基于非线性积分方程,利用井轴上阵列感应成像测井仪(AIT)的单频测量信号,将变形玻恩(Bom)迭代方法用于地球物理测井反演,用正则化方法求出地层电导率分布。文中首先给出对于未知电导率分布的非线性积分方程,然后用玻恩近似使非线性积分方程线性化,求出电导率分布。在迭代过程中,数值模式匹配法用于求解阵列感应的正演问题。数值计算表明,用井轴上 AIT 的单频测量信号得到的成像结果与真电导率剖面分布吻合较好。 Based on the nonlinear integral equation, the Bom iterative method was applied to geophysical logging inversion by using the single-frequency measurement signal of AIT on the shaft, and the regularization method was used to obtain the formation Conductivity distribution. In this paper, the nonlinear integral equation for the unknown conductivity distribution is given first, and then the nonlinear integral equation is linearized by Born approximation to find the conductivity distribution. In the iteration process, the numerical pattern matching method is used to solve the forward problem of array induction. The numerical results show that the imaging results obtained from the single-frequency measurement signal of AIT on the shaft coincides well with the distribution of true conductivity profiles.