Efficient implementation of equivalent medium parametrization in finite-difference seismic wave simulation methods

Gridpoint discretization of the model has a significant impact on the accuracy of finite-difference seismic waveform simulations. Discretizing the discontinuous velocity model using local point medium parameters can lead to artefact diffraction caused by the stair-step representation and inaccuracies in calculated waveforms due to interface errors, particularly evident when employing coarse grids. To accurately represent model interfaces and reduce interface errors in finite-difference calculations, various equivalent medium parametrization methods have been developed in recent years. Most of these methods require volume-integrated averaging calculations of the medium parameter values within grid cells. The simplest way to achieve this volume averaging is to apply numerical integration averaging to all grid cells. However, this approach demands considerable computational time. To address this computational challenge, we propose employing a set of auxiliary grids to identify which grid cells intersected by the welded interface and perform volume averaging only on these specific cells, thereby reducing unnecessary computational overhead. Additionally, we present a 3-D tilted transversely isotropic equivalent medium parametrization method, which effectively suppresses interface errors and artefact diffraction under the application of coarse grids. We also provide an approach for computing the normal direction of the interface, which is essential for the tilted transversely isotropic equivalent medium parametrization. Numerical tests validate the accuracy of the tilted transversely isotropic equivalent medium parametrization method and demonstrate the practicality of the implementation proposed in this paper for complex models.