径向速度变化地层井孔声场的快速模拟
Fast modeling of borehole acoustic p-waves in the presence of radial velocity variation

在声波测井过程中,为了精细刻画井孔附近岩石和流体特性所引起的速度径向变化规律,常用的方法是对井孔到原状地层的区域进行径向分层,然后利用传播矩阵的方法来模拟丼周的速度变化,然而,这种方法用于波形数据反演的过程中十分耗时。提出了一种利用Born近似快速模拟纵波速度径向变化的方法。推导了速度扰动时散射场积分表达式,并据此计算径向速度扰动模型下的散射声场,得到其近似解析解。数值模拟结果表明,与传统的方法相比,新的近似解能给出合理的模拟结果,提供了一种利用声波波形数据反演速度径向变化的新思路。
Traditionally, borehole acoustic modeling of radial formation changes is done with a propagator matrix method, which, however, is time-consuming in inversion processing. In this study, the use of the Born approximation for a fast modeling of the radial velocity variation is proposed. The integral expression for the perturbed acoustic wave field is derived, and an approximate analytical solution for it is obtained. Compared with exact modeling, the approximate solution gives reasonably accurate results when the Born condition is satisfied, and provides a fast forward model for the waveform inversion of radial velocity variation by using borehole acoustic data.