A Supervised Descent Learning Technique for Solving Directional Electromagnetic Logging-While-Drilling Inverse Problems

In this article, a new scheme based on the supervised descent method (SDM) for solving directional electromagnetic logging-while-drilling (LWD) inverse problems is proposed. The SDM provides us a new perspective to combine the classical gradient-based inversion and machine-learning-based inversion schemes. It iteratively learns a set of descent directions in the offline training process, where the training model set is generated in advance according to the prior information, and then updates the models with the learned descent directions as well as data residuals in the prediction stage, resulting in great flexibility to incorporate prior information, the capability of skipping local minima, and accelerated convergence. The generalization ability of the SDM to interrogate new models that are not contained in the training model set is also explored. By utilizing real-time information obtained from the logging process, the learned descent directions can be slightly revised with a higher efficiency to get closer to the true model. In addition, we probe the sensitivity of the SDM by adding different levels of random noise to the measurements. Numerical examples demonstrate that SDM-based inversion can achieve a higher resolution, faster convergence, and higher robustness than conventional schemes such as Occam's inversion.