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The Chebyshev spectral element method using staggered predictor and corrector for elastic wave simulations

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Abstract

Based on strong and weak forms of elastic wave equations, a Chebyshev spectral element method (SEM) using the Galerkin variational principle is developed by discretizing the wave equation in the spatial and time domains and introducing the preconditioned conjugate gradient (PCG)-element by element (EBE) method in the spatial domain and the staggered predictor/corrector method in the time domain. The accuracy of our proposed method is verified by comparing it with a finite-difference method (FDM) for a homogeneous solid medium and a double layered solid medium with an inclined interface. The modeling results using the two methods are in good agreement with each other. Meanwhile, to show the algorithm capability, the suggested method is used to simulate the wave propagation in a layered medium with a topographic traction free surface. By introducing the EBE algorithm with an optimized tensor product technique, the proposed SEM is especially suitable for numerical simulation of wave propagations in complex models with irregularly free surfaces at a fast convergence rate, while keeping the advantage of the finite element method.

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Authors and Affiliations

  1. State Key Laboratory of Acoustics, Institute of Acoustics, Chinese Academy of Sciences, Beijing, 100190, China

    Cheng-Xuan Che, Xiu-Ming Wang & Wei-Jun Lin

Authors
  1. Cheng-Xuan Che
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  2. Xiu-Ming Wang
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  3. Wei-Jun Lin
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Additional information

This work is supported by the National Natural Science Foundation of China (Grant No. 40774099, 10874202) and the National High Technology Research and Development Program of China (Grant No. 2008AA06Z205).

Che Chengxuan received his master degree in Geodetection and Information Technology from Northeast Petroleum University in 2007. He is currently a PhD student majoring in reservoir acoustic characterizations and borehole exploration in Institute of Acoustics, Chinese Academy of Sciences. His research interests include numerical simulation of seismic waves, numerical simulation and experimental measurement of production well-logging.

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Che, CX., Wang, XM. & Lin, WJ. The Chebyshev spectral element method using staggered predictor and corrector for elastic wave simulations. Appl. Geophys. 7, 174–184 (2010). https://doi.org/10.1007/s11770-010-0242-9

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  • DOI: https://doi.org/10.1007/s11770-010-0242-9

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