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山东大学学报（理学版） ›› 2016, Vol. 51 ›› Issue (11): 99-106.doi: 10.6040/j.issn.1671-9352.0.2016.232

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弹性介质Hamilton正则方程与声波方程辛几何算法

方刚1,2,栾锡武1,2 *,方建会3   

  1. 1.国土资源部油气资源和环境地质重点实验室, 青岛海洋地质研究所, 山东 青岛 266071;2.海洋国家实验室海洋矿产资源评价与探测技术功能实验室, 山东 青岛 266071;3.中国石油大学(华东)理学院, 山东 青岛 266580
  • 收稿日期:2016-05-23 出版日期:2016-11-20 发布日期:2016-11-22
  • 通讯作者: 栾锡武(1966— ),男,博士,研究员,研究方向为综合地球物理勘探. E-mail:xluan@cgs.cn E-mail:fanggeo@163.com
  • 作者简介:方刚(1984— ),男,博士,助理研究员,研究方向为地震成像、地震波动力学. E-mail:fanggeo@163.com
  • 基金资助:
    国家自然科学基金资助项目(41504109);山东省自然科学基金资助项目(BS2015HZ008)

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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摘要： 建立弹性介质的Hamilton正则方程,把声波介质视为特殊的弹性介质,由弹性介质Hamilton方程导出声波介质地震波方程,对声波方程Hamilton化后给出其蛙跳格式的辛差分算法。将声波方程辛算法应用于二维情况下的地震波场正演数值模拟计算,并与常规的有限差分算法进行比较。结果表明,在地震波场正演数值模拟计算中辛几何算法比常规有限差分算法更具优越性。

关键词: 弹性介质, 辛几何算法, 声波方程, Hamiltion正则方程

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

中图分类号: 

  • O316
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