Complex frequency‐shifted multi‐axial perfectly matched layer for frequency‐domain seismic wavefield simulation in anisotropic media

ABSTRACT Seismic anisotropy has an important influence on seismic data processing and interpretation. Although the frequency‐domain seismic wavefield simulation has a problem of solving the large scale linear sparse matrix due to the computational limitations, it has some advantages over the time‐domain seismic wavefield simulation including efficient inversion using only a limited number of frequency components and easy implementation of multiple sources. To accurately simulate seismic wave propagation in the frequency domain, we also need to choose the absorbing boundary conditions to absorb artificial reflections from edges of the model as we do in the time domain. Compared with the classical boundary conditions including the perfectly matched layer and complex frequency‐shifted perfectly matched layer, the complex frequency‐shifted multi‐axial perfectly matched layer has been proven to effectively suppress the unwanted reflections at grazing incidence and solve the instability problem in the time‐domain seismic numerical modelling in anisotropic elastic media. In this paper, we propose to extend the complex frequency‐shifted multi‐axial perfectly matched layer absorbing boundary condition to the frequency‐domain seismic wavefield simulation in anisotropic elastic media. To test the validity of our proposed algorithm, we compare the results (snapshots and seismograms) of the frequency‐domain seismic wavefield simulation with those of the time‐domain modelling. The model studies indicate that the complex frequency‐shifted multi‐axial perfectly matched layer absorbing boundary condition is stable in the frequency‐domain seismic wavefield simulation in anisotropic media, and provides better absorbing performance than the complex frequency‐shifted perfectly matched layer boundary condition.