横向各向同性地层倾斜井中的声场模式分析  

Mode analyses in a deviated borehole penetrating a transversely isotropic formation

作　　者：刘乐[1] 林伟军[1] 张海澜[1] 王秀明[1] 

机构地区：[1]中国科学院声学研究所声场与声信息国家重点实验室,北京100190

出　　处：《地球物理学进展》2015年第2期797-804,共8页Progress in Geophysics

基　　金：国家自然科学基金重点项目(11134011;41274134);中国科学院"十二五"信息化专项超级计算重点应用示范项目(XXH12503-02-02-05)联合资助

摘　　要：针对横向各向同性地层包围的倾斜井模型,基于有限元方法求解频率一波数域波动方程,使用卷积完全匹配层进行数值截断.从计算得到的二维谱中可以直观地看到模式波的分布,继而得到模式波的相速度.与前人的方法相比,该方法对地层各向异性的强弱程度没有要求,可以计算强各向异性介质;此外,计算不依赖于具体的声源形式,可以在较宽的频率范围内进行,且准确度高,误差基本不超过1%.计算了不同倾斜角度、不同偶极源指向性条件下快、慢地层包围的倾斜井中的弯曲模式波的相速度频散曲线.计算结果表明,当井孔倾斜时,偶极源激发的弯曲波分裂成快、慢两条弯曲波,其低频速度分别趋近于地层的SH和qSV速度.接收器接收到的快、慢弯曲波的相速度由倾斜角决定,与声源指向角无关.本文中的方法具有较好的拓展性,可以很方便地修改以分析其他模型.The wave equation was solved in the frequency-wave number domain based on the finite element method to investigate the wave propagation in a deviated borehole penetrating an transversely isotropic formation. A eonvolutional perfectly matched layer was implemented to simulate the numerical truncation. The mode distribution was shown directly and clearly on the two dimension spectrum, so the phase velocity of the mode could be obtained afterwards. Compared with the perturbation method, the weak elastic anisotropy is not necessary as the derivation asks for nothing about the anisotropy parameters. And unlike FDTD, the computation was conducted in the frequency domain without carrying a specific source form. Results are obtained in a wider frequency range and with higher accuracy. The relative error of phase velocity is mostly less than 1 percent. Using this method, we calculated the phase velocity dispersion curves of the fiexural wave in a deviated borehole surrounded by a fast or slow formation with different deviation angles and dipole orientation. The results show that for such a deviated borehole, the flexural wave splits into fast and slow flexural waves, whose phase velocities are respectively equal to that of the SH and qSV wave of the transversely isotropic formation at low frequencies. Further study show that the phase velocities of the fast and slow fiexural waves were independent of the source or receiver orientation. The method used in this paper can be extended to other similar models with little modification.

关 键 词：倾斜井 弯曲波模式 频散曲线 有限元法 

分 类 号：P631[天文地球—地质矿产勘探]