Time-Lapse Seismic and Electrical Monitoring of the Vadose Zone During a Controlled Inﬁltration Experiment at the Ploemeur Hydrological Observatory, France

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Article Time-Lapse Seismic and Electrical Monitoring of the Vadose Zone during a Controlled Inﬁltration Experiment at the Ploemeur Hydrological Observatory, France

Lara A. Blazevic 1,2,*, Ludovic Bodet 2, Sylvain Pasquet 3 , Niklas Linde 4, Damien Jougnot 2 and Laurent Longuevergne 1 1 CNRS, Géosciences Rennes—UMR 6118, Université Rennes, F-35000 Rennes, France; [email protected] 2 CNRS, EPHE, METIS, Sorbonne Université, F-75005 Paris, France; [email protected] (L.B.); [email protected] (D.J.) 3 Institut de physique du globe de Paris, CNRS, Université de Paris, F-75005 Paris, France; [email protected] 4 Institute of Earth Sciences, University of Lausanne, CH-1015 Lausanne, Switzerland; [email protected] * Correspondence: [email protected]

Received: 31 March 2020; Accepted: 21 April 2020; Published: 25 April 2020

Abstract: The vadose zone is the main host of surface and subsurface water exchange and has important implications for ecosystems functioning, climate sciences, geotechnical engineering, and water availability issues. Geophysics provides a means for investigating the subsurface in a non-invasive way and at larger spatial scales than conventional hydrological sensors. Time-lapse hydrogeophysical applications are especially useful for monitoring flow and water content dynamics. Largely dominated by electrical and electromagnetic methods, such applications increasingly rely on seismic methods as a complementary approach to describe the structure and behavior of the vadose zone. To further explore the applicability of active seismics to retrieve quantitative information about dynamic processes in near-surface time-lapse settings, we designed a controlled water infiltration experiment at the Ploemeur Hydrological Observatory (France) during which successive periods of infiltration were followed by surface-based seismic and electrical resistivity acquisitions. Water content was monitored throughout the experiment by means of sensors at different depths to relate the derived seismic and electrical properties to water saturation changes. We observe comparable trends in the electrical and seismic responses during the experiment, highlighting the utility of the seismic method to monitor hydrological processes and unsaturated flow. Moreover, petrophysical relationships seem promising in providing quantitative results.

Keywords: hydrogeophysics; seismic; electrical imaging; time-lapse; vadose zone; water saturation; inﬁltration

1. Introduction Soil moisture plays an important role in the Earth’s water balance [1–3]. After precipitation, for instance, water content increases in a soil further influencing water fluxes such as groundwater recharge, surface runoff, and evapotranspiration. These processes characterize the critical zone and are closely related to ecosystems’ productivity, climate variability, slope stability, and water availability and quality [4,5], hence the interest in measuring soil moisture and mapping its temporally varying distribution in the subsurface. The vadose zone, also termed the unsaturated zone, is governed by strong spatiotemporal variability posing important challenges for hydrological characterization [6]. Classical soil moisture

Water 2020, 12, 1230; doi:10.3390/w12051230 www.mdpi.com/journal/water Water 2020, 12, 1230 2 of 18 measuring techniques are intrusive (i.e., they are based on analyzing soil samples in the laboratory), and more modern techniques such as Time Domain Reflectometry (TDR) or Frequency Domain Reflectometry (FDR), while non-intrusive and adapted to in situ conditions, are still limited in terms of coverage and the small support volume of measurements [7]. To overcome these limitations, hydrogeologists have increasingly turned to geophysical methods over the past three decades [8,9]. The combined use of multiscale probing and imaging techniques along with the integration of hydrological, hydrogeological, and hydrogeochemical data is now commonplace for the observation and study of the surface–subsurface continuum [10]. This approach, often referred to as hydrogeophysics, can be applied non-intrusively from the surface to provide information about subsurface properties related to hydrogeological structures at appropriate scales. Moreover, time-lapse geophysical applications have proven useful for monitoring flow and water content dynamics [11]. In vadose zone hydrogeophysics, electrical and electromagnetic methods dominate due to the clear links between the physical properties they sense and water content. Being mainly dependent on mechanical properties, seismic prospecting techniques are commonly used at larger scales and for other application areas [10]. The seismic signal is by definition related to elastic wave propagation velocities that in turn depend on the material’s mineral composition, porosity, state of stress, and degree of saturation. Seismic imaging has been classically used to characterize geological structures [12–14], yet seismic responses are also influenced by hydrological properties and state variables [15], a recognition that has led to evermore studies using seismic data to constrain hydrological models. Pressure (P) and shear (S) wave velocities (VP and VS) can be estimated from various seismic techniques [16,17]. P- and S-waves are affected differently by changes in pore fluid saturation and their ratio (VP/VS) permits imaging fluids in rocks. For applications to characterize the critical zone, it is possible to combine P- and S-wave refraction tomography [18,19] or to use surface-wave profiling methods [20,21]. These approaches have been tested in further studies [22,23] and applied for quantitative estimations of hydrological parameters in hydrothermal contexts [24]. Nevertheless, there are inherent incompatibilities between P-wave tomography and surface-wave analysis as they involve distinct wavefield examinations and different assumptions about the medium and, as a result, VP and VS models have contrasting resolutions, investigation depths, and posterior uncertainties. Moreover, the inversion processes generally use a small number of layers that cannot fully describe the continuous variations of the subsurface hydrological properties, and the spatial variability of dry properties in soils can be of greater influence in seismic wave velocities than the variation of water content itself. Consequently, VP and VS models should be interpreted separately [25,26] before deriving any parameter of interest which can, in turn, lead to bias and impair monitoring applications. These challenges propel the revision of forward models and inversion approaches, promoting an advance from structural and static property imaging to process-based imaging in order to find alternative ways to detect spatiotemporal changes in water distribution. It is important to consider the hydrological information contained in the seismic data before inverting them [27–29] and also to quantify their temporal variability [26] to properly understand hydrosystems dynamics. In parallel, efforts have been made to establish physical links between seismic methods and the hydrodynamic parameters of interest, spanning theoretical and experimental approaches [30–34] together with field case studies [24,35] and empirical petrophysical models [36–38]. Nevertheless, the interpretation of the near-surface mechanical properties and the definition of their quantitative links with hydrodynamic parameters remains complex. The typical theoretical framework for studying connections between a rock’s hydrodynamic parameters and seismic properties is poroelasticity. However, most sites of interest in critical zone observatories and associated hydrosystems do not only involve consolidated rocks but also—and almost systematically—unconsolidated and partially saturated soils. In this context, the use of Effective Medium Theory (EMT) approaches (e.g., [39,40]) remains delicate as they can fail to quantitatively describe velocity profiles [41]. The use of multi-method geophysics can help overcome these limitations by decreasing ambiguities inherent to each method [42]. Regarding electrical resistivity tomography (ERT) and seismic methods, Water 2020, 12, x FOR PEER REVIEW 3 of 18

Medium Theory (EMT) approaches (e.g., [39,40]) remains delicate as they can fail to quantitatively describe velocity profiles [41]. The use of multi-method geophysics can help overcome these limitations by decreasing ambiguities inherent to each method [42]. Regarding electrical resistivity tomography (ERT) and seismic methods, previous studies have shown correlatable trends between electrical resistivity, ρ, and P-wave seismic velocity in near-surface materials (e.g., [43,44]) while others have used both methods in time-lapse settings to study ground ice degradation [45], and infiltration and dissolution processes [46]. To further investigate the electrical and seismic response in a near-surface time-lapse setting, we designed a controlled field experiment in a critical zone observatory, in Brittany, France. We infiltrated water into a defined area using overall regular injection intervals during two days with Water 2020, 12, 1230 3 of 18 buried TDR sensors providing real-time water content data with depth. Each infiltration event was followed by geophysical acquisitions along two superficial orthogonal lines crossing in the middle ofprevious the infiltration studies have area. shown Herein, correlatable we show trends not only between the relative electrical changes resistivity, in ρ ρand, and VP -wavebut also seismic their evolutionvelocity in with near-surface water saturation materials and (e.g., derived [43,44 ])infiltration while others patterns. have usedWe explore both methods correlations in time-lapse between thesettings two togeophysical study ground properties ice degradation and evaluate [45], the and agreement infiltration between and dissolution the data processes and well [-46established]. petrophysicalTo further relationships. investigate the We electrical discuss and our seismic results response in the context in a near-surface of advancing time-lapse the usage setting, and inweterpretation designed a of controlled seismic data field andexperiment multi-method in a critical geophysics zone observatory, at the near in-surface Brittany, field France. scale Wefor hydrologicalinfiltrated water applications. into a defined area using overall regular injection intervals during two days with buried TDR sensors providing real-time water content data with depth. Each infiltration event was 2.followed Materials by geophysicaland Methods acquisitions along two superficial orthogonal lines crossing in the middle of the infiltration area. Herein, we show not only the relative changes in ρ and VP but also their evolution 2.1. Site Description with water saturation and derived infiltration patterns. We explore correlations between the two geophysicalThe Ploemeur properties Hydrological and evaluate Observatory the agreement is located between in the northwest data and well-establishedFrance, on the south petrophysical coast of Brittany,relationships. 3 km We from discuss the our Atlantic results Ocean in the (Figure context of 1). advancing The crystalline the usage bedrock and interpretation aquifer in the of seismicarea is composeddata and multi-method of tectonic units geophysics developed at the during near-surface the Hercynian field scale orogeny for hydrological and marked applications. by numerous synkinematic intrusions of Upper Carboniferous leucogranites [47]. A pumping site is located at the intersection2. Materials of and (i) Methodsa contact between the Ploemeur granite and overlying mica schists dipping 30° to the2.1. North Site Description and (ii) a sub-vertical fault zone striking N 20° [48]. Since 1991, the crystalline bedrock aquifer has annually supplied 1 million m3 of drinking water to a The nearby Ploemeur population Hydrological of 20,000 Observatory inhabitants. The is located well-developed in northwest and France, highly onconnected the south fracture coast networkof Brittany, at 3depth km from makes the this Atlantic aquifer Ocean highly (Figure productive1). The compared crystalline to bedrock other bedrock aquifer in aquifers the area in Brittany.is composed Over of time, tectonic it unitshas been developed developed during into the a Hercynian well-monitored orogeny site and with marked dense by piezometric numerous coveragesynkinematic involving intrusions 50 boreholes of Upper ranging Carboniferous from 30 to leucogranites 150 m depth [47 [49]].. A The pumping mean annual site is locatedprecipitation at the andintersection potential of (i)evapotranspiration a contact between a thet the Ploemeur site are granite around and 900 overlying and 600 mica mm/year, schists dippingrespectively 30◦ to [50] the, suggestingNorth and (ii)the amaximum sub-vertical infiltration fault zone is strikingas large Nas 20300◦ [ 48mm/year,]. i.e., 30% of annual rainfall.

FFigureigure 1. 1.Geographical Geographical and and geological geological situation situation of the of Ploemeur the Ploemeur Hydrological Hydrological Observatory Observatory (modiﬁed (modifiedfrom [23]). from [23]).

Since 1991, the crystalline bedrock aquifer has annually supplied 1 million m3 of drinking water to a nearby population of 20,000 inhabitants. The well-developed and highly connected fracture network at depth makes this aquifer highly productive compared to other bedrock aquifers in Brittany. Over time, it has been developed into a well-monitored site with dense piezometric coverage involving 50 boreholes ranging from 30 to 150 m depth [49]. The mean annual precipitation and potential evapotranspiration at the site are around 900 and 600 mm/year, respectively [50], suggesting the maximum infiltration is as large as 300 mm/year, i.e., 30% of annual rainfall. We carried out an infiltration experiment consisting of successive pulses in the micaschist area near the pumping site. In 2012, a team of researchers and students [51] dug a pit and installed sensors at different depths including thermometers, tensiometers, and TDR sensors, the latter providing real-time water content estimates throughout our experiment. They also characterized the recovered soils from Water 2020, 12, x FOR PEER REVIEW 4 of 18

We carried out an infiltration experiment consisting of successive pulses in the micaschist area near the pumping site. In 2012, a team of researchers and students [51] dug a pit and installed Watersensors2020 , at12 , different 1230 depths including thermometers, tensiometers, and TDR sensors, the 4 latter of 18 providing real-time water content estimates throughout our experiment. They also characterized the recovered soils from the pit in terms of textural classes, type of soil, bulk density, ρb, and porosity, ϕ, the pit in terms of textural classes, type of soil, bulk density, ρ , and porosity, φ, as summarized in as summarized in Table 1. A cross-section picture and schematicb of the pit wall are shown in Figure Table1. A cross-section picture and schematic of the pit wall are shown in Figure2. Once the sensors 2. Once the sensors were installed, the pit was refilled with the same extracted soil. were installed, the pit was reﬁlled with the same extracted soil.

Table 1. Soil characterization from pit samples after [51]. Table 1. Soil characterization from pit samples after [51]. Horizon Clay Silt Sand Soil Sampling Horizon Horizon Soil Sampling ρb (g/cm3) ϕ (%) Horizon Clay (%) Silt (%) Sand (%) ρ (g/cm3) φ (%) LimitsLimits (m) (m) (%) (%) (%) TypeType DepthDepth (m) (m) b 0.15 1.04 ± 0.02 50 A 0–0.3 7.50 85.14 7.36 Silt 0.15 1.04 0.02 50 A 0–0.3 7.50 85.14 7.36 Silt ± 0.250.25 1.311.31 ± 0.050.05 5050 Silty 0.50 1.79 ± 0.01 30 B 0.3–1.2 2.76 68.39 28.85 Silty 0.50 1.79 0.01 30 B 0.3–1.2 2.76 68.39 28.85 ± loamloam 0.900.90 1.711.71 ± 0.020.02 3030 Silty 1.40 1.86 ± 0.02 30 Silty 1.40 1.86 0.02 30 CC 1.2–21.2–2 2.382.38 62.4362.43 32.81 32.81 ± loamloam 2.002.00 1.651.65 ± 0.050.05 3030 ±

(a) (b)

Figure 2. ((a)) Picture of the pit dug in 20122012 withwith sensorssensors installedinstalled [[51]51];; ((b)) cross-sectioncross-section schematicschematic showing sensor positions and horizons (A,(A, B,B, C)C) describeddescribed inin TableTable1 1..

2.2. Acquisition Setup

The infiltrationinfiltration experiment waswas carriedcarried outout inin SeptemberSeptember 2018.2018. WeWe firstfirst delimiteddelimited aa 2.22.2 × 2.42.4 mm22 × rectangular area for the infiltrationinfiltration using wooden planks, the western side of it being adjacent to the side of of the the pit pit with with the sensors.the sensors. We then We installed then installed electrodes electrodes and 14-Hz and vertical 14-Hz component vertical component geophones alonggeophones two orthogonalalong two orthogonal lines, named lines, NS named and WE, NS crossing and WE, in crossing the middle in the of middle the infiltration of the infiltration area. For thearea. two For geophysical the two geophysical methods, methods, the dimensions the dimensions were the samewere withthe same each with line beingeach line 14.2 being m long 14.2 with m 72long sensors with 72 spaced sensors by spaced 20 cm. by 20 cm. For the ERT acquisition, acquisition, we used a Wenner–SchlumbergerWenner–Schlumberger array with 2006 quadripole quadripole configurations.configurations. As As for for the the seismic seismic acquisition, given given the small geophone spacing and spread, the seismic source source consisted consisted of a smallof a metallic-headed small metallic- sledgehammerheaded sledgehammer hit by another hit 2-kg by sledgehammer. another 2-kg Asledgehammer. total of 14 shots A weretotal madeof 14 shots along were each made line with along a spacing each line of with 1 m starting a spacing at of0.1 1 m starting (i.e., 10 cm at − before0.1 m − the(i.e., first 10 cm geophone) before the and first ending geophone) at 14.3 mand with ending the spacing at 14.3 between m with thethe lastspacing and secondbetween last the shot last being and 40 cm. There were no shots inside the infiltration area. At each shot position, we hit four times to increase the signal-to-noise ratio. The sampling rate was 0.125 ms, and the recording time was 800 ms. A delay of 50 ms was kept before the beginning of each record to prevent early triggering issues. − Water 2020, 12, x FOR PEER REVIEW 5 of 18 second last shot being 40 cm. There were no shots inside the infiltration area. At each shot position, we hit four times to increase the signal-to-noise ratio. The sampling rate was 0.125 ms, and the recording time was 800 ms. A delay of −50 ms was kept before the beginning of each record to prevent early triggering issues. Water 2020, 12, 1230 5 of 18 To investigate the changes in geophysical data and properties with varying water content, we adopted a time-lapse approach during two measurement days in which the responses to successive infiltrationsTo investigate were targeted. the changes The in first geophysical acquisition data on and day properties 1 was with carried varying out before water content, any forced we adoptedinfiltration a time-lapse had been approach made and during it is referred two measurement to as the background days in which acquisition. the responses Each to subsequent successive infiltrationsacquisition was were made targeted. after The an infiltration first acquisition event on except day 1 for was the carried first acquisition out before any of day forced 2, which infiltration was haddone been before made resuming and it the is referredinfiltration to asevents. the background In total, we acquisition.infiltrated 9 times Each (4 subsequent times on day acquisition 1 and 5 wason day made 2), and after we an acquired infiltration geophysical event except data for at the11 individual first acquisition acquisition of day times 2, which (5 times was on done day before 1 and resuming6 on day 2). the infiltration events. In total, we infiltrated 9 times (4 times on day 1 and 5 on day 2), and we acquiredThe infiltrated geophysical water data was at 11 pumped individual from acquisition a neighboring times (5 times borehole. on day Pumping 1 and 6 on rates day 2).were continuouslyThe infiltrated measured, water wasas well pumped as pumped from a neighboringwater conductivity borehole. and Pumping temperature. rates were Since continuously the water measured,level at the assite well is at as 1 pumped5.8 m depth, water we conductivity do not expect and the temperature. pumping to Sincehave theaffected water the level vadose at the zone site isdynamics at 15.8 m or depth, the geophysical we do not expect data. We the used pumping a hose to havewith a aff shectedowerhead the vadose attached zone and dynamics an operator or the geophysicalstood along data.the wooden We used planks a hose while with ainfiltrating showerhead (see attached Figure and 3). To an operatorensure uniform stood along coverage the wooden inside planksthe infiltration while infiltrating area, we steadily (see Figure moved3). Tothe ensure hose during uniform each coverage infiltration; inside no the standing infiltration water area, surface we steadilywas created moved indicatin the hoseg that during the each injection infiltration; rate was no lower standing than water the infiltration surface was capacity created of indicating the soil that(approximately the injection 18 rate mm/h was, measured lower than during the infiltration several tests capacity using of the the Porchet soil (approximately method). The 18first mm two/h, measuredinfiltration duringvolumes several were 250 tests liters using each the (approximately Porchet method). 45 mm) The, firstand twoit took infiltration 20 minutes volumes to complete were 250each liters infiltration. each (approximately For the subsequent 45 mm), infiltrations and it took, we 20 minutesused 400 to liters complete each each(approximately infiltration. 75 For mm) the subsequenttaking 35 minutes infiltrations, to complete we used each 400 infiltration. liters each (approximatelyThe sensors in the 75 mm)subsurface taking 35continuously minutes to recorded complete eachthe volumetric infiltration. water The sensors content, in theθ, matric subsurface water continuously potential, Ψ recordedm, and temperature, the volumetric T, water throughout content, theθ, matricexperiment water as potential, shown inΨ Figurem, and 4. temperature, T, throughout the experiment as shown in Figure4.

Figure 3. Schematic of acquisition setup and picture during an inﬁltrationinfiltration event. The solid pink line along the pit area corresponds to the plane including thethe buriedburied sensors.sensors.

There was no rainfall during the experiment and the air temperature varied between 7 and 23 ◦C. The potential evapotranspiration was 3.3 mm/day, considered negligible compared to the inﬁltration volumes. The experiment data are openly available, information on where and how to access them is provided in Availability of Data and Materials. Water 2020, 12, 1230 6 of 18 Water 2020, 12, x FOR PEER REVIEW 6 of 18

FigureFigure 4. Volumetric 4. Volumetric water water content content (θ (),θ), matric matric waterwater potential (Ψ (Ψm),m and), and temperature temperature (T) throughout (T) throughout the experimentthe experiment as recordedas recorded from from the the sensorssensors at at different diﬀerent depths. depths. Markers Markers indicating indicating starting starting times of times of electricalelectrical resistivity resistivity tomography tomography (ERT) (ERT) and and seismic seismic acquisitions acquisitions are are shown shown on eachon each curve. curve. Gray Gray shadingsshadings correspond correspond to theto the periods periods of of water water inﬁltration. infiltration.

3. ResultsThere was no rainfall during the experiment and the air temperature varied between 7 and 23 °C. The potential evapotranspiration was 3.3 mm/day, considered negligible compared to the 3.1. Electricalinfiltration Resistivity volumes. TomographyThe experiment data are openly available, information on where and how to access them is provided in Availability of Data and Materials. Before inverting the raw data, we eliminated unrealistic data points such as zero values of apparent resistivity,3. Resultsρa. Figure5 shows pseudo-sections for some of the acquisitions for both lines. As we worked with time-lapse data, the electrode conﬁgurations with bad data points during one acquisition were removed3.1. Electrical from all Resistivity the others Tomography such that all acquisitions had the same number of data points using the same electrodeBefore conﬁgurations. inverting the raw This data, pruning we eliminated of the data unrealistic implied data that points the original such as 2006 zero measurements values of at eachapparent acquisition resistivity, were ρ reduceda. Figure 5 to shows 1970 andpseudo 1956-sections data pointsfor some for of the the NS acquisitions and WE lines,for both respectively, lines. beforeAs being we worked used forwith inversion. time-lapse data, the electrode configurations with bad data points during one

Water 2020, 12, x FOR PEER REVIEW 7 of 18 Water 2020, 12, x FOR PEER REVIEW 7 of 18 acquisition were removed from all the others such that all acquisitions had the same number of data acquisition were removed from all the others such that all acquisitions had the same number of data points using the same electrode configurations. This pruning of the data implied that the original points using the same electrode configurations. This pruning of the data implied that the original 2006 measurements at each acquisition were reduced to 1970 and 1956 data points for the NS and Water20062020 measurements, 12, 1230 at each acquisition were reduced to 1970 and 1956 data points for the NS and7 of 18 WE lines, respectively, before being used for inversion. WE lines, respectively, before being used for inversion.

(a) (b) (a) (b) Figure 5. Pseudo-sections of apparent resistivity for (a) NS and (b) WE lines showing the FigureFigure 5. Pseudo-sections 5. Pseudo-sections of apparent of apparent resistivity resistivity for (a ) for NS ( anda) NS (b) WEand lines (b) WE showing lines the showing background, the background, 2nd, 5th, and 11th acquisitions. 2nd,background, 5th, and 11th 2nd, acquisitions. 5th, and 11th acquisitions. To invert the ERT data we used the pyGIMLi library [52]. We first inverted the background ToTo invert invert the the ERT ERT data data we we used used the the pyGIMLi pyGIMLi librarylibrary [[52]52].. We We first first invert inverteded the the background background acquisitions for the NS and WE lines separately. To do so, we used a homogeneous starting and acquisitionsacquisition fors for the the NS NS and and WE WE lines lines separately. separately. To dodo so, we used a a homogeneous homogeneous starting starting and and reference model of 50 Ω.m. The anisotropic regularization (relative weight penalizing roughness) referencereference model model of 50of Ω50.m. Ω.m. The The anisotropic anisotropic regularization regularization (relative (relative weight weight penalizing penalizing roughness) roughness) was was set to 0.5 to favor horizontal layering and the relative error was set to 4.5% according to the setwas to 0.5 set to to favor 0.5 to horizontal favor horizontal layering layering and the and relative the relative error waserror set was to set 4.5% to according4.5% according to the to largest the largestlargest standard standard deviation deviation in in the the recorded recorded data. data. The The regularization regularization parameter parameter λλ waswas initiallyinitially setset toto standard500 and deviationdecreased inby the20% recorded at each iteration data. The until regularization convergence. parameter As the infiltrationλ was initially area only set covered to 500 anda decreased500 and bydecreased 20% at eachby 20% iteration at each until iteration convergence. until convergence As the infiltration. As the infiltration area only area covered only covered a segment a segmentsegment of of the the line line and and as as we we are are interested interested in in retrieving retrieving a a strong strong contrast contrast between between areas areas of of ofincreasing the line and water as we content are interested and areas in retrieving of constant a strong water content, contrast webetween used areas an l1- ofnorm increasing mimicking water increasing water content and areas of constant water content, we used an l1-norm mimicking contentminimization and areas scheme of constant to enhanc watere spatial content, transitions we used in an thel1 -normmodel. mimicking The data fit minimization criteria (chi-squared scheme to minimization scheme to enhance spatial transitions in the model. The data fit criteria2 (chi-squared enhance spatial2 transitions in the model. The data fit criteria (chi-squared misfit χ normalized by the misfitmisfit χ χ normalized2 normalized by by the the number number of of data data points points being being smaller smaller than than 1) 1) was was reached reached at at the the 15th15th andand number of data points being smaller than 1) was reached at the 15th and 16th iterations for the NS and 16th16th iteration iterations sfor for the the NS NS and and the the WE WE line, line, respectively. respectively. We We show show the the results results ofof thesthesee backgroundbackground theinversionsinversions WE line, inrespectively. in Figure Figure 6. 6. We show the results of these background inversions in Figure6.

(a()a ) ((bb))

FigureFigureFigure 6. 6. Background6. Background Background ERTERT ERT inversionsinversions inversions for for ( a()a )NS NS NS and and and ( (b(bb)) )WE WEWE lines. lines. Black Black Black points points points at at atthe the the surface surface surface indicate indicate indicate electrodeelectrodeelectrode positions. positions. positions.

ForForFor the the the time-lapse time time-lapse-lapseinversions inversions inversions wewe we applied applied the the ratioratio ratio inversion inversioninversion scheme scheme introduced introduced introduced by by by [53][53] [53:: ]:

′ 퐝퐝nn 퐝 ′=dn 푓(퐦 ), 퐝nn = (푓(퐦0)0), (1)(1) dn0 = 퐝퐝0f0 m0 , (1) d0 where d0 and dn are the data (in this case, apparent resistivity) for the background acquisition and the nth acquisition, respectively, f(m0) is the model response for the background acquisition, and dn’ is the new data to invert. Instead of using a uniform starting model as in [53], the starting and reference model was initially set to the resulting background model (e.g., [54]). A modiﬁed inversion approach was put into place, in which we performed the time-lapse inversions twice. In the ﬁrst round, we used the Water 2020, 12, x FOR PEER REVIEW 8 of 18

where d0 and dn are the data (in this case, apparent resistivity) for the background acquisition and Waterthe2020 nth, 12acquisition, 1230 , respectively, f(m0) is the model response for the background acquisition, and d8n of’ 18 is the new data to invert. Instead of using a uniform starting model as in [53], the starting and reference model was initially set to the resulting background model (e.g., [54]). A modified inversion l1-normapproach minimization was put into scheme place, and in setwhich the we relative performed error to the 3% time and-lapse the initial inversio lambdans twice. to 200, In decreasingthe first it byround, 20% weat each used iteration. the l1-norm Then, minimization a second time-lapse scheme and inversion set the wasrelative performed error to in 3% which and the the initial starting andlambda reference to 200, model decreasing at each time it by step 20% were at each defined, iteration. for each Then, inversion a second parameter, time-lapse as inversion the minimum was resistivityperformed between in which the model the starting obtained and from refere thence first model time-lapse at each inversion time step and were the defined, background for each model, whileinversion keeping parameter, the other as inversion the minimum parameters resistivity unchanged. between We the adopted model thisobtained approach from to the decrease first thetime prominence-lapse inversion of positive and the anomalies background around model, the infiltration while keeping area the (for other an alternative inversion parameters formulation, seeunchanged [55]). Note. We that adopted the second this approach time-lapse to decrease inversion the isprominence like any other of positive time-lapse anomalies inversion, around except the forinfiltration the fact that area the (for starting an alternative and reference formulation, model see [55] favors). Note negative that the changes second time aiming-lapse at inversion diminishing is smoothness-constrained-inducedlike any other time-lapse inversion, false-positive except for the artifacts fact that surrounding the starting the and region reference of large model decreases. favors If positivenegative increases changes are aiming needed at to diminishing fit the data, smoothness then positive-constrained changes-induced will still false appear-positive in the artifacts inversion surrounding the region of large decreases. If positive increases are needed to fit the data, then results. In Figure7, we show the time-lapse inversion results for both lines in terms of relative change positive changes will still appear in the inversion results. In Figure 7, we show the time-lapse with respect to the background inversion. The decrease in resistivity grows with each acquisition inversion results for both lines in terms of relative change with respect to the background inversion. reaching decreases of 90%. The decrease in resistivity grows with each acquisition reaching decreases of 90%.

(a) (b)

FigureFigure 7. 7.ERT ERT time-lapse time-lapse inversions inversions for for (a )( NSa) NS and and (b) ( WEb) WE lines lines showing showing the the relative relative change change in ρ in. Black ρ. pointsBlack at pointsthe surface at the indicate surface electrode indicate positions, electrode and positions the dashed, and black the dashed lines delimit black thelines infiltration delimit the area. infiltration area. 3.2. Seismic Refraction: Traveltimes and P-wave Velocity 3.2. Seismic Refraction: Traveltimes and P-wave Velocity For the seismic data, we first identified temporal changes in the seismic traces. For a given shot position,For we the extracted seismic data, the we gathers first identified at different temporal acquisition changes times in the and seismic overlapped traces. For the a traces; given ashot clear shiftposition, is observed we extracted inside thethe infiltrationgathers at different area with acquisition the first arrivalstimes and of lateroverlapped acquisitions the traces; arriving a clear later inshift time is (Figure observed8). inside To quantify the infiltration these shifts, area with we manually the first arrivals picked of the later first-arrival acquisitions traveltimes arriving later for in the wholetime dataset. (Figure Next,8). To we quantify computed these the shifts, diff erences we manually in arrival picked times thebetween first-arrival each traveltimes acquisition for and the the backgroundwhole dataset. acquisition. Next, we Figure computed9 displays the differences these di ffinerences arrival fortimes each between shot-geophone each acquisition pair to and illustrate the background acquisition. Figure 9 displays these differences for each shot-geophone pair to illustrate to which extent increases in traveltimes are due to the successive infiltration events. The increases to which extent increases in traveltimes are due to the successive infiltration events. The increases in in traveltimes sometimes extend a few meters outside the infiltration area whereas further away, traveltimes sometimes extend a few meters outside the infiltration area whereas further away, the the changes are minimal or slightly negative. The NS line shows more outliers in traveltime differences changes are minimal or slightly negative. The NS line shows more outliers in traveltime differences while the WE line has a more continuous behavior. This is likely a consequence of the noisier traces in while the WE line has a more continuous behavior. This is likely a consequence of the noisier traces the NS line, which made picking more difficult. in the NS line, which made picking more difficult. As we observed traveltime changes consistent with the infiltration, we proceeded by inverting these data to obtain a VP subsurface model using the refraction tomography module of pyGIMLi that uses Dijkstra’s algorithm [56] as the forward solver. Similarly, as for the ERT, we first inverted the background acquisitions using as starting model a gradual increase from 100 m/s at the top to 600 m/s at the bottom in accordance with expected velocity ranges in shallow soils. The reference model was the same as the starting model, and we set an absolute error of 3 ms. The regularization parameter λ Water 2020, 12, 1230 9 of 18

was set to 200, and we applied an l1-norm scheme based on iteratively reweighted least squares both forWater regularization 2020, 12, x FOR PEER and REVIEW data as we observed systematic outliers in the data (picked traveltimes).9 of For 18 bothWater 20 lines,20, 12 the, x FOR data PEER were REVIEW ﬁtted in three iterations leading to the results in Figure 10. 9 of 18

FigureFigure 8.8. Seismic traces inside the inﬁltrationinfiltration area fromfrom shotshot No.No. 3 ((xx == 1.9 m) along the NS line. We Figure 8. Seismic traces inside the infiltration area from shot No. 3 (x = 1.9 m) along the NS line. We show thethe traces from the background,background, 5th,5th, and 11th acquisitions and observe a clear positive shift in show the traces from the background, 5th, and 11th acquisitions and observe a clear positive shift in P-wave-wave ﬁrstfirst arrivalarrival times.times. P-wave first arrival times.

(a) (b) (a) (b) n Figure 9. 9.Picked Picked traveltime traveltime di ﬀ differenceserences between between the nth theacquisition nth acquisition (tn, for n (t=, 2, for 5, 8,n 11)= 2,and 5, background 8, 11) and Figure 9. Picked traveltime differences between the nth acquisition (tn, for n = 2, 5, 8, 11) and background acquisition (t1) for (a) NS and (b) WE lines for every shot-geophone pair. The black acquisition (t1) for (a) NS and (b) WE lines for every shot-geophone pair. The black dashed lines delimit background acquisition (t1) for (a) NS and (b) WE lines for every shot-geophone pair. The black thedashed geophone lines delimit positions the inside geophone the inﬁltration positions inside area. the infiltration area. dashed lines delimit the geophone positions inside the infiltration area. As we observed traveltime changes consistent with the infiltration, we proceeded by inverting As we observed traveltime changes consistent with the infiltration, we proceeded by inverting these data to obtain a VP subsurface model using the refraction tomography module of pyGIMLi that these data to obtain a VP subsurface model using the refraction tomography module of pyGIMLi that uses Dijkstra’s algorithm [56] as the forward solver. Similarly, as for the ERT, we first inverted the uses Dijkstra’s algorithm [56] as the forward solver. Similarly, as for the ERT, we first inverted the background acquisitions using as starting model a gradual increase from 100 m/s at the top to 600 background acquisitions using as starting model a gradual increase from 100 m/s at the top to 600 m/s at the bottom in accordance with expected velocity ranges in shallow soils. The reference model m/s at the bottom in accordance with expected velocity ranges in shallow soils. The reference model was the same as the starting model, and we set an absolute error of 3 ms. The regularization was the same as the starting model, and we set an absolute error of 3 ms. The regularization parameter λ was set to 200, and we applied an l1-norm scheme based on iteratively reweighted least parameter λ was set to 200, and we applied an l1-norm scheme based on iteratively reweighted least squares both for regularization and data as we observed systematic outliers in the data (picked squares both for regularization and data as we observed systematic outliers in the data (picked traveltimes). For both lines, the data were fitted in three iterations leading to the results in Figure 10. traveltimes). For both lines, the data were fitted in three iterations leading to the results in Figure 10.

Water 2020, 12, 1230 10 of 18 Water 2020, 12, x FOR PEER REVIEW 10 of 18 Water 2020, 12, x FOR PEER REVIEW 10 of 18

(a) (b) (a) (b) FigureFigure 10. 10.Background BackgroundP -waveP-wave seismic seismic refraction refraction tomography tomography model model for for (a )( NSa) NS and and (b) ( WEb) WE lines. lines. Black pointsBlackFigure at points the10. surfaceBackground at the surface indicate P- waveindicate geophone seismic geophone and refraction shot and positions. shot tomography positions. model for (a) NS and (b) WE lines. Black points at the surface indicate geophone and shot positions. AsAs for for the the ERT, ERT, we we defined defined aa ratioratio correctioncorrection (Equation 1) 1) and and continued continued with with the the time time-lapse-lapse inversionsinversionsAs for using usingthe theERT, the same we same parametersdefined parameters a ratio as for ascorrection thefor background the (Equation background inversion 1) inversionand continued except except for reducingwith for the reducing time the assumed-lapse the absoluteassumedinversions error absolute using to 2 ms. theerror We same to tried 2 parametersms. the We two-step tried as the for approachtwo the-step background approach as for the inversionas time-lapse for the excepttime ERT-lapse without for ERT reducing significantwithout the assumed absolute error to 2 ms. We tried the two-step approach as for the time-lapse ERT without improvementsignificant improvement and therefore and adhered therefore to adhered a single to time-lapse a single time inversion.-lapse inversion. Figure 11 Figure shows 11 theshows results the in resultsignificants in terms improvement of relative and change therefore with adhered respect toto thea single background. time-lapse We inversion. notice a clearFigure decrease 11 shows in theVP terms of relative change with respect to the background. We notice a clear decrease in VP inside the results in terms of relative change with respect to the background. We notice a clear decrease in VP infiltrationinside the area, infiltration which becomes area, which more becomes evident more at each evident acquisition at each in acquisition time, eventually in time, reaching eventually60%. reachinginside the − 60%. infiltration Outside area the, infiltrationwhich becomes area, in more the first evident one - atm eter each depth, acquisition one can in observe time, eventually zones− of Outside the infiltration area, in the first one-meter depth, one can observe zones of increase in VP increasereaching in − 60%.VP resulting Outside from the infiltrationsmall decreases area, inin traveltimesthe first one recorded-meter depth, at these one locations. can observe zones of resulting from small decreases in traveltimes recorded at these locations. increase in VP resulting from small decreases in traveltimes recorded at these locations.

(a) (b) (a) (b) Figure 11. Seismic time-lapse inversions for (a) NS and (b) WE lines showing the relative change in FigureVFigureP. Black 11. 11.Seismic points Seismic attime-lapse time the - surfacelapse inversions inversions indicate for geophonefor (a ()a NS) NS and and ( b( shotb)) WE WE positions lines lines showing showing, and the the the dashed relative relative black change change lines in inV P. BlackdelimitVP. points Black the points atinfiltration the surface at the area. surface indicate indicate geophone geophone and shot and positions, shot positions and the, and dashed the black dashed lines black delimit lines the inﬁltrationdelimit the area. infiltration area. 3.3. Petrophysical relationships 3.3.3.3. Petrophysical Petrophysical relationships relationships To further investigate the behavior of ρ and VP with varying water saturation, Sw, we extracted theTo resistivityTo further further investigateand investigate velocity the valuesthe behavior behavior at depths ofofρ ρ correspondingand and VVPP with varying varying to those water water of the saturation, saturation, subsurface Sw Ssensors, wwe, we extracted extractedfor all thethethe resistivity pointsresistivity inside and and velocitythe velocity infiltration values values area at at depths depthsand all corresponding correspondingacquisitions. toWe to those convertedthose of of the the the subsurface subsurface water content sensors sensors readings for for all all the pointsfromthe points insidethe TDR inside the sensors inﬁltration the infiltration to Sw areaby means andarea allofand the acquisitions. all porosity acquisitions. measurements We convertedWe converted of the the waterthe soil water (Table content content 1) such readings readings that: from from the TDR sensors to Sw by means of the porosity measurements of the soil (Table 1) such that: the TDR sensors to Sw by means of the porosity measurements휃 of the soil (Table1) such that: 푆 = , (2) 푤 휙휃 푆푤 =θ , (2) Sw = 휙, (2) and plotted ρ and VP against Sw (Figures 12 and 13φ). We compared the trends in our data with welland - plottedestablished ρ and models VP against for both Sw methods.(Figures 1We2 and define 13).d We ρ as compare the inversed the of trends the effective in our data electrical with conductivity,well-established σeff, modelsformulated for by both [57] methods. as: We defined ρ as the inverse of the effective electrical conductivity, σeff, formulated by [57] as:

Water 2020, 12, 1230 11 of 18

and plotted ρ and VP against Sw (Figures 12 and 13). We compared the trends in our data with well-established models for both methods. We defined ρ as the inverse of the effective electrical conductivity, σeff, formulated by [57] as:

Water 2020, 12, x FOR PEER REVIEW 11 of 18 Water 2020, 12, x FOR PEER REVIEW 11 of 18 1 n σe f f = [Sw σw + (F 1)σs], (3) F1 − 1 푛 휎푒푓푓 = [푆푤 푛휎푤 + (퐹 − 1)휎푠], (3) m 휎푒푓푓 = 퐹 [푆푤 휎푤 + (퐹 − 1)휎푠], (3) where F = φ− is the electrical formation factor,퐹 m and n are Archie’s first and second exponent [58], where F = ϕ−m is the electrical formation factor, m and n are Archie’s first and second exponent [58], respectively,where σFw = isϕ−m the is the electrical electrical conductivity formation factor, of them and pore n are water, Archie’s and firstσs andis the second surface exponent conduction. [58], We respectively, σw is the electrical conductivity of the pore water, and σs is the surface conduction. We comparedrespectively two diff,erent σw is the models electrical with conductivity the data, oneof the for pore the water two, shallowestand σs is the sensorsurface positionsconduction. and We another compared two different models with the data, one for the two shallowest sensor positions and one foranother the rest, one given for the the rest di, givenfferent the documented different documented porosities porosities across across these these depths. depths. For For thethe first first model another one for the rest, given the different3 documented porosities across these depths. For the first we usedmodelm = wen = use1.5d andm = nσ =s 1.5= 1and 10σs =− 1 S× /10m,−3 forS/m, the for secondthe second one, one, as as the the porositiesporosities were were lower lower and and the model we used m = n = 1.5 and× σs = 1 × 10−3 S/m, for the second one, as the porosities were lower and −4 4 soils werethe deepersoils were and deeper likely and more likely compacted, more compacted we used, we usedm = m1.7, = 1.7,n = n2, = 2, and andσ sσs= = 55 × 1010−−4 S/m.S/m. For For both the soils were deeper and likely more compacted, we used m = 1.7, n = 2, and σs = 5 × 10 S/m. For 2 −2 × modelsboth we usedmodelsσ wwe= used5 10 σw = 5S /×m 10 as−2 theS/m meanas the conductivitymean conductivity of the of the pumped pumped water water measured measured during both models we used× σw− = 5 × 10 S/m as the mean conductivity of the pumped water measured the experiment.during the experiment..

Figure 12. Electrical resistivity (ρ) versus water saturation (Sw) inside the infiltration area at the Figure 12.FigureElectrical 12. Electrical resistivity resistivity (ρ) versus (ρ) ver watersus water saturation saturation (S w(S)w inside) inside the the inﬁltration infiltration area at the depths depths of the TDR sensors. The data points come from both NS and WE lines. The black solid lines of the TDRdepths sensors. of the TDR The sensors data points. The data come points from come both from NS andboth WENS and lines. WE The lines. black The black solid solid lines lines correspond correspond to resistivity models described in the text. to resistivitycorrespond models to resistivity described models in the described text. in the text.

Figure 13. P V S Figure-wave 13. P-wave velocity velocity ( P ()V versusP) versus water water saturationsaturation (S (w) winside) inside the infiltration the inﬁltration area at area the depths at the depths Figure 13. P-wave velocity (VP) versus water saturation (Sw) inside the infiltration area at the depths of the TDRof the sensors. TDR sensors. The The data data points points come come from from both NS NS and and WE WE lines. lines. The Thesolid solidlines correspond lines correspond to to of the TDR sensors. The data points come from both NS and WE lines. The solid lines correspond to velocity models described in the text for 100% quartz (black) and 100% clay (gray). velocityvelocity models models described described in the in the text text for for 100% 100% quartzquartz (black) (black) and and 100% 100% clay clay (gray) (gray)..

Water 2020, 12, 1230 12 of 18

We modeled VP for two different compositions, 100% quartz and 100% clay, using an effective medium model based on Hertz–Mindlin contacts. We computed the dry effective bulk and shear moduli, Keff and µeff, for the absolutely frictionless case (formulation from [59], p. 247):

 1/3 2( )2 2 C 1 φ µ  3 Ke f f =  − P , µe f f = Ke f f , (4)  18π2(1 ν)2  5 − where C is the average number of contacts per grain; µ and ν are the shear modulus and the Poisson ratio of the grain material, respectively; and P is the eﬀective stress. For the 100% quartz composition we used µ = 44 GPa and ν = 0.08, and for the 100% clay composition we used µ = 9 GPa and ν = 0.34; in both cases we used C = 6. We proceeded by performing ﬂuid substitution according to Biot–Gassmann [39,40] to obtain the saturated bulk and shear moduli, Ksat and µsat, for the whole range of 0%–100% Sw (formulation also from [59], p. 273):

Ksat Ke f f K f l = + , µsat = µe f f , (5) K Ksat K Ke f f φ K K − − − f l where K is the bulk modulus of the grain material, and Kfl is the effective bulk modulus of pore fluid and as we deal with a partially saturated medium:

1 Sw 1 Sw = + − , (6) K f l Kw Ka with Kw and Ka as water and air bulk modulus, respectively (Kw = 2.2 GPa and Ka = 0.101 MPa). Together with the corresponding changes in ρb, we calculated VP as: s 4 Ksat + 3 µsat VP = . (7) ρb

4. Discussion The results obtained from ERT and seismic time-lapse inversions demonstrate the utility of geophysics in providing spatiotemporal information about hydrological processes that complement soil moisture sensors with limited spatial coverage. In Figure 14 we show the evolution of the infiltration front in the subsurface in terms of relative changes in ρ and VP. Although the choice of percentage change ( 60% for ρ and 25% for V ) is rather arbitrary, one can identify large-scale − − P similarities and smaller differences in the evolution of the two properties and between the infiltration patterns of the two lines. Previously, cross-borehole geophysics has been successfully applied to monitor tracer infiltration (e.g., cross-borehole ERT and GPR in [60]). Herein we extend this application using surface-based ERT and seismic. From the profiles in Figure 14, we can identify preferential flow paths that are consistent for both methods, where for the NS line changes tend to evolve northwards, and for the WE line, they evolve eastwards. In the case of the WE line, this might come as a result of the refilled pit on the west side of the infiltration area impeding flow. These evolutions have a greater lateral increase between the two first time-lapse acquisitions, of about 40 cm, which then reduces to around 20 cm lateral progression between acquisitions. Overall, we can say that the water tends to flow in the ENE direction. This is important for the further analysis of infiltration results, as the existence of preferential flow paths and lateral water redistribution dismiss a 1D hypothesis at scales as small as 1 m. Water 2020, 12, x FOR PEER REVIEW 12 of 18

We modeled VP for two different compositions, 100% quartz and 100% clay, using an effective medium model based on Hertz–Mindlin contacts. We computed the dry effective bulk and shear moduli, Keff and µeff, for the absolutely frictionless case (formulation from [59], p. 247):

퐶2(1 − 휙)2휇2 1/3 3 퐾 = [ 푃] , 휇 = 퐾 , (4) 푒푓푓 18휋2(1 − 휈)2 푒푓푓 5 푒푓푓 where C is the average number of contacts per grain; µ and ν are the shear modulus and the Poisson ratio of the grain material, respectively; and P is the effective stress. For the 100% quartz composition we used µ = 44 GPa and ν = 0.08, and for the 100% clay composition we used µ = 9 GPa and ν = 0.34; in both cases we used C = 6. We proceeded by performing fluid substitution according to Biot– Gassmann [39,40] to obtain the saturated bulk and shear moduli, Ksat and µsat, for the whole range of 0%–100% Sw (formulation also from [59], p. 273):

퐾푠푎푡 퐾푒푓푓 퐾푓푙 = + , 휇푠푎푡 = 휇푒푓푓, (5) 퐾 − 퐾푠푎푡 퐾 − 퐾푒푓푓 휙(퐾 − 퐾푓푙) where K is the bulk modulus of the grain material, and Kfl is the effective bulk modulus of pore fluid and as we deal with a partially saturated medium:

1 푆푤 1 − 푆푤 = + , (6) 퐾푓푙 퐾푤 퐾푎 with Kw and Ka as water and air bulk modulus, respectively (Kw = 2.2 GPa and Ka = 0.101 MPa). Together with the corresponding changes in ρb, we calculated VP as: 4 퐾 + 휇 √ 푠푎푡 3 푠푎푡 (7) 푉푃 = . 휌푏

Water 2020, 12, x FOR PEER REVIEW 13 of 18

Previously, cross-borehole geophysics has been successfully applied to monitor tracer infiltration (e.g., cross-borehole ERT and GPR in [60]). Herein we extend this application using surface-based ERT and seismic. From the profiles in Figure 14, we can identify preferential flow paths that are consistent for both methods, where for the NS line changes tend to evolve northwards, and for the WE line, they evolve eastwards. In the case of the WE line, this might come as a result of the refilled pit on the west side of the infiltration area impeding flow. These evolutions have a greater lateral increase( abetween) the two first time-lapse acquisitions, of (aboutb) 40 cm, which then reduces to around 20 cm lateral progression between acquisitions. Overall, we can say that the water Figure 14. Isochrones showing a given percentage of relative change in electrical r resistivityesistivity ( ρ) and tends to flow in the ENE direction. This is important for the further analysis of infiltration results, as P-wave-wave velocity (VP)) and and their their evolution evolution with with acquisition for for (a)) NS and (b) WEWE lines.lines. The dashed the existence of preferential flow paths and lateral water redistribution dismiss a 1D hypothesis at black lines delimit the inﬁltrationinfiltration area and the graygray arrows indicateindicate lineline crossings.crossings. scales as small as 1 m. We nownow investigateinvestigate the the correlation correlation trends trends between betweenρ and ρ andVP VasP theyas they are are both both dependent dependent on φ onand ϕ Sandw. FromSw. From Figure Figure 15, we 15, observe we observe that thethat correlation the correlation between between the two the properties two properties changes changes with Swithw, with Sw, thewith points the points being more being spread more for spread dryer for soils dryer and aligningsoils and with aligning a positive with correlation a positive when correlation saturation when is higher.saturation Understanding is higher. Understanding these trends andthese how trends they and change how with they varying change Swithw is importantvarying Sw for is important the use of multi-methodfor the use of multi geophysics-method interpretation geophysics interpretation and inversion and in hydrological inversion in contexts. hydrological contexts.

Figure 15.15. PP-wave-wave velocityvelocity ( V(VPP)) versus versus resistivity resistivity (ρ ()ρ inside) inside the the infiltration infiltration area area at the at depthsthe depths of the of TDR the sensors.TDR sensors. The data The points data comepoints from come both from NS both and WENS linesand atWE the lines background at the background and last (11th) and acquisitions. last (11th) acquisitions. The predicted electrical resistivity for a given Sw is mostly in good agreement with our data (Figure 12). For the two deepest sensor positions, however, the model underpredicts the data, which The predicted electrical resistivity for a given Sw is mostly in good agreement with our data might(Figure be 12). related For the to thetwo soil deepest being sensor more compacted positions, however, at these locations. the model Regarding underpredicts seismic the velocities data, which and petrophysicalmight be related modeling, to the thesoil behaviorbeing more of V Pcompactedin unconsolidated at these partiallylocations. saturated Regarding media seismic is still velocities not fully agreed upon, and this is reflected in the modest agreement between our predictions and the observed and petrophysical modeling, the behavior of VP in unconsolidated partially saturated media is still datanot fully (see agreed Figure 13upon). Classic, and this EMT is combinedreflected in with the Biot–Gassmannmodest agreement fluid between substitution our predictions predicts a decrease and the inobservedVP with data increasing (see FigureSw until 13). about Classic 95%–98% EMT where combined the increase with Biotin K–satGassmantakes overn fluid the increase substitution in ρb, and V starts sharply increasing. Most studies, both in the laboratory and the field, have reported a predictsP a decrease in VP with increasing Sw until about 95%–98% where the increase in Ksat takes over decreasing trend in V with S before reaching full saturation [28,31,34,61,62], even if recent laboratory the increase in ρb, andP VP startsw sharply increasing. Most studies, both in the laboratory and the field, have reported a decreasing trend in VP with Sw before reaching full saturation [28,31,34,61,62], even if recent laboratory experiments showed an opposite trend [29,38]. Moreover, some authors have pointed out that EMT fails to quantitatively describe the changes as it tends to overpredict the velocity values [15,31,34]. Our seismic results agree with the decreasing trend in velocities with Sw, as seen from the behavior inside the infiltration area depicted in Figure 11. From Figure 13, we can identify this trend for the three most shallow TDR positions whereas it is hard to recognize a trend for the other positions. Even though the deeper soil is more water saturated, the VP values are greater because the

Water 2020, 12, 1230 14 of 18 experiments showed an opposite trend [29,38]. Moreover, some authors have pointed out that EMT fails to quantitatively describe the changes as it tends to overpredict the velocity values [15,31,34]. Our seismic results agree with the decreasing trend in velocities with Sw, as seen from the behavior inside the infiltration area depicted in Figure 11. From Figure 13, we can identify this trend for the three most shallow TDR positions whereas it is hard to recognize a trend for the other positions. Even though the deeper soil is more water saturated, the VP values are greater because the soils are more compacted. In the specific case of the TDR data at z = 0.5 m, Sw seems to reach 100%; however, due to the low velocity values, we conclude that the porosity values for this layer are probably higher than documented, and it does not actually reach full water saturation. When comparing the data with the models for two different mineralogical compositions, we find that the shallow soils start with values predicted by the clay model, and with greater depths, they gradually move towards the predictions of the quartz model. This might be an indicator of different compositions for the different soils, which can come as a result of weathering, although one cannot rule out the possibility of a uniform mineralogy and under- or overprediction from the model. In addition to this analysis, and for both ERT and seismic, one has to take into account the resolution-dependent limitations of comparing field data with theoretical models [63]. Although the observed trend in velocities is consistent with theoretical predictions, it is interesting to observe that in the vicinity of the infiltration area there are also apparent increases in VP. We are confident this comes from the data as we observe shorter traveltimes at corresponding positions (Figure9). These decreases in traveltime are rather small in magnitude, but they are systematically observed at each acquisition and for both lines. This suggests that they are related to changes in Sw, which could have implications for the interpretation of near-surface time-lapse seismic in non-controlled contexts. Previous studies have investigated the complementarity of VP and VS to estimate changes in Sw in near-surface contexts [22,24]. Further research includes surface wave dispersion analysis and inversion of dispersion curves to obtain 1D VS profiles. Together with the VP results we presented above and appropriate petrophysical models, one could gain further insight in quantitative estimations of Sw from seismic data.

5. Conclusions We performed a controlled water infiltration experiment over two days where infiltration intervals were separated by times during which surface-based seismic and electrical resistivity acquisitions 3 were performed. In total, we infiltrated 629 mm of water (total volume 3.3 m ) resulting in Sw changes from 20% to 70% in the vadose zone. These increases in Sw are well detected by the ERT; decreases in electrical resistivity up to 90% are evident at each acquisition down to 1 m depth. From the seismic picks, we can identify clear increases in refracted P-wave first arrival times inside the infiltration area, reaching up to 10 ms increase at later acquisitions. These traveltime increases translate into VP decreases up to 60% when inverting the data. From the time-lapse inversion of ERT and seismic data, we observe comparable trends notably in terms of the lateral spreading of the infiltration, which is detected similarly by both methods, and we were able to identify preferential flow paths. This highlights the utility of combined surface-based ERT and seismic refraction to monitor hydrological processes and water saturation changes in the vadose zone. Moreover, understanding the correlation between ρ and VP and its evolution with Sw can be useful for the interpretation and inversion of multi-method geophysics in hydrological contexts. The petrophysical predictions are in good to fair agreement with the data. Nevertheless, it is important to have good knowledge of the soil’s properties in order to extract correct quantitative information from geophysical data while also taking into account resolution-dependent limitations.

Author Contributions: Conceptualization, L.A.B., L.B., S.P., N.L. and L.L.; methodology, L.A.B., L.B., S.P., N.L., D.J. and L.L.; formal analysis, L.A.B, L.B. and N.L.; investigation, L.A.B., L.B., S.P., N.L., D.J. and L.L.; data curation, L.A.B.; writing—original draft preparation, L.A.B.; writing—review and editing, L.A.B., L.B., S.P., N.L., Water 2020, 12, 1230 15 of 18

D.J. and L.L.; supervision, L.B., N.L., D.J. and L.L. All authors have read and agreed to the published version of the manuscript. Funding: This project is part of the PhD thesis of L.A.B. within the ENIGMA ITN funded by the European Union’s Horizon 2020 research and innovation program under the Marie Sklodowska-Curie Grant Agreement No 722028. The field experiment was supported by the SNO H+ network and OZCAR research infrastructure. The geophysical equipment was provided by the CRITEX ANR-11-EQPX-0011 project and the METIS laboratory at Sorbonne Université. Acknowledgments: We thank Joaquín Jiménez-Martínez (EAWAG, ETH Zürich) for the installation of the unsaturated zone observation system and for the soil analysis. We also thank Thomas Hermans (Ghent University) for helpful discussions regarding the ERT and Thomas Günther (Leibniz Institute for Applied Geophysics) for his support regarding the usage of the pyGIMLi library. Conflicts of Interest: The authors declare no conflict of interest. Availability of Data and Materials: Upon creating an account at http://hplus.ore.fr/en/database/acces-database, the whole dataset and description files are available at http://hplus.ore.fr/documents/ploemeur.kmz. More details on the Ploemeur Hydrological Observatory can be found at http://hplus.ore.fr/en/ploemeur and https: //deims.org/731f3ced-148d-4eb5-aa46-870fa22be713.

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