Three-dimensional finite-difference resistivity modeling using an upgridding method

The finite-difference method (FDM) for solving three-dimensional (3-D) resistivity problems has traditionally used a graded, rectangular grid whose spacings change independently in orthogonal coordinate axis directions. Small cell sizes are used to represent the field around external sources or fine resistivity features. The cell sizes are increased gradually toward the boundaries of a computational domain. Typically, cells can have very large aspect ratios, especially near the computational domain boundaries. Large round-off errors and slow convergence of (iterative) numerical solutions to the finite-difference (FD) equation system may result. In this paper, we present an upgridding approach to improve the efficiency of the FDM with a conventional rectangular grid. The upgridding process coalesces cells of extremal shapes in the directions of short dimensions to reduce cell aspect ratios and the total number of unknowns. Our experiments with a set of 3-D resistivity models show that the upgridding FDM can reduce the computation time by nearly half relative to using the FDM with a graded, rectangular grid.