旋转轴对称介质中的qP波射线追踪  

Ray-tracing for qP waves in media with rotated axis of symmetry

作　　者：杨文军[1] 孙福利[2] 

机构地区：[1]中国地质大学,北京100083 [2]中国科学院地质与地球物理研究所,北京100029

出　　处：《地球物理学进展》2011年第1期246-256,共11页Progress in Geophysics

摘　　要：本文使用qP波一阶射线追踪方程(FORT)计算光滑、非均匀旋转轴对称弱各向异性介质中qP波传播的路径和走时.此FORT方程只依赖于15个弱各向异性参数,而非标准射线方程中的21个弹性参数.通常弹性参数模型是在局部坐标系中给定的,而在实际中需要的是全局坐标系下的弹性参数,因此为了解决两个坐标系下弹性参数的变换问题,本文从Bond变换方程出发,推导出了旋转轴对称介质中的弹性参数张量变换方程.全局坐标系中的弹性参数是由局部坐标系中弹性参数通过两个坐标系间极角和方位角的正、余弦函数组合给出的,所得到的弹性参数能够完全匹配FORT方程.最后通过对旋转TI模型和正交模型进行数值模拟验证本方法的有效性和适应性,结果表明本方法对于具有不同各向异性类型、各向异性强度和旋转角度的介质都具有很高的计算精度.We use the first-order ray tracing （FORT） formulas of qP waves to calculate pathes and traveltimes of qP waves propagation in smooth, inhomogeneous and weakly anisotropic medium with arbitrarily symmetric axes. The FORT equations depend only on 15 weak-anisotropy parameters, not on the 21 elastic moduli used in the standard raytracing equations. The elastic modulus of anisotropic media is presented in the local coordinate system, while practical coordinate is in the global system, the Cartesian coordinate system. In order to solve the inconsistency problem between the global coordinate system and the local coordinate system, in this paper, the tensor transformation equations of elastic modulus in media with rotated axis of symmetry are derived from the Bond transformation equations. The weak-anisotropy parameters in the global coordinate system can be explicitly expressed as the combination with the sine and cosine functions of polar angle and azimuth between these different coordinate systems, and the weak-anisotropy parameters in the local coordinate system. The calculated weak-anisotropy parameters are completely suitable to the FORT formulas. We verify the validity and adaptability of this method used in this paper with numerical simulations for the rotated TI model and the rotated ORTHO model. The results indicate that this method has high accuracy for media with different anisotropic types, different anisotropic strength and different rotated mode.

关 键 词：弱各向异性 射线追踪 走时 qP波 张量旋转变换 

分 类 号：P631[天文地球—地质矿产勘探]