Abstract
Modeling of seismic-wave propagation in anisotropic medium with irregular topography is beneficial to interpret seismic data acquired by active and pas- sive source seismology conducted in areas of interest such as mountain ranges and basins. The major challenge in this context is the difficulty in tackling the irregular free-surface boundary condition in a Cartesian coordinate system. To implement sur- facetopography,weusetheboundary-conforminggridandmaparectangulargridonto a curved grid. We use a stable and explicit second-order accurate finite-difference scheme to discretize the elastic wave equations (in a curvilinear coordinate system) in a 3D heterogeneous transversely isotropic medium. The free-surface boundary con- ditions are accurately applied by introducing a discretization that uses boundary- modified difference operators for the mixed derivatives in the governing equations. The accuracy of the proposed method is checked by comparing the numerical results obtained by the trial algorithm with the analytical solutions of the Lamb's problem, for anisotropicmediumandatransverselyisotropicmediumwithaverticalsymmetryaxis, respectively. Efficiency tests performed by different numerical experiments illustrate clearlytheinfluenceofanirregular(nonflat)freesurfaceonseismic-wavepropagation.
Highlights
Rough topography is very common and we have to deal with it during the acquisition, processing and interpretation of seismic data
We propose a stable and explicit finite difference method to simulate with second-order accuracy the propagation of seismic waves in a 3D heterogeneous transversely isotropic medium with non-flat free surface
The accurate application of the free surface boundary conditions is done by using boundary-modified difference operators to discretize the mixed derivatives in the governing equations of the problem
Summary
Rough topography is very common and we have to deal with it during the acquisition, processing and interpretation of seismic data. Appelo and Petersson (2009) have generalized the results of Nilsson et al (2007) to curvilinear coordinate systems, allowing for simulations on non-rectangular domains They construct a stable discretization of the free surface boundary conditions on curvilinear grids, and they prove that the strengths of the proposed method are its ease of implementation, efficiency (relative to low-order unstructured grid methods), geometric flexibility, and, most importantly, the “bullet-proof” stability (Appelo and Petersson, 2009), even though they deal with 2D isotropic medium. Several numerical examples are presented to demonstrate the accuracy and efficiency of the method
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