一种弱各向异性介质地震波群速度的近似表示新方法

New approximate expressions of Seismic group velocities for weakly anisotropic media

地震各向异性介质的群速度是关于相角的复杂函数,将其表示成射线角形式较为困难,这给地震各向异性分析以及走时正演模拟等带来诸多不便;另一方面,观测资料表明实际地球介质的地震各向异性通常较弱,这为用射线角近似表示地震波群速度提供了可能.本文基于以射线角近似表示相角的思想,提出了一种弱各向异性条件下,群速度射线角近似表示的新方法.计算表明,在弱地震各向异性条件下,新方法在很宽的射线角范围内,对三种地震波的群速度都能很好地近似,在准SV波计算精度方面显著优于目前通常使用的近似方法.

Group velocities of seismic waves in anisotropic media are usually expressed as functions of phase angle instead of ray angle for it is difficult for general anisotropic media to express them in terms of the latter. However, expressions of the group velocities in terms of ray angle are needed in calculating travel times for anisotropic media and in analysis of seismic anisotropy. Fortunately, most media in the Earth＇s interior are weakly anisotropic, which makes it possible to approximately write the group velocities as functions of ray angle. In this paper, we have put forward a new method to approximately express the group velocities in terms of ray angle for weakly anisotropic media. The new method is based on the approximate expression of phase angle in terms of ray angle. Numerical examples show that the new formula can approach well the exact group velocities of the three kinds of waves during a wide range of ray angle, and, especially, it has much higher accuracy than other expressions for quasi-SV waves.