声测井中的声压—速度有限差分方法

PRESSUREVELOCITY FINITE DIFFERENCE METHOD IN ACOUSTIC LOGGING

为了解决薄互储层的声测井问题，提出了声压—速度有限差分方法：用声压和速度矢量做为场变量，分别描述井内流体和井外弹性固体或双相介质。这样选择场变量的优点是：处理脉冲点源（或线源）与套网格技术相比简单得多；在内边界上的差分格式稳定，精度得到了改进；人为边界上的吸收效果较好。用柱坐标分别给出了井壁上流体与弹性固体、流体与双相介质的声压—速度边界条件，并用守恒积分方法处理了井壁上的边界条件。通过用声压—速度有限差分方法模拟弹性固体和双相介质地层的声场，证明了声压—速度有限差分方法的有效性。

A pressurevelocity finitedifference (PVFD) method is presented for simulating the transient acoustic field of the acoustic logging problem with horizontal multilayer elastic solid or twophase media formation. In this method, the pressure and velocity are, respectively, chosen as the variables to describe the motion of media inside and outside the borehole. The boundary conditions for pressure and velocity at borehole wall are given in cylindrical coordinate, and they are treated by conservation integral method. The PVFD method has some advantages, especially for solving the acoustic logging problem. The treatment of singular point source is more simpler. Innerboundary equations at the borehole wall established with pressure and velocity is of advantage for calculating stability. The absorbing effect of the artificial boundaries can be got improvement. By comparing with the results of Fourier transform under the circumstance of the homogeneous formation outside the borehole, and simulating the acoustic pressure field with the horizontallayered elastic solid formation, the effectiveness and accuracy of this method has been examined. 