An LSM–LBM Coupling Algorithm Based on the Inverse Squared Distance Method and Its Application in Seismic Wavefield Simulation

Research on seismic wave propagation in fluid-bearing reservoirs is crucial for unconventional oil and gas exploration. While traditional wave equation-based simulations are well-established, they often struggle to accurately model fluid–solid two-phase media characterized by complex tectonic features, strong discontinuities, and intricate interfacial couplings. This article presents an advanced approach utilizing two mesoscopic discrete models: the lattice spring model (LSM) and the lattice Boltzmann model (LBM). The LSM simulates solid wavefields via the velocity Verlet algorithm, with optimized spatial distributions of springs and masses. Concurrently, the LBM is employed for fluid wavefield simulation, featuring a precisely designed lattice model and well-defined collision and streaming rules. In particular, a novel momentum exchange strategy incorporating the inverse squared distance method (ISDM) is constructed to enhance wavefield information transfer between the LSM and LBM at fluid–solid boundaries, aiming to improve accuracy and stability. The efficacy of the novel ISDM–LSM–LBM coupling algorithm is validated through simulations of layered models, fluid-filled cavity model, and river filling models. Compared with the original LSM–LBM algorithm, it exhibits enhanced computational accuracy and stability, albeit with a modest increase in computational burden and memory consumption. Comparative analysis with finite difference method (FDM) results reveals that the ISDM–LSM–LBM algorithm accurately captures wavefield characteristics. Although slight differences are observed in the depiction of reflected, transmitted, and converted waves at internal boundaries—attributable to the distinct fluid–solid interface treatments of each method—the new algorithm’s flexibility in boundary coupling and consideration of additional interaction forces offer significant improvements in accuracy and stability. This innovative simulation technique, independent of traditional wave equations, significantly enhances the precision and adaptability of wavefield calculations in fluid–solid media, providing substantial benefits for oil and gas geophysical exploration.