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.