摘要
研究了VTI-TTI介质界面上发生的反射和折射现象。利用Bond变换,证明了TTI-TTI各向异性介质界面可以用VTI-TTI介质界面的方法处理。给出了在两种不同的各向异性介质界面上产生的模式转换波的极化系数的解析表达式,推导了过第一临界角区域产生的非均匀椭圆极化折射P波的极化系数表达式;依据开尔文-克里斯托费尔方程,建立了求解VTI介质一侧反射角的四次多项式和求解TTI介质一侧折射角的八次多项式,得到了入射波/模式转换波的极化系数、界面上的反射/折射系数、界面两侧介质弹性及其各向异性参数、入射角之间的严格理论关系。研究发现,模式转换波的极化系数和界面上的反射/折射系数取决于界面两侧介质的密度和弹性参数及其各向异性,并且受入射角的影响。入射波/模式转换波的极化系数与界面上的反射/折射系数密切相关,依据能量守恒定律和声学边界条件,可以互相验证。
The reflection and refraction phenomena occurring at the VTI-TTI dielectric interface are studied.Using the Bond transform,it is proved that the TTI-TTI anisotropic medium interface can be handled by the method of the VTI-TTI medium interface.The analytical expression of the polarization coefficient of the mode-converted wave generated at the interface of two different anisotropic media is given,and the polarization of the non-uniform elliptically polarized refracted P-wave generated through the first critical angle region is deduced coefficient expression.According to Christoffel equation,the quartic polynomial for solving the reflection angle of the VTI medium side and the 8th order polynomial for solving the refraction angle of the TTI medium side are established,and the polarization coefficient of the incident wave/mode-converted wave,the polarization coefficient on the interface are obtained.Rigorous theoretical relationship between the reflection/refractive coefficients,the elasticity of the medium on both sides of the interface and its anisotropy parameters,and the angle of incidence.It is found that the polarization coefficients and the reflection/refractive coefficients of the mode-converted waves at the interface depend on the density and elastic parameters of the medium on both sides of the interface and their anisotropy,and are affected by the incident-angle.The polarization coefficients of the mode-conversion waves are closely related to the reflection and refraction coefficients at the interface and can be validated against each other from the law of energy conservation and the interfacial boundary conditions.
作者
法林
赵琳
李玉霞
邹骁
胡凯利
李晓
梁计峰
孙豪
赵梅山
FA Lin;ZHAO Lin;LI Yuxia;ZOU Xiao;HU Kaili;LI Xiao;LIANG Jifeng;SUN Hao;ZHAO Meishan(School of Information Engineering,Xi'an Institute of Translation and Interpretation,Xi'an 710105,China;School of Electronic Engineering,Xi'an University of Posts and Telecommunications,Xi'an 710121,China;CNPC Logging Company Limited,Xi'an 710061,China;The Department of Chemistry,James Franck Institute,The University of Chicago,Chicago 60637,USA)
出处
《西安邮电大学学报》
2022年第2期40-51,共12页
Journal of Xi’an University of Posts and Telecommunications
基金
国家自然科学基金项目(41974130,40974078)
中国石油天然气集团有限公司重大现场试验项目(2020F-46)。
