Modelling elastic-wave propagation in inhomogeneous anisotropic media by the pseudo-spectral method

Abstract

The paper presents a numerical approach called the pseudo-spectral method to model elastic-wave propagation in inhomogeneous anisotropic media. In the pseudo-spectral method, spatial derivatives in the wave equations are computed by multiplication in the wavenumber domain, which can be accomplished efficiently by Fast Fourier Transform (FFT). The pseudo-spectral method is global in the sense of involving a summation of continuous differentiable Fourier basis functions, and as a result the pseudo-spectral method is able to yield highly accurate approximations of smooth solutions with substantially fewer grid points than would be required by local methods such as finite-element or finite-difference methods. The method also has relatively faster computation speed than other numerical methods because of the use of FFT. By employing the pseudo-spectral method, it is feasible and cost-effective to evaluate wave propagation in 3-D arbitrary anisotropic media with present-day supercomputers. The paper shows wave modelling results in 2-D inhomogeneous anisotropic media which are numerically solved in a Sun-Sparc workstation. The modelling results give clear 2-D and 3-D views of the propagating wave phenomena like shear-wave splitting, wave-type coupling and wave diffraction in the inhomogeneous anisotropic media. This modelling technique can provide a useful tool to study and interpret complicated wave propagation in realistic materials and structures such as hydrocarbon reservoirs in the earth.