用迭代反演算法进行二维井间电磁成像

Two dimensional Crosshole Electromagnetic Imaging with an Iterative Inversion Method

魏宝君，张中庆，张庚骥．用迭代反演算法进行二维井间电磁成像．测井技术，１９９８，２２（６）：４０７～４１１提出了一种基于逐次逼近解法的迭代反演算法对井间地层电导率的构造进行成像。该方法应用一阶Ｂｏｒｎ近似将积分方程线性化，得到对电导率分布的初始估计，在迭代反演中应用高阶Ｂｏｒｎ近似对井间地层电导率构造作更精确的估计。数值计算结果表明，这种迭代反演算法与基于Ｂｏｒｎ近似、二阶Ｂｏｒｎ近似和扩展Ｂｏｒｎ近似的反演算法相比提高了成像分辨率，而计算效率相当。应用该方法还可以对井间电导率分布进行二次成像。

An iterative inversion method based on SAM is developed to image the earth′s conductivity structure between two holes. The method employs the first Born approximation to linearize the integral equation formulation, and an initial estimate of the conductivity is obtained. A higher order Born approxiamation is applied in an iterative manner to achieve better estimates of the structure. Numerical results indicate that the iterative inversion method improves resolution compared with other inversion methods based on Born approximation or second Born approximation or extended Born approximation, and has the same computational efficiency. The method can also be applied to re image the earth′s conductivity structure.