Modeling ground displacement above reservoirs undergoing fluid withdrawal/injection based on an ellipsoidal inhomogeneity model

We propose a procedure to efficiently monitor the geomechanical behavior of underground porous reservoirs undergoing fluid withdrawal/injection. We apply the inhomogeneity problem and invert geodetic data on subsidence/uplift to calibrate and specify parameters used for geomechanical models. Based on pressure changes, we first calculate the poroelastic strain of the reservoirs, then we test it assuming uniaxial deformation on a three-dimensional ellipsoidal inhomogeneity with different semi-axes, in a full space isotropic elastic domain and finally we apply a simple half space approximation to account for the tractions-free ground surface. Despite its simplicity and the initial full space approximation, the semi-analytical model derived in this study replicates well poroelastic strains inferred by geodetic data or obtained with other analytical and numerical techniques. Our model is a good approximation for predicting the profile of surface deformation (i.e. geodetic strain) and, once calibrated, its magnitude.