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 inversion model comprising convolutional and recurrent neural layers is used to invert seismic data for EI. The proposed workflow uses well-log data to guide the inversion. In addition, it uses seismic forward modeling to regularize the training and to serve as a geophysical constraint for the inversion. The proposed workflow achieves an average correlation of 98% between the estimated and target EI using 10 well logs for training on a synthetic data set.
Seismic inversion refers to the process of estimating reservoir rock properties from seismic reflection data. Conventional and machine learning-based inversion workflows usually work in a trace-by-trace fashion on seismic data, utilizing little to no information from the spatial structure of seismic images. We propose a deep learning-based seismic inversion workflow that models each seismic trace not only temporally but also spatially. This utilizes information-relatedness in seismic traces in depth and spatial directions to make efficient rock property estimations. We empirically compare our …
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…
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…
We discuss the concept of cloaking for elastic impedance tomography, in which, we seek information on the elasticity tensor of an elastic medium from the knowledge of measurements on its boundary. We derive some theoretical results illustrated by some numerical simulations.
Direction-Aware Masked Pretraining on 3D Seismic Data with Transfer to Cross-Area Acoustic Impedance Inversion
State Key Laboratory of Deep Oil and Gas, China University of Petroleum (East China)（中国石油大学（华东）油气藏地质与开发国家重点实验室）；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）
Seismic inversion helps geophysicists build accurate reservoir models for exploration and production purposes. Deep learning-based seismic inversion works by training a neural network to learn a mapping from seismic data to rock properties using well log data as the labels. However, well logs are often very limited in number due to the high cost of drilling wells. Machine learning models can suffer overfitting and poor generalization if trained on limited data. In such cases, well log data from other surveys can provide much needed useful information for better generalization. We propose a lea…
Seismic inversion plays a very useful role in detailed stratigraphic interpretation of seismic data. Seismic inversion enables estimation of rock properties over the complete seismic section. Traditional and machine learning-based seismic inversion workflows are limited to inverting each seismic trace independently of other traces to estimate impedance profiles, leading to lateral discontinuities in the presence of noise and large geological variations in the seismic data. In addition, machine learning-based approaches suffer the problem of overfitting if there is a small number of wells on wh…
Original GLM (Gel'fand-Levitan-Marchenko) theory is for scattering potential recovery of Schrödinger equation. In this paper, we formulate the GLM impedance solution of oblique incidence for simultaneous inversion of velocity and density including boundary jumps based on acoustic wave equation. In addition to the use of reflection amplitude, traveltime information of reflection arrivals is also utilized for inversion based on the focusing principle. Numerical tests demonstrate the recovery of velocity and density, verified the validity of the theory and method. The theory of Schrödinger impeda…
We have formulated elastic seismic full waveform inversion (FWI) within a deep learning environment. In our formulation, a recurrent neural network is set up with rules enforcing elastic wave propagation, with the wavefield projected onto a measurement surface acting as the synthetic data to be compared with observed seismic data. Gradients for iterative updating of an elastic model, with a variety of parameterizations and misfit functionals, can be efficiently constructed within the network through the automatic differential method. With this method, the inversion based on complex misfits can…
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 …
In exploration seismology, seismic inversion refers to the process of inferring physical properties of the subsurface from seismic data. Knowledge of physical properties can prove helpful in identifying key structures in the subsurface for hydrocarbon exploration. In this work, we propose a workflow for predicting acoustic impedance (AI) from seismic data using a network architecture based on Temporal Convolutional Network by posing the problem as that of sequence modeling. The proposed workflow overcomes some of the problems that other network architectures usually face, like gradient vanishi…
The three electromagnetic properties appearing in Maxwell's equations are dielectric permittivity, electrical conductivity and magnetic permeability. The study of point diffractors in a homogeneous, isotropic, linear medium suggests the use of logarithms to describe the variations of electromagnetic properties in the earth. A small anomaly in electrical properties (permittivity and conductivity) responds to an incident electromagnetic field as an electric dipole, whereas a small anomaly in the magnetic property responds as a magnetic dipole. Neither property variation can be neglected without …
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…
Full waveform inversion (FWI) strongly depends on an accurate starting model to succeed. This is particularly true in the elastic regime: The cycle-skipping phenomenon is more severe in elastic FWI compared to acoustic FWI, due to the short S-wave wavelength. In this paper, we extend our work on extrapolated FWI (EFWI) by proposing to synthesize the low frequencies of multi-component elastic seismic records, and use those "artificial" low frequencies to seed the frequency sweep of elastic FWI. Our solution involves deep learning: we separately train the same convolutional neural network (CNN) …
Elastic full-waveform inversion (FWI) when successfully applied can provide accurate and high-resolution subsurface parameters. However, its high computational cost prevents the application of this method to large-scale field-data scenarios. To mitigate this limitation, we propose a target-oriented elastic FWI methodology based on a redatuming step that relies upon an extended least-squared migration process. In our approach, the surface-reflection data can be attributed to a given subsurface portion when mapped into the image space. This process allows us to reconstruct reflection data genera…
$\mathbf{\mathbb{E}^{FWI}}$: 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）
Source footprint elimination in full-waveform inversion by model extension: Application to elastic guided waves recorded by distributed acoustic sensing in unconventional reservoir
Geostatistical seismic inversion is commonly used to infer the spatial distribution of the subsurface petro-elastic properties by perturbing the model parameter space through iterative stochastic sequential simulations/co-simulations. The spatial uncertainty of the inferred petro-elastic properties is represented with the updated a posteriori variance from an ensemble of the simulated realizations. Within this setting, the large-scale geological (metaparameters) used to generate the petro-elastic realizations, such as the spatial correlation model and the global a priori distribution of the pr…
In this work, we propose a full-waveform technique for the spatial reconstruction and characterization of (micro-) seismic events via joint source location and moment tensor inversion. The approach is formulated in the frequency domain, and it allows for the simultaneous inversion of multiple point-like events. In the core of the proposed methodology is a grid search for the source locations that encapsulates the optimality condition on the respective moment tensors. The developments cater for compactly supported elastic bodies in $\mathbb{R}^2$; however our framework is directly extendable to…
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…
Iterative geostatistical seismic inversion integrates seismic and well data to infer the spatial distribution of subsurface elastic properties. These methods provide limited assessment to the spatial uncertainty of the inverted elastic properties, overlooking alternative sources of uncertainty such as those associated with poor well-log data, upscaling and noise within the seismic data. We express uncertain well-log samples, due to bad logging reads and upscaling, in terms of local probability distribution functions (PDFs). Local PDFs are used as conditioning data to a stochastic sequential si…
Reservoir models are numerical representations of the subsurface petrophysical properties such as porosity, volume of minerals and fluid saturations. These are often derived from elastic models inferred from seismic inversion in a two-step approach: first, seismic reflection data are inverted for the elastic properties of interest (such as density, P-wave and S-wave velocities); these are then used as constraining properties to model the subsurface petrophysical variables. The sequential approach does not ensure a proper propagation of uncertainty throughout the entire geo-modelling workflow a…
Structural seismic interpretation and quantitative characterization are historically intertwined processes. The latter provides estimates of properties of the subsurface which can be used to aid structural interpretation alongside the original seismic data and a number of other seismic attributes. In this work, we redefine this process as a inverse problem which tries to jointly estimate subsurface properties (i.e., acoustic impedance) and a piece-wise segmented representation of the subsurface based on user-defined macro-classes. By inverting for the quantities simultaneously, the inversion i…
Seismic amplitude-variation-with-offset inversion using an algebraically equivalent formulation of the exact Zoeppritz equations and a matrix-free adjoint-state framework
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）
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…
Efficient assessment of convolved hidden Markov models is discussed. The bottom-layer is defined as an unobservable categorical first-order Markov chain, while the middle-layer is assumed to be a Gaussian spatial variable conditional on the bottom-layer. Hence, this layer appear as a Gaussian mixture spatial variable unconditionally. We observe the top-layer as a convolution of the middle-layer with Gaussian errors. Focus is on assessment of the categorical and Gaussian mixture variables given the observations, and we operate in a Bayesian inversion framework. The model is defined to make inve…
In seismic waveform inversion, the reconstruction of the subsurface properties is usually carried out using approximative wave propagation models to ensure computational efficiency. The viscoelastic nature of the subsurface is often unaccounted for, and two popular approximations--the acoustic and linearized Born inversion--are widely used. This leads to reconstruction errors since the approximations ignore realistic (physical) aspects of seismic wave propagation in the heterogeneous earth. In this study, we show that the Bayesian approximation error approach can be used to partially recover f…
