometry (e.g.Miled andMiller,2007). Pidlisecky et al. (2011) formulated the inverse

. (2013) to understand aquifer/river interaction along theColumbia River at thees were collected on electrode lines 1–3. Statistics for line 1 are shown below.mple image pixel locations shown in (B). (B) Maximum correlation betweenand aquifer betweenERI lines aremost hydraulically connected. (C) Lag timeis indicative of flow velocity, (D) coefficient of variation of bulk conductivityr interaction, (E) peak-to-peak time shift between stage and conductivity timeoints are located over former waste infiltration galleries



problem for distribution-based parameters, i.e. the param-eters of a Gaussian and/or log-Gaussian plume. Laloy et al.(2012) parameterized a tomographic inverse problem usingspatial orthogonal moments, which are linear combinationsof the conventional geometric moments (Equations (25) and(26)). These alternative parameterizations effectively con-dense the information captured in the time-lapse geophys-ical datasets to a handful of summary statistics, each ofwhich provides direct insight into the transport process andmay be more interpretable than an over-parameterizedimage. For example, the zeroth-order geometric momentgives the total mass (controlled by decay processes), the firstand zeroth together give the centre of mass (controlled byadvection), and the second and zeroth together give thespread (controlled by dispersion and heterogeneity). Inprinciple, it is possible to calculate parameters controllingsolute transport directly from temporal moments. Forexample, for solute transport with dual-domain masstransfer, the mass-transfer rate coefficient and the ratio ofimmobile to mobile porosity can be calculated as simplelinear combinations of the temporal moments of electricaland fluid data (Day-Lewis and Singha, 2008). BothPidlisecky et al. (2011) and Laloy et al. (2012) foundimproved recovery of plume morphology and mass usingthis new paradigm for inversion of time-lapse ERI data.Knowledge of plume moments (or effective CDE

parameters) provides quantitative insight into hydrologicprocesses and controlling parameters. Although valuable asa final result of analysis, such condensed information maybe useful in further analysis involving model calibration. Asreviewed subsequently, calibration of process models to afew inferred moments or CDE parameters is an efficientalternative to calibration to time-lapse ERI results consistingof time series for the hundreds or thousands of pixels orvoxels a tomogram comprises.

Calibration of hydrologic process models

It is reasonable to expect that changes in geophysicallyimaged properties coincide, in space and time, withchanges in hydrologic parameters, such as moisturecontent and salinity. Rather than seek to convert thegeophysical tomogram to a cross section (or volume) ofthe hydrologic parameter, the calibration strategy seeks touse the geophysical images as calibration data for thehydrologic process model. In our definition and catego-rization of translation strategies, we draw an importantdistinction between calibration and coupled inversion,explained in more detail subsequently.The hydrologic model may be calibrated to the

geophysical information in various ways, some involvinga petrophysical relation and conversion step and othersnot. The level or rigour in calibration ranges from manualcalibration to formal parameter estimation using optimi-


zation algorithms [e.g. PEST (Doherty and Hunt, 2010)and UCODE (Poeter et al., 2005)]. In some cases,calibration may be to summary statistics derived fromgeophysical images. For example, Binley et al. (2002)calibrated a vadose zone model to estimate saturatedhydraulic conductivity using spatial moments (i.e. centreof mass) of cross-hole electrical resistivity images. Deianaet al. (2008) converted resistivity tomograms to watercontent and used moments from the resulting watercontents to calibrate an infiltration model and estimatesaturated hydraulic conductivity. Briggs et al. (2013) usedUCODE to calibrate a MT3D (Zheng and Wang, 1999)solute-transport model with dual-domain mass transfer toboth concentration data and apparent conductivities.Doetsch et al. (2013) calibrated a TOUGH2 (Pruess et al.,1999) flow and transport model for CO2 migration to time-lapse electrical resistivity tomograms using a petrophysicalrelation to link gas saturation and resistivity.

Coupled inversion

Coupled inversion has the potential to directly translategeophysical data into hydrologic information during ahydrologic inversion procedure. There is no inversion forgeophysical parameters (e.g. conductivity), post-inversionconversion of geophysical inversion results, or calibrationof a hydrologic process model to geophysical inversionresults. The term ‘coupled inversion’ has variousdefinitions in the literature, with synonyms sometimesincluding joint inversion, data fusion, and data integra-tion. We stress, however, that these terms have differentmeanings in different publications. In the followingdiscussion, we attempt a review of definitions found inthe recent literature and clarify important differences.The goal of coupled inversion, by any common

definition of the term, is to reduce uncertainty and betterconstrain estimation of hydrologic properties or statescompared with inversion conditioned to a single datatype. The philosophy underlying coupled inversionstrategies is not new and goes back decades in thehydrologic literature, with numerous papers combining,for example, temperature and head data (e.g. Stallman,1965; Woodbury and Smith, 1988; Lapham, 1989;Woodbury, 2007) and tracer and head data (e.g. Grahamand McLaughlin, 1989a; Graham and McLaughlin,1989b; Carrera, 1993; Harvey and Gorelick, 1995a).Similarly, the geophysical literature is replete with articlesin which multiple data types are inverted simultaneouslyto better constrain estimates of parameters common to themultiple underlying forward models. We focus thisreview on work in which ERI is used within a coupledinversion framework, but emphasize that seminal work usingsimilar approaches with other data types (e.g. Kowalskyet al., 2005) is outside the scope of this paper.


K. SINGHA ET AL.

In recent years, considerable effort within thehydrogeophysics community has been dedicated todevelopment and application of techniques of coupledinversion, called by other names depending on the author.Yeh and Simunek (2002) proposed two levels of ‘datafusion’ in the context of a study in which ERI is used toinform estimation of hydrologic parameters governingvariably saturated flow. In Level 1 data fusion, thehydrologic estimation problem is conditioned on resultsfrom the geophysical image (i.e. calibration in ourterminology). In Level 2 data fusion (Figure 5), theinverse problem is solved using both types of data, with astrong coupling between the two forward models, inwhich resistivity data are used alongside hydrologic datato estimate hydrologic parameters, and the hydrologicmodel output is used as input to the geophysical forwardmodel. Whereas calibration uses the geophysicalinversion results (i.e. the image) as additional data forestimation of hydrologic parameters, Level 2 data fusion(i.e. coupled inversion) uses geophysical data asadditional hydrologic data. The disadvantage of Level 1data fusion is that geophysical images are resolution-limited and bear the imprint of regularization, priorinformation, temporal smearing, mapping of data errorsinto the model, and limited survey geometry.More recently, Hinnell et al. (2010) coined the term

‘hydrogeophysical coupled inversion’, for a workflow,which functionally is identical to that of Yeh and Simunek’s

Figure 5. Workflow for hydrogeophysical inversion, adapted from Level 2data fusion as outlined by Yeh and Simunek (2002) and functionallyidentical to ‘coupled hydrogeophysical inversion’ as defined by

Hinnel et al. (2010)


Level 2 data fusion. Coupled hydrogeophysical inversionfocuses on similar linkages between a hydrologic processmodel (i.e. flowor transport) with geophysical data sensitiveto the hydrologic process (e.g. electrical conductivity).Coupling as outlined by Hinnell et al. (2010) and in Level 2data fusion as outlined by Yeh and Simunek (2002) isachieved in the inversion of data by explicitly accountingfor the effect of the hydrologic state on the geophysicalproperty. Output from the hydrologic forward model (e.g. atransport model to simulate a tracer test) is fed through apetrophysical relation, and the result is used as input to thegeophysical forward model (e.g. electrical conduction tosimulate ERI data). The primary limitation of this approachis that the petrophysical relationship is rarely known atthe field scale. The inverse solution will tend to producehydrological parameter estimates consistent with thepetrophysical model assumed, resulting in biased estimatesif the petrophysical model is inaccurate. Johnson et al.(2009) proposed and synthetically demonstrated anapproach that bypasses the petrophysical relation bymaximizing the correlation between observed ERI dataand that produced by the coupled model. Irving andSingha (2010) demonstrated a stochastic coupled-inversion framework using Markov chain Monte Carlo(MCMC) algorithm for ERI and tracer data. Suchstochastic approaches are amenable to modifications thatenable uncertainty in the petrophysical relationship to beappropriately accounted for. Ultimately, petrophysicaluncertainty is one of the primary factors limiting theutility of coupled inversion approaches. Resolving thisproblem remains an area of active research.Whereas most examples of coupled inversion to date

have focused on fusion of information consideringgeophysical data and hydrologic data as contributing todifferent terms in the inverse problem’s fitting criteria orobjective function, Pollock and Cirpka (2008; 2012)presented a coupled inversion framework in which thephysics of the two data types are linked at a more basiclevel. For the specific problem of monitoring ionic tracerswith ERI, Pollock and Cirpka (2008) derived temporalmoment generating equations for concentration andelectrical potential perturbations as a function of theunderlying hydraulic conductivity field.At the time of this writing, coupled inversion remains

an active area of research in hydrogeophysics, with newtools being developed to facilitate applications to realdatasets. For example, Lawrence Berkeley Laboratory’sMPiTOUGH2 (Commer et al., 2013) now explicitlysupports coupled inversion. Recent developments inparameter estimation codes such as PEST (Doherty andHunt, 2010) and UCODE_2005 (Poeter et al., 2005)similarly allow for consideration of multiple data types.With such advancements, we foresee proliferation ofcoupled inversion studies in the literature.



TECHNOLOGICAL ADVANCES

Instrumentation

Advances in time-lapse electrical imaging capabilitieshave been enabled in part by the development of autonomousmulti-electrode, multi-channel instrumentation. Modern daysurvey instruments are capable of accommodating many tensof electrodes using a single control unit, which can beexpanded with additional switching units to accommodatemany hundreds to thousands of electrodes, each capable ofeither transmitting current or measuring potential. Inaddition,multi-channel instruments enable the simultaneousmeasurement of potential across many pairs of electrodesfor a given current injection, which has the potential todecrease survey times by the reciprocal of the number ofchannels, thereby substantially improving temporalresolution. Most systems also allow fully customizedmeasurement sequences that are completed withoutuser intervention. System control and data transferthrough wireless internet connection facilitate long-termfield deployment and enable remote, continuous, andautonomous time-lapse monitoring of subsurface processesfrom data collection to offsite transmission for processing.Coupled with equally autonomous data processing andinversion on the software end, this provides the opportunityto execute real-time autonomous monitoring of subsurfaceprocess through time-lapse ERI (Versteeg et al., 2006;Johnson et al., 2010a). In addition to commercially availablesystems, the availability of highly customizable ‘smart’electrical hardware components and advanced, high-levelcontrol software have facilitated the development of capableand inexpensive custom ‘home grown’ ERI surveyinstruments (Sherrod et al., 2012).

High-performance computing

Advances in survey instrumentation have enabledapplications using large numbers of electrodes and havereduced survey times between time-lapse surveys,providing the opportunity to monitor over larger areasand to improve spatial and temporal resolution. In manycases, fully utilizing the monitoring capabilities affordedby these systems is cumbersome or impossible with non-scalable or limited scalability computing systems due tothe computationally intensive nature of ERI, TDIP, or CRinversion, particularly for 4-D imaging applications.Several practitioners have addressed the computationaldemands of large-scale applications by developinginversion software capable of using parallel computinghardware. For example, Loke et al. (2010) demonstrated areduction in computing time of more than two orders ofmagnitude by optimizing memory usage and leveragingthe parallel computation capabilities of the graphicalprocessor unit when optimizing measurement sequences


for 2-D ERI arrays on a commonly available microcom-puter. In addition, most inversion codes are capable ofutilizing the shared-memory parallelism naturally provid-ed by modern multi-core processors and/or sharedmemory multi-CPU computing hardware.Given the high cost of massively parallel shared-memory

systems, most high-performance parallel computing systemsare distributedmemory, wherebymanymachines comprisingindependent CPUs and memory are linked together byhigh-speed networking hardware. This enables relativelyinexpensive access to large numbers of processors and largevolumes of memory, but requires parallelized inversionsoftware written specifically to run on distributed memorysystems. Commer et al. (2011)modified a parallel frequency-domain EM inversion code to invert time-lapse SIP data.They used the code to image 4-D changes in conductivitymagnitude and phase during a bioremediation experimentusing 250 CPUs on a distributed memory parallel computingsystem. In addition, Johnson et al. (2010b) described aparallel inversion algorithm designed to invert 3-D and 4-DERI datasets, which has facilitated temporally dense 4-Dmonitoring applications over extended periods requiringhundreds to thousands of inversions (Johnson et al., 2012;Truex et al., 2013; Wallin et al., 2013).

Survey design optimization

Survey design is the process whereby the number ofelectrodes, electrode layout, and set of measurementscomprising a survey is selected. Many survey types havebeen used, with practitioners often choosing from one(or a combination) of traditional array types that weredefined in the early days of electrical prospection beforethe advent of imaging. Five such arrays are the Wenner,Schlumberger, dipole–dipole, pole–pole, and pole–dipoleconfigurations. Most of these arrays were designed toaddress a particular issue. For example, the Wenner arrayprovides a high signal-to-noise ratio, whereas theSchlumberger array is particularly sensitive to horizontalcontacts. The general advantages and disadvantages ofeach array are well understood and have been publishedin previous literature (Ward, 1990) and each continues tobe used today. However, it is also well recognizedthat, for a given electrode layout and subsurfaceconductivity, there are likely non-standard arrays thatcan optimize imaging resolution for a given number ofmeasurements. This can be especially important intime-lapse imaging applications because the maximumpossible temporal resolution is equal to the time requiredto complete a survey, and therefore to the number ofmeasurements collected in a survey. Reducing the numberof measurements in a survey increases temporal resolu-tion, but in general will decrease spatial resolution. It isalso important to consider efficient sequences for


K. SINGHA ET AL.

collecting error measurements, in particular reciprocalmeasurements (Slater et al., 2000).The number of four-electrode non-reciprocal

measurements nd to choose from given ne electrodes is(Noel and Xu, 1991)

nd ¼ ne ne� 1ð Þ ne� 2ð Þ ne� 3ð Þ=8 (27)

which represents a remarkable number of possibilities, evenfor a modest number of electrodes. For example, for 24electrodes, nd is equal to almost 32 000. For a givenelectrode layout, survey optimization methodologies ingeneral seek to identify sets of measurement sequences thatoptimize spatial resolution with a minimum number ofmeasurements, thereby also optimizing temporal resolution.Several approaches have been proposed for survey

optimization, with most research as of late focusing onmethods that increase the diagonal of the resolution matrix(Menke, 1989; Lehmann, 1995; Stummer et al., 2004; Zheet al., 2007; Maurer et al., 2010; Blome et al., 2011;Wilkinson et al., 2012). Wilkinson et al. (2006) alsoproposed an optimization scheme that, in addition tooptimizing the diagonal of the resolution matrix, also seeksto minimize electrode polarization effects by allowingsufficient time between when a particular electrode is usedto inject current and subsequently measure potential. Suchan approach is potentially valuable when collecting TDIP orCR data. It is worth noting, however, that the resolutionmatrix is dependent upon the conductivity distribution,so optimized surveys generated using an erroneousconductivity distributionmay not be optimal at all, althoughthe papers referenced earlier have demonstrated goodimprovements in resolution, in synthetic and field studies,when optimizing about a homogeneous conductivity field.In many time-lapse studies, while the conductivity willchange during the monitoring period, it may not changesubstantially, which allows this exercise to remain valuable.Other possibilities for improved experimental designinclude making sequential measurements that reduce thesize of the null space (e.g. Coles, 2008).Although survey design methods proposed to date have

demonstrated impressive spatial resolution with a rela-tively small number of measurements, optimizationschemes that rely on calculating the resolution matrixare computationally demanding, even with the moreefficient updating schemes (Wilkinson et al., 2006; Lokeet al., 2010), and have only been demonstrated on modest2-D arrays to date. These can be used as a starting pointfor 3-D survey optimization, but efficient methods for full3-D optimization have not yet been demonstrated. Giventhe computational demands of optimization, the value ofoptimizing surveys for conductivity characterization (asopposed to collecting and inverting a more comprehen-sive survey that provides similar resolution) is debatable.However, optimized surveys may be needed in time-lapse


imaging applications where subsurface conductivity isevolving quickly and high temporal resolution is needed.Regardless of the method used to design a time-lapse

survey, the resulting survey should be synthetically tested toensure the survey meets design objectives. Unfortunately,this important step is often overlooked. Such a testincludes modelling subsurface conductivity distributionsrepresentative of those anticipated during the fieldexperiment, generating the synthetic data resulting fromthose distributions for the designed survey through forwardmodelling and assessing forward model accuracy, addingnoise to the data consistent with that expected in the field,inverting the data, and analysing the resulting imagesagainst the design criteria. If possible, a pre-design surveyshould be conducted to provide information concerning thebackground conductivity distribution and noise conditions.These can be used in the design and synthetic testing phaseas described earlier to provide an accurate assessment ofsurvey performance under field conditions. An assessmentof survey time should also be conducted to ensure the surveydesign provides adequate time resolution. In this regard, onesensible strategy is to first identify the maximum number ofmeasurements that can be collected and still satisfy timeresolution requirements, and then design the survey to thatnumber of measurements.

Emerging applications

Developments in measurement technology, inversion, andjoint inversion methods have lead to a tremendous growth inapplication of electrical methods. Here, we highlight a fewmajor areas where process monitoring is being increasinglyperformed with ERI, TDIP and/or CR: (1) groundwaterresources and exchange processes, (2) vadose zone processes,(3) solute and contaminant transport, (4) ecological processes,(5) biogeochemistry and remediation, and (6) carbon dioxidestorage. The multi-dimensionality of these methods and theirstrength for long-term continuous monitoring, givensemi-permanently emplaced electrodes, can be highlyadvantageous over traditional point-based methods forstudies of time-varying processes.

Groundwater resources and exchange

Electrical resistivity imaging has been particularlysuccessful in monitoring the movement of water atinterfaces, including exchange between surface water andgroundwater, or groundwater and the ocean or estuaries.Recent work has used ERI methods to build relationshipsbetween electrical conductivity, hyporheic exchange, andalluvial deposits (Crook et al., 2008; Slater et al., 2010;Bianchin et al., 2011; Doro et al., 2013) or to directlymonitor exchange between groundwater and surfacewater (Nyquist et al., 2008; Coscia et al., 2011). Manyauthors have used tracers to image these exchange



processes (Figure 6) (Ward et al., 2010b; Ward et al.,2010a; Cardenas and Markowski, 2011; Doetsch et al.,2012; Ward et al., 2012a; Ward et al., 2013). ERI and CRhave also been used to image natural exchange processes(Slater and Sandberg, 2000; Breier et al., 2005), includingthe exchange of seawater with a freshwater sand aquiferin a tidewater stream (Acworth and Dasey, 2003) andexchange associated with daily dam operations (Cosciaet al., 2012; Johnson et al., 2012; Wallin et al., 2013).ERI has additionally been used to image groundwaterexchange with bays and oceans, and studies have shownthat ERI can be used to determine areas of discharge,which can have important implications for nutrientloading and water management (Bratton et al., 2003;Day-Lewis et al., 2006b; Henderson et al., 2010).Electrical resistivity imaging has also been used to image

transport between fast and slow paths in groundwatersystems, such as fractured rock or karst. Quantifying thelocation of the fast flow paths in these heterogeneoussettings, how they may change in time, and the fluidinteractions between fast paths and a lower permeabilitymatrix that may include substantial storage capacity isimportant to understanding the vulnerability of theseaquifers to contamination. In the case of karst systems,targets may be large air-filled or fluid-filled conduits ofsufficient contrast to be easily mapped (e.g. Šumanovac

Figure 6. Electrical resistivity imaging of solute transport in a stream and anfrom Ward et al. (2010b). Transects shown are perpendicular to the stream,model. Areas of high resistivity at an elevation of 3-m local datum are suggephysical location. (C–G) Time-lapse ERI results, at time elapsed after beginni

bulk resistivity from background condition


and Weisser, 2001; van Schoor, 2002; Deceuster et al.,2006; Youssef et al., 2012). An overview of geophysicaltechniques applicable to karst systems was recentlypublished by Chalikakis et al. (2011). Fractured rockcontinues to be an area of characterization difficult for ERImethods, which are often of poor enough resolution thatimaging specific features is difficult. Despite this issue,recent contributions have highlighted possible approachesto better imaging fractures and transport in fractures byfocusing onmore appropriate inversion parameterization forfractured rock settings given an understanding of fracturelocations from borehole logging data (Robinson et al.,2013a; Robinson et al., 2013b).It is important, especially in hydrologic systems, to account

for temperature effects on resistivitymeasurements. Electricaldata are often calibrated to remove changes associated withtemperature changes in the subsurface (e.g. Hayley et al.,2007). In the absence of calibration, electrical measurementsmay produce confounding signals in complicated settingswhere temperature as well as other properties controllingresistivity is changing (Rein et al., 2004; Revil et al., 2004).That said, many have capitalized on this change to use ERIto directly image changes in temperature in hydrogeologicsettings (Ramirez et al., 1993; Ramirez and Daily, 2001;Musgrave and Binley, 2011). Temperature changes of afew degrees have produced resistivity changes of 10–20%

abandoned stream channel during a 21-h tracer injection in Pennsylvaniawith flow directed out of the page. (A) Pre-injection electrical resistivitysted to be an abandoned cobble bed. (B) Model sensitivity as a function ofng the conservative solute injection. Colour indicates the percent change ins. (H) Interpretation of resistivity images


K. SINGHA ET AL.

in controlled studies (Revil et al., 1998). Additionally,ERI associated with geothermal fields has occurred overthe past many years; only recently have these methodsbeen used to help calibrate fluid and heat flow models(Hermans et al., 2012).

Vadose zone moisture dynamics

Electrical resistivity imaging has been frequently usedto monitor moisture dynamics in the vadose zone, goingback to early work by Daily et al. (1992). ERI is generallyused in the vadose zone to image infiltration, defineinterface geometries, or map preferential flow paths.Binley et al. (2002), for instance, monitored seasonaldynamics of moisture within a sandstone aquifer, andused ERI to map wetting and drying fronts. French et al.(2002) used ERI to monitor tracer transport andinfiltration associated with snowmelt and quantifiedmovement with moment analysis. More recently,Travelletti et al. (2012) used ERI in a simulated 67-hrainfall experiment to monitor water infiltration andsubsurface flow to pinpoint when steady-state conditionswere reached, and determine bedrock depth and potentialpreferential flow paths. Gasperikova et al. (2012) usedboth cross-well and surface ERI to examine the impactsof recharge on subsurface contamination, primarilynitrate. Some recent work has used ERI to help look atlongstanding issues in hydrology where spatially exhaus-tive data may contribute, for example, to the idea that theassumption of 1-D piston flow associated with recharge isnot valid (Nimmo et al., 2009; Arora and Ahmed, 2011).Some authors have also explored new inversion tech-niques given a vadose zone motivation; Yeh et al. (2002)developed geostatistically based inversion, and Mitchellet al. (2011) explored different inversion techniques formonitoring the decreasing effectiveness of a rechargepond through time.Recent work has also explored partially saturated flow

in alpine watersheds using ERI, including quantificationof storage and flow. Sass (2004) used ERI to image porewater being pushed away from the freezing frontassociated with increasing hydraulic pressure duringfreezing in the Alps. Langston et al. (2011) imagedperched water and focused infiltration, which could beused to quantify the timing of alpine watershed discharge.McClymont et al. (2010; 2011) used multiple geophysicaltools, including ERI, to image subsurface sedimentpackages and bedrock topography, which controlledavailable storage and the location of springs, respectively,in the Canadian Rockies. Two recent studies outlineinformation provided from ERI about flow dynamics onlonger scales than are commonly considered. Hilbich et al.(2008) describe continuous ERI monitoring of permafrost


within the Swiss Alps for 7 years and found short-term,seasonal, and interannual changes associated withchanges in melt and radiation. Both vertical andhorizontal infiltration of water affected these measure-ments, and the authors noted that moisture measurementswould be needed to separate moisture from temperaturechanges. Scherler et al. (2010) explore infiltration alongheterogeneous flow paths to investigate energy and masstransfer in Switzerland and found an interesting cycle ofdecreased surface permeability from freezing, increasedpressure heads, and then infiltration and heat transfer, andused ERI to constrain moisture content ignoring changesin temperature.Electrical resistivity imaging has also been successfully

used to explore vadose zone remediation, includingengineered vadose zone desiccation, which was recentlytested at the Hanford Site as a remediation technology forslowing the migration of contaminants toward the watertable (Truex et al., 2013). Relying on the petrophysicalrelationship between saturation and electrical conducti-vity, 4-D cross-hole ERI was used to monitor thedesiccation zone with time, providing detailed informa-tion concerning the subsurface structure and desiccationperformance (Figure 7).

Contaminant transport

Electrical resistivity imaging has been a successfultool for monitoring contaminant transport in the case ofimaging electrically conductive contaminants like land-fill leachates (e.g. Chambers et al., 2006; Mansoor andSlater, 2007). Other contaminants are more difficult todetect. For example, non-aqueous phase liquids(NAPLs) are challenging targets for electrical methodsas the electrical properties of NAPLs change over time inresponse to biodegradation (see, for review, Atekwanaand Atekwana, 2010). CR has been repeatedly exploredas a potential technology for characterization andmonitoring of NAPL contaminants in the subsurface;early CR monitoring experiments focused on thepotential of CR to monitor the transport of dense non-aqueous phase liquid (DNAPL) (Daily et al., 1998;Chambers et al., 2004). Such efforts were motivated bylaboratory experiments suggesting that reactionsbetween DNAPL and clay minerals (clay–organicinteractions) could be sensed with CR (e.g. Olhoeft,1985). However, contrary to such laboratory studies, CRmonitoring experiments on recently spilled DNAPLfound the phase as measured by CR to be relativelyinsensitive to the presence and/or transport of DNAPL,with more information coming from |σ| as a result of theresistive DNAPL replacing the electrolyte within thepore space (Daily et al., 1998; Chambers et al., 2004).More recent laboratory experiments indicate that CR


Figure 7. (Top) Pre-desiccation 3-D baseline ERI image showing bulk electrical conductivity along selected iso-surfaces modified from Truex et al.(2013). Higher electrical conductivity lenses are diagnostic of fine-grained, elevated moisture units that tend to harbour contaminated pore water. Lowerelectrical conductivity lenses represent coarser-grained, higher-permeability units that likely provide preferred flow pathways between gas injection andextraction wells. (Bottom) Three-dimensional view of the change in volumetric water content (WC) over time derived from 3-D cross-hole ERI. Two

tomograms were produced per day over the 70-day monitoring period


Copyright © 2014 John Wiley & Sons, Ltd. Hydrol. Process. (2014)

K. SINGHA ET AL.

signals of clay–organic interactions are uncertain andsometimes small (Ustra et al., 2012). This in partexplains the limited success of these early CR imagingexperiments.

Ecological processes

Electrical resistivity imaging has been successfullyused in recent years to image processes driven by orimportant to biology, from the microbiological scales upto ecosystem dynamics. For example, ERI has been usedto image root uptake in variably vegetated systems(Jayawickreme et al., 2008; Jayawickreme et al., 2010);the authors found differences in soil moisture distributionbetween forested and grassland ecosystems throughoutthe growing season that are important for parameterizingroots in global climate and hydrological models(Figure 8). On shorter time scales, Robinson et al.(2012) monitored ERI in an oak–pine forest, findingresults indicative of hydraulic lift, whereby trees pumpwater from deep within the vadose zone and release itnear the surface. al Hagrey (2007) used ERI todiscriminate between types of roots (soft vs woody) aswell as imaging moisture content within the root zone andin tree trunks (al Hagrey, 2006), inspiring similar workdifferentiating sapwood from heartwood (Guyot et al.,2013). Other authors have similarly used ERI to look atmoisture dynamics and its importance on vegetation, fromMediterranean southern France (Nijland et al., 2010) tothe Mojave Desert (Nimmo et al., 2009).

Figure 8. Two-dimensional ERI across a sharp ecotone in Michigan from Jayathe peak of the growing season (August). ERI data show a significantly larg

deeper effec


Biogeochemistry and remediation

Significant research has recently explored the electricalsignatures resulting from microbial growth and interac-tions between microbes and mineral surfaces. Themonitoring of biogeochemical processes associated withthe natural or stimulated biodegradation of contaminantsis a promising application of CR monitoring. Numerousrecent laboratory experiments have indicated that CR issensitive to microbe-mineral interactions (see for reviewAtekwana and Slater, 2009), particularly biomineraliza-tion associated with the sequestration of heavy metals(Williams et al., 2005; Slater et al., 2007). Flores Orozcoet al. (2011) built on these laboratory findings andsuccessfully demonstrated the feasibility of monitoringbiogeochemical changes accompanying stimulation ofindigenous aquifer microorganisms known to sequesteruranium during and after acetate injection (Figure 9).Spatiotemporal changes in the phase response of aquifersediments were shown to correlate with increases in Fe(II)and precipitation of metal sulfides (e.g. FeS) followingthe iterative stimulation of iron and sulfate-reducingmicroorganisms. In contrast, only modest changes in |σ|were observed over the monitoring period and could notbe clearly related to the biomineralization. Chen et al.(2012) suggested a Bayesian framework for estimatingthe geochemical parameters directly from the frequency-dependent CR response observed by Flores Orozco et al.(2011), although they recognized that the approach waslimited by the need for more robust petrophysical

wickreme et al. (2008) before the start of the growing season (May) and iner seasonal change in soil moisture for the forest and also that trees havetive roots


Figure 9. (a) Schematic representation of the experimental setup for a biostimulation experiment using CR. Monitoring wells upgradient (open circles)and downgradient (solid circles) of the injection gallery (solid black rectangle) are referred to the direction of the groundwater flow (solid arrow). Thedashed lines represent the location and extent of array A and B. All dimensions are given in metres. (b) CR images for the measurements collected alongarray A (red line in part a) in 2007 after an injection of 5mM acetate and 2mM bromide. Elapsed time in days is referenced to the start of acetateinjection. (left) Resistivity images for data collected at 1Hz. Phase images computed for data collected at (middle) 1 and (right) 4Hz. Modified from

Flores Orozco et al. (2011)


relations for quantifying biomineral concentration fromcomplex resistivity data.Electrical resistivity imaging has also been successful

in some situations for imaging solid phase transforma-tions and the emplacement and migration of amendmentsfor remediation (e.g. Ramirez et al., 1993; Dailyand Ramirez, 1995). For example, ERI was recentlydemonstrated as an effective bioremediation long-termbioremediation monitoring tool at a site contaminatedwith chlorinated solvents in Brandywine, Maryland, USA(Johnson et al., 2010b). A lactate-based amendment andpH buffer (sodium hydroxide) were injected into thesubsurface to moderate pH levels and stimulate thebio-activity of reducing organisms. A 3-D cross-boreholeERI array was installed at the site with the objective ofmonitoring the injection and subsequent transport ofamendment to determine which regions had been treated.The system operated autonomously for approximately3 years, collecting one 3-D ERI dataset approximatelyevery 2 days. Extensive sampling was also conducted inorder to relate changes in conductivity with changes inbiogeochemical conditions. A set of selected ERI imagesshowing the change in conductivity with time frombaseline conditions is shown in Figure 10. The ERIimages show the amendment plume sinking and spread-ing from the injection zone over a lower confining unitand slowly diluting from day 2 to day 371. Changes inbulk conductivity were consistent with changes in fluidconductivity during this period. From day 371 to 762, alarge secondary increase in conductivity was observed


that was not associated with a corresponding increase influid conductivity. Geochemical indicators sampledduring this period revealed enhanced bioactivity andprovided evidence for the formation of FeS precipitates.Furthermore, fine FeS particulates were observed inseveral wellbore samples during this period, suggestingthe large secondary increase in conductivity from day 371to 762 was caused by FeS precipitation. Thus, in this case,the ERI images provided detailed spatial and temporalinformation concerning both the transport of injectedamendments, and concerning the distribution and timingof corresponding biological activity, and stage ofbioremediation progress.

Carbon dioxide storage

ERI, TDIP, and CR can also be useful technologies formonitoring processes associated with climate change. Forexample, while capturing and storing CO2 has become apopular idea for controlling greenhouse gas emissions tothe atmosphere, long-term storage of CO2 requiresmonitoring for possible CO2 migration and leakage.ERI is a promising method for these studies because CO2

displaces conductive brine in many storage areas. Anumber of studies have used ERI to monitor CO2

propagation in storage sites (Ramirez et al., 2003; Gieseet al., 2009; Kiessling et al., 2010; Bergmann et al., 2012;Doetsch et al., 2013), including a recent study thatimaged CO2 injection into an oil-and-gas field at 3000mdepth (Carrigan et al., 2013).


Figure 10. Four-dimensional ERI monitoring images during enhancedbioremediation at a site in Brandywine, Maryland. The images show thesodium enriched, lactate amendment plume sinking and spreading fromthe injection zone over a lower confining unit, and slowly diluting fromday 2 to day 371. Changes in bulk conductivity were consistent withchanges in fluid conductivity during this period. From day 371 to 762, alarge secondary increase in conductivity was observed resulting fromincreased bioactivity and subsequent FeS precipitation, which was

validated by sampling

K. SINGHA ET AL.

Monitoring geochemical transformations associatedwith CO2 storage and sequestration in aquifers representsanother promising application of CR monitoring. Forexample, Dafflon et al. (2013) performed a CRmonitoring experiment on a test site where dissolvedCO2 was injected into the subsurface. The data were notof sufficient quality to generate reliable time-lapse imagesof phase, highlighting the challenges of acquiring reliableCR data as stressed earlier. Dafflon et al. (2013) did


suggest that the ϕ recorded on sets of electrodes thatsample the subsurface properties close to the boreholeshowed some evidence for additional information beyondwhat was obtained from |σ| alone. They suggested thatthis resulted from changes in the surface charge density,along with possible mineral dissolution and ion exchange.However, changes in ϕ largely tracked changes in |σ| inthis experiment, which can occur in the presence of onlychanges in electrical conduction (i.e. σ′). Consequently,this experiment was inconclusive in demonstrating theadditional information on geochemical transformationsthat can potentially be extracted from CR measurementsrelative to measuring |σ| alone.

DISCUSSION AND FUTURE DIRECTIONS

In this paper, we outline the state of the science withrespect to time-lapse electrical data collection, inversion,interpretation, and application. ERI methods have becomemainstream geophysical tools, with recent innovationsdriven by the development of multichannel, autonomoustools and improved inversion methodologies. Thesedevelopments have been applied to a wide range ofapplications, from imaging changes in water quality orquantity to mapping the moisture content of tree trunks tomapping CO2 injection for sequestration. Despite all ofthis work, there are a number of areas where thesetechnologies have not been used to their full potential.SIP largely remains a research technology outside of itslong-standing use for mineral exploration. Application ofERI/TDIP/CR methods to biological systems, in partic-ular, is an area where a substantial amount of fundamentalresearch still remains to be conducted. Also, while thesemethods are being more regularly applied for monitoring,a largely missing step is to use these tools to developdecision-support systems and improve environmentalstewardship; for example, these instruments could beused to image changes in moisture content as a functionof climate change, or saline intrusion along coastalaquifers as shown by the Automated Time-LapseElectrical Resistivity Tomography (ALERT) system(Kuras et al., 2009; Ogilvy et al., 2009). In terms oftools, the development of wireless receivers may changethe field; while recently on the market these remain rarelyused, but would be fundamental to mapping processesover large scales, such as watersheds.Major improvements have come with the development of

alternative parameterizations, for example to discretizeboreholes and regularization that allows for sharp bound-aries, important where such contrasts are expected.New inversion tools that move beyond over-parameterizedvoxel models to solving for process-indicative parametersdirectly also show promise. Parameterization based on the



physics of plume shape evolution, for example, appears apromising direction for future research to translate ERI results tohydrologic information. Indeed, the medical imaging literatureoffers many approaches to moment-based (e.g. Milanfar et al.,1996) and shape-basedparameterizations (e.g.Dorn et al., 2000;Miller et al., 2000) that might prove useful in hydrogeophysics.As a community, it is worth continuing to push towardalternative inversion and regularization techniques; ideas such assteering filters or prediction error filters (Schwab et al., 1996;Clapp et al., 1998) from seismic processing may be used toimprove tomograms and thus geological understanding of Earthsystems. Another challenge is how to balance different types ofdata within coupled inversion, where wemay have hundreds orthousands of geophysical measurements but only tens ofhydrologic observations. Future opportunities include furtherrefinement and continued adoption of joint inversion methodsfor estimating parameters or processes of interest directly, anddevelopment of rock physics relations for time-lapse inversions,where sensitivity and measurement errors change with time.

ACKNOWLEDGEMENTS

This research was supported in part by National ScienceFoundation Grant EAR-0747629 and Environmental Pro-tection Agency Region 1 and the U.S. Geological Survey’sToxic Substances Hydrology Program and GroundwaterResources Program.We thank two anonymous reviews andBurke Minsley for thoughtful feedback. Any use of trade,firm, or product names is for descriptive purposes only anddoes not imply endorsement by the US Government.

AcronymsCDE

Copyright © 2
0
Convection–dispersion equation
CR Complex resistivity CRI Complex resistivity imaging DC Direct current EDL Electrical double layer EI Electrical impedance ER Electrical resistivity ERI Electrical resistivity imaging FISt Full inverse statistical IP Induced polarization NAPL Non-aqueous phase liquid PFE Percentage frequency effect RFA Random field averaging RMS Root-mean-square SIP Spectral induced polarization TDIP Time-domain induced polarization
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