Speed and Accuracy in 3-D Resistivity Modeling
Accuracy in finite-difference (FD) modeling is closely related to the discretization scheme, whereas speed depends mainly on the equation solvers. We compare the accuracy of five FD discretization schemes for 3-D resistivity modeling. Three schemes yield good results: a method using volume-weighted averages from conductivities assigned to neighboring grid cells, a method that integrates over elemental volumes, and a resistivity network approach. Discretization by elemental volume leads to coupling coefficients that are similar to those derived from the volume-weight method. The coefficients only differ by a real factor. In the second section, the cumulative amount of numerical work as a measure of speed is compared for five different equation solvers with and without preconditioning. The most efficient equation solver for symmetric matrices is the preconditioned conjugate gradient method. General matrix solution methods for both symmetric and nonsymmetric matrices—such as ORTHOMIN and the methods of stabilized biconjugate gradients and squared conjugate gradients—also achieve satisfactory convergence rates.