Pseudo‐spectral method using rotated staggered grid for elastic wave propagation in 3D arbitrary anisotropic media

Abstract

A B S T R A C TStaggering grid is a very effective way to reduce the Nyquist errors and to suppress the non-causal ringing artefacts in the pseudo-spectral solution of first-order elastic wave equations. However, the straightforward use of a staggered-grid pseudo-spectral method is problematic for simulating wave propagation when the anisotropy level is greater than orthorhombic or when the anisotropic symmetries are not aligned with the computational grids. Inspired by the idea of rotated staggered-grid finitedifference method, we propose a modified pseudo-spectral method for wave propagation in arbitrary anisotropic media. Compared with an existing remedy of staggeredgrid pseudo-spectral method based on stiffness matrix decomposition and a possible alternative using the Lebedev grids, the rotated staggered-grid-based pseudo-spectral method possesses the best balance between the mitigation of artefacts and efficiency. A 2D example on a transversely isotropic model with tilted symmetry axis verifies its effectiveness to suppress the ringing artefacts. Two 3D examples of increasing anisotropy levels demonstrate that the rotated staggered-grid-based pseudo-spectral method can successfully simulate complex wavefields in such anisotropic formations.Key words: Arbitrary anisotropy, Wave propagation, Pseudo-spectral method, Rotated staggered grid. I N T R O D U C T I O NThe numerical modelling of the seismic wave propagation in realistic media is a key element in earthquake and exploration seismology. Several approaches have been developed with different physical model approximations, different complexity levels of the numerical schemes, and different usage of computational resources; see, for example, Carcione et al. (2002) for an overview. The finite-difference method (FDM) remains the most popular numerical method for seismic modelling because it is robust and relatively simple to implement, and it offers a good balance between accuracy and efficiency (Moczo et al. 2007;Yang et al. 2010;Virieux et al. 2011;Liu 2013). Other methods such as the pseudo-spectral (Kosloff and Baysal 1982;Sun et al. 2016a), finite-element (Eriksson * E-mail: 923458778@qq.com and Johnson 1991), spectral elements (Komatitsech et al. 2000), discontinuous Galerkin (Chung and Engquist 2006;De Basabe et al. 2008), finite-volume (Benjemaa et al. 2007, and grid methods (Zhang and Liu 1999) are used to various extent in the geophysical community. Wave propagation simulation has attracted a renewed interest mainly because the so-called (acoustic or elastic) full-wave equation approaches have become a fundamental tool in seismic migration and waveform inversion, considering the new challenges in exploration, especially anisotropy (Operto et al. 2009;Lisitsa and Vishnevskiy 2010;Bartolo et al. 2015;Cheng et al. 2016).The pseudo-spectral method (PSM) (Kosloff and Baysal 1982) we used here is an attractive alternative to the FDM that exploits the fast Fourier transform (FFT) algorithm for computing the spatial derivatives. Its main advantage is that ...

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