用阵列感应测井曲线重建二维电阻率剖面

Reconstructing Two dimensional Resistivity Profile Using Array Induction Logs

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。

A new method is presented to reconstruct resistivity profile σ(ρ,z) in this paper. The two dimensional meridian ellipse is divided into rectangular intervals, which can be considered as pixels if the divisions are fine enough. The matrix for calculating apparent conductivities is obtained from the calculated integral geometrical factors of the pixels. On the bisis of quasi linear approximation theory, two dimensional resistivity profile can be reconstructed using the real time inversion of array induction synthetic matrix. In synthesizing the inverse matrix, singular value decomposition (SVD) and Tikhonor regularization method (TRM) are used for solving a question which is not propely posed. In essence, it is a problem of restoration and reconstruction of imcomplete observation data.