A mesh-free finite-difference scheme for frequency-domain acoustic wave simulation with topography

With the increasing complexity of seismic exploration objects, numerical simulation methods that can accurately describe topographical surfaces and complex geological structures are very important. In this study, we propose a mesh-free finite-difference method for frequency-domain numerical simulation with topography. The mesh-free nodes method theoretically applies to any surface and geological structure, whereas the finite-difference scheme has the advantages of high calculation efficiency, small memory occupation, and high simulation accuracy. Therefore, the mesh-free finite-difference method ensures high efficiency and is suitable for irregular surfaces. In addition, we introduce the perfectly matched layer (PML) absorbing boundary condition into the mesh-free numerical simulation, and we compare the performance of the simplified PML, the classical PML, and the complex frequency-shifted PML methods in suppressing boundary reflections. Then, the complex frequency-shift PML method, which is more accurate in suppressing boundary reflections under topographical surface conditions, is applied to the comparison of the mesh-free and regular grid numerical simulations. The comparisons reflected in snapshots, seismic records, and seismic wavelets demonstrate the effectiveness of the proposed mesh-free finite-difference method. Finally, the proposed numerical simulation method is applied to the Marmousi model and field data with topography to further demonstrate its effectiveness.