Marine electrical resistivity imaging of submarine groundwaterdischarge: sensitivity analysis and application in Waquoit Bay,Massachusetts, USA

Rory D. Henderson & Frederick D. Day-Lewis &

Elena Abarca & Charles F. Harvey & Hanan N. Karam &

Lanbo Liu & John W. Lane, Jr.

Abstract Electrical resistivity imaging has been used incoastal settings to characterize fresh submarine groundwaterdischarge and the position of the freshwater/salt-water inter-face because of the relation of bulk electrical conductivity topore-fluid conductivity, which in turn is a function of salinity.Interpretation of tomograms for hydrologic processes iscomplicated by inversion artifacts, uncertainty associatedwith survey geometry limitations, measurement errors, andchoice of regularization method. Variation of seawater overtidal cycles poses unique challenges for inversion. Thecapabilities and limitations of resistivity imaging are pre-sented for characterizing the distribution of freshwater andsaltwater beneath a beach. The experimental results providenew insight into fresh submarine groundwater discharge atWaquoit Bay National Estuarine Research Reserve, EastFalmouth, Massachusetts (USA). Tomograms from theexperimental data indicate that fresh submarine groundwaterdischarge may shut down at high tide, whereas temperaturedata indicate that the discharge continues throughout the tidalcycle. Sensitivity analysis and synthetic modeling provideinsight into resolving power in the presence of a time-varyingsaline water layer. In general, vertical electrodes and cross-

hole measurements improve the inversion results regardlessof the tidal level, whereas the resolution of surface arrays ismore sensitive to time-varying saline water layer.

Keywords Electrical resistivity imaging . Coastalaquifers . Groundwater/surface-water relations .Submarine groundwater discharge . Equipment/fieldtechniques . USA

Introduction

Fresh groundwater resources are threatened by salineintrusion (Foyle et al. 2002; Barlow 2003), and estuaries arethreatened by nutrient loading from fresh submarine ground-water discharge (FSGD) (Johannes 1980; Simmons 1992;Moore 1999; Burnett et al. 2003; Colman et al. 2004; Millerand Ullman 2004; Slomp and Van Cappellen 2004). Withresidential development in coastal areas, increased ground-water extraction has led to numerous examples of saltwaterintrusion (Buxton and Smolensky 1999; LaCombe andCarleton 2002), and increasing nutrient loading has exacer-bated eutrophication of estuaries (Colman et al. 2004).Understanding freshwater/salt-water dynamics and the pro-cesses influencing FSGD is essential to effective watermanagement and treatment using, for example, artificialrecharge to prevent saline intrusion or permeable reactivebarriers to reduce nutrient loading to estuaries. Traditionalmethods of sampling coastal groundwater and measuringdischarge rates (e.g., borehole sampling or seepage meters)suffer from sparse spatial coverage and therefore providelimited information for placement of injection wells orremediation systems. Recently, electrical and electromagneticgeophysical methods have been used to complement conven-tional measurement approaches and clarify the spatial andtemporal distribution of freshwater and saltwater in coastalsettings (e.g., Slater and Sandberg 2000; Frohlich and Urish2002; Schultz 2002; Bratton et al. 2004; Taniguchi et al. 2006;Day-Lewis et al. 2006; Swarzenski et al. 2006, 2007;Marksammer et al. 2007; Schultz et al. 2007). Severalpermanent, large-scale electrical monitoring efforts are under-way in Europe to detect coastal saline intrusion in support of

Received: 30 December 2008 /Accepted: 25 June 2009Published online: 10 September 2009

© Springer-Verlag (outside the USA) 2009

R. D. Henderson ()) : F. D. Day-Lewis : J. W. LaneUS Geological Survey, Office of Groundwater,Branch of Geophysics,11 Sherman Place, Unit 5015, Storrs, CT 06269, USAe-mail: rhenders@usgs.govTel.: +860-377-7663Fax: +860-487-8802

R. D. Henderson : L. LiuCenter for Integrative Geosciences,University of Connecticut,Beach Hall, Unit 2045, Storrs, CT 06269, USA

E. Abarca :C. F. Harvey :H. N. KaramDepartment of Civil and Environmental Engineering,MIT,77 Massachusetts Avenue, Cambridge, MA 02139, USA

, Jr.

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water-resource protection—e.g., in Almeria, Spain (Nguyenet al. 2009). Electrical geophysical monitoring can aid in therapid assessment of freshwater/salt-water dynamics and serveto identify areas for further sampling or engineering controls.

In coastal settings, direct-current electrical resistivityimaging (ERI) has been performed in two modes: marineelectrical resistivity (MER), where the electrodes rest onor are installed into marine sediments, and continuousresistivity profiling (CRP), where floating electrodes aretowed by a vessel. MER data have been used incombination with automated seepage meter measurementsto identify displacement of salt-water by freshwater(Taniguchi et al. 2007), and in combination with geo-chemical sampling to identify where freshwater exits thebeach face at low tide (Swarzenksi et al. 2006, 2007).

Vessel-towedCRP is effective in reconnaissance efforts tocover large areas and identify potential areas of enhancedFSGD for additional sampling (Day-Lewis et al. 2006).Manheim et al. (2004) conducted CRP surveys and sedimentsampling in coastal bays of the Delmarva (Delaware,Maryland, and Virginia) Peninsula. Krantz et al. (2004) useda suite of geophysical techniques, including CRP, to map thespatial distribution of subsurface freshwater and likelygeologic controls. Several reconnaissance surveys wereperformed by Belaval et al. (2003) to map the extent offreshwater underlying coastal embayments inMassachusetts.

Despite the proven capabilities of ERI in coastal settings,the method has important limitations. Whereas in medicalimaging it is possible to surround a target with electrodes, inwater-borne geophysical experiments, electrode locations inmarine environments generally are limited to the watersurface, the water bottom, or boreholes. Because of surveylimitations and measurement errors, the ERI inverse problemis commonly underdetermined, and regularization and (or)prior information are necessary to calculate a unique,tomographic solution. Tomograms, consequently, representblurry, blunted versions of reality. Although the issue oftomographic resolving power has been studied in detail forcross-hole (Day-Lewis et al. 2005) and land-based (Dahlinand Loke 1998; Miller and Routh 2007) survey geometries,less attention has been devoted to MER and CRP, for whichthe time-varying layer of seawater poses a unique challenge.Day-Lewis et al. (2006) investigated the role of the water-layer on CRP and showed that resolution and depth ofinvestigation vary inversely with both water thickness andwater conductivity. In addition, these authors showed thatalthough inversion constraints based on water-columnresistivity or thickness improve inversion results in principle(Loke and Lane 2004), small errors in constraint values cantranslate into large errors in estimated resistivity. Comparedto CRP, MER is generally considered to provide improvedresolution and inversion results because electrode posi-tions are known more accurately, electrodes are closer tothe subsurface target, and reciprocal data may be collected(Day-Lewis et al. 2006). Still, Nguyen et al. (2009)demonstrated the critical importance of interpreting MERtomograms within the context of ERI sensitivity.

Here, inversions and sensitivity analyses for MER fieldexperiments performed at the Waquoit Bay National Estuar-

ine Research Reserve (WBNERR), East Falmouth, Massa-chusetts are presented. The experimental objectives includethe characterization of the freshwater and seawater dynamicsinduced by tidal fluctuations. Toward this end, continuoustime-lapse MER and fiber-optic distributed temperaturemeasurements were collected for a 30-day period in June–July 2007. This work focuses on an approximate 12-h subsetof these data collected during spring tide conditions, when allthe electrodes along the study transect are submerged at hightide. To facilitate interpretation of tomograms for indicationsof FSGD, sensitivity analyses and synthetic modeling areperformed. In addition to the site-specific objectives, thiswork attempts to provide general insight into survey designand inversion strategies for MER. Forward and inversemodeling of synthetic datasets for hypothetical subsurfacemodels help to assess the resolving power of ERI in thecontext of monitoring coastal FSGD.

Background

The application of MER for characterization and monitor-ing salt-water intrusion and FSGD is based on thedependence of fluid electrical conductivity on salinity. Inthis section, a brief review is presented of the processescontrolling FSGD and petrophysical relations underlyingthe interpretation of MER tomograms for the timing andspatial distribution of FSGD.

Submarine groundwater dischargeFresh submarine groundwater discharge (FSGD) is drivenby the difference in head between the fresh, coastal aquiferand the bay water level and by buoyancy of freshwater.While these two mechanisms drive FSGD, at least fourhydrologic processes act to modulate FSGD and control thestructure of the freshwater/salt-water interface: (1) wave andtide run-up, which introduce salt water into the beach face;(2) tide action on several time scales, including daily highand low tides and monthly variation of spring and neap tides,which act to shift the interface and FSGD area; (3) seasonalpatterns of inland recharge, which control the flow of freshgroundwater to the coast; and (4) storms, which can bothincrease the head of the freshwater aquifer by precipitationand increase tidal and wave run-up on the beach. The roles ofthese processes have been studied extensively, and the readeris referred for additional background to Cooper (1959),Kohout (1960), Shum (1992), Ataie-Ashtiani et al. (1999),Jeng et al. (2001), Liu (2002), Taniguchi (2002), Urish andMcKenna (2004), Michael et al. (2005), Swarzenski et al.(2007), and Smith et al. (2008). Reilly and Goodman (1985)offer an historical review of early quantitative analyses of thefreshwater/salt-water interface.

The basis for application of marine electricalresistivity in coastal settingsMarine electrical resistivity distinguishes saline and freshgroundwater through the dependence of bulk electrical

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resistivity on fluid electrical conductivity, and the depend-ence of fluid electrical conductivity on salinity. For theformer relation, Archie’s Law (Archie 1942) is commonlyassumed:

�e ¼ a��mS�n��1w ð1Þ

Where ρe is the bulk resistivity; a is a constant between0.5 and 2.5; φ is the porosity; m is a constant between 1.3and 2.5; S is the saturation of the material; n is a constant,assumed here equal to 2; and σw is the water conductivity(Telford et al. 1990). Archie’s Law is an empirical law thatis generally valid in resistive granular materials (i.e. verylittle or no clay). In a saturated system, where porosity isassumed not to change over time, changes in resistivitycan be attributed to changes in porewater salinity. Anumber of relations between fluid electrical conductivityand salinity, as total dissolved solids (TDS), are found inthe literature, including, for example:

TDS ¼ Asw ð2Þ

(after Hem 1970; Freeze and Cherry 1979) where TDS isexpressed in mg/l, σw is fluid conductivity in µS/cm, andA is a conversion factor, commonly between 0.55 and 0.75depending on the ionic composition of the groundwater.

Marine electrical resistivity

Electrical resistivity data acquisition involves currentinjection between two electrodes, and measurement ofpotential difference between another pair of electrodes.Numerous combinations (commonly hundreds or thou-sands) of current and potential pairs are used for a singlesurvey. Discussions of electrical resistivity theory andapplications to time-lapse imaging are provided by Kemnaet al. (2006) and Binley and Kemna (2005). This workfocuses on the MER geometry, in which electrodes aredeployed at a fixed spacing at the water/sediment inter-face. Current flow in the earth is a diffusive process and isdescribed by the Poisson equation:

r � rV

r

� �¼ I d x� xs; y� ys; z� zsð Þð Þ ð3Þ

where V is the electrical potential (volts); ρ is the electricalresistivity (ohm-m); x, y and z are Cartesian coordinates;xs, ys and zs are Cartesian coordinates of current sources orsinks; and I is the current (amperes), positive or negative,at the source or sink location (Telford et al. 1990).

Electrical resistivity inversionResistivity data are commonly inverted to estimatesubsurface resistivity patterns by solving a regularized,non-linear, least squares regression problem (Binley andKemna 2005). The objective function to be minimized

consists of two weighted terms, one for the data misfit andone for the model complexity:

F ¼ d � f mð Þ½ �TWTW d � f mð Þ½ � þ amTDTDm ð4Þ

where d is a vector of the measured resistances (ratio of V/I, in ohms); f(m) is the vector of the forward problemsolution based on m (calculated resistances); m is thevector of model parameters, the logarithms of resistivity;W is a diagonal weighting matrix of the reciprocal ofmeasurement standard deviations; α is a tradeoff param-eter to scale the smoothing constraint and is found using aline search to minimize the objective function; and D is amodel weighting operator. Here, D is the matrix of spatialsecond-derivatives of the model parameters m determinedby a finite-difference filter, used for Tikhonov regulariza-tion of the otherwise underdetermined inverse problem.The estimated resistivity field is composed of the vector ofresistivity values m that minimizes the objective function.The tradeoff between the two terms in Eq. 4 (i.e., α) isdetermined using Occam’s approach (Constable et al.1987; deGroot-Hedlin and Constable 1990); the inversionfits the measurements to a degree consistent with an errormodel (W) based on either observed reciprocal or repeatmeasurements (Binley et al. 1996). The inversions areperformed with the R2 inversion code (Binley and Kemna2005) which uses a “2.5-D” approximation to solve forthree-dimensional electrical conduction in the forwardproblem while limiting heterogeneity to the two-dimen-sional (X-Z) plane of the cross section (Xu et al. 2000). Inother words, heterogeneity in the X-Z plane of interestextends infinitely in the third dimension, Y. The 2.5-Dapproach allows for realistic representation of currentdistribution while limiting the number of model nodes/elements to the plane of interest. At each iteration of theinversion, the solution is updated according to:

JTWTWJ þ aDTD� �

Dmk ¼ JTWTW d � f mkð Þ½ �� aDTDmk ð5Þ

mkþ1 ¼ mk þ Dmk ð6Þ

where J is the Jacobian of simulated measurements withrespect to model parameters; mk+1 is the updated model atthe start of iteration k+1; and Δmk is the model updatecalculated during iteration k. As discussed previously, theinversion iterates until the forward modeled data matchthe observed data to the root mean square error consistentwith the error model W.

Interpretation and sensitivity analysisInterpretation of resistivity tomograms is often compli-cated by the spatially—and in the case of time-lapseinversion, temporally—variable resolving power of elec-

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trical resistivity tomography (Day-Lewis et al. 2005,2006, 2007). Where resolution is good, inverted resistivityvalues closely approximate earth resistivity. Conversely,where resolution is poor, the inverted resistivity is stronglyaffected by choices of starting model, regularizationcriteria, and (or) prior information; hence the relationbetween inverted resistivity and salinity may be weak incertain regions of tomograms or for whole tomograms atcertain times. Quantitative tools for evaluating resolutioninclude (1) the model resolution matrix (e.g., Menke 1984;Day-Lewis and Lane 2004), (2) the cumulative sensitivitymatrix (e.g., Nguyen et al. 2009), and (3) syntheticmodeling. This work focuses on the second and thirdtechniques.

The model resolution matrix acts as a filter throughwhich the inversion sees the subsurface. Although themodel resolution matrix is a more rigorous measure ofresolving power, its calculation is more computationallyintensive than that of S (Menke 1984). The cumulativesensitivity matrix, S, is:

S ¼ JTWTWJ ð7Þ

The diagonal of S (of length equal to the number ofparameters) provides insight into how the model parametersaffect the modeled measurements f(m). In general, param-eters with higher sensitivity are more accurately estimated.

For synthetic modeling exercises, resistivity data aresimulated for numerical time-lapse models for WaquoitBay, add random or systematic error to the data, and invertthe synthetic data to develop time-series tomograms.Comparison of these tomograms with the syntheticresistivity cross sections used to generate hypotheticaldata help to assess the resolution of the inversion and

identify possible artifacts. This approach is also used toinvestigate how inclusion of borehole electrodes mayimprove resolution of the subsurface electrical resistivitydistribution for future work.

Application

A time-lapse MER field experiment was conducted atWBNERR, East Falmouth, Cape Cod, Massachusetts(Fig. 1). Cape Cod comprises remnant glacial deposits fromthe Wisconsin deglaciation approximately 12,000–15,000 years ago (Oldale 1981). The bay is approximately3 km2 and has an average depth of about 1 m (Cambareriand Eichner 1998). In general, the Cape Cod aquifer isunconfined, 100–120-m thick and receives about 46 cm ofrecharge annually (Cambareri and Eichner 1998). In theWaquoit Bay area, an approximately 11-m-thick permeablelayer overlies a less permeable layer of fine sand, silt, andclay. Glacial till and bedrock underlie the upper sediments atapproximately 33 m depth (Cambareri and Eichner 1998).

Field experimental setupAt WBNERR, a resistivity cable with 48 graphite electro-des spaced at 1-m intervals was installed beneath the bay/sediment interface. The cables were buried under thebeach and out under the bay along a 47-m shore-perpendicular transect (Figs. 1 and 2a). Onshore, thecables terminate inside a research facility, where datacollection instruments were installed. The cable wasweighted with small fishing weights and armored withflexible, corrugated tubing, which was slit length-wise toallow direct contact with the marine sediments. The cable

Fig. 1 Site location map and experimental setup at Waquoit Bay, Falmouth, Massachusetts

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was buried 0.5 m below the water/sediment interface nearshore and shallower offshore to minimize the possibilityof the cable being snagged or damaged by human oranimal activity and to reduce cable movement by watercurrents between surveys or site visits.

Resistivity measurements were made with a single-channel control unit and multiplexer manufactured byMulti-Phase Technologies, LLC1 that were interfaced with alaptop computer for instrument control and data storage.Resistivity data collection was performed according to adipole-dipole survey geometry, i.e. one electrical dipole forthe current injection between two electrodes and one for thevoltage measurement between two electrodes. Each surveyconsisted of 1,890 measurements including normal andreciprocal data. Reciprocal measurements were performedin sequential order after each survey rather than immediatelyfollowing the corresponding measurement in an attempt tomaximize the temporal resolution of each survey. Eachsurvey was collected over about 50 min with both the normalmeasurements and their reciprocals each taking about 25min.Nearly continuous data acquisition was achieved withminimal interruption, except in cases of power failure duringthe 30-day period during June and July 2007.

In addition to resistivity data, hydrologic and meteoro-logical data were collected to provide context for data

interpretation. The tidal level of the bay was recorded at15-min intervals by a pressure transducer east of theshore-perpendicular transect. Observations of tide run-upon the beach face and water-level measurements from amanual tide gauge were recorded approximately everyhour during daylight hours. Bathymetry data weremeasured at discrete locations adjacent to the resistivitytransect to infer the water column thickness for each time-lapse inversion. Temperature data were collected along theresistivity transect with a fiber-optic distributed temper-ature sensor (FODTS) at 1-m spatial and 30-s temporalresolution. A subset of the FODTS data is included here.For description of the FODTS experiment, the reader isreferred to Henderson et al. (2009).

Inversion of field MER dataPrior to inversion, several preprocessing steps wereperformed: (1) identification of bay water level at themiddle of each survey data collection period; (2) creationof finite-element meshes to match various tidal stages; (3)time-stamping of resistivity data and parsing into time-lapse input files; (4) checks for bad data and calculation ofdata error weights; (5) creation of inversion input files;and (6) creation of a batch file for sequential inversion ofresistivity data.

For inversion of MER and CRP data, it is common toapply constraints on the resistivity of the water column

(b) Marine electrical resistivity crosshole geometry for synthetic experiments

(a) Marine electrical resistivity surface-electrode geometry used in field experiments

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1 Any use of trade, product, or firm names in this publication is fordescriptive purposes only and does not imply endorsement by theUS Government.

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and to fix the water-column/sediment boundary in theinversion (Loke and Lane 2004). In principle, suchconstraints can improve resolution and thus inversionresults; however, small errors in constraint values cantranslate into large errors in inversions (Day-Lewis et al.2006). A two-part strategy is used to allow for a sharp,resistivity boundary at the water/sediment interface whileaccurately representing the water column and bathymetry.First, a series of high-resolution finite-element meshes isused to accurately represent the beach profile. In all, 56finite-element meshes are used, each consisting ofapproximately 25,000 elements and 12,500 nodes, torepresent conditions at various tide stages and accountfor 11 m of tidal run-up on the beach face (Fig. 3). Toillustrate the temporal evolution of the water layer, Fig. 3shows the beach face portion of the mesh where the salt-water layer extension changes according to the seawaterelevation (tide). The mesh used for calculations extendswell beyond the MER survey area. Second, a parameter-ization that includes two regularization zones, such thatthe inversion does not penalize development of a sharpcontrast in resistivity across the water/sediment interfaceis used. In the calculation of model roughness (i.e., thesecond term in Eq. 4), only differences between cells inthe same regularization zone contribute. Every elementwithin the sediment layer is an individual inversionparameter, whereas elements in the water layer aregrouped laterally with distance from shore into fivepatches, each corresponding to one inversion parameter.Fewer parameters are used in the water column becausewater column resistivity is not expected to vary greatly.

Measurements are weighted in the inversion procedureaccording to their errors, as assessed through reciprocalmeasurements. Although reciprocal measurements areconsidered to provide a better approximation of measure-ment error than repeat measurements (Daily et al. 2004),they do not incorporate all sources of error expected in atime-lapse survey. Temporal changes in resistivity—in thewater column or sediment—during the course of a givensurvey will result in inconsistent data, as measurementslate in a survey will “see” a different reality thanmeasurements early in the same survey (Day-Lewis et al.2002). In addition, model error arises from discrepanciesbetween field conditions and assumptions of the forwardmodel, e.g., homogeneity perpendicular to the crosssection of the tomogram. Based on inspection of the dataand the convergence observed for preliminary inversions,reciprocal errors are multiplied by a coefficient of 2.5 toincrease the smoothing and enable convergence to theOccam’s criterion. Very noisy data (>10% of the recip-rocal error) are suppressed further by diminishing theirweights by a factor of 200 because large reciprocal errorsmay indicate extremely poor measurement quality or largechanges in subsurface resistivity between the time of themeasurement and the corresponding reciprocal measure-ment. Observed standard errors during data acquisition(stacked data from each measurement) did not exceed 2%.

The time-lapse inversion is performed sequentially,using the result of one inversion as the starting model forthe next; this procedure involves interpolation from onefinite-element mesh to another, because the mesh changesfrom survey to survey according to the tide. This

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Fig. 3 Representative sections of finite-element meshes for a high tide and b low tide. Fifty-six total meshes account for 11 m of tidal run-up on the beach face. Each mesh consists of approximately 25,000 elements and 12,500 nodes. Blue represents salt water, yellow representssediment layer, and black represents the sediment/water interface (bathymetry)

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interpolation applies only to the water layer elements,whereas the size, shape and location of the sedimentelements do not change from one mesh to another.

Results

The data for the sequence presented here was collected on14–15 June 2007, near the maximum, spring tidal range for

Waquoit Bay. This sequence presents the results of 12inversions collected over an approximately 12-h windowduring which the tidal range is ~1 m (Fig. 4). In addition tothe MER tomograms, concurrent temperature transects(Henderson et al. 2009) are included to facilitate interpre-tation. As the tide falls, an electrically resistive zonedevelops, expands spatially, and grows in contrast. Sim-ilarly, a cold temperature anomaly develops near theresistivity anomaly and broadens as the tide falls. This cold

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anomaly is consistent with the presence of groundwaterdischarge, which is colder than surface water in summer.This zone, which extends between 9 and 13 m from the firstelectrode, is interpreted as an indication of FSGD. As thetide rises, the large resistive anomaly and the temperaturetrough appear to decrease in magnitude. For this particularsequence, the resistivity anomaly appears to have amaximum resistivity of greater than 100 ohm-m and persistsfor ~3–4 h, whereas the temperature anomaly persiststhrough the whole tidal cycle. Based on the tomogramsalone, it is difficult to interpret whether the FSGD iscontinuous in time or shuts down at high tide, or whetherthe resistivity anomaly diminishes at high tide becauseresolution degrades with increasing water column depth.The persistence of the cold anomaly in the FODTS transectssupports the second explanation. As stated previously anddemonstrated in the next section, reliable interpretation oftomograms requires consideration of sensitivity and resolv-ing power from synthetic modeling and resolution analysis.

It is worth noting that temperature influences themagnitude of electrical conductivity/resistivity. For theresults displayed here, the temperature variation alongthe length of the resistivity survey did not vary by more thanapproximately 4°C/day. Although some of the observedresistivity changes can be attributed to temperature dynamics,the observed temperature variations are not sufficient toexplain fully the observed resistivity changes.

Sensitivity analysis and image appraisal

Synthetic modeling exercises are used to answer threequestions arising from the field-experimental results:

1. How does water column thickness affect sensitivityand, in particular, the ability to resolve subsurfacefreshwater?

2. How do errors in assumed water column thicknessaffect inversion results?

3. Could resolution be improved by the addition of cross-hole measurements?

For construction of synthetic models, the same bathy-metry as used for the field-experiment is considered. Indesigning synthetic models to address the first twoquestions, the experiment assumes the same surveygeometry as used for the field experiment. Inversionsettings for the synthetic sequence (i.e. batch, time-lapseprocessing) are consistent with the procedure described insection Inversion of field MER data.

Effect of seawater-column thicknessTo evaluate the effect of baywater column thickness, i.e.,tide elevation, on resolution of subsurface freshwater,three synthetic models representing a sequence of con-ditions along a portion of a tidal cycle (Fig. 5a–c), fromhigh to low tide, are considered. Synthetic models weredefined by numerical simulations completed using thefinite-element density-dependent flow and transport codeTRANSDENS (Hidalgo et al. 2004). Modifications wereperformed to the code to represent the transient tidalboundary condition on the beach face. Model performancewas previously tested reproducing the numerical resultsproposed by Robinson et al. (2006). A two-dimensionalcross-sectional model of the Waquoit Bay unconfinedaquifer was developed. An irregular grid with smallerelements is used near the areas of interest (intertidal zoneand surroundings of the freshwater/salt-water interface) todiscretize the problem domain (300 m×10 m).

The boundary conditions implemented in the model are(1) a prescribed freshwater inflow of 0.15 m/d through theinland boundary; and (2) a fluctuating prescribed headapplied to the upper boundary in contact with the bay

Synthetic models of electrical resistivity Inversions with surface measurements Inversions with cross-hole measurements

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Fig. 5 a–c Defined subsurface resistivity structure for the synthetic forward modeling and inversion. d–f Inversion results with surfaceresistivity measurements. g–i Inversion results with cross-hole measurements

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water. The boundary on the beach face changes dynam-ically as the water layer advances and recedes due to tidalchanges. While the beach face is not submerged, aprescribed head of equivalent pressure equal to 0 isapplied. The hydraulic parameters used in the simulationsare: equivalent freshwater hydraulic conductivity = 100 m/d,porosity = 0.25, fluid viscosity = 0.001 kg/m-s, longi-tudinal dispersivity coefficient = 0.1 m, transversedispersivity coefficient = 0.01 m, and molecular diffusioncoefficient = 8.64 e-5 m2/d.

A long, transient simulation was run until a pseudosteady state was reached (600 days). A simulation with asmaller time-step (0.0041 days) was performed to increasethe temporal resolution of the results to study the effect ofthe tidal fluctuations. Here, only the portion of the solutetransport model that overlaps with the resistivity inversionmesh is shown (Fig. 5a–c). The models represent afreshwater body whose discharge zone remains relativelyconstant; a salt-water wedge intruding below the fresh-water and a salt-water tidal recirculation zone of approx-imately 2 m in thickness formed on the beach face.

Concentrations from the numerical models were trans-formed to bulk resistivity using Archie’s Law (Eq. 1)assuming saturated conditions a=1, m=1.3, and φ=0.25.Prior to inverting the forward model results, random error(Gaussian noise based on forward model resistances) wasadded to the data to simulate uncertainty in measurementsand discretization. Ten percent Gaussian noise was addedto the synthetic surface measurements to reflect theapproximate level of noise in the field data, whereas 6%Gaussian noise was added to the synthetic cross-holemeasurements because, based on experience, cross-holemeasurements are expected to provide cleaner data. Theassumed resistivity values correspond to minimum andmaximum TDS of 1 g/l and 36 g/l for freshwater and salt

water, respectively. Synthetic models are included inFig. 5a–c.

The time-lapse inversion scheme follows the progres-sion of the pore-fluid resistivity distribution and fresh-water/salt-water interface over a portion of one tidal cycle(Fig. 5a–c), from high to low tide. These spatialdistributions are qualitatively consistent with direct meas-urements of salinity using piezometers and seepage meters(Michael et al. 2003) as well as results from other fieldsites (Robinson et al. 2006). The initial high-tide tomo-gram (Fig. 5d) poorly recovers the subsurface resistivitydistribution at depth. Whereas the tomogram resolves thehigh resistivity features immediately adjacent to theelectrodes, it shows only weak evidence of the deepersubsurface freshwater. As the tide falls (Fig. 5d–f) and thesaline layer over the beach face contracts, the resistiveFSGD is better resolved in the tomograms.

In land-surface resistivity surveys, depth of investiga-tion is estimated, as a rule of thumb, as being one third toone fifth of the maximum electrode separation, withresolution of fine scale features dependent on the electrodespacing. Here, at much smaller fractions of the maximumseparation, resolution is very weak because the injectedcurrent is channeled into the conductive seawater abovethe electrodes; thus, sensitivity is observed to rapidlydecay with depth, as shown in Fig. 6. In poorly resolvedareas, estimated resistivity is more strongly affected by thestarting model, regularization, and prior information.

Effect of errors in assumed water-column thicknessIn principle, application of inversion constraints for water-column thickness can improve resolution (Loke and Lane2004), but even small errors in constraint values canproduce large errors in tomograms (Day-Lewis et al. 2006).

DISTANCE, IN METERS

(b) Sensitivity for surface electrode geometry at low tide

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Fig. 6 Calculated sensitivity of surface measurement surveys at a high and b low tide from field data

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1 10 100RESISTIVITY, IN OHM-M

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Fig. 7 a Synthetic model of subsurface resistivity for low tide simulation. b Results after forward and inverse modeling with correct watercolumn constraints, low tide mesh for surface measurements only. c Results after forward and inverse modeling with incorrect watercolumn constraints, high tide mesh for surface measurements only

DISTANCE, IN METERS

(b) Sensitivity for crosshole electrode geometry at high tide

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Fig. 8 Calculated sensitivity of synthetic surface a and cross-hole measurement b surveys high tide

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For a single, hypothetical subsurface resistivity model(Fig. 7a), inversions are performed using the correct, low-tide mesh (Fig. 7b) and an incorrect high-tide mesh(Fig. 7c) with the same survey geometry, parameterization,and regularization as used for analysis of field data. Usingthe high-tide mesh for the simulated low-tide dataset resultsin spurious anomalies in the tomogram that easily could bemisinterpreted. The freshwater and salt-water resistivityvalues are too high and the true anomaly appearsdisconnected from another resistive feature closer to shore.

Value of cross-hole measurementsTo assess the potential value of cross-hole measurementsover surface measurements , the simulated tidal sequencein Fig. 5a–c was inverted with the addition of threeboreholes at 4, 9 and 14 m from shore, with verticallyaligned electrodes spaced at approximately 1-m intervals(Fig. 2b). Small variations in vertical electrode spacingresulted from slight irregularities in the finite-elementmeshes. Compared to the inversions incorporating surfacemeasurements, the cross-hole measurements increaseresolution of the subsurface resistivity structure over thetidal cycle, enabling much better tomograms at high tides(Fig. 5g) and superior sensitivity with depth (Fig. 8).

The improvements in resolving power are demonstra-ted by comparing the sensitivities for the surface-only andcross-hole electrode configurations for high-tide condi-tions (Fig. 8a,b). The sensitivity plot indicates strongsensitivity to the seawater and the higher subsurfacesensitivity is generally confined to the areas immediatelyadjacent to the electrodes, presumably because electriccurrent is focused in the more conductive seawater layer.The cross-hole measurements provide substantialimprovement in resolution (Fig. 8b) and results inresolution that is less variable with depth, a conditionwhich facilitates interpretation for hydrologic processes.The non-symmetric features in the sensitivity plot areattributed to a combination of the non-symmetric surveygeometry; variations in sensitivity due to the spatialpattern of resistivity; and the random errors added to thesynthetic data, which translate into a W with variablemeasurement weights.

Discussion and conclusions

Electrical geophysical methods have been used in anumber of studies to monitor freshwater/salt-water inter-action and coastal processes including submarine ground-water discharge and salt-water intrusion. Here, time-lapsemarine electrical resistivity and temperature results arepresented for an experiment to study fresh groundwaterdischarge to an estuary. Although the inverted time-lapsetomograms revealed the zone of freshwater discharge atlow tide, tomograms at high tide indicated uniformlysaline conditions under the electrode array in contradictionto other data including continuous fiber-optic temperature(Henderson et al. 2009).

Sensitivity analysis and synthetic modeling indicatethat at high-tide conditions, current is preferentiallyfocused in the conductive surface-water layer, and,consequently, the inversion cannot resolve resistive sub-surface freshwater. Indeed, the estimated shape andmagnitude of the freshwater anomaly in tomograms canvary substantially over time, as a result of shifts in thehighly conductive seawater layer. In poorly resolved areas,or at high tide conditions, the estimated resistivity is morestrongly affected by the starting model, regularization, andprior information. Through synthetic models, the potentialvalue of cross-hole measurements to better resolve subsur-face freshwater during high-tide conditions was shown.The addition of cross-hole measurements results in morespatially uniform resolution, which should facilitate theuse of tomograms for understanding shifting patterns ofsubmarine groundwater discharge and seawater intrusion.These findings are specific to the experimental surveylayout considered here; nonetheless, the results underscorethe general importance of interpreting MER tomograms inthe context of spatially and temporally variable resolution.

Acknowledgements This work was funded by the US GeologicalSurvey Groundwater Resources and Toxic Substances HydrologyPrograms, and by NSF grant EAR 0548706, the Singapore MITAlliance for Research and Technology, and the Kuwait-MIT Alliance(to CFH). The authors are grateful to M. Charette and A. Mulligan(Woods Hole Oceanographic Institution) for transducer data; A. Binley(Lancaster University) for access to the R2 inversion code executable;C. Weidman and the WBNERR staff for field support and site access;and Hydrogeology Journal’s Associate Editor V. Post and reviewersS. Kruse and E. Gasperikova for useful comments on the draftmanuscript. The first author is also grateful to the University ofConnecticut Civil and Environmental Engineering Department for agraduate fellowship to support his MSci research.

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