关键词: 声测井, 有限差分, 流体声压, 速度矢量

Abstract: 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.

Key words: acoustic logging, finite-difference, fluid pressure, velocity vector