Groundwater Monitoring with Passive Seismic Interferometry

Passive seismic interferometry takes advantage of natural ambient seismic noise generated by the wind, the storms and the human activities (e.g. cars, trains and hereafter pumps) to recover the slight variations of the seismic wave velocity induced by changes in the groundwater level. Here we compare the seismic measurements with actual piezometric data acquired on the Crépieux-Charmy (Lyon, France) groundwater exploitation field. We show the excellent correspondance between variations in the groundwater level and seismic velocity variations. We present hereafter the time and space monitoring of an hydraulic dome formed to prevent biological and chemical pollutions to enter the exploitation field. The horizontal resolution is solely limited by the number of seismic stations used, and is about 30 m in the present study. The vertical resolution of seismic measurement is impaired by spurious artifacts linked to the intermittent sources of noise. In average, the sensitivity of the seismic velocity change corresponds to a 50 cm change of waterlevel. This study confirms the possibility of groundwater monitoring in an industrial context with ambient seismic noise.

). In case of upstream incoming pollution, these basins are filled up with water and form a series of hydraulic domes below them. Each dome represents a local increase of a few meters of the water table, supposed to invert the local water flow from the channel to the uptake area. In the present study, we will focus on the hydraulic dome formed under the infiltration basin 5.2, used for different scientific and experimental studies by the research platform of "Eau du Grand Lyon".

The Hydraulic Dome of Basin 5.2
The infiltration basin 5.2 has dimensions of 370 by 100 meters. It is bounded by an earthen dam of 4 meters high. The basin is equipped with several piezometers ( Figure 1) among which P96 that is located in the vicinity of the supposed maximum of the hydraulic dome formed when the basin is filled-up with water.
Piezometer B10, located on the western bank, is used as a control of the elevation of the hydraulic dome. French regulations enforce a minimum infiltration distance for water of 1 meter. Because of the uncertainty on the position of the maximum of the dome that represents the minimum infiltration distance, the water supply to basin 5.2 is stopped when B10 indicates a groundwater level of 2 meters below the surface level (mbsl). It is started again when B10 indicates a groundwater level of 2.6 mbsl. As a consequence, the water level inside basin 5.2 oscillates around a mean elevation of 1.8 meters. Figure 2 presents a schematic

Passive Seismic Monitoring of Groundwater
Passive seismic monitoring leans on the recording of the mechanical waves that propagate into the subsurface (Figure 3(a)). These waves originate from natural sources such as the wind, the storms, the rivers, and from anthropogenic sources such as cars, trains and hereafter pumps. The mechanical seismic waves are classified as body waves (P and S waves) and surface waves (Rayleigh and Love waves). All of them are characterized by a given velocity that depends on different parameters of the medium such as the shear modulus, the stiffness and the density for elastic parameters; fluid composition, porosity and saturation for poroelastic parameters. The waves velocity is accurately determined by cross-correlating the recordings of the ambient seismic wave field at two seismic stations. The result is formed by a series of waves arriving at different times, depending on their velocity and on the path they followed. We differentiate between the ballistic waves that propagate directly from station A to station B and the coda waves that propagate indirectly from station A to station B. The passive seismic monitoring consists on the repetition of this measurement over consecutive time windows. The results form a correlogram (Figure 3(b)). Any change of the subsurface properties linked to water table variations for instance will result in a slight change of velocity: the arrival time of the waves will be changed accordingly. The first application was shown on the Merapi volcano [2]. The authors demonstrated that the late phases (for time lapse greater than 2 s) reconstructed by the noise correlations are dominated by body waves. They also proved that the temporal decay of these waves is reminiscent of the decay of the coda waves, opening the way for noise coda-wave interferometry. Using precipitation data at the regional scale and a hydrologic model, they linked the annual velocity variations to variations in the water when the distribution of noise sources is stable in space and time [4].
In the following, we apply the very same technique in an industrial context,

Seismic and Piezometric Data
During 9 days from April 26, 2017 to May 06, 2017, nine seismic stations (Rauex by Sercel) equipped with vertical geophones with a nominative frequency of 5 Hzwere installed around basin 5.2. They continuously recorded the ground motion generated by the natural and anthropogenic noise sources at a sampling frequency of 250 Hz. The precise dating of the samples was insured by a continuous GPS synchronization of the seismic station. The waveforms recorded by each station are chopped into one hour windows (Figure 3(a)). During these 9 days of experiment, the basin 5.

Seismic Velocity Changes
For each seismic station and each one-hour trace, the signal processing operations are the following: the data is filtered between 3 and 20 Hz and is whitened in the spectral domain to correct for the differences of spectrum of the different noise sources. On a field experiment with standalone stations, it may happen that from time to time the seismic stations stop acquiring data; the missing data are replaced by zeros in order to complete the time series. Unfortunately in our experiment, station 1 stopped acquiring data early in the experiment. For this reason this station is not included in the analysis. For the pairs of stations of interest (linked by red paths in Figure 1) the one-hour data records are correlated to produce a correlogram similar to the one presented in Figure 3(b). The slight velocity changes are observable as slight changes of arrival time of the ballistic waves. Windowed crosscorrelation (or moving-window cross spectral method in the frequency domain) and trace stretching are two techniques commonly used to estimate local time shifts in seismic signals [5]. Within this study, we use the stretching technique [2]  Many different values of the stretching factor ε are tested. The one retained is the one that maximizes the zero-lag crosscorrelation coefficient between the reference and the velocity variation of each hour. The optimal stretching factor ε is either positive (i.e., the seismic phases arrive later than their reference time) or negative (i.e., the seismic phases arrive before their reference time). Finally, the seismic velocity change curve is defined as the opposite of the vector of the hourly stretching factor.

Piezometric Changes
The velocity changes retrieved following the processing described in the previous section are relative to the reference, chosen here as the average of all 1 h correlations. In order to compare the results with the piezometric data, we simply need to remove the average of each piezometric curve provided for the instruments B10, P96, S20 and M25.

Depth Dependence of the Velocity Changes
The seismic velocity changes presented in Figure 5    "best frequency range" are coherent at the exception of the last pair of stations (3 -4) that shows a large frequency range. This is possibly due to the path between the two stations mostly formed by the eastern dam that limits the basin 5.2.
The relationship that links the frequency bandwidth with the "equivalent depth" is depending on the local shear wave velocity profile with depth. In the context of this study, different active seismic experiments have been performed around the basin 5.2 to retrieve the velocity profile in the first tens of meters. The outcome of these profiles is that the shear wave velocity in the subsurface is quite low but highly variable. For the sake of simplicity the shear wave velocity is considered as constant over the first 5 meters and equal to 300 m·s −1 . The depth z is computed according to the relation z = 0.15*c/f, where c is the local shear wave velocity and f is the frequency [7]. This depth corresponds to the maxi- imposes a supernumerary layer that modifies the free surface conditions. For these reasons, the simple approach of the maximum energy and the results of equivalent depth presented in Table 1 must be considered as gross approximations.

3D Representation of the Hydraulic Dome
For practical reasons the seismic stations were installed around the basin 5.2.
The seismic velocity change curves obtained in Figure 5 integrate  Figure 7 presents a 3D representation of the results obtained in this study. It includes on the same scale the relative piezometric changes (in meters) and the seismic velocity changes (in percentage) as a function of the distance to B10 and as a function of the time of the experiment. As for Figure 5, the overall agreement between the two independent measurements is acceptable. There seems to exist a difference in the behaviors of the virtual piezometers. Points A, B is not pronounced or is not even present in the data. This has to be related to the initial water level conditions of the basin 5.2 at the beginning of the seismic recordings ( Figure 4). It is very likely that the hydraulic dome is locally much less expressed (as seen in piezometer M25 during the filling stage) and vanishes quite rapidly, hence the small relative changes of seismic velocity mostly governed by the regional groundwater flow. The filling stage of basin 5.2 turns into a small

Limitations of the Approach
If the overall agreement between piezometric measurements and seismological measurements is acceptable, some discrepancies appear when it comes to the fine details of the time evolution of the water table. As illustrated in Figure 3(b), the monitoring of the water table based on seismological measurements requires a stable distribution of the sources of noise. This requirement is hardly achieved in the industrial context of the exploitation, where water pumping and injection happens at different times and locations in the 11 hectares of the field. The nonstationary distribution of the sources of noise creates spurious artifacts in the velocity changes. This might become an issue when trying to identify the depth dependence of the velocity change, because most of the industrial noise sources have a frequency content of a few Hertz. Activation of such sources creates strong energetic seismic body waves that are refracted inside the medium and may arrive simultaneously with the surface waves of interest for the monitoring of the water table. An example of this is provided in Figure 3(b).

Conclusion
We have shown here the potential of the seismic noise for the monitoring of the water table in an industrial context. The seismic velocity changes presented in this study integrates the information along the path between the pairs of stations, i.e. horizontally. They also integrate information vertically because of the finite frequency band of analysis that scans the medium at different depths that include fully and partially saturated horizons. However, the velocity change is largely governed by the position of the saturation front (i.e. the water table): an analysis in different frequency bands helps to constrain the depth of this front through time. The nonstationary source of noise distribution impacts the retrieval of the details of the water table evolution. The interpretation of the seismic velocity changes might be impaired by spurious artifacts. Nonetheless, the seismic noise monitoring allows retrieving the major features of the water table evolution. The lateral resolution of the technique is limited by the distance between the seismic stations, with a minimum in this study of 30 meters. The spurious artifacts limit the vertical resolution of the retrieved changes.