Title

The research on unsplit PML absorbing boundary conditions of acoustic equation for VTI 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

针对垂直横向各向同性(VTI)介质声波波动方程的特点,研究了VTI介质非分裂式完全匹配层(Unsplit perfectly matched layer,UPML)吸收边界条件。首先从VTI介质波场传播稳定性和减少伪横波噪声的角度对常见的几种VTI介质声波波动方程进行了归纳和对比,发现VTI介质声波近似方程更适用于VTI介质情形。然后以VTI介质声波近似二阶波动方程为基础,推导出UPML波动方程,并给出求解该波动方程的具体数值实现方法。数值模拟结果表明,UPML吸收边界条件能达到很好的人工边界反射吸收效果,相比于优化海绵吸收边界条件,其人工边界反射吸收效果明显提高。

Abstract

We study unsplit perfectly matched layer (UPML) absorbing boundary conditions for vertical transversely isotropic (VTI) media based on the characteristics of VTI media acoustic wave equation.We firstly summarize several common VTI media acoustic wave equations and compare these wave equations in detail from the perspective of wavefield propagation stability and pseudo SV-wave noise reduction for VTI media.We conclude that the VTI acoustic approximation equation is applicable for VTI media.Then we derive the UPML wave equation from the VTI acoustic approximation second-order wave equation.Afterwards we give the concrete numerical implementation method.The numerical modeling examples show that the UPML boundary condition can absorb the artificial boundary reflection very well.The boundary reflection absorbing effect of the proposed UPML algorithm is much better compared with the optimal sponge boundary condition.

关键词：

VTI介质; 非分裂式完全匹配层; 伪横波噪声; 声波近似方程; 二阶波动方程;

Keywords:

VTI media,unsplit perfectly matched layer (UPML),pseudo SV-wave noise,acoustic approximation equation,second-order wave equation;

基金项目

国土资源部海底矿产资源重点实验室开放基金(No.KLMMR-2015-A-14)、国家自然科学基金项目(41604110)、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.1000-1441.2016.06.002

VTI介质声波方程非分裂式PML吸收边界条件研究