Dispersion Analysis and 3-D Wavefield Modeling of Lattice Boltzmann Model

When the structure of the media is complex or there are strong interfaces, the simulated seismic waves obtained by the traditional forward modeling methods are often difficult to fit the real wavefields. To get more accurately simulated waves, in this article, we utilize the widely used 3-D lattice Boltzmann model (LBM) in fluid mechanics as a new tool for seismic wavefield simulation. In order to establish a general framework for the LBM in the 3-D case, first, we introduce an improved LBM scheme in 3-D form considering the reflection and transmission effects. Then, we carry out a systematic dispersion analysis of the LBM with different lattices by analogizing the dispersion derivation of the finite-difference method (FDM) and comparing the results of the LBM with those of the FDM. Finally, we explore the stability conditions and present the treatment of initial and boundary conditions. To verify the feasibility of this 3-D-LBM strategy, we perform 3-D wavefield simulation tests on a homogeneous model, a cavity model, and a five-layer model, respectively. By comparing the results obtained by LBM and FDM, we conclude that the accuracy of this improved LBM scheme is acceptable. This 3-D-LBM modeling scheme provides a new option for seismic wavefield simulation for complex media due to its flexibility of boundary processing and efficient parallelism capability.