TI介质中的相速度和群速度及射线参数

Phase velocity,group velocity,and ray parameters in transversely isotropic media

根据横向各向同性(TI)介质中体波相速度的解析表达式,分析了不同各向异性参数条件下相速度曲线的特征。分析结果表明,随着各向异性参数所满足的条件不同,相速度曲线既可能单调递增,也可能单调递减,或在一定相角范围递增而在其它相角范围递减。相速度曲线的单调性决定群对相的偏离方向,当相速度递减时,群向TI对称轴方向偏离,群相偏离角为负;当相速度递增时,群向背离TI对称轴的方向偏离,群相偏离角为正。利用相表示的射线参数表达式和群相关系得出了群、相联合表示的射线参数表达式,并用数值算例进行了验证。

According to analytic expressions of phase velocities for body wave in transversely isotropic(TI)media,the characteristics of phase-velocity curves are discussed for different sets of anisotropic parameters.The phase-velocity curve can be either monotonic in- creasing or monotonic decreasing,or increasing in a certain range of phase angle while decreasing in another range.The deviation of group velocity from phase velocity is relevant to the monotonicity of phase-velocity curve.The deviation directs toward the symmetry axis of TI media for decreasing phase velocities,the deviation angle is negative.The deviation directs away from the symmetry axis of TI media for increasing phase velocities,and the deviation angle is positive.The ray parameter expression in the form of combination with phase and group can be derived from the phase-group relation- ship and the ray parameter expression in terms of phase.