Study On Mesh-free Finite Difference Method For Seismic Wave Equations

Numerical modeling of seismic wave propagation is an important means of underground exploration.Among numerous modeling methods,the finite difference method has become one of the most popular methods in recent years for its simplicity and stability.However,there are also some deficiencies for the traditional finite difference method.The grid cells are usually rectangles which cannot exactly fit curved interfaces or irregular model boundaries.The local refinement in critical areas is hardly to achieve.With the increasingly complex of exploration target,the mesh-free finite difference method has attracted more and more attention for its high geometric flexibility.Without complex meshing process or lattice mapping,the distribution process of mesh-free nodes is simple and direct,which reduces the cost of improving geometric flexibility.As one of the most widely used mesh-free finite difference methods,the radial-basis-funtion-generated finite difference(RBF-FD)method can accurately simulate seismic wave propagation in an irregular computational domain,ensure the modeling accuracy and improve the computational efficiency.Since the irregular computational domain generally has irregular boundaries,this thesis proposed the perfectly matched layer(PML)method and the complex-frequency-shifted perfectly matched layer(CFS-PML)method for the irregular boundary.Besides,the thesis achieved Kelvin-Voigt viscoelastic media modeling based on the mesh-free finite difference method and analyzed the attenuation effect of different viscous coefficient media towards seismic waves.The frequency-domain modeling is suitable for multi-shot parallel computations and has no error accumulation.Using RBF-FD,this thesis realized frequency-domain mesh-free finite difference modeling for acoustic wave equation.The proposed PML is applicable for the irregular boundary and has a good absorption effect.The proposed CFS-PML can effectively absorb low frequency waves and near-grazing incident waves.With the increase of viscosity coefficient,seismic waves attenuate significantly,the dominant frequency moves towards the low frequency and the effective bandwidth becomes narrower,which results in resolution reduction.Furthermore,by adopting the non-uniform nodal distribution or cutting off the unnecessary computational domain,the mesh-free finite difference method can reduce the memory consumption and improve the computational efficiency.