3-D FINITE-DIFFERENCE MODELING OF ELASTIC-WAVES IN BOREHOLE ENVIRONMENTS

Full-wavefield sonic logs may be simulated for arbitrarily complicated three-dimensional (3-D) borehole environments using 3-D elastic finite differences. To ensure reliability through large contrasts in Poisson's ratio (across mud-casing-lithology contacts), a staggered grid finite-difference formulation is used. Cylindrical symmetry is not assumed so the responses of features such as asymmetrical washouts and dipping structure are easily obtained. When features are asymmetrical, seismic responses vary significantly at various points around the hole circumference at any depth. Even for simple hole geometries, observed responses are complicated because of coupling between waves inside and outside the hole. Observations are also sensitive to the source-receiver separation. Output formats include fixed-time snapshots of displacement, divergence, and curl, and seismograms for the center and edge of a borehole; this allows detailed arrival identification and interpretation. To our knowledge, this is the most comprehensive and flexible scheme for modeling borehole waves that has been implemented to date.