3D seismic modeling using staggered-grid OcTree mesh

Summary Because the grid spacing is fixed in the finite-difference method (FDM), the numerical dispersion usually imposes the use of restrictive small grid spacing (given by the lower velocity) in the whole model. Then, the number of grid points per wave-length is too large in deep layers, resulting in loss of efficiency of the FDM. Although the use of high-order operators allows bigger grid spacing and could make FDM more efficient, this does not solve the problem. In this paper, we develop a new 3D explicit scheme based on finite-volume method (FVM) that addresses the aforementioned problem in an efficient way. The algorithm is constructed using a general formalism with sparse matrices and allows both the use of different grid spacing in layers with different velocities and the refinement in regions of interest using OcTree meshes. Oc-Tree is easy to generate using regular grids, avoiding additional complications in meshing. Computational tools for parallel processing on the GPU were used for the algebraic manipulation of the sparse matrices. The numerical scheme can be seen as an extension of the staggered-grid scheme; actually, it reduces to the classical staggered-grid scheme for the case of regular grids. Finally, an example is presented to show the effectiveness of the method.