Error Control and Loss Functions for the Deep Learning Inversion of Borehole Resistivity Measurements
Software Competence Center Hagenberg (SCCH)（哈根贝格软件能力中心（SCCH））；Euskampus Fundazioa（巴斯克校园基金会）；University of the Basque Country (UPV/EHU)（巴斯克大学（UPV/EHU））；Ikerbasque (Basque Foundation for Sciences)（伊克巴斯克（巴斯克科学基金会））；The University of Texas at Austin（德克萨斯大学奥斯汀分校）；Tecnalia（泰克纳利亚）；Basque Research & Technology Alliance（巴斯克研究与技术联盟）；Pontificia Universidad Católica de Valparaíso（瓦尔帕莱索天主教大学）；Curtin University（科廷大学）
M. Shahriari, D. Pardo, J. A. Rivera, C. Torres-Verdín, A. Picon, J. Del Ser, S. Ossandón, V. M. Calo
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.
Full-waveform inversion (FWI) is a technique having the potential for building high-resolution elastic velocity models. We proposed to apply this technique to wireline monopole acoustic logging data to obtain the near wellbore formation velocity structures, which can be used in wellbore damage or fluid intrusion evaluation. A 2D FWI using monopole acoustic logging data is presented. The FWI is established in cylindrical coordinates instead of Cartesian coordinates in order to adapt to the borehole geometry. A preconditioner is designed for suppressing the influence of the strong borehole guide…
With the rapid development of deep learning, intelligent scheme is gradually introduced to solve various nolinear inverse problems. In this paper, we combine an efficient adaptive deep neural network (ADNN) framework with adaptive modified Levenberg-Marquardt (AMLM) algorithm based on three-layer inversion model to exact formation resistivity and invasion depth from array laterolog resistivity measurements. ADNN presented in this paper can realize the 2D/3D fast forward modeling of array laterolog. AMLM algorithm and hierarchical inversion scheme are adopted to improve the anti-noise ability a…
In Paris Basin, we evaluate how HTEM data complement the usual borehole, geological and deep seismic data used for modelling aquifer geometries. With these traditional data, depths between ca. 50 to 300m are often relatively ill-constrained, as most boreholes lie within the first tens of meters of the underground and petroleum seismic is blind shallower than ca. 300m. We have fully reprocessed and re-inverted 540km of flight lines of a SkyTEM survey of 2009, acquired on a 40x12km zone with 400m line spacing. The resistivity model is first "calibrated" with respect to ca. 50 boreholes available…
We develop a quantitative predictive model for the state of stress of a volume of crust encompassing the Duvernay Formation with a spatial extent of over 150 km x 150 km centred near the municipality of Fox Creek. An average direction of the maximum horizontal compression SH is of N43°E, determined from analysis of 20 borehole image logs. A model of the vertical stress SV, corrected for topographic variations, is provided from the integration of a 3D density volume constructed from 1125 density logs. The minimum horizontal compressions Sh and pore pressures PP are evaluated through analysis of…
The advent of fast sensing technologies allows for real-time model updates in many applications where the model parameters are uncertain. Bayesian algorithms, such as ensemble smoothers, offer a real-time probabilistic inversion accounting for uncertainties. However, they rely on the repeated evaluation of the computational models, and deep neural network (DNN) based proxies can be useful to address this computational bottleneck. This paper studies the effects of the approximate nature of the deep learned models and associated model errors during the inversion of extra-deep borehole electromag…
Deep Learning (DL) inversion is a promising method for real time interpretation of logging while drilling (LWD) resistivity measurements for well navigation applications. In this context, measurement noise may significantly affect inversion results. Existing publications examining the effects of measurement noise on DL inversion results are scarce. We develop a method to generate training data sets and construct DL architectures that enhance the robustness of DL inversion methods in the presence of noisy LWD resistivity measurements. We use two synthetic resistivity models to test three approa…
The standard smooth electrical resistivity tomography inversion produces an estimate of subsurface conductivity that has blurred boundaries, damped magnitudes, and often contains inversion artifacts. In many problems the expected conductivity structure is well constrained in some parts of the subsurface, but incorporating prior information in the inversion is not a trivial task. In this study we developed an electrical resistivity tomography inversion algorithm that combines parametric and smooth inversion strategies. In regions where the subsurface is well constrained, the model was parameter…
Current methods of estimating the change in stress caused by injecting fluid into subsurface formations require choosing the type of constitutive model and the model parameters based on core, log, and geophysical data during the characterization phase, with little feedback from operational observations to validate or refine these choices. It is shown that errors in the assumed constitutive response, even when informed by laboratory tests on core samples, are likely to be common, large, and underestimate the magnitude of stress change caused by injection. Recent advances in borehole-based strai…
University of Cagliari（卡利亚里大学）；GEUS—Geological Survey of Denmark and Greenland（丹麦和格陵兰地质调查局）；Aarhus Geophysics ApS（奥胡斯地球物理公司）；University of Oulu（奥卢大学）
The possibility to have results very quickly after, or even during, the collection of electromagnetic data would be important, not only for quality check purposes, but also for adjusting the location of the proposed flight lines during an airborne time-domain acquisition. This kind of readiness could have a large impact in terms of optimization of the Value of Information of the measurements to be acquired. In addition, the importance of having fast tools for retrieving resistivity models from airborne time-domain data is demonstrated by the fact that Conductivity-Depth Imaging methodologies a…
Probabilistic inversion methods based on Markov chain Monte Carlo (MCMC) simulation are well suited to quantify parameter and model uncertainty of nonlinear inverse problems. Yet, application of such methods to CPU-intensive forward models can be a daunting task, particularly if the parameter space is high dimensional. Here, we present a two-dimensional (2D) pixel-based MCMC inversion of plane-wave electromagnetic (EM) data. Using synthetic data, we investigate how model parameter uncertainty depends on model structure constraints using different norms of the likelihood function and the model …
School of Qilu Transportation, Shandong University（山东大学齐鲁交通学院）；Geotechnical and Structural Engineering Research Center, Shandong University（山东大学岩土与结构工程研究中心）；Data Science Institute, Shandong University（山东大学数据科学研究院）
The inverse problem of electrical resistivity surveys (ERSs) is difficult because of its nonlinear and ill-posed nature. For this task, traditional linear inversion methods still face challenges such as suboptimal approximation and initial model selection. Inspired by the remarkable nonlinear mapping ability of deep learning approaches, in this article, we propose to build the mapping from apparent resistivity data (input) to resistivity model (output) directly by convolutional neural networks (CNNs). However, the vertically varying characteristic of patterns in the apparent resistivity data m…
The reliability of surface-based electrical resistivity tomography (ERT) for quantifying resistivities for shallow subsurface water processes is analysed. A method comprising numerical simulations of water movement in soil and forward-inverse modeling of ERT surveys for two synthetic data sets is presented. Resistivity contrast, e.g. by changing water content, is shown to have large influence on the resistivity quantification. An ensemble and clustering approach is introduced in which ensembles of 50 different inversion models for one data set are created by randomly varying the parameters for…
Within the framework of a global French program oriented towards the development of renewable energies, Martinique Island (Lesser Antilles, France) has been extensively investigated (from 2012 to 2013) through an integrated multi-methods approach, with the aim to define precisely the potential geothermal ressources, previously highlighted (Sanjuan et al., 2003). Amongst the common investigation methods deployed, we carried out three magnetotelluric (MT) surveys located above three of the most promising geothermal fields of Martinique, namely the Anses d'Arlet, the Montagne Pel{é}e and the Pito…
Fluid flow in the vadose zone is governed by Richards equation; it is parameterized by hydraulic conductivity, which is a nonlinear function of pressure head. Investigations in the vadose zone typically require characterizing distributed hydraulic properties. Saturation or pressure head data may include direct measurements made from boreholes. Increasingly, proxy measurements from hydrogeophysics are being used to supply more spatially and temporally dense data sets. Inferring hydraulic parameters from such datasets requires the ability to efficiently solve and deterministically optimize the n…
When solving inverse problems in geophysical imaging, deep generative models (DGMs) may be used to enforce the solution to display highly structured spatial patterns which are supported by independent information (e.g. the geological setting) of the subsurface. In such case, inversion may be formulated in a latent space where a low-dimensional parameterization of the patterns is defined and where Markov chain Monte Carlo or gradient-based methods may be applied. However, the generative mapping between the latent and the original (pixel) representations is usually highly nonlinear which may cau…
Geophysical inversion attempts to estimate the distribution of physical properties in the Earth's interior from observations collected at or above the surface. Inverse problems are commonly posed as least-squares optimization problems in high-dimensional parameter spaces. Existing approaches are largely based on deterministic gradient-based methods, which are limited by nonlinearity and nonuniqueness of the inverse problem. Probabilistic inversion methods, despite their great potential in uncertainty quantification, still remain a formidable computational task. In this paper, I explore the pot…
A Jacobian-free inversion method is presented to accelerate Electrical Resistivity Tomography (ERT) for shallow aquifer characterization. The ERT problem typically implements the adjoint state method to efficiently compute Jacobian during the inversion. However, the adjoint state method needs intrusive forward model code changes and may not be computationally scalable with many observations especially when one performs 3D ERT surveys with dense multi-electrode arrays. Here the Principal Component Geostatistical Approach (PCGA), a fast and scalable Jacobian-free inverse modeling method, is appl…
3-D Magnetotelluric Deep Learning Inversion Guided by Pseudo-Physical Information
Key Laboratory of Earth Exploration and Information Techniques of Ministry of Education, College of Geophysics, Chengdu University of Technology（教育部地球探测与信息技术重点实验室，成都理工大学地球物理学院）；College of Computer Science and Cyber Security, Chengdu University of Technology（成都理工大学计算机科学与网络security学院）
Electrical Resistivity Tomography (ERT) has been extensively used for imaging the subsurface resistivity distribution and structure. Over the years, many algorithms have been developed in order to solve the subsurface resistivity distribution from the ERT measurements. In this paper a new method for interpreting the ERT measurements is presented. Using supervised learning to train a neural network, we are able to interpret the ERT measurement into a 2D image of the underground resistivity up to depths of 50 meters while using a simple Wenner-Schlumberger survey of 96 electrodes with 1 meter sp…
Airborne transient electromagnetic (TEM) is a cost-effective method to image the distribution of electrical conductivity in the ground. We consider layered earth inversion to interpret large data sets of hundreds of kilometre. Different strategies can be used to solve this inverse problem. This consists in managing the a priori information to avoid the mathematical instability and provide the most plausible model of conductivity in depth. In order to obtain fast and realistic inversion program, we tested three kinds of regularization: two are based on standard Tikhonov procedure which consist …
Seawater intrusion (SWI) is a complex process, where 3D modeling is often necessary in order to monitor and manage the affected aquifers. Here, we present a synthetic study to test a joint hydrogeophysical inversion approach aimed at solving the inverse problem of estimating initial and current saltwater distribution. First, we use a 3D groundwater model for variable density flow based on discretized flow and solute mass balance equations. In addition to the groundwater model, a 3D geophysical model was developed for direct current resistivity imaging and inversion. The objective function of t…
A Targeted Quadrature Framework for Simulating Large-Scale 3D Anisotropic Electromagnetic Measurements
Uppsala University（乌普萨拉大学）；Worcester Polytechnic Institute（伍斯特理工学院）；DEM Holding（3DEM控股公司）；The University of Texas at Austin（德克萨斯大学奥斯汀分校）；Equinor（挪威国家石油公司）
Physically Guided Deep Unsupervised Inversion for 1D Magnetotelluric Models
Universidad Industrial de Santander（桑坦德工业大学）；King Fahd University of Petroleum and Minerals（法赫德国王石油与矿产大学）；College of Petroleum Engineering and Geosciences（石油工程与地球科学学院）
Enhancing Deep Learning based RMT Data Inversion using Gaussian Random Field
Indian Institute of Technology (Indian School of Mines)（印度理工学院（印度矿业学院））；UiT The Arctic University of Norway（挪威北极大学）；Indian Institute of Petroleum & Energy（印度石油与能源研究院）；Transmute AI Lab (Texmin Hub)（Transmute AI实验室（Texmin中心））
本文针对深度学习 RMT 反演中的分布外泛化问题，提出用 Gaussian Random Fields 生成地下电阻率模型并端到端训练网络，在合成与现场数据中验证了其抗噪和泛化优势。
We present an algorithm for focusing inversion of electrical resistivity tomography (ERT) data. ERT is a typical example of ill-posed problem. Regularization is the most common way to face this kind of problems; it basically consists in using a priori information about targets to reduce the ambiguity and the instability of the solution. By using the minimum gradient support (MGS) stabilizing functional, we introduce the following geometrical prior information in the reconstruction process: anomalies have sharp boundaries. The presented work is embedded in a project (L.A.R.A.) which aims at the…
Pacific Northwest National Laboratory（太平洋西北国家实验室）；Virginia Tech（弗吉尼亚理工大学）
Time-lapse electrical resistivity tomography (ERT) is a popular geophysical method to estimate three-dimensional (3D) permeability fields from electrical potential difference measurements. Traditional inversion and data assimilation methods are used to ingest this ERT data into hydrogeophysical models to estimate permeability. Due to ill-posedness and the curse of dimensionality, existing inversion strategies provide poor estimates and low resolution of the 3D permeability field. Recent advances in deep learning provide us with powerful algorithms to overcome this challenge. This paper present…
