Inverse problems appear in multiple industrial applications. Solving such inverse problems require the repeated solution of the forward problem. This is the most time-consuming stage when employing inversion techniques, and it constitutes a severe limitation when the inversion needs to be performed in real-time. In here, we focus on the real-time inversion of resistivity measurements for geosteering. We investigate the use of a deep neural network (DNN) to approximate the forward function arising from Maxwell’s equations, which govern the electromagnetic wave propagation through a media. By doing so, the evaluation of the forward problems is performed offline, allowing for the online real-time evaluation (inversion) of the DNN.

In some geological formations, borehole resistivity measurements can be simulated using a sequence of 1D models. By considering a 1D layered media, we can reduce the dimensionality of the problem from 3D to 1.5D via a Hankel transform. The resulting formulation is often solved via a semi-analytic method, mainly due to its high performance. However, semi-analytic methods have important limitations such as, for example, their inability to model piecewise linear variations on the resistivity. Herein, we develop a multi-scale finite element method (FEM) to solve the secondary field formulation. This numerical scheme overcomes the limitations of semi-analytic methods while still delivering high performance. We illustrate the performance of the method with numerical synthetic examples based on two symmetric logging-while-drilling (LWD) induction devices operating at 2 MHz and 500 KHz, respectively.

In the last decade, industry’s demand for deep learning (DL) has increased due to its high performance in complex scenarios. Due to the DL method’s complexity, experts and non-experts rely on blackbox software packages such as Tensorflow and Pytorch. The frameworks are constantly improving, and new versions are released frequently. As a natural process in software development, the released versions contain improvements/changes in the methods and their implementation. Moreover, versions may be bug-polluted, leading to the model performance decreasing or stopping the model from working. The aforementioned changes in implementation can lead to variance in obtained results. This work investigates the effect of implementation changes in different major releases of these frameworks on the model performance. We perform our study using a variety of standard datasets. Our study shows that users should consider that changing the framework version can affect the model performance. Moreover, they should consider the possibility of a bug-polluted version before starting to debug source code that had an excellent performance before a version change. This also shows the importance of using virtual environments, such as Docker, when delivering a software product to clients.

Modern geosteering is heavily dependent on real-time interpretation of deep electromagnetic (EM) measurements. We have developed 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 data set. The data set size is limited because the simulator provided by the vendor is optimized for sequential execution. Therefore, we design a training data set that embraces the geologic rules and geosteering specifics supported by the forward model. We use this data set 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 using a relatively small training set size, the resulting DNN forward model is quite accurate for the considered examples: a multilayer 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.

Deep neural network (DNN)-based methods are suitable for the rapid inversion of borehole resistivity measurements. They approximate the forward and the inverse problem offline during the training phase, and they only require a fraction of a second for the online evaluation (aka prediction). Herein, we have adopted a DNN-based iterative algorithm to design a borehole instrument such that the inverse solution is unique for a given earth parameterization. We select a large set of electromagnetic measurement systems routinely used in logging operations, and our DNN algorithm selects a subset of measurements that are suitable for inversion purposes. Numerical results with synthetic data confirm that this approach can provide valuable insight when designing borehole-logging instruments.