Pyramid-shaped grid for elastic wave propagation

Abstract

Elastic wave propagation is elemental to wave-equation-based migration and modeling. Conventional simulation of wave propagation is done on a grid of regular rectangular shape, though other styles, like spherical or ray-family-based, do exist. One of the previously proposed rectangular grid schemes is an irregular vertical (z) grid size. As an extension of this irregular z grid, we design a new grid system, a Pyramid-shaped grid (P-grid), and develop a numerical scheme associated with the elastic wave propagation that can reduce the number of grids, thus improving the efficiency of elastic wave propagation. In our scheme, the grid shape is non-rectangular, and the grid size changes vertically while remaining constant horizontally. For 3D wave propagation, our proposal has a simple transform/interpolation relationship to a regular rectangular grid in all 3 dimensions. Therefore, it yields a very low cost for high order interpolation and allows easy parallelization. In comparison with our previous variable vertical grid size scheme, our proposed scheme uses only a quarter of number of grid points. With numerical benchmarks, we demonstrate a reduction in runtimes of up to ∼79% using real 3D data and sub-optimized code.