Probabilistic model-error assessment of deep learning proxies: an application to real-time inversion of borehole electromagnetic measurements

Abstract

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 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 measurements, which are usually obtained from logging while drilling (LWD). 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 electromagnetic 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 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 deep learning models, it is widely known that the deep neural networks can contain some type of model-error in the regions not covered by the training data, which are unknown and training specific. When the deep learning models are utilized during inversion of electromagnetic 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 electromagnetic 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 multi-modality and propose possible solutions to alleviate it in real-time.

Verification of a real-time ensemble-based method for updating earth model based on GAN

“…The future work is to integrate the DA developed in this paper with the decision framework developed in [8], allowing DSS under a much more complex geological setting. Furthermore, the method can be extended to account for model errors present in machine learning approximations in real-time [13].…”

“…The proposal is sampled from the proposal distribution q ( m * | m). The move is performed with probability b ( m, m * ) = min (1, r ( m, m * )) (13) where the Hastings ratio is defined as…”

“…The forward deep neural network (FDNN) trained on synthetic data for extra-deep electromagnetic measurements [10] enabled the real-time ensemble-based update of layered models in 1.5D [11], and 3D [12]. Moreover, [13] showed that the model errors present in the FDNN approximation can be alleviated during the ensemble based inversion for the layered case.…”

Electromagnetic imaging and deep learning for transition to renewable energies: a technology review

“…Real-time DL inversion techniques also have the potential to perform statistical or probabilistic inversion processes (Alyaev et al, 2021). Real-time DL probabilistic inversion greatly improves the practicability of data-driven forward modeling in practical applications (Rammay et al, 2022). In addition, DL inversion methods also have great application potential in geophysical monitoring (Puzyrev, 2019).…”

Neural network architecture optimization using automated machine learning for borehole resistivity measurements

“…Some traditional methods to solve inverse problems include gradient-based and statistics-based approaches (Malinverno & T orres-Verd ín 2000 ;T arantola 2005 ;W atzenig 2007 ;Ijasana et al 2013 ;Pardo & Torres-Verd ín 2014 ;Jahani et al 2022 ). Artificial intelligence (AI) algorithms, particularly deep learning (DL), have recently become popular to solve inverse problems (Jin et al 2019b ;Puzyrev 2019 ;Shahriari et al 2020c , b ;Moghadas 2020 ;Hu et al 2020 ;Rammay et al 2022 ). In this work, we use a deep neural network (DNN) to approximate the solution of an inverse problem.…”