Since the start of production in 1968 in the Groningen gas field (Netherlands) considerable land subsidence (>30 cm) has occurred above the field. Variability in reservoir compaction has led to earthquakes on reactivated Mesozoic age reservoir faults. Even though the impact of this seismicity (M_W ≤3.6) on society has been large, due to substantial structural damage to buildings, surface deformation induced by the co-seismic slip has been too small to detect using geodetic data. It is possible that differential compaction across faults is not only accommodated by seismic slip, but also by aseismic slip (e.g., creep). Aseismically slipping reservoir faults would relax the stresses in the reservoir and, thus, reduce the severity of the seismicity. In this study we explore the potential occurrence of aseismic slip on the reservoir faults. We perform a sensitivity analysis to investigate whether aseismic slip on the different reservoir faults has the capacity to produce detectable surface signals. We use the analytical Okada (1992) model of slip on a discrete dislocation in a uniform elastic half-space to simulate the deformations originating from slip on a wide range of fault geometries, representing the variability in the field. Unsurprisingly, laterally extensive faults with strong compaction contrasts across them (large differential slip magnitudes) produce the largest surface signals. To determine which potentially aseismically slipping faults produce surface signals that could be detectable in persistent scatterer InSAR time series, we analyze the surface patterns for large differential displacements across large length scales, since InSAR observations are most sensitive to spatially extensive patterns with high spatial gradients. We use the results of the sensitivity analysis to guide our search for patterns originating from aseismically slipping reservoir faults in PS-InSAR time series data of the Groningen area. First results show that these specific patterns are rare, indicating that the amount of aseismic slip is limited. For faults lacking surface signals related aseismic slip, the results of sensitivity analysis are used to determine upper limits for the aseismic differential slip magnitudes.