Open AccessModelling elastic‐wave propagation in inhomogeneous anisotropic media by the pseudo‐spectral method
Author(s) -
Lou Min,
Rial J. A.
Publication year - 1995
Publication title -
geophysical journal international
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.302
H-Index - 168
eISSN - 1365-246X
pISSN - 0956-540X
DOI - 10.1111/j.1365-246x.1995.tb05910.x
Subject(s) - pseudo spectral method , spectral method , fast fourier transform , wave propagation , wavenumber , spectral element method , fourier transform , anisotropy , computation , mathematical analysis , computational physics , finite difference , finite difference time domain method , physics , finite element method , mathematics , optics , fourier analysis , algorithm , mixed finite element method , thermodynamics
SUMMARY 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.