中文摘要：

相速度和群速度是研究地震波传播规律和描述介质特性的重要参数，是弹性波传播理论中的核心内容，在理论研究和实际应用中有重要作用．本文根据VTI介质的刚度矩阵，利用Bond变换建立了TTI介质刚度矩阵．再利用TTI介质刚度矩阵，结合弹性动力学的本构方程、牛顿运动微分方程和几何方程，得到了三维TTI介质弹性波波动方程和Christoffel方程．通过本征值方法求解Christoffel方程，推导了三维TTI介质弹性波相速度的解析表达式．利用Berryman和Crampin推导各向异性介质群速度公式，根据三维TTI介质的相速度解析式推导了三维TTI介质群速度解析表达式．数值试例表明，随着各向异性介质参数改变，TI介质弹性波相速度变化较为平缓，群速度变化较为剧烈，qP波和SH波速度变化较为平缓，qSV波速度变化较为剧烈．

英文摘要：

Phase and group velocity are the important parameters for researching seismic wave propagation and describing the media property, and they are key contents in theory of elastic wave propagation and play a role in theory and application. Based on stiffness matrix in vertical transverse isotropy （VTI） media and Bond transform, this paper found the stiffness matrix in tilted transverse isotropy （TTI） media. Using the stiffness matrix in TTI media, constitutive equation, Newton＇s motion differential equation and geometry equation, we obtain the elastic wave equation and Christoffel equation in 3D TTI media. Solving the Christoffel equation by eigenvalue method, we derive an analytic expression for phase velocity in 3D TTI media. On the basis of the group velocity equation derived by Berryman and Crampin, we derive an analytic expression for group velocity in 3D TTI media from the analytic expression for phase velocity. The result of numerical examples indicates that the change of elastic wave phase velocity in TI media is smoothout with anisotropic parameters, and the change of group velocity is acuteness. The change of velocity for qP wave and SH wave is smoothout, and the change of velocity for qSV wave is acuteness.