Viscoacoustic wave simulation with the lattice Boltzmann method

Abstract

The lattice Boltzmann method (LBM), widely used in computational fluid mechanics, is introduced as a novel mesoscopic numerical scheme for viscoacoustic wavefield simulation. Through mathematical derivation, a mapping model between the relaxation time of LBM and the quality factor based on the Kelvin-Voigt model is established, which provides a theoretical background for the comparison of the viscoacoustic wavefields obtained, respectively, by LBM and finite-difference method (FDM) formulated on the traditional wave equation. By defining the transmission and reflection coefficients and adopting a Newton interpolation algorithm to modify the streaming process of the LBM, we have extended the conventional LBM to simulate the wavefields in complex media with acceptable accuracy. A 2D homogeneous model, two 2D layered models, and the modified Marmousi model are tested in the numerical simulation experiments. The simulation results of LBM are comparable to those of FDM, and the relative errors are all within a reasonable range, which can verify the effectiveness of the forward modeling kernel. The modified LBM offers a new numerical scheme in seismology to simulate viscoacoustic wave propagation in complex media and even in porous media considering its flexible boundary condition and high discrete characteristic.