Optimal Symplectic Scheme and Generalized Discrete Convolutional Differentiator for Seismic Wave Modeling

In this paper, seismic wave equation is transformed into the Hamiltonian system, and a new symplectic numerical scheme is developed, which is called the optimal symplectic algorithm and generalized discrete convolutional differentiator (OSGCD). For temporal discretization, OSGCD introduces Lie opera...

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Bibliographic Details
Published in:Chinese journal of geophysics 2013-09, Vol.56 (5), p.623-635
Main Authors: Shao-Lin, LIU, Xiao-Fan, LI, Wen-Shuai, WANG, Ming-Wen, LU, Mei-Gen, ZHANG
Format: Article
Language:English
Subjects:
Differentiators
Discretization
Generalized convolutional differentiator
Geometry
Geophysics
Mathematical analysis
Mathematical models
Numerical modeling
Operators (mathematics)
Optimization
Seismic wave
Seismic waves
Symplectic scheme
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Summary:In this paper, seismic wave equation is transformed into the Hamiltonian system, and a new symplectic numerical scheme is developed, which is called the optimal symplectic algorithm and generalized discrete convolutional differentiator (OSGCD). For temporal discretization, OSGCD introduces Lie operators to construct two‐stage and second‐order symplectic scheme and adopts the optimal symplectic scheme based on the minimum error principle. For the spatial discretization, OSGCD employs the generalized discrete convolution differentiator to approximate the spatial differential operators and uses derivative approximation to obtain stable operator coefficients. We obtain the stability condition for a 2D case. In numerical experiments, OSGCD is compared with different methods, showing advantages in both accuracy and efficiency. The OSGCD also has the ability for modeling long‐term seismic wave propagation and modeling seismic waves in heterogeneous media.
ISSN:0898-9591
2326-0440
DOI:10.1002/cjg2.20058