2-D and 3-D interpretation of electrical tomography measurements, Part 1: The forward problem

Abstract

We have developed a computer code to model the electrical potential field for borehole‐to‐borehole measurements. This scheme supports a large class of model geometries including 2-D and 3-D structures embedded in a homogeneous half‐space. It enables the computation of the electrical potential at any point due to a direct current injection at any source point within the model. A new boundary integral formulation is used that generates a sparse linear system. The sparsity is exploited in order to optimize the memory size and the computation time needed to solve the forward problem. This formulation is new because two unknown quantities—the electrical potential and a current‐related quantity—are solved for each interface. The numerical accuracy of this code has been extensively tested. Simulations of a simple model geometry are used to gain insight on when 3-D phenomena differ from those of 2-D models.