A Robust Inversion of Induction Logging Responses in Anisotropic Formation Based on Supervised Descent Method

Abstract

In this letter, a novel inversion scheme based on the supervised descent method (SDM) for the logging responses interpretation of anisotropic formations is proposed. The inversion scheme combines the characteristics of traditional gradient-based methods and machine learning techniques. In the inversion process, the model parameters can be updated directly according to the descent directions collected from the training phase. Therefore, the inversion can flexibly incorporate the prior information and overcome the dependence of convergence on the initial values. It can also avoid local minima and accelerate global convergence. Moreover, the dynamic regularization scheme is adopted to reduce the ill-posedness of the problem, and the bagging algorithm is incorporated into the training process to reduce the overfitting and enhance the generalization ability. A series of numerical examples are investigated to test the inversion performance in anisotropic formations. Results show that the proposed inversion scheme for anisotropic formations has high accuracy, fast convergence, and strong robustness.