Frequency-Domain Finite-Difference Elastic Wave Modeling in the Presence of Surface Topography

Seismic numerical modeling in the presence of surface topography has become a valuable tool to characterize seismic wave propagation in basin or mountain areas. Regarding advantages of frequency-domain seismic wavefield simulations (e.g., easy implementation of multiple sources and straightforward extension of adding attenuation factors), we propose a frequency-domain finite-difference seismic wavefield simulation in 2D elastic media with an irregular free surface. In the frequency domain, we first transform second-order elastic wave equations and first-order free surface boundary conditions from the Cartesian coordinate system to the curvilinear coordinate system. Then we apply complex frequency-shifted perfectly matched layer (CFS-PML) absorbing boundary condition to second-order elastic wave equations in the curvilinear coordinate. To better couple free surface boundary conditions and CFS-PML absorbing boundary condition, we also apply the complex coordinate stretching method used in CFS-PML to free surface boundary conditions in the curvilinear coordinate. In the first numerical test, the comparison of the seismograms calculated by our algorithm with an analytical solution indicates that our algorithm can accurately simulate seismic wavefield in the frequency domain. Finally, we choose three more elastic models with different types of surface topographies to further characterize seismic wave propagation.