Generalized Geertsma Solution for Isotropic Layered Medium

Abstract

We report a generalized Geertsma solution with which we can calculate the surface deformation from a subsurface made of an arbitrary number of isotropic homogeneous layers and a thick reservoir at any depth. We validate the generalized Geertsma solution by solving simple numerical examples and comparing the results with a reference finite-element solution. Then, we apply the generalized Geertsma solution to more realistic subsurface models to study the effect of subsurface layering on surface deformation and the impact of acquisition-processing accuracy on inverted reservoir pressure. The modelling demonstrates the surface deformation (both magnitude and shape) is most influenced by the reservoir stiffness. Finally, the inversion exercise demonstrates that for the case of In Salah-inspired synthetic model, 3% noise resulting from data acquisition-processing error may introduce 15% deviation in the inverted pressure compared to the true reservoir pressure.