水平层状介质中双侧向测井资料的迭代Tikhonov正则化反演

Iterative Tikhonov regularization inversion for duai-laterolog in horizontally stratified media

根据非线性反演理论与Morozov偏差原理研究建立从双侧向测井(DLL)资料中同时重构地层原状电阻率、侵入带电阻率、侵入半径、层界面位置以及井眼泥浆电阻率的迭代正则化算法.首先利用Tikhonov正则化反演理论将双侧向测井资料的反演问题转化为含有稳定泛函的非线性目标函数的极小化问题,并利用Gauss-Newton算法确定极小化解.为得到稳定的反演结果并有效实现测井资料的最佳拟合,在迭代过程中将Morozov偏差原理和Cholesky分解技术相结合,建立了一套后验选择正则化因子的方法.最后通过理论模型和大庆油田实际测井资料的处理结果,验证了该算法能够取得更为满意的反演效果.

In this paper, we present an iterative regularization algorithm to simultaneously reconstruct all the model parameters, including the virgin formation resistivity, flushed zone resistivity, invasion radius, horizontal boundary depth and mud resistivity per bed, from duallaterolog （DLL） data based on nonlinear inversion theory and Morozov discrepancy principle. We firstly adopt Tikhonov regularization inversion theory to transform the inversion problem into the minimization problem of non-quadratic objective function with the stabilizing functional defined on model space, and use Gauss-Newton method to obtain the minimization of objective function. Then, the combination of Morozov discrepancy principle and Cholesky decomposition is executed to propose an a-posteriori regularization factor choice strategy in order to obtain a stable inversion solution as well as to realize best fit of input data with modeling logs. Finally, the inversion results of theoretical modeling data and field logs measured from Daqing oil field prove that the inversion method can produce more satisfactory effect.