Resistivity Modelling with Topography

Abstract

A major difficulty of electrical resistivity forward modelling is caused by the singularity of the potential occurring at the source location. To avoid large numerical errors, the total potential is split into a primary part containing the singularity and a secondary part. The primary potential is defined analytically for flat topography, but is classically computed numerically in the presence of topography: in that case, an accurate solution requires expensive computations. We propose to select for the primary potential the analytic solution defined for homogeneous models and flat topography, and to modify accordingly the free surface boundary condition for the secondary potential, such that the total potential still satisfies the Poisson equation. The modified singularity removal technique thus remains fully efficient even in the presence of topography, without any additional numerical computation. The modified secondary potential in a homogeneous model is not null in the case of topography as it would be in the classical approach. We implement the approach with the Generalized Finite Difference method. We present a 2.5D inversion example on a simple synthetic data set.