井孔压力与地层应力集中诱导的偶极弯曲波的分裂

利用在大形变基础上叠加小扰动的非线性波动理论——声弹性理论，数值考察了井外均匀各向同性固体介质同时受井孔静压力和井外单轴水平压力作用时，Stoneley波和两种偏振的偶极弯曲波的相速度频散曲线，并研究了计算中用到的灵敏系数随频率的变化. 数值结果表明，模式波相速度频散曲线的变化主要受灵敏系数中对应的3个三阶弹性常数的项控制；由井孔周围应力集中引起的沿单轴压力方向和垂直于该方向偏振的弯曲波发生分裂，同时随频率的增大，两条频散曲线产生交叉；井孔静压力的作用使两条频散曲线交叉点的位置发生变化，交叉点相速度值随井孔压力的增加而增大，但对应的频率值不变.

DIPOLE FLEXURAL WAVES SPLITTING INDUCED BY BOREHOLE PRESSURIZATION AND FORMATION STRESS CONCENTRATION

Based on the theory of acoustoelasticity, which is concerned with small deformation superimposed upon large initial strain, we numerically calculate the Stoneley and flexural mode dispersion curves in a fluid-filled borehole which is pressurized by fluid and uniaxially stressed solid formation. Computational results show that the fractional changes in the phase velocity are most sensitive to frequency sensitivity coefficient C m_2 , C m_3 and C m_4 , corresponding to three third-order elastic constant c_ 111 , c_ 112 and c_ 123 , respectively, for formations with higher degree of nonlinearity. The results also indicate that the velocity increases at the crossover point of dispersion curves for both flexural waves polarized parallel and perpendicular to the stress direction along with borehole pressure increase.