Qing-Huo Liu
Eric Schoen
Francois Daube
Curt Randall
Hsui-lin Liu
Ping Lee
Schlumberger-Doll Res., Old Quarry Rd., Ridgefield, CT 06877
Elastic wave propagation in realistic borehole environments is very complex because of the presence of borehole, dipping beds, and other irregular scatterers. In order to understand this complex wave propagation phenomenon for sonic logging applications, a three-dimensional finite-difference (FD) method was used to simulate elastic wave propagation on a parallel computing architecture. The FD scheme solves the first-order elastic wave equations with central differencing in both space and time via staggered grids. Liao's absorbing boundary condition is used to reduce artificial reflections from the finite computational domain. In this work, uniform grids in Cartesian coordinates are used to discretize the inhomogeneous medium. Because of the staircase approximation of the circular borehole, it is observed that the discretization requirement is quite different for monopole and dipole sources. Several methods are suggested to remedy this problem. The results from the FD method were validated by other methods available for several special geometries. Numerical examples will be shown to demonstrate the interaction of elastic waves with borehole and the surrounding geologic structures. Applications to interpretation of sonic logging will be illustrated.