Wavenumber sampling strategies for 2.5-D frequency-domain seismic wave modelling in general anisotropic media

The computational efficiency of 2.5-D seismic wave modelling in the frequency domain depends largely on the wavenumber sampling strategy used. This involves determining the wavenumber range and the number of the sampling points, and overcoming the singularities in the wavenumber spectrum when taking the inverse Fourier transform to yield the frequency-domain wave solution. In this paper, we employ our newly developed Gaussian quadrature grid numerical modelling method and extensively investigate the wavenumber sampling strategies for 2.5-D frequency-domain seismic wave modelling in heterogeneous, anisotropic media. We show analytically and numerically that the various components of the Green's function tensor wavenumber-domain solutions have symmetric or antisymmetric properties and other characteristics, all of which can be fully used to construct effective and efficient sampling strategies for the inverse Fourier transform. We demonstrate two sampling schemescalled irregular and regular sampling strategies for the 2.5-D frequency-domain seismic wave modelling technique. The numerical results, which involve calibrations against analytic solutions, comparison of the different wavenumber sampling strategies and validation by means of 3-D numerical solutions, show that the two sampling strategies are both suitable for efficiently computing the 3-D frequency-domain wavefield in 2-D heterogeneous, anisotropic media. These strategies depend on the given frequency, elastic model parameters and maximum wavelength and the offset distance from the source.