TTI介质刚度矩阵的分解  

Decomposition of stiffness matrix for TTI media

作　　者：金世勋 印兴耀[1] 梁锴[1] KIM Sehun;YIN Xing-yao;LIANG Kai(China University of Petroleum （East China） , Shandong Qingdao 266580, Chin)

机构地区：[1]中国石油大学(华东),山东青岛266580

出　　处：《地球物理学进展》2018年第2期644-652,共9页Progress in Geophysics

基　　金：国家重点基础研究发展计划(973)项目(2013CB228604)资助

摘　　要：刚度矩阵是表征传播介质特性的重要参数.TTI介质的刚度矩阵由VTI/HTI介质的刚度矩阵转换而得,因而TTI介质与VTI/HTI介质之间存在着某种联系.本文将TTI介质的刚度矩阵表示成VTI/HTI介质的刚度矩阵与一个‘扰动'矩阵之和的形式,从另一个角度揭示了TTI介质与VTI/HTI介质的关系.本文在TTI介质刚度矩阵分解的基础上,将TTI介质的波动方程分解成VTI/HTI介质波动方程和‘扰动介质'波动方程,然后对VTI/HTI介质波动方程和‘扰动'介质波动方程分别进行了模拟.将两个模拟结果进行合成并与TTI介质的波动方程模拟结果进行了对比,验证了方法的准确性和有效性.理论分析与数值模拟结果表明,TTI介质可认为是VTI/HTI介质的一种延伸.Stiffness matrix is very important parameter that characterizes propagation media. Stiffness matrix of TTI media is based on VTI/HTI media,so that there are some relations between two media. On this paper,we have expressed stiffness matrix of TTI media as the sum of VTI/HTI media and ‘disturbance ＇,so that indicated relations between TTI and VTI/HTI media from another point of view. We have decomposed the wave equation of TTI media as the sum of VTI/HTI media wave equation and ‘disturbance ＇media wave equation following decomposition of stiffness matrix for TTI media,and simulated above two equations. We have verified the accuracy and effectiveness of this method during compare the result of TTI media wave equation simulating with the combination of VTI/HTI media and ‘disturbance＇ media wave equation simulating.Theoretical analysis and numerical simulation results show that TTI media can be considered as an extension of VTI/HTI media.

关 键 词：刚度矩阵分解 TTI介质 Bond变换 有限差分 

分 类 号：P631[天文地球—地质矿产勘探]