Dithering of absorbers for efficient finite‐difference modeling of viscoelastic wave propagation

Abstract

Viscoelastic modeling traditionally uses multiple relaxation mechanisms (absorbers) per wave type in each cell of the numerical grid. We show that one absorber per cell suffices when the absorbers of different relaxation frequencies and absorption strengths are dithered in a supercell, i.e., a very small area of several nearby cells. The relaxation frequencies used in a supercell can be preselected to cover the bandwidth required in the modeling and distributed locally in a random manner to minimize numerical scattering. The absorption strengths, however, must be found iteratively to yield an average absorption that matches the desired medium over the bandwidth. We have tested the dithered‐absorber method for modeling a variety of 2-D media using a staggered‐grid finite‐difference scheme. For a uniform medium, our result agrees well with the exact analytic solution. For inhomogeneous models, the dithered‐absorber solution agrees well with the finite‐difference solution computed with five absorbers per cell. The computer time and memory requirements of the dithered‐absorber method are only ≈60% and ≈40% of those with five absorbers per cell. In all cases, random numerical scattering is very small—typically less than similar types of error because of model discretization.