Adaptive Mesh Refinement(AMR) Finite-Difference Methods For Seismic Wave Propagation Modelling In Strongly Heterogeneous Media

Seismic numerical modelling is an important tool for simulating strong ground motion and imaging subsurface structure.Strong ground motion simulation and full wave inversion require hundreds of thousands of broadband forward calculations,imposing high computing resource demands.Finite-difference method(FD)is currently widely used for its simple implementation and high efficiency.The structured grid in FD is easy to generate for complex models,and it is also suitable for massive parallel computation to achieve higher computation effiency.Orthodox finite-difference method applies uniform grid to discretize the model and the grid size is usually determined by the worst case,lowest wave velocity and pinchout,for example.Therefore,for complex models in practice,applying uniform grid will cause severe spatial and temporal oversampling,squandering computation resources.By discretizing zones with lower velocities or complex geometries with finer grid size,the non-uniform grid can improve calculation efficiency while ensuring accuracy,and is widely discussed.Strongly heterogeneous media discussed in this paper refers to the models with strong velocity heterogeneity.Compared with classical layered-based or block-based discontinuous grid,adaptive mesh refinement(AMR)organizes grid refinement zones with more flexible geometries and can utilize the compotational resources more efficiently.However,the AMR algorithm is sophisticated,including its multi-level grid data management,mesh generation and computational load balancing on high-performance computing platforms.We implement AMR for seismic wave simulation.According to the features of FD implementation,we choose patch-structured AMR in this work.One of the existing mature AMR frameworks in computaional fluid dynamics saves us the trouble of designing specific data structures and interfaces.When generating meshes,we use finer grid size to discretize the lower velocities zones and coarser grid size to discretize those with higher velocities.The refinement ratio between adjacent grid level is fixed and grid levels change gradually at interfaces with high velocity contrast.The computation process is similar with that of discontinous grid:at every time step,update the wavefield according to the following steps:(1)solve the wave equations from base level to the maximum level in the inner part of grid boxes;(2)interpolate the ghost values in the finer grid(the missed values for the FD stencils at the boundary of different level grid)with the values in the coarser grid;(3)restrict the ghost values in the coarser grid(the values in coarser grid in the overlapping zones)with the values in the finer grid to ensure the calculation accuracy and stability.In this work,we apply AMR in staggered-grid finite-difference method to simulate two-dimensional acoustic wave.We then apply AMR in collocated-grid finite-difference method to simulate two-dimensional and three-dimensional elastic wave.The results of numercial tests verify the stability,accuracy and efficiency of our method for strongly heterogeneous model.Considering the overhead due to the AMR data structure and overlapping multi-level grid structure,we discuss the factors influencing the computational efficiency.