JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2016, Vol. 51 ›› Issue (11): 99-106.doi: 10.6040/j.issn.1671-9352.0.2016.232

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Hamiltonian canonical equations of elastic medium and symplectic geometric algorithm of acoustic wave equation

FANG Gang1,2, LUAN Xi-wu1,2 *, FANG Jian-hui3   

  1. 1. Key Laboratory of Marine Hydrocarbon Resources and Environmental Geology, Ministry of Land and Resources, Qingdao Institute of Marine Geology, Qingdao, 266071, Shandong, China;
    2. Laboratory for Marine Mineral Resources, Qingdao National Laboratory for Marine Science and Technology, Qingdao, 266071, Shandong, China;
    3. School of Science in China University of Petroleum, Qingdao 266580, Shandong, China
  • Received:2016-05-23 Online:2016-11-20 Published:2016-11-22

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Abstract: The Hamilton canonical equations is built for elastic medium. Taking the acoustic medium as a special kind of elastic medium, the acoustic wave equation can be derivate from elastic Hamilton canonical equations. The symplectic geometric algorithm with leapfrog schemes can be obtained with the Hamiltonian of acoustic wave equation. The symplectic geometric algorithm of acoustic wave equation can be applied for 2D seismic wave fields numerical modeling. Comparing with the conventional finite differences algorithm, the results indicated that the symplectic geometric algorithm is more advantageous in seismic wave fields numerical modeling.

Key words: acoustic wave equation, Hamilton canonical equations, symplectic geometric algorithm, elastic medium

CLC Number: 

  • O316
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