TTI介质弹性波相速度与偏振特征分析

相速度和偏振方向是研究地震波传播规律和描述介质特性的重要参数,在理论研究和实际应用中有重要作用.本文假定倾斜横向各向同性(TTI)介质对称轴位于观测坐标系XOZ面内,在此观测坐标系下直接推导了TTI介质弹性波相速度和偏振方向的解析表达式,再进一步利用Thomsen弱各向异性理论,推导了弱各向异性近似条件下弹性波相速度以及qP波和qSV波偏振方向表达式.理论分析和数值试例表明,在相速度方面,随着各向异性介质参数改变,qP波和qSH波速度变化较为平缓,qSV波速度变化较为剧烈.弹性波相速度近似式误差均较小,能较好地近似精确相速度.在偏振方向方面,SH波偏振方向只是传播方向和对称轴倾角的函数,而与各向异性参数无关,SH波偏振方向既垂直于传播方向,又垂直于TTI介质对称轴方向.除特定方向外,qP波和qSV波的偏振方向与传播方向均成一定角度,并且随TTI介质对称轴倾角的改变而改变;在精确和近似情况下,qP波和qSV波的偏振方向始终垂直;在精度允许范围内,偏振方向的弱各向异性近似式与理论解析式吻合较好.

The analysis of phase velocity and polarization feature for elastic wave in TTI media

Phase velocity and polarization direction are the important parameters for studying seismic wave propagation and describing the media property, and they play essential roles in theory and application. This paper assumes that the symmetry axis of tilted transverse isotropy (TTI) media lies in the XOZ plane in observed coordinate system and we directly derive an analytic expression for phase velocity and polarization direction in TTI media in this system. Based on the Thomsen dimensionless anisotropic parameters and weak anisotropy approximation theory, we also derive the approximate expressions of phase velocity for elastic wave, polarization direction for qP wave and qSV wave. The result of analysis and numerical examples indicate that the change of velocity for qP wave and qSH wave is gentle, and the change of velocity for qSV wave is dramatic. The errors between exact and approximate value are small, so the approximation expression is a good approximation for exact phase velocity. The polarization direction of SH wave is the function of propagation angle and tilted angle of symmetry axis instead of anisotropic parameters. The polarization direction of SH wave is not only perpendicular to propagation direction, but also perpendicular to the direction of symmetry axis. The polarization directions of qP wave and qSV wave are neither parallel nor perpendicular to propagation direction except some special directions, and changes as the angle of symmetry axis in TTI media. For both exact and approximate expressions the polarization directions of qP wave and qSV wave are always perpendicular. In a given range of error the weak anisotropic approximate and analytic expressions match well.