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张中庆，张庚骥，储昭坦，谢树棋，等．用阵列感应测井曲线重建二维电阻率剖面．测井技术，１９９７，２１（２）：１１９～１２４采用阵列感应测井资料重建二维电导率剖面σ（ρ，ｚ），把二维子午面划分为矩形区间。如果区域划分足够精细，则可以视之为象素（ｐｉｘｅｌ），计算这些区域的积分几何因子，形成计算视电导率的矩阵。采用准线性近似，反求出阵列感应合成矩阵，用合成矩阵进行实时反演，获得二维电阻率剖面。在求合成矩阵的过程中，利用奇异值分解（ＳＶＤ）和吉洪诺夫正则化法来解决问题的不适定性。其实质是不完全观测数据的复杂重建问题。
Zhang Zhongqing, Zhang Gengji, Chu Zhaotan, Xie Shuqi, and so on. Reconstruction of two - dimensional resistivity profile with array induction logging curve. Logging Technology, 1997,21 (2): 119-124 Two-dimensional conductivity profile σ (ρ, z) is reconstructed using array-induced logging data and the two-dimensional meridian plane is divided into rectangular sections. If the regions are fine enough, they can be considered as pixels and the integral geometry of these regions can be calculated to form a matrix for calculating apparent conductivity. Using the quasi-linear approximation, the array-induced composite matrix is obtained inversely and the composite matrix is used for real-time inversion to obtain the 2D resistivity profile. In the process of finding the synthesis matrix, the singular value decomposition (SVD) and the Jikunov regularization method are used to solve the ill-posed problem. The essence is incomplete reconstruction of the observed data.