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.