# 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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## Abstract

**:**

## 1. Introduction

_{P}and V

_{S}) 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 (V

_{P}/V

_{S}) 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, V

_{P}and V

_{S}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, V

_{P}and V

_{S}models should be interpreted separately [25,26] before deriving any parameter of interest which can, in turn, lead to bias and impair monitoring applications.

_{P}but also their evolution with water saturation and derived infiltration patterns. We explore correlations between the two geophysical properties and evaluate the agreement between the data and well-established petrophysical relationships. We discuss our results in the context of advancing the usage and interpretation of seismic data and multi-method geophysics at the near-surface field scale for hydrological applications.

## 2. Materials and Methods

#### 2.1. Site Description

^{3}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.

_{b}, and porosity, ϕ, as summarized in Table 1. A cross-section picture and schematic of the pit wall are shown in Figure 2. Once the sensors were installed, the pit was refilled with the same extracted soil.

#### 2.2. Acquisition Setup

^{2}rectangular area for the infiltration using wooden planks, the western side of it being adjacent to the side of the pit with the sensors. We then installed electrodes and 14-Hz vertical component geophones along two orthogonal lines, named NS and WE, crossing in the middle of the infiltration area. For the two geophysical methods, the dimensions were the same with each line being 14.2 m long with 72 sensors spaced by 20 cm.

_{m}, and temperature, T, throughout the experiment as shown in Figure 4.

## 3. Results

#### 3.1. Electrical Resistivity Tomography

_{a}. Figure 5 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 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 2006 measurements at each acquisition were reduced to 1970 and 1956 data points for the NS and WE lines, respectively, before being used for inversion.

_{1}-norm mimicking minimization scheme to enhance spatial transitions in the model. The data fit criteria (chi-squared misfit χ

^{2}normalized by the number of data points being smaller than 1) was reached at the 15th and 16th iterations for the NS and the WE line, respectively. We show the results of these background inversions in Figure 6.

**d**

_{0}and

**d**

_{n}are the data (in this case, apparent resistivity) for the background acquisition and the nth acquisition, respectively, f(

**m**

_{0}) is the model response for the background acquisition, and

**d**

_{n}’ 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 l

_{1}-norm minimization scheme and set the relative error to 3% and the initial lambda to 200, decreasing it by 20% at each iteration. Then, a second time-lapse inversion was performed in which the starting and reference model at each time step were defined, for each inversion parameter, as the minimum resistivity between the model obtained from the first time-lapse inversion and the background model, while keeping the other inversion parameters unchanged. We adopted this approach to decrease the prominence of positive anomalies around the infiltration area (for an alternative formulation, see [55]). Note that the second time-lapse inversion is like any other time-lapse inversion, except for the fact that the starting and reference model favors negative changes aiming at diminishing smoothness-constrained-induced false-positive artifacts surrounding the region of large decreases. If positive increases are needed to fit the data, then positive changes will still appear in the inversion results. In Figure 7, we show the time-lapse inversion results for both lines in terms of relative change with respect to the background inversion. The decrease in resistivity grows with each acquisition reaching decreases of 90%.

#### 3.2. Seismic Refraction: Traveltimes and P-wave Velocity

_{P}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 was set to 200, and we applied an l

_{1}-norm scheme based on iteratively reweighted least 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.

_{P}inside the infiltration area, which becomes more evident at each acquisition in time, eventually reaching −60%. Outside the infiltration area, in the first one-meter depth, one can observe zones of increase in V

_{P}resulting from small decreases in traveltimes recorded at these locations.

#### 3.3. Petrophysical relationships

_{P}with varying water saturation, S

_{w}, we extracted the resistivity and velocity values at depths corresponding to those of the subsurface sensors for all the points inside the infiltration area and all acquisitions. We converted the water content readings from the TDR sensors to S

_{w}by means of the porosity measurements of the soil (Table 1) such that:

_{P}against S

_{w}(Figure 12 and Figure 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, σ

_{eff}, formulated by [57] as:

^{−m}is the electrical formation factor, m and n are Archie’s first and second exponent [58], respectively, σ

_{w}is the electrical conductivity of the pore water, and σ

_{s}is the surface conduction. We compared two different models with the data, one for the two shallowest sensor positions and another one for the rest, given the different documented porosities across these depths. For the first model we used m = n = 1.5 and σ

_{s}= 1 × 10

^{−3}S/m, for the second one, as the porosities were lower and the soils were deeper and likely more compacted, we used m = 1.7, n = 2, and σ

_{s}= 5 × 10

^{−4}S/m. For both models we used σ

_{w}= 5 × 10

^{−2}S/m as the mean conductivity of the pumped water measured during the experiment.

_{P}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, K

_{eff}and µ

_{eff}, for the absolutely frictionless case (formulation from [59], p. 247):

_{sat}and µ

_{sat}, for the whole range of 0%–100% S

_{w}(formulation also from [59], p. 273):

_{fl}is the effective bulk modulus of pore fluid and as we deal with a partially saturated medium:

_{w}and K

_{a}as water and air bulk modulus, respectively (K

_{w}= 2.2 GPa and K

_{a}= 0.101 MPa). Together with the corresponding changes in ρ

_{b}, we calculated V

_{P}as:

## 4. Discussion

_{P}. Although the choice of percentage change (−60% for ρ and −25% for V

_{P}) is rather arbitrary, one can identify large-scale similarities and smaller differences in the evolution of the two properties and between the infiltration patterns of the two lines.

_{P}as they are both dependent on ϕ and S

_{w}. From Figure 15, we observe that the correlation between the two properties changes with S

_{w}, with the points being more spread for dryer soils and aligning with a positive correlation when saturation is higher. Understanding these trends and how they change with varying S

_{w}is important for the use of multi-method geophysics interpretation and inversion in hydrological contexts.

_{w}is mostly in good agreement with our data (Figure 12). For the two deepest sensor positions, however, the model underpredicts the data, which might be related to the soil being more compacted at these locations. Regarding seismic velocities and petrophysical modeling, the behavior of V

_{P}in unconsolidated partially saturated media is still not fully agreed upon, and this is reflected in the modest agreement between our predictions and the observed data (see Figure 13). Classic EMT combined with Biot–Gassmann fluid substitution predicts a decrease in V

_{P}with increasing S

_{w}until about 95%–98% where the increase in K

_{sat}takes over the increase in ρ

_{b}, and V

_{P}starts sharply increasing. Most studies, both in the laboratory and the field, have reported a decreasing trend in V

_{P}with S

_{w}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].

_{w}, 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 V

_{P}values are greater because the soils are more compacted. In the specific case of the TDR data at z = 0.5 m, S

_{w}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].

_{P}. We are confident this comes from the data as we observe shorter traveltimes at corresponding positions (Figure 9). 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 S

_{w}, which could have implications for the interpretation of near-surface time-lapse seismic in non-controlled contexts.

_{P}and V

_{S}to estimate changes in S

_{w}in near-surface contexts [22,24]. Further research includes surface wave dispersion analysis and inversion of dispersion curves to obtain 1D V

_{S}profiles. Together with the V

_{P}results we presented above and appropriate petrophysical models, one could gain further insight in quantitative estimations of S

_{w}from seismic data.

## 5. Conclusions

^{3}) resulting in S

_{w}changes from 20% to 70% in the vadose zone. These increases in S

_{w}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 V

_{P}decreases up to 60% when inverting the data.

_{P}and its evolution with S

_{w}can be useful for the interpretation and inversion of multi-method geophysics in hydrological contexts.

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## Availability of Data and Materials

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

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

**Figure 4.**Volumetric water content (θ), matric water potential (Ψ

_{m}), and temperature (T) throughout the experiment as recorded from the sensors at different depths. Markers indicating starting times of electrical resistivity tomography (ERT) and seismic acquisitions are shown on each curve. Gray shadings correspond to the periods of water infiltration.

**Figure 5.**Pseudo-sections of apparent resistivity for (

**a**) NS and (

**b**) WE lines showing the background, 2nd, 5th, and 11th acquisitions.

**Figure 6.**Background ERT inversions for (

**a**) NS and (

**b**) WE lines. Black points at the surface indicate electrode positions.

**Figure 7.**ERT time-lapse inversions for (

**a**) NS and (

**b**) WE lines showing the relative change in ρ. Black points at the surface indicate electrode positions, and the dashed black lines delimit the infiltration area.

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

**Figure 9.**Picked traveltime differences between the nth acquisition (t

_{n}, for n = 2, 5, 8, 11) and background acquisition (t

_{1}) for (

**a**) NS and (

**b**) WE lines for every shot-geophone pair. The black dashed lines delimit the geophone positions inside the infiltration area.

**Figure 10.**Background P-wave seismic refraction tomography model for (

**a**) NS and (

**b**) WE lines. Black points at the surface indicate geophone and shot positions.

**Figure 11.**Seismic time-lapse inversions for (

**a**) NS and (

**b**) WE lines showing the relative change in V

_{P}. Black points at the surface indicate geophone and shot positions, and the dashed black lines delimit the infiltration area.

**Figure 12.**Electrical resistivity (ρ) versus water saturation (S

_{w}) inside the infiltration area at the depths of the TDR sensors. The data points come from both NS and WE lines. The black solid lines correspond to resistivity models described in the text.

**Figure 13.**P-wave velocity (V

_{P}) versus water saturation (S

_{w}) inside the infiltration area at the depths 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).

**Figure 14.**Isochrones showing a given percentage of relative change in electrical resistivity (ρ) and P-wave velocity (V

_{P}) and their evolution with acquisition for (

**a**) NS and (

**b**) WE lines. The dashed black lines delimit the infiltration area and the gray arrows indicate line crossings.

**Figure 15.**P-wave velocity (V

_{P}) versus resistivity (ρ) inside the infiltration area at the depths of the TDR sensors. The data points come from both NS and WE lines at the background and last (11th) acquisitions.

**Table 1.**Soil characterization from pit samples after [51].

Horizon | Horizon Limits (m) | Clay (%) | Silt (%) | Sand (%) | Soil Type | Sampling Depth (m) | ρ_{b} (g/cm^{3}) | ϕ (%) |
---|---|---|---|---|---|---|---|---|

A | 0–0.3 | 7.50 | 85.14 | 7.36 | Silt | 0.15 0.25 | 1.04 ± 0.02 1.31 ± 0.05 | 50 50 |

B | 0.3–1.2 | 2.76 | 68.39 | 28.85 | Silty loam | 0.50 0.90 | 1.79 ± 0.01 1.71 ± 0.02 | 30 30 |

C | 1.2–2 | 2.38 | 62.43 | 32.81 | Silty loam | 1.40 2.00 | 1.86 ± 0.02 1.65 ± 0.05 | 30 30 |

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## Share and Cite

**MDPI and ACS Style**

Blazevic, L.A.; Bodet, L.; Pasquet, S.; Linde, N.; Jougnot, D.; Longuevergne, L.
Time-Lapse Seismic and Electrical Monitoring of the Vadose Zone during a Controlled Infiltration Experiment at the Ploemeur Hydrological Observatory, France. *Water* **2020**, *12*, 1230.
https://doi.org/10.3390/w12051230

**AMA Style**

Blazevic LA, Bodet L, Pasquet S, Linde N, Jougnot D, Longuevergne L.
Time-Lapse Seismic and Electrical Monitoring of the Vadose Zone during a Controlled Infiltration Experiment at the Ploemeur Hydrological Observatory, France. *Water*. 2020; 12(5):1230.
https://doi.org/10.3390/w12051230

**Chicago/Turabian Style**

Blazevic, Lara A., Ludovic Bodet, Sylvain Pasquet, Niklas Linde, Damien Jougnot, and Laurent Longuevergne.
2020. "Time-Lapse Seismic and Electrical Monitoring of the Vadose Zone during a Controlled Infiltration Experiment at the Ploemeur Hydrological Observatory, France" *Water* 12, no. 5: 1230.
https://doi.org/10.3390/w12051230