2.5-D acoustic wave modelling in the frequency-wavenumber domain

Abstract

3-D acoustic wave propagation in a 2-D model is simulated in the frequency-wavenumber domain. Fourier transforms are used to reduce the problem of solving the 3-D equation to the solution of multiple 2-D boundary-value problems. Each of these 2-D boundary-value problems is associated with a frequency?wavenumber pair, and its discretisation via a finite-difference approximation leads to a sparse system of linear algebraic equations. The sparse linear system is repeatedly solved by an LU decomposition method for different pairs of wavenumber and frequency. The 3-D response for a specific frequency is obtained by an inverse Fourier transformation of these solutions with respect to the wavenumber. Time-domain synthetic seismograms are obtained by a further temporal inverse Fourier transformation of the frequency response. A 2.5-D absorbing boundary condition is derived from the paraxial approximation of the 3-D wave equation. It is more efficient than the 2-D boundary condition in suppressing the artificial reflections from the edges of the computational domain. The numerical singularity is avoided by allowing the frequency to become complex. The Fourier transform with respect to the wavenumber can be accelerated by a non-uniform sampling in the wavenumber domain.