A discrete representation and the implementation for the finite-difference seismic waveform simulation with coarse grid

The model discretization by the grid points has a great influence on the accuracy of the finite-difference seismic waveform simulation. Discretizing the discontinuous velocity model by the medium parameters of local points will lead to artefacts diffraction from stair-step representation and the inaccuracy of the calculated waveforms due to the interface error. To accurately represent layered models and reduce the interface error of finite-difference calculation, many equivalent medium parametrization methods have been developed in recent years. Most of these methods are developed for the fourth-order staggered-grid scheme and may not be accurate enough for coarse grids when applying higher-order and optimized schemes.

In this work, we develop a tilted transversely isotropic equivalent medium parametrization method to suppress the interface error and the artefact diffraction caused by the staircase approximation under the application of coarse grids. We also present an efficient algorithm for implementing equivalent medium parameterization methods for complex layered models.