Estimation of unsaturated hydraulic parameters in ...basin.earth.ncu.edu.tw/Course/SeminarII... · the time-lapse ERT data, 2) Establishing an in-situ approach to convert time-lapse

Journal of Applied Geophysics 121 (2015) 71–83

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Journal of Applied Geophysics

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Estimation of unsaturated hydraulic parameters in sandstone usingelectrical resistivity tomography under a water injection test

Mohammad Farzamian a,⁎, Fernando A. Monteiro Santos a, Mohamed A. Khalil a,b

a IDL-Universidade de Lisboa, Faculdade de Ciências, Campo Grande, Ed. C8, Lisboa, Portugalb National Research Institute of Astronomy and Geophysics, Helwan, Cairo, Egypt

⁎ Corresponding author.E-mail address: [email protected] (M. Fa

http://dx.doi.org/10.1016/j.jappgeo.2015.07.0140926-9851/© 2015 Elsevier B.V. All rights reserved.

a b s t r a c t

Article history:Received 11 February 2015Received in revised form 13 July 2015Accepted 19 July 2015Available online 23 July 2015

Keyword:Water injection testERTMoment analysisUnsaturated sandstoneHydraulic conductivity

Hydraulic conductivity is an important soil propertywhen determining the potential forwatermovement in top-soil and in spite of its importance; soil hydraulic conductivity remains one of themost difficult of soil properties toassess. Laboratorymethods have limitations due to the size of the samples and taking undisturbed soil samples isusually difficult in sandy soil and in-situ methods are required to estimate hydraulic conductivity.This study was conducted to estimate saturated hydraulic conductivity in unsaturated sandstone using theground surface electrical resistivity tomography (ERT). The site is characterized by a deep Arenosol soil withhigh permeability and a low water retention capacity located at the Semora-Correia, the east of Lisbon. EightERT snapshots were collected during a water injection test to produce a sequence of 2D resistivity images.Time-lapse ERT data were inverted using independent data inversion, the difference inversion and simultaneousspace–time inversionmethods. Afterward, using an in-situ approach resistivity variationmodels were convertedto water content images. By comparing first and second spatial moments of water movement images inferredfrom the ERT method with unsaturated flow simulation predicted from a numerical solution of Richards' equa-tion, the range of saturated hydraulic conductivity is estimated to be in 0.5–0.7 (cm/min).The evaluation of ERT approachwasmade using a synthetic test. The results of synthetic test showed that the es-timated parameters were significantly influenced by the ERT inversion method and an overprediction of spatialmoments and consequently saturated hydraulic conductivity was observed in all inversion methods; howeverthe resistivity models obtained by simultaneous space–time inversion method was more successful in watermovement monitoring.

© 2015 Elsevier B.V. All rights reserved.

1. Introduction

Improved understanding of unsaturated flow and identifying hy-draulic parameters is limited by the lack of appropriate in situ measure-ment techniques. Traditional methods are usually invasive, sometimesrequiring boreholes, covering only a small and localized investigationandmay not be representative of the soil properties at themanagementscales.

Recent research has shown that ERT surveys as non-invasive andcost-effective method is a promising alternative to traditional tech-niques for unsaturated zone characterization. The capability of ERT sur-veys have been demonstrated in many studies (e.g. Kemna et al., 2002;Looms et al., 2008a, 2008b; Daily et al., 1995; Müller et al., 2010). Time-lapse ERT survey is a popular tool for unsaturated zone monitoring todetermine those hydrologic variables that are time dependent, such assoil water content variations. The dependence of electrical resistivity

rzamian).

variations on changes in soil water content through empirical or semi-empirical relationships (e.g., Archie, 1942) or established in-situ rela-tionships (e.g., Farzamian et al., 2015) is the key mechanism thatpermits the use of time-lapse ERT to monitor water movement intime-lapse mode. Several studies have been conducted to monitor salttracer tests or water infiltration through the unsaturated zone usingground surface ERT (e.g., Barker and Moore, 1998; Park, 1998; Hayleyet al., 2009) and crosshole ERT (e.g., Slater et al., 1997; Daily et al.,1992; Binley et al., 2002a, 2002b; Deiana et al., 2007). Also, ground sur-face ERT (e.g., Robert et al., 2012; Cassiani et al., 2006) and crosshole ERT(e.g., Binley et al., 1996; Slater et al., 2000, 2002; Singha and Gorelick,2005) are extensively used in saturated zone study.

ERT approach has several limitations in unsaturated zone character-ization. These limitations are partly due to technical limitations of theERT method associated with resolution and inversion artifacts reportedin many studies (e.g., Deiana et al., 2007; Cassiani et al., 2006). Inade-quate petrophysical relationship to convert electrical resistivity valuesto soil water content is another source of uncertainty and necessity ofdetermining site-specific relationships was discussed in several studies(e.g., Looms et al., 2008a). The temperature dependence of electrical

72 M. Farzamian et al. / Journal of Applied Geophysics 121 (2015) 71–83

resistivity is also a source of error for time-lapse resistivity monitoringand the effect of temperature changes over ERT images must be takeninto account (Hayley et al., 2007).

Since the most unsaturated zone studies focused mainly oncrosshole ERT, we performed an experiment to explore the potentialof ground surface ERT in capturing water movement during a water in-jection test in order to estimate the saturated hydraulic conductivity.We also measured the subsurface temperature variations during thewater injection test using suitably placed sensors for temperature cor-rection over time-lapse ERT models.

In this study, we examined several time-lapse inversion methodsand attempted to evaluate the artifacts associated with each inversionmethod by performing a synthetic test. In addition, we established anin-situ approach based on resistivity and volumetric water content var-iations as proposed by Farzamian et al. (2015) to convert resistivity var-iations to water content distribution images. The method we used inthis study is similar to Farzamian et al. (2015) work, which used time-lapse ERT andmulti-height EM38data collectedunder natural conditionfor unsaturated hydraulic parameters characterization. They comparedthe unsaturated flow simulation predicted from a numerical solutionof Richards' equation with equivalent statistics from 2D resistivity im-ages inferred from ERT andmulti-height EM38 data to estimate the sat-urated hydraulic conductivity. To improve this comparison, we usedmoment analysis (Ye et al., 2005) in this study to estimate the firstand second spatial moment of the water tracer. This method is widelyused in hydrogeophysical study. One of the first applications ofmomentanalysiswas described by Binley et al. (2002b). They calculatedfirst andsecond spatial moments of changes in moisture content predicted froma numerical simulation of vadose zone flow with two- and three-dimensional ERT and cross-borehole radar profiles to estimate hydraulicconductivity. Singha andGorelick (2005) also used themoment analysisto estimate horizontal and vertical hydraulic conductivity. More recent-ly, Looms et al. (2008a) calculated the zeroth,first, and secondmomentsto estimate thewater loss and illustrate how small structural changes inlayered sediments can result in capillary barriers and affects the down-ward migration.

2. Field site and field experiment

2.1. Study area

The study area is located at the state of Campanhia das Lezirias —Samorra Correia, approximately 50 km east of Lisbon. The soil is adeep Arenosol (FAO, 1988) with high permeability and a low water re-tention capacity. A field site with 40 m length and 6 m width wasestablished to conduct the experiment, on a 2 m unsaturated soil,consisting mainly of sands. Also, an experimental transect with 12 mlengthwas designed in themiddle of the filed site for geophysical mon-itoring and soil sampling (Fig. 1).

2.2. Sampling and laboratory analysis

Eight soil cores down to a depth of approximately 2 mwere extract-ed along the experimental transect before the water injection test. Thelocations of soil cores were shown in Fig. 1. These cores were sectionedinto 0.2 m lengths and prepared for laboratory analysis of soil physicalproperties namely particle density, bulk density, texture and also gravi-metric water content. Standard set of sieves were used to divide sandinto classes, and to separate sand fractions from silt and clay fractionsin the soil. The particle size distribution analysis along transect indicateda sand texture class with less than five percent clay and silt, on average.The observed average particle density and bulk density were 2.65 and1.66 respectively and the porosity value was equal to 37%. As the soiltexture and bulk density exhibited a low degree of variation along thefield site, the site was considered homogeneous and the porosity wasfixed at 37%.

2.3. Water injection test and ERT monitoring

An artificialwater injection testwas carried out at a rate of 8.96 cm/hover a 12.6 by 2.1 m2 area of the field site, using drippers spaced every30 cm over the surface (344 drippers) for about 3 h. Therefore, about0.71m3 ofwaterwas injected during the experiment. Pressure compen-satingdripperswith drip rate of 8 l per hourwere used for all drippers inthis experiment to guarantee uniform water distribution along the en-tire lines. The water supplied from a nearby groundwater access wasused in this test in order to injectwaterwith the same electrical conduc-tivity of the in-situ water. The water was supplied to a water tank andwas distributed to the drippers by using pump to ensure constantflow during the experiment. A water flow meter was connected to thesystem to verify a constant flow rate of water and also measured thefinal amount of injected water. In addition, 14 soil temperature sensorswere installed in 2 boreholes at depths of 0.1m, 0.3 m, 0.5 m, 0.7m, 0.9,1.1 and 1.3 m. The sensors monitored temperature changes minutelyduring the experiment.

The evolution of the injected water was monitored by the groundsurface time-lapse ERT survey using 4POINTLIGHT_10Wdevice. Geotestsoftwarewas used for remote controlling of 4POINTLIGHT_10W in com-bination with active boxes for geoelectric tomography using multi-electrodes. ERT surveys were performed using Schlumberger electrodeconfiguration with the maximum current electrode (AB/2) expansionof 6 m and electrode spacing of 0.30 m respectively. 40 electrodeswere used in this experiment and a total of 361 data were collectedfor each image. The required time for each acquisition was about22 min and 8 data sets were obtained during the water injection.

3. Material and methods

The saturated hydraulic conductivity estimation from time-lapseERT data consists of fourmain elements (outlined in Fig. 2); 1) Invertingthe time-lapse ERT data, 2) Establishing an in-situ approach to converttime-lapse ERT model to water content images, 3) Simulating unsatu-rated flow, 4) Using moment analysis to evaluate mass balance and es-timate the saturated hydraulic conductivity. These elements will beseparately discussed in the following sections.

3.1. Time-lapse ERT inversion

We inverted the time-lapse ERT data using three differentapproaches: independent data inversions, difference inversion(LaBrecque and Yang, 2001) and simultaneous space–time inversion(Kim et al., 2009). In independent inversion, independent data inver-sions are carried out separately and changes in ERT models with timeare obtained by subtraction of pixel-by-pixel values from a backgroundimage (Deiana et al., 2007). The difference inversionmethodminimizesthe misfit between the difference in two datasets and the differencebetween two model responses and smoothness is imposed directlyon the time-lapse model change. This method is widely used forinverting time-lapse ERT data as suggested by several published works(e.g., Kemna et al., 2002; Deiana et al., 2007). In simultaneous space–time algorithm, subsurface structure and the entire monitoring dataare defined in the space–time domain to obtain a simultaneous space–time model using just one inversion process. The method introducesthe regularizations not only in the space domain but also in time to re-duce inversion artifacts and improve stability of the inverse solution(Kim et al., 2009). A description and comprehensive comparison ofthese methods were presented in Hayley et al. (2011).

In order to map water content variation inferred from time-lapseERT inversion, the temperature fluctuations that affect the unsaturatedzone during water injection test must be taken into account (Hayleyet al., 2009). It is common practice in electrical geophysics to assume alinear variation in resistivity with temperature over the typical rangeof temperatures encountered in shallow surveys (Musgrave and

Fig. 1. a) Location of the study area at the state of Campanhia das Lezirias— Samorra Correia, the east of Lisbon. b) Schematic diagram of thewater injection test showing the location of thedrippers, ERT transect, temperature sensors and soil cores.

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Binley, 2011). For instance Hayley et al. (2007) and Scott and Kay(1988) using a variety near surface materials discovered the slopeof the linear model is quite consistent and a value between 0.018and 0.022 can be used if no other information is available. In thisstudy we have corrected the time-lapse ERT data for temperatureprior to inversion using the method described in Hayley et al. (2010).As shown by Hayley et al. (2010), correcting for temperature priorto inversion, as opposed to correcting inversion models, allows for theuse of time-lapse inversion methods with less inversion artifacts. Tocorrect the time-lapse ERT data for temperature, we first inverted all8 datasets and then we adjusted ERT images to a standard temperatureimage by applying a value of 2% change per degree. Afterward, weperformed forward simulations using the uncompensated inversionand the standard temperature equivalent model for each dataset.Subtracting the temperature-compensated simulated resistance datafrom the uncompensated simulated resistance data, we obtained thedata correction terms for each dataset. The data correction terms werefinally subtracted from the measured data to obtain temperature-compensated data.

3.2. In-situ resistivity and water content relationship

To convert the time-lapse resistivitymodel towater content change,we established an in-situ approach based on resistivity and volumetricwater content variations by plotting the inverted value of resistivity ofextracted sample as a function of the degree of saturation (S). S is de-fined as:

S ¼ θ∅

ð1Þ

where θ is the volumetric water content and∅ is the porosity. The plotallowed us to obtain an empirical relationship between resistivity and Sfrom the best match of the experimental data. To achieve this objective,6 ERT datasets were collected during one year along the same experi-mental transect before the water injection test. Soil samples were col-lected immediately after each ERT survey and were analyzed for watercontent. ERT data was inverted and the inverted resistivity values of re-lated extracted samples have been extracted and then plotted as a

Fig. 2. Analysis flowcharts for integration of time-lapse ERT and hydrologic data to estimate the saturated hydraulic conductivity.

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function of the degree of saturation in Fig. 3 to find out the bestmatch ofresistivity vs S variation. The obtained relationship is given by the fol-lowing equation:

ρ ¼ 36:618 s−2:408 ð2Þ

where S is the degree of saturation and ρ is the resistivity of the porousmedium in relevant degree of saturation. It is worth mentioning that,we averaged the resistivity values around each sample to obtain this re-lationship. The error bar of resistivity data was included in Fig. 3.

Fig. 3. Electrical resistivity of extracted sample

3.3. Unsaturated flow simulation

Unsaturated flow simulations were built using HYDRUS2D softwarepackage (Šimůnek et al., 2006) which solves Richards' equation using afinite-element formulation. Two-dimensional Richards' equation isexpressed as:

∂.

∂xKH hð Þ ∂h

∂x

� �þ ∂

.∂z

Kv hð Þ ∂ hþ zð Þ∂z

� �¼ ∂θ

∂tð3Þ

s as a function of the degree of saturation.

75M. Farzamian et al. / Journal of Applied Geophysics 121 (2015) 71–83

where h [L] is pressure head, z [L] is elevation, θ is volumetric water con-tent, KH(h) and KV(h) are the horizontal and vertical unsaturated hy-draulic conductivity [L/T] respectively as a function of pressure head.We assumed here that the retention and hydraulic conductivityfunctions can be represented by the parametric models of vanGenuchten (1980) who used the statistical pore-size distributionmodel of Mualem (1976) to obtain a predictive equation for the unsat-urated hydraulic conductivity function in terms of soil water retentionparameters:

θ hð Þ ¼ θr þ θs−θrð Þ1þ αhj jn� �m h b 0

θs h ≥ 0

8<: ð4Þ

K hð Þ ¼ KsSle 1− 1−S1=me

� �mh i2ð5Þ

Se ¼ θ−θrθs−θr

ð6Þ

m ¼ 1−1=n ; nN1 ð7Þ

where θs is the saturatedwater content, θr is the residualwater content,defined as the water content for which the gradient dθ/dh becomeszero, α and n are empirical parameters and Ks is the saturated hydraulicconductivity. The pore connectivity parameter l in the hydraulic con-ductivity function was estimated to be about 0.5 as an average formany soils (Šimůnek et al., 2006).

3.4. Moment analysis

2D spatial moments were calculated from the resistivity images ac-cording to

Mij tð Þ ¼ ∬ΓΔθ x; zð Þxiz jdxdz: ð8Þ

The zeroth, first and second spatial moments correspond to i + j =0, 1, and 2 respectively.Δθ is thewater content changes based on the re-sistivity changes estimation inferred from time-lapse ERTmodel, wherethe background water content has been removed. Γis the volume of in-terest (for a description of moment analysis, see e.g., Ye et al., 2005).

In moment analysis, the mass of the system and location of the cen-ter of mass and how the mass spread at consecutive times is quantified.

Fig. 4. In situ temperature variations during the wa

The zeroth moment, M00, is the changes in mass within the domain.The firstmoment,M01 normalized by themass, defines the vertical cen-ter of mass and finally the spread of the mass about its center is relatedto the second spatial moment. The vertical spread of water is definedusing following equation:

σ2xx ¼

M02

M0−

M01

M0

� 2

: ð9Þ

4. Results and discussion

4.1. Time-lapse ERT model

The inversion of time-lapse ERT data was carried out usingRES2DINV software (Loke, 2002a).

The ERT data was corrected for temperature prior to inversion usingthe data temperature correction method outlined earlier. Fig. 4 illus-trates changes in temperature of the first borehole during water injec-tion. The temperature graphs for sensors in depths over 30 cm show asharp decrease at the beginning of water injection and followed by agradual rise as water injection went on. Sensors with less than 30 cmbutmore than 10 cmdepths show increasing trends duringwater injec-tion. Pattern of changes in temperature for the second borehole (notshown here) showed a very similar result.

The background resistivity model is shown in Fig. 5. The modelingresult shows fairly high resistivity values along the profile which indi-cates the soil was very dry before the water injection test. Inversion oftime–lapse data was then carried out using independent data inver-sions, the difference inversion and simultaneous space–time inversionmethods. The results of resistivity model inferred from simultaneousspace–time inversion method after two iterations are shown in Figs. 6and 7. Fig. 6(a–h) show the results of resistivity inversions, in terms ofpercentage resistivity changes with respect to background in 32, 54,75, 97, 119, 140, 162 and 182 min after injection respectively. Two iter-ationswere only used to invert data since it appears to be some noise inthe first dataset that causes distortions in the model when we tried toreduce the datamisfit below 5%. Using Eq. (2), we then converted resis-tivity changes to water content variations. The results of percentagewater content changes with respect to background in 32, 54, 75, 97,119, 140, 162 and 182 min after injection are shown in Figs. 7a, b, c,6d, e, f, g and h respectively. The infiltrating water front into the

ter injection, inferred from the first borehole.

Fig. 5. 2D vertical resistivity image of background before the water-injection test.

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unsaturated zone is clearly visible in Fig. 7 shortly after water injection.Focusing on the subsequent eight images indicates that the sedimentsare highly permeable and the infiltration process is very fast in a down-ward movement and vertical spreading. There is no sign of water frontmovement ceasing or changing which again confirms that the soil isfairly homogenous.

4.2. Estimating the saturated hydraulic conductivity

Themass balance, center of mass vertical motion and vertical spreadof injected water inferred from time-lapse ERT models were estimatedusing Eqs. (8) and (9). The results of these analyses are plotted inFig. 8(a–c). The percent mass was obtained after removing the massfrom background. Fig. 8a shows a very poor resolution at simulatingwater mass and only about 20% of the injected water was recovered inthis study. The trend of themass percent is fairly steady over the exper-iment with a gradual decrease from 21.5% to 19.5%. The center of massverticalmotion, computed fromERT images is shown in Fig. 8b. The cen-ter ofmass verticalmotion indicates clearly the very fast infiltration andvertical downwardmigration. The center ofmassmoved approximately53 cm from the injection source over 182 min. The vertical spread ofinjected water is plotted in Fig. 8c. The graph shows a fairly monotonictrend of increase in vertical spread over the experiment as water mi-grates downward. The vertical spread of injected water show a greaterscatter compared to the first moment. It is not unexpected due to thehigh sensitivity of the second moment computation to smoothness op-timization method used in the inversion process.

In order to constrain the hydrological model, we simulated unsatu-rated flow using HYDRUS 2D software. Five van Genuchten's parame-ters (θr, θs, α, n, and Ks) were predicted based on the particle sizedistribution and bulk density of the extracted samples using ROSETTAsoftware (Schaap et al., 2001). The obtained values from ROSETTA

software are given in Table 1a. Consequently, van Genuchten's equa-tions with the estimated values were used as input to the unsaturatedflow simulation. Initial conditions were developed based on the watercontent of the extracted samples. Concerning soil texture analysis, a ho-mogenous soil was selected for simulations. The upper and bottomboundaries of the soil were simulated by implementing specified fluxof 8.96 cmh−1 corresponding to the applied irrigation and free drainageboundary conditions respectively. The simulation was carried out for182 min and the evaporation was neglected in all simulations.

The center of mass vertical motion of the flow simulation was calcu-lated and is shown in Fig. 9a. The center ofmass is in preference to othermeasures, such as the position of the tracer front, because (a) it has aphysical basis, and (b) will be sensitive to the hydraulic conductivityof the sandstone for gravity dominated flow (Binley et al., 2002b). Acomparison of the center of mass vertical motion inferred from flowsimulation with ERT images (Fig. 9a) shows that the water trace sinksfaster in the graph derived from ERT images.

Since among van Genuchten's parameters, the saturated hydraulicconductivity plays the most important role in dynamics of the vadosezone and in particular, it controls the speed of water infiltration, wefixed all others van Genuchten's parameters to be the same values ofthe Table 1a and then several new simulations were carried out bychanging saturated hydraulic conductivity value to find the bestmatch on the basis of the sinking process of the water during water in-jection test. Several values of saturated hydraulic conductivity fromROSETTA database range for sand (Table 1b)were used for new simula-tions. The results of center of mass vertical motion shown in Fig. 9a in-dicate that saturated hydraulic conductivity values in 0.5–1 cm/mincan well reproduce the center of mass vertical motion of injectedwater during the period of measurements. The vertical spread ofinjected water resulting from simulating models is also plotted inFig. 9b. The scatter pattern of vertical spread inferred from ERT images

Fig. 6. Sequence of resistivity changes inferred from simultaneous space–time inversion results with respect to background in 32, 54, 75, 97, 119, 140, 162 and 182 min after injectionrespectively.

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Fig. 6 (continued).

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make this comparison inaccurate; however hydraulic conductivityvalues in 0.5–1.5 cm/min range can better reproduces the verticalspread of injected water during the period of measurements.

5. Synthetic test

Synthetic numerical experimentwas performed to examinehow theERT method could inherently alter the spatial moment analysis results

Fig. 7. Sequence of percentagewater content changes inferred from simultaneous space–time ininjection respectively.

and thereby influence the result of hydrologic parameters characteriza-tion. A 2D forward hydrologic simulation ofwatermovement during thewater injectionwas performed for 182min. A homogenous soil with thevanGenuchten's parameters listed in Table 1a and Ks equal to 0.65wereused in this synthetic test. The same initial and boundary conditionswere developed as used in the previous simulations. The thermal pro-files of the soil were also taken into account in these simulations. After-ward, the development of water infiltration in 32, 54, 75, 97, 119, 140,

version resultswith respect to background in32, 54, 75, 97, 119, 140, 162 and182min after

Fig. 7 (continued).

79M. Farzamian et al. / Journal of Applied Geophysics 121 (2015) 71–83

162 and 182 min after injection was inverted to electrical resistivitymaps using Eq. (2). The electrical resistivity distribution maps werethen used as input for a forward model calculation using theRES2DMOD program (Loke, 2002b). We used the same measurementconfiguration as used in the field site. The forward models obtainedwith RES2DMOD program were subsequently used as input for

inversion. 5% random errors were added to the synthetic data andwere then inverted using RES2DINV. Using the temperature-correction method described in Section 3.1, we corrected the datafrom each time for the temperature variations. The inversion of thetemperature-compensated synthetic data was carried out using inde-pendent inversion, the difference inversion and simultaneous space–

Fig. 8. Results of the moment analysis inferred from the time-lapse ERT model. a) The percent mass; b) The center of mass vertical motion c) The vertical spread of injected water.

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time methods in order to provide an insight into different inversionmethod resulting in spatial moment analysis. Finally, the invertedmodels were used to calculate spatial moment analysis. The samediscretization was used for all inversion process as well as simulatedmodel. The synthetic test was designed only to be used as a mean toidentify errors associated with the ERT method and inversion processand therefore cannot be compared with the moment analysis resultsconducted on the real data.

The estimated values of mass, center of mass vertical motion andvertical spread based on the simulation of water movement and thesynthetic data are shown in Fig. 10a, b and c respectively. (I) in Fig. 10

Table 1a) Van Genuchten's parameters estimated by ROSETTA software, b) range of vanGenuchten's parameters for sand found in the ROSETTA database, computed from the av-erage and one standard deviation of 308 sand samples.

θr α (cm−1) n ks (cm/min)

a) 0.0489 0.0330 3.56 0.25b) 0.024–0.082 0.02–0.06 2.10–4.81 0.115–1.735

indicates the spatial moment analysis inferred from the simulatedmodel and (II), (III) and (IV) were inferred from the synthetic datainverted by independent inversion, the difference inversion and simul-taneous space–time methods respectively. Fig. 10a illustrates that theinjected water mass is overpredicted by the ERT method. All inversionmethods used in the synthetic test overestimated the mass in system;however, the simultaneous space–time model yielded a better resolu-tion in mass recovery particularly at the beginning of the experiment.

The center of mass vertical motion inferred from the synthetic testshown in Fig. 10b is ahead of the simulatedmodel. There is a significantdifference between the simultaneous space–time model and two otherinverted models at the beginning of the experiment in Fig. 10b. Al-though the center of mass vertical motion inferred from the simulta-neous space–time model was overpredicted, the estimated values arenonetheless quite close to the true value (difference b25%). On theother hand, the vertical spread is more difficult to determine correctly.Fig. 10c shows a drastic difference between the values inferred fromthe synthetic test and simulated model. This result is not surprising,since the ERT data were inverted using a smoothness optimizationmethod which spreads the water tracer location more widely over thearea of interest.

Fig. 9.Comparison of themoment analysis inferred from ERTwith simulatingmodel based on the VanGenuchten's parameters listed in Table 1a and several hydraulic conductivity values.a) The center of mass vertical motion; b) The vertical spread of injected water.

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6. Discussion

The water injection test conducted at the Samorra Correia provesthat fast infiltration in permeable sediments can bemonitored by groundsurface ERT. In spite of poor resolution of ERT images to reproduce theprecise injected water mass, a joint consideration of the first and secondmoments aimed to constrain the saturated hydraulic conductivity.

The ERT-estimated water mass was dramatically underestimatedand only about 20% of the injected water was recovered in this study.The poor sensitivity of ERT method, particularly the ground surfaceERT, in imagingwater content amountmight be explained by the lateralwatermovement out of themeasurement area in the ground surface 2Dsurvey, the noise level in the background resistivity image, the inversionprocess and more importantly the large contrast between the electricalconductivity of injected water and background.

The synthetic test results and moment analysis calculations indicatethat the determination of the center of mass vertical motion is fairly ro-bust when the water tracer penetrated to deeper zone. In contrary,predicting the vertical spread of the water tracer is more troublesome.The high sensitivity of the second moment analysis computation dueto inversion process and noisy dataset in borehole ERT survey werealso reported in several studies (e.g., Binley et al., 2002b; Singha andGorelick, 2005; Looms et al., 2008a). Since the vertical spread in this

experiment was significantly overestimated and distorted, the first mo-ment is a more reliable tool to estimate the hydraulic conductivity. Re-garding the fact that, the first moment was also slightly overestimatedby ERT method, the range of 0.5–0.7 cm/min could be a more accurateestimation for saturated hydraulic conductivity.

We have used three different inversion methods to present howthese approaches capture the water movement during water injectiontest and investigate whether the recent simultaneous space–time regu-lation can better resolve the water infiltration. The results of the syn-thetic test reveals a significant difference between the spatial momentanalyses inferred from simultaneous space–time inversion model andtwo others inversion models at the beginning of the experiment. Thewater tracer is a small target at the beginning to capture properly inthe inversion process and the large contrast between the electrical con-ductivity of injected water and background also makes the inversionprocess more difficult to recover the sharp anomaly accurately; howev-er, the simultaneous space–timemodel did a better job and the result ofthis method is closer to the simulated model. As the water tracer pene-trated deeper and becamemore dispersed, the results of other inversionmethods becomemore similar and stable and ERTmodels aremore suc-cessful in capturing the water movement and therefore the center ofmass vertical motion and the vertical spread were estimated moreaccurately.

Fig. 10. Results of the moment analysis inferred from synthetic test: a) The percent mass; b) The center of mass vertical motion; c) The vertical spread of injected water.

82 M. Farzamian et al. / Journal of Applied Geophysics 121 (2015) 71–83

7. Conclusions

The use of non-invasive ground surface ERT data to characterizechanges in water content due to water injection into the unsaturatedsandstone is an invaluable tool to derive unsaturated hydraulic param-eters under in-situ conditions. It is extremely difficult to derive similarestimates in the sandy soil fromdirectmeasurements, which are heavilyaffected by soil disturbance and other errors.

The synthetic test in this study shows how ERT method and inver-sion process inherently changes the shape and magnitude of the watertracer during the experiment. The findings in this study stress the im-portance of a careful consideration in inverse problem to avoid the ef-fects of overparameterization and smoothing from regularization thatcan impact the quantitative estimates of hydrogeologic parametervalues. It was difficult to apply the difference inversion on our datadue to the presence of noise in the initial data set and the results ofthis approach was only slightly better than independent inversion.This is not surprising, since the difference inversion method requiresan independent inversion of the first dataset. Therefore, artifacts in the

initial independent inversion will introduce artifacts into the time-lapse inversion. In our experience, the simultaneous space–time inver-sion could effectively reducing the inversion artifacts and was signifi-cantly more successful in mapping resistivity changes; however thesynthetic test reveals that even this technique can lead to uncertainestimates of soil hydraulic properties. Future attempts can be madeon finding ways to deal with these shortcomings. Applying new ap-proaches such as coupled hydrogeophysical inversion (e.g. Hinnellet al., 2010) can significantly improve the parameters estimation byconsidering all of the hydrologic and geophysical data in a single inver-sion process simultaneously and avoiding geophysical resolution prob-lems related to the data inversion.

The simple conversion of electrical conductivity to water contentbased on Archie's law could underestimate the water mass in thisstudy. The method used in this study has the advantage of using an ap-proach similar to ERT models to calibrate field data which could effec-tively reduce heterogeneity in water content distribution mapping. Inaddition, collecting undisturbed samples to conduct a laboratory exper-iment was an impractical issue in our case study since the soil was a

83M. Farzamian et al. / Journal of Applied Geophysics 121 (2015) 71–83

loose deposit of sand. In contrast, the degree of saturation of extractedsample was limited and did not cover 0–1 range and also localizingthe electrical conductivity of the related samples based on the invertedmodel was another source of uncertainty which made impractical toachieve a more accurate relationship.

As the temperature varies during the water injection significantlyand affects the electrical resistivity of soil, the thermal profiles of thesoil were taken into account in the calculation. The thermal profilesshow variations of 6co during the water injection experiment which af-fects significantly in ERT images and was required to be modified for aquantitative model. Neglecting temperature fluctuations leads to errorsin interpretation of ERT images particularly when a quantitative esti-mate of water content is required. In this study, we corrected the datafor temperature before inversion to avoid adverse effects of imperfectERI inversion resolution on the temperature correction.

Acknowledgment

The authors sincerely acknowledge the financial support from thegrant of FCT (Referencia da bolsa: SFRH/BD/66665/2009) that madethis study possible. We are grateful to Jorge Simoes from “Companhiadas Lezírias” for continued support for our work in Semora Correira.Thanks also to Vera Lopes (Geology Department, University of Lisbon)who provided the laboratory facilities and useful guidance for sampleanalysis. The work would not have been possible without agreementof site access by “Companhia das Lezírias”. Thanks to Ivo ManuelBernardo, Jamil Al-Halbouni and Antonio Soares who have contributedto data collection and equipment preparation and installation.

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