One way to improve our understanding of the reservoir behavior at depth is to analyze the ground surface response during reservoir exploitation. During reservoir exploitation, pressure changes can lead to compaction/dilation at depth resulting in ground surface displacements. Disentangling the information encrypted in the surface displacement data should therefore provide information about the reservoir behavior at depth. In the last decade we developed a workflow imbricating fast geomechanical forward models and a surface displacement data assimilation scheme to improve our (i) understanding of the subsurface processes and (ii) improve predictions of reservoir behavior in terms of reservoir management. Here we present two case studies to illustrate the versatility and robustness of the workflow. The first case study identified undepleted gas compartments in a strongly faulted and compartmentalized reservoir in a Dutch gas field through inversion of combined surface levelling and InSAR data. The second case study constrained spatial variation in aquifer activity around another Dutch gas field by directly employing ascending and descending PS-InSAR line-of-sight data. We also show the benefit of using multiple data assimilation for constraining parameters in forward models that contain non-linearity. Additionally, we present a novel approach for an inversion workflow that includes uncertainties in every step of the inversion process in a single integrated inversion procedure.