A stability criterion of elastic wave modelling by the Fourier method
Abstract
Forward modelling of wave equations by Fourier transform is widely regarded for its high precision, small memory and moderate calculation time. In forward modelling, the stability problem must be considered. This paper derives a stability criterion for the simulation of elastic wave propagation by Fourier transform. The derived stability condition is v^{2}k^{2}Δt^{2} <= 4, where v is the phase velocity, k is the wavenumber and Δt is the time interval. Furthermore, stability is discussed for onedimensional, twodimensional and threedimensional modelling respectively. For mdimensional modelling by Fourier transform in elastic media, for a grid of cube, square or line segments where each side length of the grid is Δd, then, when the modelling parameters satisfy v_{\max } \Delta t/\Delta d \le 2/(\sqrt m \pi ), the modelling process is stable.
 Publication:

Journal of Geophysics and Engineering
 Pub Date:
 June 2005
 DOI:
 10.1088/17422132/2/2/010
 Bibcode:
 2005JGE.....2..153L
 Keywords:

 stability criterion elastic wave modelling Fourier method