The salt mining industrial exploitation located in Vauvert (France) has been injecting water at high pressure into wells to dissolve salt layers at depth. The extracted brine has been used in the chemical industry for more than 30 years, inducing a subsidence of the surface. Yearly leveling surveys have monitored the deformation since 1996. This dataset is supplemented by synthetic aperture radar (SAR) images, and since 2015, global navigation satellite system (GNSS) data have also continuously measured the deformation. New wells are regularly drilled to carry on with the exploitation of the salt layer, maintaining the subsidence. We make use of this careful monitoring by inverting the geodetic data to constrain a model of deformation. As InSAR and leveling are characterized by different strengths (spatial and temporal coverage for InSAR, accuracy for leveling) and weaknesses (various biases for InSAR, notably atmospheric, very limited spatial and temporal coverage for leveling), we choose to combine SAR images with leveling data, to produce a 3-D velocity field of the deformation. To do so, we develop a two-step methodology which consists first of estimating the 3-D velocity from images in ascending and descending acquisition of Sentinel 1 between 2015 and 2017 and second of applying a weighted regression kriging to improve the vertical component of the velocity in the areas where leveling data are available. GNSS data are used to control the resulting velocity field. We design four analytical models of increasing complexity. We invert the combined geodetic dataset to estimate the parameters of each model. The optimal model is made of 21 planes of dislocation with fixed position and geometry. The results of the inversion highlight two behaviors of the salt layer: a major collapse of the salt layer beneath the extracting wells and a salt flow from the deepest and most external zones towards the center of the exploitation.

Rock salt (halite) is a sedimentary rock formed by the evaporation of seawater under specific conditions at different geological times.
Halite deposits are located underground or inside mountains, though some can also be found on the surface in arid regions.
They mainly contain crystals of sodium chlorite (NaCl) but can also include impurities such as clay, anhydrite, or calcite.
The distribution of salt deposits worldwide is very localized, spread over areas ranging from a few up to several hundred square kilometers.
In Europe, countries such as Germany, Denmark, and the Netherlands have a large amount of salt

The difference between geostatic pressure and brine (or hydrocarbons) at cavern depth produces a change in stress equilibrium that leads to elastic and visco-elastic deformation of the surrounding medium

Along with spatially dense InSAR and leveling data, a complete description of the 3-D surface displacement rates can be assessed by combining the geodetic datasets.
Indeed, all three geodetic techniques measuring the subsidence in Vauvert are complementary regarding their spatial and temporal attributes.
The combination of deformation data measured according to different geometries is not trivial.
The displacement values are indeed projected along the line of sight of the satellite for InSAR, along the vertical for leveling, and in 3-D for GNSS.
Different combination techniques have already been tested at different stages of data processing: first, different satellite acquisition geometries (e.g., ascending, descending, and ascending of parallel orbit) can be used to estimate the three components of the displacement

From the combined velocity field, models of the salt layer (e.g., analytical, numerical, or geomechanical) can be derived in order to improve the brine productivity and to predict the evolution of subsidence.
A software has already been developed for the Solution Mining Research Institute to evaluate and predict surface subsidence over underground openings

In our study, we aim at characterizing the deformation of salt reservoir using Sentinel-1 images, leveling lines, and GNSS data.
We propose a two-step methodology to combine geodetic data measuring the bowl of subsidence induced by the salt extraction in Vauvert

The salt deposit of Vauvert is located on the NW margin of the on-shore half graben of the extensional Camargue basin in southern France.
This graben results from the Oligo-Aquitanian rifting of the margin during the Mediterranean Sea expansion

the clay series brings together two sub-series – the “gray series” (2000 m thick of deposit of clay, sand, limestone, marl, conglomerate, and lignite) and the “red series” (200 m of clay and gypsiferous marls with several intervals of marl and sand from palustrine environment);

The saliferous series (900 m thick) with four formations – the infra-saliferous, the lower saliferous, the intermediate marl, and the upper saliferous formations; these formations lie between 1500 and 3000 m deep and are affected by normal faults and two thrust surfaces, i.e., decollements D1 and D2 (Fig.

The marine clay series range from 800 to 1500 m thick and correspond to three sequences of Aquitanian deposits, mainly composed of clay with intervals of limestones, sandstones, or layers of dolomite.

Geological structural scheme of area under study crossing the numbered wells (Derrick symbols at the surface, pf is for Pierrefeu well) at Vauvert (from

The deep salt deposit of Vauvert was discovered during the 1952–1962 oil survey conducted by ELF

The monitoring of subsidence above salt extraction in Vauvert has been performed since 1996 by IGN using leveling surveys along with a collection of InSAR data acquired by various satellite missions (ERS, ENVISAT, SENTINEL; Fig.

The height differences between two points of the network were determined by direct geodetic leveling (double run) carried out using an electronic level LEICA WILD NA3003, on a round trip pattern.
This instrument has an accuracy of 0.1 mm, and the standard deviation of measurements for 1 km of round-trip leveling is 0.4 mm (manufacturer data).
IGN has conducted the processing using the Geolab least squares adjustment program (version 2001.9.20.0).
This type of tool makes it possible to provide for each of the points an elevation as well as an indicator of the accuracy of the result.
The accuracy is estimated from the observations and not only from manufacturer nominal features.
The mean data uncertainties from the 2019 survey reaches 1.34 mm.
Figure

Radar images from Sentinel constellation imaging satellites (Sentinel-1a and Sentinel-1b) are recorded on the C-band frequency (similarly to Envisat) and present a short temporal redundancy of about 6 d, limiting the temporal decorrelation.
The perpendicular baseline between the images is very short, a few tens of meters, which also limits the spatial decorrelation.
Sentinel constellation images have a swath of 250 km wide and a resolution of

Once the interferograms are created under SNAP, they are imported and processed with StaMPS processing software

Mean velocity in LOS direction in

Four permanent GNSS stations (Fig.

Figure

Time series of the three components

Terrestrial (e.g., leveling, inclinometry) and satellite-based (e.g., GNSS, InSAR) geodetic measurements are complementary in terms of accuracy and spatial or temporal resolution, from slow ground displacement monitoring (e.g.,

Although these hypotheses may be false for other cases, in the case of Vauvert, and given the previous available information from InSAR

Algorithm of the two-step methodology developed to combine deformation velocities estimated from interferograms and leveling surveys. (1) Three-dimensional geometrical estimation is performed to derive east, north, and vertical components from ascending and descending InSAR geometries. (2) The vertical component and leveling data are combined using a weighted regression-kriging technique.

The first step of the approach consists of interpolating the ascending and descending InSAR data by ordinary kriging, in order to densify the spatial distribution of PS points, so that they can be virtually colocated with leveling benchmarks.
The kriging interpolation models the best linear unbiased prediction of the intermediate values by a Gaussian variogram model (driven by prior covariances).
The number of data points, position, and uncertainties are considered in the interpolation, leading to interpolated values of the data distribution along with uncertainties (kriging variance that accounts for the data uncertainties).
By applying a weighting function based on the correlation between the data and the distance between them, the kriging method allows canceling the effect of a high-density area, typically cities, where PSs are more concentrated than elsewhere, notably poorly anthropized areas where the number of data points can be low.
We use ordinary kriging to densify the spatial distribution of PSs

The velocity

The 3-D components of the velocity field derived from InSAR can be defined as

In the second step of our combination approach, we use a regression-kriging method (e.g.,

On Fig.

The three components (east, north, and vertical) of the velocity field calculated using the two-step methodology described in this section

The combination of InSAR ascending and descending data with leveling data produces a 3-D velocity field measuring the deformation above the salt exploitation of Vauvert.
The vertical velocity computed through this combination is fairly similar to the one estimated by

Three components of the velocity from GNSS and the Dual InSAR geometry–leveling combined dataset observed at GNSS locations (VAU1, VAU2, VAU3, VAUV; see Fig.

The salt formation lies between 1500 and 3000 m deep in sheet-like layers dipping at 30

First, we use a simple Mogi source

Second, we consider a 2-D plane of dislocation (model 2) with parameters (position, depth, dimensions, dip, azimuth) set according to the salt layer properties for a more realistic model.
The forward model uses three-dimensional, elastic dislocation theory in a homogeneous half space

The combined velocity field suggests a more complex source deformation and a single source may not be sufficient to explain the surface subsidence.
Thus, we discretize the salt layer into several dislocation patches, to increase the degrees of freedom for the sources to model the surface deformation.
The single rectangular plane is subdivided into 21 square planes (model 3) of 1 km side. The orientation is the same for the 21 patches and locations and depths are set accordingly to the salt layer characteristics, all these parameters are fixed (Fig.

For model 4, we add a fourth row of planes (dashed orange line in Fig.

Representations of the dislocation planes (numbering from 1 to 28) are displayed in shaded orange modeling the salt layer (darker shading for deeper planes), along with the currently known boreholes (red dots). The decollements are represented by the double line and listric faults by black lines beneath the site of salt exploitation in Vauvert (France). The allochthonous saliferous unity is represented by the gray dotted area. The limits of Vauvert and Beauvoisin cities are represented by blue areas, and the Vauvert normal fault is displayed using black lines (modified from

For model 1, the position of the source is sought in the

To determine the model parameter uncertainties, we implement the approach developed by

We compute the difference between the observations and the model to obtain the residual values. These residuals are used with the data uncertainties to estimate how the model fits the dataset using the normalized rms (NRMS)

Inversion results for the four models described in Sect.

Considering model 1, the inversion leads to an optimal point source located 1971 m deep at the north end of the Parrapon site, associated with a volume change of

The 2-D dislocation plane of model 2 provides a solution with high residuals (Table

To check this hypothesis, we discretize the salt layer into several planes of dislocation. In doing so, we increase the degrees of freedom of the sources to model the surface deformation. Model 3 presents the lowest values of residuals, NRMS, and WRMS for the east and vertical components, suggesting that horizontal displacements at depth are needed to explain the observations.
However, the north component remains partly unexplained, certainly due to the high uncertainties related to the method we use to extract the north component from the InSAR signal.
We estimate a volume change of

Increasing the number of planes to 28 in the model by adding a fourth row at greater depth does not improve the residuals nor the fit to the horizontal components.
Besides, the volume change associated with this model reaches

The geometry of 21 dislocation planes model, the residuals (NRMS and WRMS), the estimated volume loss, and the agreement with the geological setting of the salt layers (Fig.

The inversion leads to a distribution of strike-slip, dip-slip, and tensile dislocations associated with each plane of the model (black dots in Fig.

Interval of confidence (2

We represent the distribution of dislocation values associated with each plane in Fig.

Planes 1 to 7 are the shallowest (the centers of the planes are at

Planes 8 to 14 are located right beneath the extracting wells (

Planes 15 to 21 are the deepest planes (

Distribution of the significant optimal dislocation parameters:

In Fig.

In this work, the level of fit for our dataset is NRMS

The methodology of combination requires specific conditions (see Sect.

Analytical models offer simple models to test first whether the surface deformation is only related to subsidence at depth due to the extraction of salt or whether creep occurs in the salt layers. A series of models has been computed to select the most appropriate model given the deep geometry of the reservoir and the fit to the observations. The collection of 21 planar dislocations is the best we have found considering the available datasets and their uncertainties. The inversion of the combined velocities allows us to constrain at first order the displacements of the salt layer using model 3.

The global slip displacement (Fig.

The strong collapse observed at planes 11 and 12 is produced by the high pumping rate at extracting wells.
Besides, at such depth, wells are drilled through a system of normal faults (Fig.

Based on our model, creep occurs in the salt layers, the next step would be to produce a more global model, with an increase in the level of complexity by considering (1) the strain source with six free parameters which generate a volumetric and shear deformation

In addition, the model can be validated using the available GNSS data (red arrows in Fig.

The model constrained by the inversion of geodetic data allows us to estimate stress tensor. This modeled tensor could be compared to in situ horizontal stress orientations from the analysis of borehole breakout. They generally occur at the azimuth of the minimum horizontal stresses and perpendicular to the maximum horizontal stress. These borehole failures are generated by compressive failure of the borehole wall and result in its enlargement in the minimum horizontal stress direction. Several logs were conducted in some of Vauvert's exploitation wells and need to be analyzed. Comparing the modeled and observed stresses would permit us to assess the reliability of our model.

The microseismic activity of the exploitation was monitored between 1992 and 2007 with magnitude events ranging from

We developed a two-step methodology combining ascending and descending LOS with leveling data in order to overcome the difference in resolution and accuracy associated with the measurement methods. This process is specific to near-radial deformation measured by geodetic techniques whose periods of observation are consistent with each other and whose density in space and time are adequate to achieve the monitoring goals (only vertical or also horizontal). The incorporation of leveling data allowed refining the InSAR-derived deformation in height. Satellite lines of sight and flight directions must also be symmetrical enough from one acquisition geometry to the other, to extract the east component of the deformation in a first approximation. The resulting 3-D velocity field gives a spatially dense measurements of the deformation whose uncertainties are all the most reliable in those areas covered by several geodetic techniques. Due to their period of availability, slightly shifted and quite short, GNSS stations could only provide a control in a first approximation. Along with the salt layer modeling, this result demonstrated the great interest for combining timely and compliant geodetic measurements with InSAR.

We inverted this combined dataset to constrain a kinematic model of the salt layer. Because we focus on a 2-year interval for the dataset, the deformation induced by the extraction largely dominates the salt creep and an elastic model is acceptable. Hence, we proposed to assimilate the salt layer to a collection of 21 planes of dislocation with fixed positions, geometries, and orientations consistently with the salt layer characteristics. The results of the inversion indicate a collapse of the planes located beneath the exploitation and the adjacent ones at the same depth. We also identified a salt flow from the deepest and most external part of the salt layer towards the center of the exploitation due to the connections between the wells and the exploited layer. Although this model gives a first approximation of the deep deformation of the salt layer, it needs to be improved to be able to predict the deformation induced by the exploitation in the future. We suggest three levels of model improvements, involving a collection of strain sources or finite elements and elasto-viscoplastic laws for the long-term prediction.

The geodetic dataset processed and combined in the work and the optimization code are available on request from the corresponding author.
The RESIF data are available from the RESIF website (DOI:

SD developed the concept of geodetic data combination under the supervision of PV, CC, and JLC. SD performed the two-step combination of InSAR and leveling data. SLF built the inversion algorithm based on the available global optimization code. SLF designed and performed the numerical calculations for the experiments. SLF wrote the paper and designed the figures with the support of SD, PV, CC, and JLC.

The authors declare that they have no conflict of interest.

The authors want to thank the KemOne company for sharing production data and for allowing the installation of various instruments on the site and more specifically Marc Valette for sharing the geological information essential to building and interpreting the model presented in the paper. We thank the REseau NAtional GNSS Permanent, RENAG, France

This paper was edited by Simon McClusky and reviewed by three anonymous referees.