Three‐dimensional anisotropic seismic wave modelling in spherical coordinates by a collocated‐grid finite‐difference method
TL;DR: In this paper, an optimized, collocated-grid finite-difference scheme was proposed to solve the anisotropic velocity-stress equation in spherical coordinates by using a non-uniform grid to discretize the computational domain.
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Abstract: SUMMARY
To simulate seismic wave propagation in the spherical Earth, the Earth’s curvature has to be taken into account. This can be done by solving the seismic wave equation in spherical coordinates by numerical methods. In this paper, we use an optimized, collocated-grid finite-difference scheme to solve the anisotropic velocity–stress equation in spherical coordinates. To increase the efficiency of the finite-difference algorithm, we use a non-uniform grid to discretize the computational domain. The grid varies continuously with smaller spacing in low velocity layers and thin layer regions and with larger spacing otherwise. We use stress-image setting to implement the free surface boundary condition on the stress components. To implement the free surface boundary condition on the velocity components, we use a compact scheme near the surface. If strong velocity gradient exists near the surface, a lower-order scheme is used to calculate velocity difference to stabilize the calculation. The computational domain is surrounded by complex-frequency shifted perfectly matched layers implemented through auxiliary differential equations (ADE CFS-PML) in a local Cartesian coordinate. We compare the simulation results with the results from the normal mode method in the isotropic and anisotropic models and verify the accuracy of the finite-difference method.
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Citations
Three-dimensional elastic wave numerical modelling in the presence of surface topography by a collocated-grid finite-difference method on curvilinear grids
TL;DR: In this paper, the authors used generalized curvilinear grids that can fit the surface topography to discretize the computational domain and described the implementation of a collocated grid finite-difference scheme, a higher order MacCormack scheme, to solve the first-order hyperbolic velocity-stress equations on the curvilanear grid.
Upper mantle structure of the Cascades from full-wave ambient noise tomography: Evidence for 3D mantle upwelling in the back-arc
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A mixed-grid finite element method with PML absorbing boundary conditions for seismic wave modelling
TL;DR: In this paper, a mixed-grid finite element method (MGFEM) is proposed to simulate seismic wave propagation in 2D structurally complex media, which divides the physical domain into two subdomains.
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