Borehole Wave Propagation In Isotropic And Anisotropic Media I: Finite Difference Method

Abstract

In this paper we developed a 3-D finite difference method to simulate wave propagations in an isotropic medium. The wave equation is formulated into the first-order hyperbolic equations by using velocity and stress and then discretizing it on a staggered grid. The 3-D time domain finite difference scheme is second order accurate in time and fourth order accurate in space. The grid dispersion and anisotropy are analyzed and the stable condition of the scheme is obtained. Higdon's absorbing boundary condition is discussed and generalized to the anisotropic medium. The scheme can provide realistic 3-D wave propagation simulation by the use of a parallel computer. The scheme is tested in the homogeneous medium. The finite difference results agree excellently with the analytic solutions of a point explosion source in the acoustic medium and a point force source in the elastic medium. The finite difference method accurately models not only the far field P and S waves, but also the near field term. It demonstrates that the second-order Higdon's absorbing boundary condition works very well in an acoustic and elastic medium.