Automated machine learning for borehole resistivity measurements

Deep neural networks (DNNs) offer a real-time solution for the inversion of borehole resistivity measurements to approximate forward and inverse operators. It is possible to use extremely large DNNs to approximate the operators, but it demands a considerable training time. Moreover, evaluating the network after training also requires a significant amount of memory and processing power. In addition, we may overfit the model. In this work, we propose a scoring function that accounts for the accuracy and size of the DNNs compared to a reference DNN that provides a good approximation for the operators. Using this scoring function, we use DNN architecture search algorithms to obtain a quasi-optimal DNN smaller than the reference network; hence, it requires less computational effort during training and evaluation. The quasi-optimal DNN delivers comparable accuracy to the original large DNN.

Design of borehole resistivity measurement acquisition systems using deep learning

Borehole resistivity measurements recorded with logging-while-drilling (LWD) instruments are widely used for characterizing the earth's subsurface properties. They facilitate the extraction of natural resources such as oil and gas. LWD instruments require real-time inversions of electromagnetic measurements to estimate the electrical properties of the earth's subsurface near the well and possibly correct the well trajectory. Deep Neural Network (DNN)-based methods are suitable for the rapid inversion of borehole resistivity measurements as they approximate the forward and inverse problem offline during the training phase and they only require a fraction of a second for the evaluation (aka prediction). However, the inverse problem generally admits multiple solutions. DNNs with traditional loss functions based on data misfit are ill-equipped for solving an inverse problem. This can be partially overcome by adding regularization terms to a loss function specifically designed for encoder-decoder architectures. But adding regularization seriously limits the number of possible solutions to a set of a priori desirable physical solutions. To avoid this, we use a two-step loss function without any regularization. In addition, to guarantee an inverse solution, we need a carefully selected measurement acquisition system with a sufficient number of measurements. In this work, we propose a DNN-based iterative algorithm for designing such a measurement acquisition system. We illustrate our DNN-based iterative algorithm via several synthetic examples. Numerical results show that the obtained measurement acquisition system is sufficient to identify and characterize both resistive and conductive layers above and below the logging instrument. Numerical results are promising, although further improvements are required to make our method amenable for industrial purposes.

Error Control and Loss Functions for the Deep Learning Inversion of Borehole Resistivity Measurements

Deep learning (DL) is a numerical method that approximates functions. Recently, its use has become attractive for the simulation and inversion of multiple problems in computational mechanics, including the inversion of borehole logging measurements for oil and gas applications. In this context, DL methods exhibit two key attractive features: a) once trained, they enable to solve an inverse problem in a fraction of a second, which is convenient for borehole geosteering operations as well as in other real-time inversion applications. b) DL methods exhibit a superior capability for approximating highly-complex functions across different areas of knowledge. Nevertheless, as it occurs with most numerical methods, DL also relies on expert design decisions that are problem specific to achieve reliable and robust results. Herein, we investigate two key aspects of deep neural networks (DNNs) when applied to the inversion of borehole resistivity measurements: error control and adequate selection of the loss function. As we illustrate via theoretical considerations and extensive numerical experiments, these interrelated aspects are critical to recover accurate inversion results.