Abstract:The phase velocities of elastic wave in TTI media can be obtained by solving the Christtoffel equation. But the exact equations are complicated and difficult to use. Starting from the 3D exact expression of phase velocities of elastic wave in TTI media characterized by Thomsen anisotropic parameters, the 3D approximation of qP- and qSV-wave phase velocities in TTI media is derived by an approximate match method. Substituting the approximation into the Berryman's group velocity equation, we can obtain the approximation of qP- and qSV-group velocity. Theoretical analysis and numerical calculations show that the approximation of phase and group velocities based on the approximate match method are in good agreement with the exact value within some ranges, and can be applied to the conditions of moderated and strong anisotropy. The closer the ε and δ are, the higher the approximation accuracy is. Meanwhile, the relative error along the symmetric axis and the vertical symmetric axis of the TTI media is the smallest, but increases near the direction at 45° to the symmetric axis. The relative error of approximate phase and group velocities of qP wave are smaller than qSV wave when the anisotropy is similar.
孙上饶, 梁锴, 印兴耀, 曹丹平, 李坤. 三维TTI介质弹性波相、群速度的近似配方表征法[J]. 石油地球物理勘探, 2021, 56(3): 496-504,518.
SUN Shangrao, LIANG Kai, YIN Xingyao, Cao Danping, LI Kun. Approximate 3D phase and group velocities for elastic wave in TTI media based on an approximate match method. Oil Geophysical Prospecting, 2021, 56(3): 496-504,518.
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