Mesh grading approach for wave propagation in high velocity-contrast media

•A mesh grading approach based on unstructured grids is proposed for wave propagation.•It is flexible to deal with the irregular interface of high-velocity contrast media.•The key feature is the construction of investigated lump on the media interface.•The coarse and fine grids are used for the high and low velocity media respectively.•Mesh grading ratio can be arbitrary odd number on the interface of coarse-fine grids.

A mesh grading approach based on investigated lump method has been presented for simulating wave propagation in high velocity-contrast media. Unstructured fine grids are used to discretize the low wave-velocity medium in order to ensure the accuracy of numerical computation, and unstructured coarse grids are used for the high wave-velocity medium in order to substantially reduce the computational cost. On the interface, one coarse grid can match the fine grids of arbitrary odd number. The key feature of the proposed method is the constructions of investigated lumps on the interfaces of media. The transition zone, which is commonly used in the discontinuous grid scheme based on the staggered-grid finite-difference method, will not be used any more. Moreover, the computational instability that the discontinuous grid schemes frequently encountered does not arise in the proposed method. The comparisons with the analytical solutions and the application in studying the effects of sedimentary basin demonstrated that the mesh grading approach is a valid, accurate, convenient and flexible algorithm in simulating wave propagations in high velocity-contrast media with irregular interfaces.