Applied Geophysics

, Volume 14, Issue 2, pp 258–269 | Cite as

Seismic wavefield modeling based on time-domain symplectic and Fourier finite-difference method

  • Gang Fang
  • Jing Ba
  • Xin-xin Liu
  • Kun Zhu
  • Guo-Chang Liu


Seismic wavefield modeling is important for improving seismic data processing and interpretation. Calculations of wavefield propagation are sometimes not stable when forward modeling of seismic wave uses large time steps for long times. Based on the Hamiltonian expression of the acoustic wave equation, we propose a structure-preserving method for seismic wavefield modeling by applying the symplectic finite-difference method on time grids and the Fourier finite-difference method on space grids to solve the acoustic wave equation. The proposed method is called the symplectic Fourier finite-difference (symplectic FFD) method, and offers high computational accuracy and improves the computational stability. Using acoustic approximation, we extend the method to anisotropic media. We discuss the calculations in the symplectic FFD method for seismic wavefield modeling of isotropic and anisotropic media, and use the BP salt model and BP TTI model to test the proposed method. The numerical examples suggest that the proposed method can be used in seismic modeling of strongly variable velocities, offering high computational accuracy and low numerical dispersion. The symplectic FFD method overcomes the residual qSV wave of seismic modeling in anisotropic media and maintains the stability of the wavefield propagation for large time steps.


symplectic algorithm Fourier finite-difference Hamiltonian system seismic modeling anisotropic 


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We are grateful to Dr. Xiaolei Song from BP for vivid discussions and valuable suggestions. We also thank the developers of the Madagascar open-source software package ( (Fomel et al., 2013a).


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Copyright information

© Editorial Office of Applied Geophysics and Springer-Verlag GmbH Germany 2017

Authors and Affiliations

  • Gang Fang
    • 1
    • 2
  • Jing Ba
    • 3
  • Xin-xin Liu
    • 1
    • 2
  • Kun Zhu
    • 4
  • Guo-Chang Liu
    • 5
  1. 1.The Key Laboratory of Gas Hydrate, Ministry of Land and ResourcesQingdao Institute of Marine GeologyQingdaoChina
  2. 2.Laboratory for Marine Mineral ResourcesQingdao National Laboratory for Marine Science and TechnologyQingdaoChina
  3. 3.School of Earth Sciences and EngineeringHohai UniversityNanjingChina
  4. 4.School of GeosciencesChina University of Petroleum (East China)QingdaoChina
  5. 5.State Key Laboratory of Petroleum Resources and ProspectingChina University of Petroleum-BeijingBeijingChina

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