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

The finite-difference method (FDM) for solving three-dimensional (3-D) resi stivity problems has traditionally used a graded, rectangular grid whose sp acings 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 bo undaries of a computational domain. Typically, cells can have very large as pect ratios, especially near the computational domain boundaries. Large rou nd-off errors and slow convergence of (iterative) numerical solutions to th e finite-difference (PD) equation system may result. In this paper, we pres ent an upgridding approach to improve the efficiency of the FDM with a conv entional rectangular grid. The upgridding process coalesces cells of extrem al shapes in the directions of short dimensions to reduce cell aspect ratio s and the total number of unknowns. Our experiments with a set of 3-D resis tivity models show that the upgridding FDM can reduce the computation time by nearly half relative to using the FDM with a graded, rectangular grid.