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" (MTP) 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 than 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.
In groundwater hydrology, geophysical imaging holds considerable promise for improving parameter estimation, due to the generally high resolution and spatial coverage of geophysical data. However, inversion of geophysical data alone cannot unveil the distribution of hydraulic conductivity. Jointly inverting geophysical and hydrological data allows us to benefit from the advantages of geophysical imaging and, at the same time, recover the hydrological parameters of interest. We have applied a coupling strategy between geophysical and hydrological models that is based on structural similarity co…
In the geophysical joint inversion, the gradient and Bayesian Markov Chain Monte Carlo (MCMC) sampling-based methods are widely used owing to their fast convergences or global optimality. However, these methods either require the computation of gradients and easily fall into local optimal solutions, or cost much time to carry out the millions of forward calculations in a huge sampling space. Different from these two methods, taking advantage of the recently developed unscented Kalman method in computational mathematics, we extend an iterative gradient-free Bayesian joint inversion framework, i…
Electromagnetic induction methods are a common means for geophysical survey. For soil structures that are invariant in one spatial dimension such as trench structures, we propose a fast forward model based on a 2D response function, taking into account sharp horizontal and vertical transitions in the electrical conductivity. The 2D model is used to invert trench structures from a synthetic dataset. The propsed method can determine trench parameters (width, height, steepness of the slope) more accurately than methods based on regularization of the 1D response function.
Los Alamos National Laboratory（洛斯阿拉莫斯国家实验室）；Microsoft Research（微软研究院）；Lawrence Berkeley National Laboratory（劳伦斯伯克利国家实验室）
Multi-physical inversion plays a critical role in geophysics. It has been widely used to infer various physical properties~(such as velocity and conductivity). Among those inversion problems, some are explicitly governed by partial differential equations~(PDEs), while others are not. Without explicit governing equations, conventional multi-physical inversion techniques will not be feasible and data-driven inversion requires expensive full labels. To overcome this issue, we develop a new data-driven multi-physics inversion technique with extremely weak supervision. Our key finding is that the p…
The near-surface environment is often too complex to enable inference of hydrological and environmental variables using one geophysical data type alone. Joint inversion and coupled inverse modeling involving numerical flow- and transport simulators have, in the last decade, played important roles in pushing applications towards increasingly challenging targets. Joint inversion of geophysical data that is based on structural constraints is often favored over model coupling based on explicit petrophysical relationships. More specifically, cross-gradient joint inversion has been applied to a wide…
Many flexible parameterizations exist to represent data on the sphere. In addition to the venerable spherical harmonics, we have the Slepian basis, harmonic splines, wavelets and wavelet-like Slepian frames. In this paper we focus on the latter two: spherical wavelets developed for geophysical applications on the cubed sphere, and the Slepian "tree", a new construction that combines a quadratic concentration measure with wavelet-like multiresolution. We discuss the basic features of these mathematical tools, and illustrate their applicability in parameterizing large-scale global geophysical (i…
This paper presents a new method of constructing physical models in a geophysical inverse problem, when there are only a few possible physical property values in the model and they are reasonably known but the geometry of the target is sought. The model consists of a fixed background and many small "particles" as building blocks that float around in the background to resemble the target by clustering. This approach contrasts the conventional geometric inversions requiring the target to be regularly shaped bodies, since here the geometry of the target can be arbitrary and does not need to be kn…
$\mathbf{\mathbb{E}^{FWI}}$: Multi-parameter Benchmark Datasets for Elastic Full Waveform Inversion of Geophysical Properties
Los Alamos National Laboratory（洛斯阿拉莫斯国家实验室）；Rutgers University（罗格斯大学）；Colorado School of Mines（科罗拉多矿业学院）；University of Pennsylvania（宾夕法尼亚大学）；The Pennsylvania State University（宾夕法尼亚州立大学）；Microsoft（微软）
Geophysical models usually contain both sharp interfaces and smooth variations, and it is difficult to accurately account for both of these two types of medium parameter variations using conventional full-waveform inversion methods. In addition, sparse geometry, noisy data and source encoding usually lead to strong inversion artifacts. We develop a novel full-waveform inversion method for acoustic and elastic waves using a total generalized p-variation regularization scheme to address these challenging problems. We decompose the full-waveform inversion into two subproblems and solve these two …
We propose a new approach to measuring the agreement between two oscillatory time series, such as seismic waveforms, and demonstrate that it can be employed effectively in inverse problems. Our approach is based on Optimal Transport theory and the Wasserstein distance, with a novel transformation of the time series to ensure that necessary normalisation and positivity conditions are met. Our measure is differentiable, and can readily be employed within an optimization framework. We demonstrate performance with a variety of synthetic examples, including seismic source inversion, and observe sub…
Global probabilistic inversion within the latent space learned by a Generative Adversarial Network (GAN) has been recently demonstrated. Compared to inversion on the original model space, using the latent space of a trained GAN can offer the following benefits: (1) the generated model proposals are geostatistically consistent with the prescribed prior training image (TI), and (2) the parameter space is reduced by orders of magnitude compared to the original model space. Nevertheless, exploring the learned latent space by state-of-the-art Markov chain Monte Carlo (MCMC) methods may still requir…
Variational Bayesian experimental design for geophysical applications: seismic source location, amplitude versus offset inversion, and estimating CO2 saturations in a subsurface reservoir
本文将变分贝叶斯实验设计引入地球物理，通过震源定位、AVO 反演和 CO2 储层饱和度估计验证其可同步计算并优化实验价值、降低计算成本。
In a variety of scientific applications we wish to characterize a physical system using measurements or observations. This often requires us to solve an inverse problem, which usually has non-unique solutions so uncertainty must be quantified in order to define the family of all possible solutions. Bayesian inference provides a powerful theoretical framework which defines the set of solutions to inverse problems, and variational inference is a method to solve Bayesian inference problems using optimization while still producing fully probabilistic solutions. This chapter provides an introductio…
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…
Full Waveform Inversion (FWI) plays a vital role in reconstructing geophysical structures. The Uncertainty Quantification regarding the inversion results is equally important but has been missing out in most of the current geophysical inversions. Mathematically, uncertainty quantification is involved with the inverse Hessian (or the posterior covariance matrix), which is prohibitive in computation and storage for practical geophysical FWI problems. L-BFGS populates as the most efficient Gauss-Newton method; however, in this study, we empower it with the new possibility of accessing the inverse…
In a previous paper, we introduced a framework for carrying out petrophysically and geologically guided geophysical inversions. In that framework, petrophysical and geological information is modelled with a Gaussian Mixture Model (GMM). In the inversion, the GMM serves as a prior for the geophysical model. The formulation was confined to problems in which a single physical property model was sought, with a single geophysical dataset. In this paper, we extend that framework to jointly invert multiple geophysical datasets that depend on multiple physical properties. The petrophysical and geologi…
Self-Supervised Knowledge-Driven Deep Learning for 3D Magnetic Inversion
Beijing National Research Center for Information Science and Technology (BNRist), Department of Automation, Tsinghua University（清华大学自动化系北京国家信息科学技术研究中心）；School of Civil Engineering, Changsha University of Science and Technology（长沙理工大学土木工程学院）
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…
Recent applications of machine learning algorithms in the seismic domain have shown great potential in different areas such as seismic inversion and interpretation. However, such algorithms rarely enforce geophysical constraints - the lack of which might lead to undesirable results. To overcome this issue, we have developed a semi-supervised sequence modeling framework based on recurrent neural networks for elastic impedance inversion from multi-angle seismic data. Specifically, seismic traces and elastic impedance (EI) traces are modeled as a time series. Then, a neural-network-based inversio…
In addition to reducing anthropogenic emissions of CO$_2$, it is increasingly clear we also need to remove CO$_2$ from the atmosphere in order to avoid some of the worst case scenarios for climate change. Geologic sequestration of CO$_2$ is among the most attractive approaches because of the large global capacity and long-time scales for storage. One mechanism of geologic storage is through carbon mineralization. Some mafic and ultramafic rocks contain minerals that will react with CO$_2$ in a carbonation reaction and convert it to carbonated minerals. This is effectively a permanent CO$_2$ st…
Geophysical inversion should ideally produce geologically realistic subsurface models that explain the available data. Multiple-point statistics is a geostatistical approach to construct subsurface models that are consistent with site-specific data, but also display the same type of patterns as those found in a training image. The training image can be seen as a conceptual model of the subsurface and is used as a non-parametric model of spatial variability. Inversion based on multiple-point statistics is challenging due to high nonlinearity and time-consuming geostatistical resimulation steps …
A critical decision process in data acquisition for mineral and energy resource exploration is how to efficiently combine a variety of sensor types and to minimize total cost. We propose a probabilistic framework for multi-objective optimisation and inverse problems given an expensive cost function for allocating new measurements. This new method is devised to jointly solve multi-linear forward models of 2D-sensor data and 3D-geophysical properties using sparse Gaussian Process kernels while taking into account the cross-variances of different parameters. Multiple optimisation strategies are t…
Applying deep-learning models to geophysical applications has attracted special attentions during the past a couple of years. There are several papers published in this domain involving with different topics primarily focusing on synthetic data. Based on the presented results, reaching the satisfaction from geophysicists is largely far away the performance of the conventional algorithms. Moreover, it is extremely hard to find documents with detailed illustrations about what are the best practices that researchers should follow regarding how to design appropriate deep-learning models to effecti…
Online learning of eddy-viscosity and backscattering closures for geophysical turbulence using ensemble Kalman inversion
Union College（联合学院）；The University of Chicago（芝加哥大学）；California Institute of Technology（加州理工学院）；Peking University（北京大学）；University of Wisconsin–Madison（威斯康星大学麦迪逊分校）；Google Research（谷歌研究）
Bayesian deep learning integration of geophysical and drilling data for 3D prediction of copper mineralization and drill targeting: a case study from the Kogodai prospect, Rudny Altai
Terra Quantum AG（泰拉量子公司）；Kogodai Joint Venture LLP（科戈代合资有限责任合伙公司）
A strategy is presented to incorporate prior information from conceptual geological models in probabilistic inversion of geophysical data. The conceptual geological models are represented by multiple-point statistics training images (TIs) featuring the expected lithological units and structural patterns. Information from an ensemble of TI realizations is used in two different ways. First, dominant modes are identified by analysis of the frequency content in the realizations, which drastically reduces the model parameter space in the frequency-amplitude domain. Second, the distributions of glob…
Harbin Institute of Technology（哈尔滨工业大学）；Peking University（北京大学）
Understanding the principles of geophysical phenomena is an essential and challenging task. "Model-driven" approaches have supported the development of geophysics for a long time; however, such methods suffer from the curse of dimensionality and may inaccurately model the subsurface. "Data-driven" techniques may overcome these issues with increasingly available geophysical data. In this article, we review the basic concepts of and recent advances in data-driven approaches from dictionary learning to deep learning in a variety of geophysical scenarios. Explorational geophysics including data pr…
Scientific curiosity, exploration of georesources and environmental concerns are pushing the geoscientific research community toward subsurface investigations of ever-increasing complexity. This review explores various approaches to formulate and solve inverse problems in ways that effectively integrate geological concepts with geophysical and hydrogeological data. Modern geostatistical simulation algorithms can produce multiple subsurface realizations that are in agreement with conceptual geological models and statistical rock physics can be used to map these realizations into physical proper…
Geophysical methods offer several key advantages over conventional subsurface measurement approaches, yet their use for hydrologic interpretation is often problematic. Here, we introduce theory and concepts of a novel Bayesian approach for high-resolution soil moisture estimation using traveltime observations from crosshole Ground Penetrating Radar (GPR) experiments. The recently developed Multi-try DiffeRential Evolution Adaptive Metropolis with sampling from past states, MT-DREAM(ZS) is being used to infer, as closely and consistently as possible, the posterior distribution of spatially dist…
ContrasInver: Ultra-Sparse Label Semi-supervised Regression for Multi-dimensional Seismic Inversion
College of computer science and technology, China University of Petroleum (East China)（中国石油大学（华东）计算机科学与技术学院）；Department of Automation, University of Science and Technology of China（中国科学技术大学自动化系）；College of Intelligence and Computing, Tianjin University（天津大学智能与计算学院）
Most geophysical inverse problems are nonlinear and rely upon numerical forward solvers involving discretization and simplified representations of the underlying physics. As a result, forward modeling errors are inevitable. In practice, such model errors tend to be either completely ignored, which leads to biased and over-confident inversion results, or only partly taken into account using restrictive Gaussian assumptions. Here, we rely on deep generative neural networks to learn problem-specific low-dimensional probabilistic representations of the discrepancy between high-fidelity and low-fid…
Recent applications of deep learning in the seismic domain have shown great potential in different areas such as inversion and interpretation. Deep learning algorithms, in general, require tremendous amounts of labeled data to train properly. To overcome this issue, we propose a semi-supervised framework for acoustic impedance inversion based on convolutional and recurrent neural networks. Specifically, seismic traces and acoustic impedance traces are modeled as time series. Then, a neural-network-based inversion model comprising convolutional and recurrent neural layers is used to invert seis…
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…
Harbin Institute of Technology（哈尔滨工业大学）；Tsinghua University（清华大学）
Seismic impedance inversion can be performed with a semi-supervised learning algorithm, which only needs a few logs as labels and is less likely to get overfitted. However, classical semi-supervised learning algorithm usually leads to artifacts on the predicted impedance image. In this artical, we improve the semi-supervised learning from two aspects. First, by replacing 1-d convolutional neural network (CNN) layers in deep learning structure with 2-d CNN layers and 2-d maxpooling layers, the prediction accuracy is improved. Second, prediction uncertainty can also be estimated by embedding the…
The objective is to study the feasibility of predicting subsurface rock properties in wells from real-time drilling data. Geophysical logs, namely, density, porosity and sonic logs are of paramount importance for subsurface resource estimation and exploitation. These wireline petro-physical measurements are selectively deployed as they are expensive to acquire; meanwhile, drilling information is recorded in every drilled well. Hence a predictive tool for wireline log prediction from drilling data can help management make decisions about data acquisition, especially for delineation and producti…
Regularization methods improve the stability of ill-posed inverse problems by introducing some a priori characteristics for the solution such as smoothness or sharpness. In this contribution, we propose a multidimensional, scale-dependent wavelet-based L1-regularization term to cure the ill-posedness of the airborne (time-domain) electromagnetic induction inverse problem. The regularization term is flexible, as it can recover blocky, smooth and tunable in-between inversion models, based on a suitable wavelet basis function. For each orientation, a different wavelet basis function can be used, …
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…
