Methods and systems for finite-difference wave equation modelling

摘要

A method of determining a seismic wavefield in a region of a subsurface of the Earth by eliminating temporal dispersion from a finite difference, FD, wavefield generated from seismic wave propagation data. The method comprises obtaining the FD wavefield containing temporal dispersion by solving a discretized wave equation using the seismic data; transforming the FD wavefield from a time domain to a frequency domain using a Fourier transform; and inverse transforming the FD wavefield from the frequency domain using an inverse Fourier transform, wherein the inverse Fourier transform uses a modified frequency based on a temporal discretization of the FD wavefield, to give the seismic wavefield in the time domain. Another aspect relates to a method of adding temporal dispersion to a seismic wavefield comprising transforming the seismic wavefield from a time to frequency domain using a Fourier transform which uses a modified frequency based on a temporal discretization of a FD wavefield. The wavefield is then inverse transformed back to time domain wherein the transform uses an unmodified frequency.