A joint absorbing boundary for the multiple-relaxation-time lattice Boltzmann method in seismic acoustic wavefield modeling

Abstract

Conventional seismic wave forward simulation generally uses mathematical means to solve the macroscopic wave equation, and then obtains the corresponding seismic wavefield. Usually, when the subsurface structure is finely constructed and the continuity of media is poor, this strategy is difficult to meet the requirements of accurate wavefield calculation. This paper uses the multiple-relaxation-time lattice Boltzmann method (MRT-LBM) to conduct the seismic acoustic wavefield simulation and verify its computational accuracy. To cope with the problem of severe reflections at the truncated boundaries, we analogize the viscous absorbing boundary and perfectly matched layer (PML) absorbing boundary based on the single-relaxation-time lattice Boltzmann (SRT-LB) equation to the MRT-LB equation, and further, propose a joint absorbing boundary through comparative analysis. We give the specific forms of the modified MRT-LB equation loaded with the joint absorbing boundary in the two-dimensional (2D) and three-dimensional (3D) cases, respectively. Then, we verify the effects of this absorbing boundary scheme on a 2D homogeneous model, 2D modified British Petroleum (BP) gas-cloud model, and 3D homogeneous model, respectively. The results reveal that by comparing with the viscous absorbing boundary and PML absorbing boundary, the joint absorbing boundary has the best absorption performance, although it is a little bit complicated. Therefore, this joint absorbing boundary better solves the problem of truncated boundary reflections of MRT-LBM in simulating seismic acoustic wavefields, which is pivotal to its wide application in the field of exploration seismology.