Title

The research on split PML absorbing boundary conditions of acoustic equation for TTI media

单位

(1.国土资源部海底矿产资源重点实验室,中国地质调查局广州海洋地质调查局,广东广州510075;2.中国科学院地质与地球物理研究所,中国科学院油气资源研究重点实验室,北京100029;3.中国石油化工股份有限公司石油物探技术研究院,江苏南京211103;4.山东科技大学地球科学与工程学院,山东青岛266590)

Organization

(1.MLR Key Laboratory of Marine Mineral Resources,Guangzhou Marine Geological Survey,China Geological Survey,Guangzhou 510075,China;2.Key Laboratory of Petroleum Resources Research,Institute of Geology and Geophysics,Chinese Academy of Sciences,Beijing 100029,China;3.Sinopec Geophysical Research Institute,Nanjing 211103,China;4.College of Earth Science and Engineering,Shandong University of Science and Technology,Qingdao 266590,China)

摘要

针对倾斜横向各向同性(TTI)介质声波波动方程的特点,研究了TTI介质分裂式完全匹配层(Split perfectly matched layer,SPML)吸收边界条件。首先对常见的几种TTI介质声波波动方程进行了归纳,并从TTI介质波场传播稳定性的角度进行对比分析,结果表明,引入横波分量的TTI介质纵横波耦合方程适用于TTI介质。然后从TTI介质纵横波耦合二阶波动方程出发,推导得到其一阶波动方程的形式,进而推导出一阶波动方程形式的SPML波动方程,并给出了高阶交错网格有限差分算法的具体实现过程。数值模拟结果表明,SPML吸收边界条件能达到很好的人工边界反射吸收效果,相比优化海绵吸收边界条件,其人工边界反射吸收效果更好。

Abstract

We study split perfectly matched layer (SPML) absorbing boundary conditions for TTI media based on the characteristics of TTI media acoustic wave equation.We firstly summarize several common TTI media acoustic wave equations and compare these wave equations in detail from the perspective of wavefield propagation stability for TTI media.We conclude that the TTI acoustic approximation equation introduced SV-wave component is applicable for TTI media.Then we derive the TTI media first-order acoustic wave equation based on the SPML boundary condition from the TTI P-wave and SV-wave coupled second-order wave equation.Afterwards we give the concrete implementation method for high-order staggered-grid finite-difference algorithm.The numerical modeling examples show that the SPML boundary condition can absorb the artificial boundary reflection very well.The boundary reflection absorbing effect of the proposed SPML algorithm is much better compared with the optimal sponge boundary condition.

关键词：

TTI介质; 分裂式完全匹配层; 纵横波耦合方程; 一阶波动方程; 高阶交错网格有限差分;

Keywords:

TTI media,; split perfectly matched layer,; P-wave and SV-wave coupled equation,; first-order wave equation,; high-order staggered-grid finite-difference;

基金项目

国家自然科学基金项目(41604110)、国土资源部海底矿产资源重点实验室开放基金项目(KLMMR-2015-A-14)、国家高技术研究发展计划(863计划)项目(2013AA092501)和国家科技重大专项(2011ZX05003-003)联合资助。

DOI

10.3969/j.issn.1000-1441.2017.03.005

TTI介质声波方程分裂式PML吸收边界条件研究