Resistivity modelling with topography

Abstract

A major difficulty of electrical resistivity forward modelling is the singularity of the potential occurring at the source location. To avoid large numerical errors, the potential is split into a primary part containing the singularity and a secondary part. The primary potential is defined analytically for flat topography, and is classically computed numerically in the presence of topography: in that case, an accurate solution requires expensive computations.We propose to define the primary potential as the analytic solution valid for a homogeneous model and flat topography, and to modify accordingly the free surface boundary condition for the secondary potential, such that the overall potential still satisfies the Poisson equation. The modified singularity removal technique thus remains fully efficient for any acquisition geometries, without any additional numerical computation, and also applicable in the presence of a buried cavity. This approach is implemented with the generalized finite difference method developed on unstructured meshes and validated through the comparison with analytical solutions. Finally, we illustrate in simple 2-D and 3-D cases how the potential depends on the shape of the topography and on the electrode positions. © The Authors 2013. Published by Oxford University Press on behalf of The Royal Astronomical Society.