TTI equivalent medium parametrization method for the seismic waveform modelling of heterogeneous media with coarse grids

Abstract

In recent years, many higher-order and optimized schemes have been developed to reduce the dispersion error with the use of large grid spacing in finite-difference seismic waveform simulations. However, there are two problems in the application of coarse grids for heterogeneous media: the generation of artefact diffraction from the stair-step representation of non-planar interfaces and the inaccuracy of the calculated waveforms due to the interface error. Several equivalent medium parametrization approaches have been proposed to reduce the interface error of the finite-difference method in heterogeneous media. However, these methods are specifically designed for the standard (2,4) staggered-grid scheme and may not be accurate enough for coarse grids when higher-order and optimized schemes are used. In this paper, 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 use four models to demonstrate the effectiveness of the proposed method, and analyse the accuracy of each seismic phase related to the interface. The results show that our method can be used with higher-order and optimized schemes at 3 points per wavelength and produce satisfactory results.