Mostafa Shahriari

M. Shahriari, A. Hazra, D. Pardo

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.

Sergey Alyaev, Mostafa Shahriari, David Pardo et al.

Modern geosteering is heavily dependent on real-time interpretation of deep electromagnetic (EM) measurements. We present a methodology to construct a deep neural network (DNN) model trained to reproduce a full set of extra-deep EM logs consisting of 22 measurements per logging position. The model is trained in a 1D layered environment consisting of up to seven layers with different resistivity values. A commercial simulator provided by a tool vendor is used to generate a training dataset. The dataset size is limited because the simulator provided by the vendor is optimized for sequential execution. Therefore, we design a training dataset that embraces the geological rules and geosteering specifics supported by the forward model. We use this dataset to produce an EM simulator based on a DNN without access to the proprietary information about the EM tool configuration or the original simulator source code. Despite employing a relatively small training set size, the resulting DNN forward model is quite accurate for the considered examples: a multi-layer synthetic case and a section of a published historical operation from the Goliat Field. The observed average evaluation time of 0.15 ms per logging position makes it also suitable for future use as part of evaluation-hungry statistical and/or Monte-Carlo inversion algorithms within geosteering workflows.

M. Shahriari, D. Pardo, J. A. Rivera et al.

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.

M. Shahriari, D. Pardo, A. Picón et al.

We use borehole resistivity measurements to map the electrical properties of the subsurface and to increase the productivity of a reservoir. When used for geosteering purposes, it becomes essential to invert them in real time. In this work, we explore the possibility of using Deep Neural Network (DNN) to perform a rapid inversion of borehole resistivity measurements. Herein, we build a DNN that approximates the following inverse problem: given a set of borehole resistivity measurements, the DNN is designed to deliver a physically meaningful and data-consistent piecewise one-dimensional layered model of the surrounding subsurface. Once the DNN is built, we can perform the actual inversion of the field measurements in real time. We illustrate the performance of DNN of logging-while-drilling measurements acquired on high-angle wells via synthetic data.