Preprint of the extended abstract submitted to the Near Surface Geoscience'24 Conference & Exhibition by the European Association of Geoscientists & Engineers (EAGE)
本文提出基于 CNN 的 PINNs 反演直流电阻率数据，并用 Monte Carlo dropout 量化不确定性，在合成与现场 Schlumberger 数据上取得与文献相当的结果。
摘要：
直流电阻率数据反演是一种广泛用于近地表表征的方法。近年来，基于深度学习的反演技术因其能够阐明地球物理数据与模型参数之间复杂的非线性关系而受到广泛关注。然而，这些方法面临训练数据可用性有限以及生成地质上不一致解等挑战。通过融合物理信息方法，可以缓解这些问题。此外，预测不确定性的量化至关重要，但在基于深度学习的反演方法中却常被忽视。本研究采用基于卷积神经网络（CNNs）的物理信息神经网络（PINNs）反演合成与现场 Schlumberger 测深数据，并通过 Monte Carlo dropout 估计预测不确定性。在合成案例和现场案例研究中，PINNs 估计的中位数剖面与现有文献结果相当，同时还能提供不确定性估计。因此，PINNs 在近地表表征的更广泛应用中展现出巨大潜力。
英文摘要：
The inversion of DC resistivity data is a widely employed method for near-surface characterization. Recently, deep learning-based inversion techniques have garnered significant attention due to their capability to elucidate intricate non-linear relationships between geophysical data and model parameters. Nevertheless, these methods face challenges such as limited training data availability and the generation of geologically inconsistent solutions. These concerns can be mitigated through the integration of a physics-informed approach. Moreover, the quantification of prediction uncertainty is crucial yet often overlooked in deep learning-based inversion methodologies. In this study, we utilized Convolutional Neural Networks (CNNs) based Physics-Informed Neural Networks (PINNs) to invert both synthetic and field Schlumberger sounding data while also estimating prediction uncertainty via Monte Carlo dropout. For both synthetic and field case studies, the median profile estimated by PINNs is comparable to the results from existing literature, while also providing uncertainty estimates. Therefore, PINNs demonstrate significant potential for broader applications in near-surface characterization.
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…
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…
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 …
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 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…
When hydrocarbon reservoirs are used as a CO2 storage facility, an accurate uncertainty analysis and risk assessment is essential. An integration of information from geological knowledge, geological modelling, well log data, and geophysical data provides the basis for this analysis. Modelling the time development of stress/strain changes in the overburden provides prior knowledge about fault and fracture probability in the reservoir, which in turn is used in seismic inversion to constrain models of faulting and fracturing. One main problem in solving large scale seismic inverse problems is hig…
Wavefield reconstruction inversion (WRI) formulates a PDE-constrained optimization problem to reduce cycle skipping in full-waveform inversion (FWI). WRI often requires expensive matrix inversions to reconstruct frequency-domain wavefields. Physics-informed neural network (PINN) uses the underlying physical laws as loss functions to train the neural network (NN), and it has shown its effectiveness in solving the Helmholtz equation and generating Green's functions, specifically for the scattered wavefield. By including a data-constrained term in the loss function, the trained NN can reconstruct…
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…
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）
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 …
California Institute of Technology（加州理工学院）；Purdue University（普渡大学）
We introduce a scheme for probabilistic hypocenter inversion with Stein variational inference. Our approach uses a differentiable forward model in the form of a physics informed neural network, which we train to solve the Eikonal equation. This allows for rapid approximation of the posterior by iteratively optimizing a collection of particles against a kernelized Stein discrepancy. We show that the method is well-equipped to handle highly multimodal posterior distributions, which are common in hypocentral inverse problems. A suite of experiments is performed to examine the influence of the var…
We propose a new approach to the solution of the wave propagation and full waveform inversions (FWIs) based on a recent advance in deep learning called Physics-Informed Neural Networks (PINNs). In this study, we present an algorithm for PINNs applied to the 2D acoustic wave equation and test the model with both forward wave propagation and FWIs case studies. These synthetic case studies are designed to explore the ability of PINNs to handle varying degrees of structural complexity using both teleseismic plane waves and seismic point sources. PINNs meshless formalism allows for a flexible imple…
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 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…
Accelerating physics-informed neural networks for full waveform inversion using a hybrid quantum-classical finite-basis architecture
Department of Geophysics, Colorado School of Mines（地质学系，科罗拉多矿业学院）；Department of Energy Science and Engineering, Stanford University（能源科学与工程系，斯坦福大学）；Department of Petroleum Engineering, Colorado School of Mines（石油工程系，科罗拉多矿业学院）
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…
Physics-informed waveform inversion using pretrained wavefield neural operators
Physical Science and Engineering division, King Abdullah University of Science and Technology（国王 Abdullah 科学与技术大学物理科学与工程部门）；School of Engineering and Applied Science, University of Pennsylvania（宾夕法尼亚大学工程与应用科学学院）
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…
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…
Curtin University（科廷大学）；Colorado School of Mines（科罗拉多矿业学院）
Inversion of electromagnetic data finds applications in many areas of geophysics. The inverse problem is commonly solved with either deterministic optimization methods (such as the nonlinear conjugate gradient or Gauss-Newton) which are prone to getting trapped in a local minimum, or probabilistic methods which are very computationally demanding. A recently emerging alternative is to employ deep neural networks for predicting subsurface model properties from measured data. This approach is entirely data-driven, does not employ traditional gradient-based techniques and provides a guess to the m…
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）
Geoelectrical techniques are widely used to monitor groundwater processes, while surprisingly few studies have considered audio (AMT) and radio (RMT) magnetotellurics for such purposes. In this numerical investigation, we analyze to what extent inversion results based on AMT and RMT monitoring data can be improved by (1) time-lapse difference inversion; (2) incorporation of statistical information about the expected model update (i.e., the model regularization is based on a geostatistical model); (3) using alternative model norms to quantify temporal changes (i.e., approximations of l1 and Cau…
Solving inverse problems involving measurement noise and modeling errors requires regularization in order to avoid data overfit. Geophysical inverse problems, in which the Earth's highly heterogeneous structure is unknown, present a challenge in encoding prior knowledge through analytical expressions. Our main contribution is a generative-model-based regularization approach, robust to out-of-distribution data, which exploits the prior knowledge embedded in existing data and model pairs. Utilizing an amortized variational inference objective, a conditional normalizing flow (NF) is pretrained on…
Seismic inversion using hybrid quantum neural networks
Stanford University（斯坦福大学）；Indian Institute of Technology (Indian School of Mines) Dhanbad（印度理工学院（印度矿业学院）丹巴德分校）；The University of Texas at Austin（德克萨斯大学奥斯汀分校）
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。
Solving the wave equation numerically constitutes the majority of the computational cost for applications like seismic imaging and full waveform inversion. An alternative approach is to solve the frequency domain Helmholtz equation, since it offers a reduction in dimensionality as it can be solved per frequency. However, computational challenges with the classical Helmholtz solvers such as the need to invert a large stiffness matrix can make these approaches computationally infeasible for large 3D models or for modeling high frequencies. Moreover, these methods do not have a mechanism to trans…
Seismic traveltime tomography using transmission data is widely used to image the Earth's interior from global to local scales. In seismic imaging, it is used to obtain velocity models for subsequent depth-migration or full-waveform inversion. In addition, cross-hole tomography has been successfully applied for a variety of applications, including mineral exploration, reservoir monitoring, and CO2 injection and sequestration. Conventional tomography techniques suffer from a number of limitations, including the use of a smoothing regularizer that is agnostic to the physics of wave propagation. …
