基于Tsvankin的VTI介质qP波精确相速度公式,利用坐标变换的方法,导出了三维空间TTI介质qP波的精确相速度公式;结合Thomsen的弱各向异性假设以及泰勒展开式,简化了三维TTI介质qP波的精确相速度公式,建立了近似相速度公式;TTI模型的计算结果表明,近似相速度公式能较好地逼近精确相速度公式.从近似相速度公式出发,推导了三维qP波的频散关系以及时间—波数域波动方程,构建了纯qP波时间—波数域波场递推格式,分析了递推公式的稳定性条件.最后,基于伪谱法对三维均匀(VTI、TTI)模型、Hess VTI模型以及BP 2007TTI模型进行qP波正演模拟.结果表明,利用所提方法得到的波场快照没有伪横波干扰,波场计算结果稳定.
Based on Tsvankins exact phase velocity for VTI media,we obtain the exact phase velocity of qP-wave for 3DTTI media with the coordinate transformation. Then following Thomsen anisotropic parameters,we gain the approximate formula of phase velocity for 3D TTI media with Taylor series.The phase velocity analysis shows that the approximate formula could well fit the exact formula.From the approximate formula of phase velocity,we derive the qP-wave dispersion relation and wave equation in the time-wavenumber domain for 3DTTI media.The stability of the wave equation is analyzed.Numerical examples demonstrate that the solution of the wave equation proposed in this paper is stable and free of S-wave artifacts.