Injection of CO2 into deep aquifers may cause surface heave of several millimetres / year. This was revealed by the interferometry analysis of satellite images from the descending orbit (ASAR-sensor of ENVISAT mission) over the period 2003-2009 during CO2 injection at KB-501 well of In Salah (Algeria). These data are of high interest for getting better insight in the characterisation of both the host reservoir and overburden rock materials via a history-matching exercise using geomechanical numerical simulations. Yet, this analysis is hindered by the high number of unknown model parameters. In the case of In Salah, the calibration should handle ten parameters including the elastic parameters of four rock formations and the initial stress state. To reduce this number, we adopted a variance-based global sensitivity analysis to evaluate the contribution of each parameter to the differences between observations and numerical results over the injection period at each spatial location. Since running the geomechanical reservoir model was time consuming (several hours), we relied on a response-surface-based approach (here of type kriging) to compute the Sobol’ sensitivity indices using a limited number of long-running geomechanical simulations (here 100). On this basis, we brought two evidences. First, the dominant influence of the reservoir’s stiffness on the observed surface displacements was highlighted. Second, the heterogeneous nature of the spatial distribution of this property was studied.