横向各向同性地层斜井中正交偶极子激发声场的数值模拟

本文采用三维应力-速度有限差分(SV-FD)方法,数值模拟了横向各向同性(TI)地层对称主轴与井轴斜交情况下正交偶极子声源激发的井孔声场.主要解决了与倾斜角有关的三维空间弹性模量矩阵的推导,柱坐标系下应力-速度有限差分方程组的建立,井轴上场点奇异性与内边界处理等几个关键问题,提高了计算精度.在横向各向同性地层对称主轴与井轴平行的情况下,与实轴积分法所得结果进行了对比,验证了本文方法的正确性.计算了不同倾角情况下xx和yy两分量的弯曲波,并用频域加权相似法提取了弯曲波频散曲线,结果显示了横向各向同性介质中不同方向偏振的弯曲波传播的分裂现象,其频散曲线在低频段分裂,随频率增大而逐渐重合.弯曲波低频截止频率处速度与理论公式得到的横波速度基本符合.

Numerical simulation of acoustic fields excited by cross-dipole source in deviated wells in transversely isotropic formation

The acoustic fields excited by cross-dipole acoustic source in borehole surrounded by transversely isotropic (TI) formation, whose symmetry axis is oblique, are numerically simulated by 3D stress velocity finite difference (SV-FD) method. Several key problems are resolved to improve the computational accuracy, such as derivation of modulus matrix related to oblique angle, establishment of SV-FD equations under cylindrical coordinates, and treatment of singular points on borehole axis. The method is validated by comparing numerical result with that obtained by real axis integration method, when the symmetry axis of TI formation is parallel with borehole axis. The flexural waveforms of xx and yy components of borehole acoustic fields with various dip angles are simulated, and the dispersion curves of flexural waves are obtained by weighted spectral semblance method. The results show obvious splitting of flexural wave with different polarization in TI formation. The dispersion curves of xx and yy split at low-frequency, and overlap at high-frequency. The velocities at low-frequency cut-off frequencies agree with those calculated by theoretical formula.