Some refinements on the finite-difference method for 3-D dc resistivity modeling

Two basic refinements of the finite-difference method for 3-D de resistivity modeling are presented. The first is a more accurate formula for the source singularity removal. The second is the analytic computation of the source terms that arise from the decomposition of the potential into the primary potential because of the source current and the secondary potential caused by changes in the electrical conductivity. Three examples are presented: a simple two-layered model, a vertical contact, and a buried sphere. Both accurate and approximate Dirichlet boundary conditions are used to compute the secondary potential. Numerical results show that for all three models, the average percentage error of the apparent resistivity obtained by the modified finite-difference method with accurate boundary conditions is less than 0.5%. For the vertical contact and the buried sphere models, the error caused by the approximate boundary condition is less than 0.01%.