倾斜地层中的井孔声场研究

研究声波在倾斜充液井孔中的传播对于声波测井数据处理和解释具有重要意义.应用三维交错网格有限差分方法模拟了处于倾斜各向同性分层地层中的井孔声场.首先，针对均匀地层中单极子声源在裸眼井中激发的声场，将有限差分的结果和实轴积分法的结果进行对比验证.然后，采用单极子和偶极子两种声源，针对地层分界面和井轴间的不同倾角，计算了相应的声场分布和井轴上的接收波形.数值计算的结果表明，当声源处于倾斜分界面以下，即处于快速（下方）地层，接收器处于倾斜分界面以上（慢速）地层时，随着地层倾斜角度的加大，测得的慢度值从接近上方慢速地层值逐渐减小直至接近下方快速地层的值.任何源距情况下测得的首波慢度均小于上方地层实际的纵波慢度.并且，慢度与源距的关系曲线随源距的加大逐渐平缓.用偶极子声源激发得到的横波慢度与纵波结果相同，并表现得比纵波对倾角的改变更敏感.上述结论在本文中用声场快照和利用合成接收波列的慢度计算得以清楚显示，并且用射线声学理论验证.

Acoustic wave propagation in a borehole penetrating an inclined layered formation

Understanding acoustic wave propagation in an inclined fluid-filled borehole embedded in 3-D media is essential for acoustic wave logging data processing and interpretation. A 3-D staggered finite-difference (FD) method is used to simulate borehole sonic waves in isotropic inclined layered formations. First, the FD results are compared with those obtained by a Real Axis Integration method for a monopole source in an open borehole vertically imbedded in homogeneous formation. A good agreement has been made for the two methods. Consequently, the FD solutions are confirmed by the analytical solutions. Then, the waveforms for a borehole with various deviations between the borehole axis and the formation interface are calculated. Those for dipole sources are also simulated at a low source centre frequency. The numerical results show that, when the source is under the inclined interface, equivalently going up in a fast (downward) formation, and also as the interface inclined angle increases, the determined slowness curves decreases from the slowness approximately correspondent to that of the slow (upward) formation, to the one in downward formation, and never reaches the real compressional slowness in the upward formation. The corresponding slowness curve, with respect to record points, and above the formation interface, becomes flatter for a long spacing; while the short spacing detection makes the curve sharper. For all spacing with receivers in the upward formation, and the source under the interface in the downward formation, the apparent slowness becomes smaller than the real wave slowness in the upward formation. The larger the inclined angle, the flatter the curves away from the interface range for the large spacing. The shear wave slowness appears the similar features but more sensitive to the inclined angle than the compressional slowness. Also, this effect is controlled by the velocity contrast between the upward and downward formations. The above phenomenon is shown clearly in both snapshot visualization and in slowness calculations with synthetic waveforms, and is well explained with the ray acoustics.