不完全LU分解预条件BICGSTAB算法实现感应测井二维FDFD快速正演模拟

摘要

The difference scheme of the 2D induction logging in cylindrical coordinates was derived, and the finite deference frequency-domain method was employed to solve the induction logging forward modeling problem. Based on the fact that the coefficient matrix was a large sparse, complex and ill-posed matrix and the linear system was difficult to solve, the bi-conjugate gradient stabilized (BICGSTAB) algorithm with incomplete LU factorization precondictioning was employed to solve this ill-posed linear system. The results show that this algorithm has advantages of high performance, high precision and stability and can improve the performance and the precision of induction logging forward modeling.%在柱坐标系下推导了二维感应测井差分格式,采用频率域有限差分方法求解感应测井正演问题.针对差分近似得到的线性方程组系数矩阵是大型稀疏复系数病态矩阵求解困难等问题,采用不完全LU分解预条件的稳定双共轭梯度( BICGSTAB)算法求解该线性方程组.研究结果表明,本算法具有速度快、精度高和稳定性好等优点,能有效提高感应测井正演模拟的效率和精度.