Time-lapse studies not only allow to monitor the reservoir but are also useful to access risk in the overburden. They usually assume that the velocity change during reservoir depletion is isotropic, but, from a geomechanical perspective, velocity changes have no reason to be isotropic. Numerous authors observe that the velocity changes in the overburden suggest rock damage such as crack opening which implies anisotropic elastic property changes. Rock damage depends on several geomechanical parameters such as the initial rock elastic properties, the in situ stress, the stress state change, the crack shapes and their orientations, etc. We show that retrieving an anisotropic time-lapse velocity change is possible using a pre-stack seismic tomographic approach. The anisotropic time-lapse velocity change is decomposed into a functions basis which respects the travel-time perturbation symmetries. The anisotropic time-lapse velocity change predicted by the rock physics models can be expressed in this general basis with some algebra. We apply the proposed tomographic inversion on a cross-section of a real reservoir and we relate the anisotropic time-lapse velocity change to horizontal crack distribution in the overburden. Results show a good qualitative consistency between the prediction of the rock physics model and the tomography results.