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


Zou, Peng
Cheng, Jiubing

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Staggering 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 finite-difference method, we propose a modified pseudo-spectral method for wave propagation in arbitrary anisotropic media. Compared with an existing remedy of staggered-grid 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.

Zou P, Cheng J (2017) Pseudo-spectral method using rotated staggered grid for elastic wave propagation in 3D arbitrary anisotropic media. Geophysical Prospecting 66: 47–61. Available:

The first author appreciates T. F. Wang, C. L. Wang, and W. J. He for their fruitful discussion in this study. The authors would like to thank the National Natural Science Foundation of China for the support under grants 41630964, 41474099, and 41674117. This publication is also based upon work supported by King Abdullah University of Science and Technology (KAUST) Office of Sponsored Research (OSR) under Award 2230. We appreciate the support of Madagascar open-source software for reproducible research (Fomel et al. 2013).


Geophysical Prospecting


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