基于P-SV波分离的VTI介质射线追踪方法

doi:10.11867/j.issn.1001-8166.2015.09.1028

近年来,VTI介质参数建模和成像技术发展迅速,其中VTI介质射线追踪是基础,其精度和稳定性直接影响建模和成像的效果。VTI介质射线追踪大多通过前人提出的频散关系推导出程函方程和射线方程,该方法主要基于纵横波相互独立的假设,采用令横波速度等于零的手段,在某些特殊情况下精度较低、稳定性较差。针对其缺点提出一种新的射线追踪方法,该方法基于P=SV波分离得到的qP波频散关系,从而推导出程函方程和射线方程,提高了精度和稳定性。最后通过模型试算验证该方法的正确性和稳定性。

关键词: VTI介质, 射线追踪, 频散关系, 程函方程, 射线方程

In recent years, modeling and imaging techniques for VTI medium have developed rapidly. Ray tracing in VTI medium is the key issue, whose precision and stability directly affect the results of modeling and imaging. Ray tracing in VTI medium is usually based on the eikonal equation and ray equation derived from the dispersion relation of Alkhalifah (2000). The assumption is that the P wave and S wave are independence, and the velocity of S wave is zero. Thus, in some particular cases, this method is lack of accuracy and stability. In this paper, a new ray tracing method was proposed to overcome this problem. We separated P-SV waves to get the phase velocity of the qP wave, and then to get the eikonal equation and ray equation of qP wave, through which the precision and stability were improved. At the end, numerical tests were made to prove the effectiveness of this method.

Key words: VTI medium, Ray tracing, Dispersion relation, Eikonal equation, Ray equation.

中图分类号:

P631.4

图1 新射线方程旅行时等值线图

Fig.1 Traveltime contours using new ray equation

图2 各向同性介质相速度曲线(ε=δ=0) 黑线表示准确相速度曲线;红线表示V_SO=0时的相速度曲线;绿线表示P-SV波分离后的相速度曲线

Fig.2 The curves of phase velocity for isotropic medium Black expresses the exact phase velocity curve;Red expresses the phase velocity curve when V_SO=0;Green expresses the phase velocity curve of separated P-SV waves

图3 ε=0.065,δ=0.059时的VTI介质相速度曲线黑线表示准确相速度曲线;红线表示V_SO=0时的相速度曲线;绿线表示P-SV波分离后的相速度曲线

Fig.3 The curve of phase velocity for Mesa clay Shale VTI medium Black expresses the exact phase velocity curve;Red expresses the phase velocity curve when V_SO=0;Green expresses the phase velocity curve of separated P-SV waves

图4 ε=0.11,δ=-0.035时的VTI介质相速度曲线黑线表示准确相速度曲线;红线表示V_SO=0时的相速度曲线;绿线表示P-SV波分离后的相速度曲线

Fig.4 The curve of phase velocity for Taylor Sand VTI medium Black expresses the exact phase velocity curve,red expresses the phase velocity curve when V_S0=0,green expresses the phase velocity curve of separated P=SV waves

图5 VTI介质ε=0.065,δ=-0.059常梯度速度模型等值线图（a）Alkhalifah射线方程旅行时等值线;（b）新射线方程旅行时等值线;（c）二者叠合对比结果

Fig.5 Analysis on VTI medium velocity isoline in constant gradient model and composite （a）Travel time isoline of Alkhalifah ray function;（b）travel time isoline of new ray function;（c）composite of two functions

图6 VTI介质ε=0.11,δ=-0.035常梯度速度模型等值线图（1）Alkhalifah射线方程旅行时等值线;（b）新射线方程旅行时等值线;（c）二者叠合对比结果

Fig.6 Analysis on VTI medium velocity isoline in constant gradient model and composite （a）Travel time isoline of Alkhalifah ray function;（b）Travel time isoline of new ray function;（c）Composite of two functions

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摘要

A New Ray Tracing Method for VTI Medium Based on Separated P-SV Waves