横向各向同性介质中纵波和转换横波的快速射线追踪方法

Fast Ray-tracing Method for Compressional and Converted Waves in Transversely Isotropic Media

1. 石油勘探开发科学研究院,北京100083;2. 河南石油勘探局技工学校,南阳473000

Deng Huaiqun, The Academy of Exploration and Development for Petroleum, Beijing 100083

首先根据横向各向同性介质中群速度与相速度的关系,以及横向各向同性介质中射线参数的表达式,推导出适用于做射线追踪的射线参数解析表达式。在介质的对称平面内,利用逐段迭代的射线追踪方法导出了任意形态光滑界面反射点和透射点的一阶修正量公式,可适用于纵波、转换横波的射线路径及旅行时的计算。公式推导未做弱各向异性的假设,对任意强度的各向异性介质都适用。通过用水平界面各向异性介质时距曲线公式 (Tsvankin 1994)和波面计算法对相同模型的对比计算表明,本文的算法计算速度快,计算精度高,对介质不需做任何假设。

In this paper an analytic expression of ray parameter which is suitable to ray tracing is deduced based on the relationship between group velocity and phase velocity and expressions of ray parameters in transversely isotropic media. In the symmetric plane of the medium, a one order correction formula is derived for any reflection and transmission point on any smooth interface via piecewise ray tracing without assumption of weak anisotropy. The formula is applicable in the calculation of ray paths and travel times of P waves and converted waves in any strong anisotropic medium rather just in weak anisotropic media. Comparison between results from time distance curve of horizontal surfaces(Tsvankin 1994) and the wave face method in isotropic media with horizontal interfaces shows that the method is faster and more accurate.