We present a new method to invert variable stress changes of fractures from InSAR ground displacements. Fractures can be either faults or magma intrusions, embeded in a 3D heterogeneous crust with prominent topographies. The method is based on a fictituous domain approach using a finite element discretization of XFEM type. A cost function involves the misfit between the solution of the physical problem and the observed data together with the smoothing terms. Regularization parameters are determined by using L-curves. The method is then reformulated to be applied to InSAR data (masked and noisy), projected in Earth-Satellite directions. Synthetic tests confirm the efficiency and effectiveness of our method.