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.

Geosteering of wells requires fast interpretation of geophysical logs which is a non‐unique inverse problem. Current work presents a proof‐of‐concept approach to multi‐modal probabilistic inversion of logs using a single evaluation of an artificial deep neural network (DNN). A mixture density DNN (MDN) is trained using the ”multiple‐trajectory‐prediction” loss functions, which avoids mode collapse typical for traditional MDNs, and allows multi‐modal prediction ahead of data. The proposed approach is verified on the real‐time stratigraphic inversion of gamma‐ray logs. The multi‐modal predictor outputs several likely inverse solutions/predictions, providing more accurate and realistic solutions compared to a deterministic regression using a DNN. For these likely stratigraphic curves, the model simultaneously predicts their probabilities, which are implicitly learned from the training geological data. The stratigraphy predictions and their probabilities obtained in milliseconds from the MDN can enable better real‐time decisions under geological uncertainties.

SUMMARY: The advent of fast sensing technologies allow for real-time model updates in many applications where the model parameters are uncertain. Once the observations are collected, Bayesian algorithms offer a pathway for real-time inversion (a.k.a. model parameters/inputs update) because of the flexibility of the Bayesian framework against non-uniqueness and uncertainties. However, Bayesian algorithms rely on the repeated evaluation of the computational models and deep learning (DL) based proxies can be useful to address this computational bottleneck. In this paper, we study the effects of the approximate nature of the deep learned models and associated model errors during the inversion of borehole electromagnetic (EM) measurements, which are usually obtained from logging while drilling. We rely on the iterative ensemble smoothers as an effective algorithm for real-time inversion due to its parallel nature and relatively low computational cost. The real-time inversion of EM measurements is used to determine the subsurface geology and properties, which are critical for real-time adjustments of the well trajectory (geosteering). The use of deep neural network (DNN) as a forward model allows us to perform thousands of model evaluations within seconds, which is very useful to quantify uncertainties and non-uniqueness in real-time. While significant efforts are usually made to ensure the accuracy of the DL models, it is widely known that the DNNs can contain some type of model-error in the regions not covered by the training data, which are unknown and training specific. When the DL models are utilized during inversion of EM measurements, the effects of the model-errors could manifest themselves as a bias in the estimated input parameters and as a consequence might result in a low-quality geosteering decision. We present numerical results highlighting the challenges associated with the inversion of EM measurements while neglecting model-error. We further demonstrate the utility of a recently proposed flexible iterative ensemble smoother in reducing the effect of model-bias by capturing the unknown model-errors, thus improving the quality of the estimated subsurface properties for geosteering operation. Moreover, we describe a procedure for identifying inversion multimodality and propose possible solutions to alleviate it in real-time.

Hydrocarbon reservoirs are often located in spatially complex and uncertain geologic environments, where the associated costs of drilling wells for exploration and development are notoriously high. These costs may be reduced with an optimized well-placement strategy based on real-time geologic information, known as well geosteering. To effectively place the well in an updated geomodel and support well geosteering decisions in real time, we apply an iterative inversion approach based on the Levenberg-Marquardt form of the ensemble randomized maximum likelihood method. The method estimates geomodel properties together with their uncertainties by reducing the statistical misfit between the measurements acquired with well-logging tools and the predicted measurements from numerical simulations. Analyses of synthetic cases indicate that the method’s reliability and computational speed depend on the distance from the logging tool to formation boundaries, the contrast of model properties, and the thickness of formation layers. Our method delivers reliable estimates of model properties with only 40 ensemble members and 2–10 iterations; hence, it is approximately 10–125 times faster than Metropolis-Hastings Monte Carlo, which we use as a baseline condition given its proven track record. Likewise, our method is amenable to parallelization to further reduce computational times. Implementation of the method with a synthetic example inspired by a historical well geosteering operation yields accurate formation evaluation and verifies its accurate and reliable performance under complex geologic conditions.