摘要
It is still argued whether we measure phase or group velocities using acoustic logging tools. In this paper, three kinds of models are used to investigate this problem by theoretical analyses and numerical simulations. First, we use the plane-wave superposition model containing two plane waves with different velocities and able to change the values of phase velocity and group velocity. The numerical results show that whether phase velocity is higher or lower than group velocity, using the slowness-time coherence （STC） method we can only get phase velocities. Second, according to the results of the dispersion analysis and branch-cut integration, in a rigid boundary borehole model the results of dispersion curves and the waveforms of the first-order mode show that the velocities obtained by the STC method are phase velocities while group velocities obtained by arrival time picking. Finally, dipole logging in a slow formation model is investigated using dispersion analysis and real-axis integration. The results of dispersion curves and full wave trains show similar conclusions as the borehole model with rigid boundary conditions.
声波测井过程中获取的速度到底是相速度还是群速度,目前仍存在一些争议,本文从理论分析和数值模拟的角度,使用三种模型对这一问题进行了研究。首先,构造一个相速度与群速度可调的稳态声波传播模型——不同声速的两个平面波叠加模型,利用慢度时间相关(STC)方法提取声波波速,数值模拟结果表明,无论相速度较大或是群速度较大,STC方法提取出来的波速都是相速度;其次,通过频散分析和割线积分得到刚性壁圆柱流体模型中的频散曲线与分波波形,使用STC方法得到的速度与相速度的频散曲线吻合较好,而直接读取波至获得的速度与群速度的频散曲线趋势一致;最后,利用频散分析和实轴积分方法,获得偶极子在慢地层中激发的模式及全波波形,得到的结果再次验证了刚性壁圆柱流体模型中的结论。
基金
supported by the National Natural Science Foundation of China (Grant No. 40774099, 10874202 and 11134011)
National 863 Program of China (Grant No. 2008AA06Z205)
