Incorporating prior knowledge on model unknowns of interest is essential when dealing with ill-posed inverse problems due to the nonuniqueness of the solution and data noise. Unfortunately, it is not trivial to fully describe our priors in a convenient and analytical way. Parameterizing the unknowns with a convolutional neural network (CNN), and assuming an uninformative Gaussian prior on its weights, leads to a variational prior on the output space that favors "natural" images and excludes noisy artifacts, as long as overfitting is prevented. This is the so-called deep-prior approach. In seismic imaging, however, evaluating the forward operator is computationally expensive, and training a randomly initialized CNN becomes infeasible. We propose, instead, a weak version of deep priors, which consists of relaxing the requirement that reflectivity models must lie in the network range, and letting the unknowns deviate from the network output according to a Gaussian distribution. Finally, we jointly solve for the reflectivity model and CNN weights. The chief advantage of this approach is that the updates for the CNN weights do not involve the modeling operator, and become relatively cheap. Our synthetic numerical experiments demonstrate that the weak deep prior is more robust with respect to noise than conventional least-squares imaging approaches, with roughly twice the computational cost of reverse-time migration, which is the affordable computational budget in large-scale imaging problems.
We consider seismic imaging to include seismic inversion. Imaging could use approximate operator or time instead of depth. Processing in time is an important part of seismic imaging as well as processing in depth. We can classify seismic imaging as quantitative versus qualitative methods. Quantitative method uses numerical methods to find the solution whose modeled seismic data approximates the input seismic records. Then we will progress to qualitative methods which have three aspects. The first aspect will be topology and geometry. The second aspect is semigroup method. The third aspect is t…
We present three imaging modalities that live on the crossroads of seismic and medical imaging. Through the lens of extended source imaging, we can draw deep connections among the fields of wave-equation based seismic and medical imaging, despite first appearances. From the seismic perspective, we underline the importance to work with the correct physics and spatially varying velocity fields. Medical imaging, on the other hand, opens the possibility for new imaging modalities where outside stimuli, such as laser or radar pulses, can not only be used to identify endogenous optical or thermal co…
This abstract presents a serverless approach to seismic imaging in the cloud based on high-throughput containerized batch processing, event-driven computations and a domain-specific language compiler for solving the underlying wave equations. A 3D case study on Azure demonstrates that this approach allows reducing the operating cost of up to a factor of 6, making the cloud a viable alternative to on-premise HPC clusters for seismic imaging.
Matrix imaging as a tool for high-resolution monitoring of deep volcanic plumbing systems with seismic noise
Institut Langevin, ESPCI Paris, PSL University, CNRS（朗之万研究所，巴黎高等物理化工学院，巴黎文理研究大学，法国国家科学研究中心）；Institut de Physique du Globe de Paris, Université Paris Cité, CNRS（巴黎地球物理研究所，巴黎西岱大学，法国国家科学研究中心）
Seismic imaging is an ill-posed inverse problem that is challenged by noisy data and modeling inaccuracies -- due to errors in the background squared-slowness model. Uncertainty quantification is essential for determining how variability in the background models affects seismic imaging. Due to the costs associated with the forward Born modeling operator as well as the high dimensionality of seismic images, quantification of uncertainty is computationally expensive. As such, the main contribution of this work is a survey-specific Fourier neural operator surrogate to velocity continuation that m…
Accurate characterization of subsurface geophysical properties and detection of the fault system are essential for geothermal energy exploration and production. The Soda Lake geothermal field is in western Nevada with a complex fault system. Previous seismic characterization only produced a low-resolution, smooth velocity model along with a simple, conceptual fault model. Using optimized correlation-based full-waveform inversion, wavefield-separation-based reverse-time migration, and automatic fault detection techniques, we present 3D seismic characterization for the Soda Lake geothermal field…
Enhancing the frequency bandwidth of the seismic data is always the pursuance at the geophysical community. High resolution of seismic data provides the key resource to extract detailed stratigraphic knowledge. Here, a novel approach, based on deep learning model, is introduced by extracting reflections from well log data to broaden spectrum bandwidth of seismic data through boosting low and high frequencies. The corresponding improvement is observed from the enhancement of resolution of seismic data as well as elimination of sidelobe artifacts from seismic wavelets. During the training stage …
The primary use of technical computing in the oil and gas industries is for seismic imaging of the earth's subsurface, driven by the business need for making well-informed drilling decisions during petroleum exploration and production. Since each oil/gas well in exploration areas costs several tens of millions of dollars, producing high-quality seismic images in a reasonable time can significantly reduce the risk of drilling a "dry hole". Similarly, these images are important as they can improve the position of wells in a billion-dollar producing oil field. However seismic imaging is very data…
The interpretation of seismic images faces challenges due to the presence of several uncertainty sources. Uncertainties exist in data measurements, source positioning, and subsurface geophysical properties. Understanding uncertainties' role and how they influence the outcome is an essential part of the decision-making process in the oil and gas industry. Geophysical imaging is time-consuming. When we add uncertainty quantification, it becomes both time and data-intensive. In this work, we propose a workflow for seismic imaging with quantified uncertainty. We build the workflow upon Bayesian to…
Unveiling magma plumbing systems for volcanic eruptions and crustal accretion via active-seismic matrix imaging
Institut Langevin, ESPCI, PSL University, CNRS（朗之万研究所，ESPCI巴黎高等物理化工学院，PSL大学，法国国家科学研究中心）；Institut de Physique du Globe de Paris, Université Paris Cité, CNRS UMR 7154（巴黎地球物理研究所，巴黎西岱大学，法国国家科学研究中心）
Seismic imaging faces challenges due to the presence of several uncertainty sources. Uncertainties exist in data measurements, source positioning, and subsurface geophysical properties. Reverse time migration (RTM) is a high-resolution depth migration approach useful for extracting information such as reservoir localization and boundaries. RTM, however, is time-consuming and data-intensive as it requires computing twice the wave equation to generate and store an imaging condition. RTM, when embedded in an uncertainty quantification algorithm (like the Monte Carlo method), shows a many-fold inc…
Deep learning applications of seismic reservoir characterization often require generation of synthetic data to augment available sparse labeled data. An approach for generating synthetic training data consists of specifying probability distributions modeling prior geologic uncertainty on reservoir properties and forward modeling the seismic data. A prior falsification approach is critical to establish the consistency of the synthetic training data distribution with real seismic data. With the help of a real case study of facies classification with convolutional neural networks (CNNs) from an o…
We report precursory seismic patterns prior to the 2016 Kumamoto earthquakes, as measured by four different methods based on changes in seismicity that can be used for earthquake forecasting: the b-value method, two methods of seismic quiescence evaluation, and an analysis of seismicity density in space and time. The spatial extent of precursory patterns differs from one method to the other and ranges from local scales (typically, asperity size) to regional scales (e.g., 2 degree x 3 degree around the source zone). The earthquakes were preceded by periods of pronounced anomalies, which lasted …
Multiple scattering of seismic waves is often seen as a nightmare for conventional migration techniques that generally rely on a ballistic or a single scattering assumption. In heterogeneous areas such as volcanoes, the multiple scattering contribution limits the imaging-depth to one scattering mean free path, the mean distance between two successive scattering events for body waves. In this Letter, we propose a matrix approach of passive seismic imaging that pushes back this fundamental limit by making an efficient use of scattered body waves drowned into a noisy seismic coda. As a proof-of-c…
Unsupervised Posterior Sampling for Seismic Data Recovery via Score-Based Generative Priors
Xi’an Jiaotong University（西安交通大学）；The National Engineering Research Center for Offshore Oil and Gas Exploration（海洋油气勘探开发国家工程研究中心）；School of Information and Communications Engineering（信息与通信工程学院）；School of Mathematics and Statistics（数学与统计学院）
We propose a predictive neural network architecture that can be utilized to update reference velocity models as inputs to the full waveform inversion. Deep learning models are explored to augment velocity model building workflows during processing the 3D seismic volume in salt-prone environments. Specifically, a neural network architecture, with 3D convolutional, de-convolutional layers, and 3D max-pooling, is designed to take standard amplitude 3D seismic volumes as an input. Enhanced data augmentations through generative adversarial networks and a weighted loss function enable the network to…
We present a methodology for quantifying seismic velocity and pore pressure uncertainty that incorporates information regarding the geological history of a basin, rock physics, well log, drilling and seismic data. In particular, our approach relies on linking velocity models to the basin modeling outputs of porosity, mineral volume fractions and pore pressure through rock physics models. We account for geological uncertainty by defining prior probability distributions on uncertain parameters and performing Monte Carlo basin simulations. We perform probabilistic calibration of the basin model o…
Seismic migration is the core step of seismic data processing which is important for oil exploration. Poststack depth migration in frequency-space (f-x) domain is one of commonly used algorithms. The wave-equation solution can be approximated as FIR filtering process to extrapolate the raw data and extract the subsurface image. Because of its computational complexity, its parallel implementation is encouraged. For calculating the next depth level, previous depth level is required. So, this part cannot be parallelized because of data dependence. But at each depth level there is plenty of roam f…
The biggest risk to operations in Polish copper is high-energy seismic tremors where hypocenters are located within the main roof strata. These phenomena occur often in the areas which are virtually free of tectonic disturbances. They are extremely difficult to both predict and analyze due to their short duration and unpredictable time of occurrence. The objective of the presented analysis was to determine the overall stress/deformation states within the considered mining panel prior to the selected archival seismic event and afterwards to judge how the progress of mining could affect the occu…
Adapting the cloud for high-performance computing (HPC) is a challenging task, as software for HPC applications hinges on fast network connections and is sensitive to hardware failures. Using cloud infrastructure to recreate conventional HPC clusters is therefore in many cases an infeasible solution for migrating HPC applications to the cloud. As an alternative to the generic lift and shift approach, we consider the specific application of seismic imaging and demonstrate a serverless and event-driven approach for running large-scale instances of this problem in the cloud. Instead of permanentl…
The goal of inversion is to estimate the model which generates the data of observations with a specific modeling equation. One general approach to inversion is to use optimization methods which are algebraic in nature to define an objective function. This is the case for objective functions like minimizing RMS of amplitude, residual traveltime error in tomography, cross correlation and sometimes mixing different norms (e.g. L1 of model + L2 of RMS error). Algebraic objective function assumes that the optimal solution will come up with the correct geometry. It is sometimes difficult to understa…
We consider the high-resolution seismic imaging method called full-waveform inversion (FWI). FWI is a data fitting method aimed at inverting for subsurface mechanical parameters. Despite the large adoption of FWI by the academic and industrial communities, and many successful results, FWI still suffers from severe limitations. From a mathematical standpoint, FWI is a large scale PDE-constrained optimization problem. The misfit function that is used, which measures the discrepancy between observed seismic data and data calculated through the solution of a wave propagation problem, is non-convex…
Reflection seismic imaging usually suffers from a loss of resolution and contrast because of the fluctuations of the wave velocities in the Earth's crust. In the literature, phase distortion issues are generally circumvented by means of a background wave velocity model. However, it requires a prior tomography of the wave velocity distribution in the medium, which is often not possible, especially in depth. In this paper, a matrix approach of seismic imaging is developed to retrieve a three-dimensional image of the subsoil, despite a rough knowledge of the background wave velocity. To do so, pa…
We propose to use techniques from Bayesian inference and deep neural networks to translate uncertainty in seismic imaging to uncertainty in tasks performed on the image, such as horizon tracking. Seismic imaging is an ill-posed inverse problem because of bandwidth and aperture limitations, which is hampered by the presence of noise and linearization errors. Many regularization methods, such as transform-domain sparsity promotion, have been designed to deal with the adverse effects of these errors, however, these methods run the risk of biasing the solution and do not provide information on unc…
The classical approach of solvability using group theory is well known and one original motivation is to solve polynomials by radicals. Radicals are square, cube, square root, cube root etc of the original coefficients for the polynomial. A polynomial is solvable by radicals if the permutation group is solvable. This is exact solvability via group theory. With modern computers, we might need to relax our definition of exact solvability and move towards practical solvability. We will address seismic imaging as an example of practical solvability by semigroup theory. The difference between semig…
Uncertainty quantification provides quantitative measures on the reliability of candidate solutions of ill-posed inverse problems. Due to their sequential nature, Monte Carlo sampling methods require large numbers of sampling steps for accurate Bayesian inference and are often computationally infeasible for large-scale inverse problems, such as seismic imaging. Our main contribution is a data-driven variational inference approach where we train a normalizing flow (NF), a type of invertible neural net, capable of cheaply sampling the posterior distribution given previously unseen seismic data f…
Earthquake hypocenters form the basis for a wide array of seismological analyses. Pick-based earthquake location workflows rely on the accuracy of phase pickers and may be biased when dealing with complex earthquake sequences in heterogeneous media. Time-reversal imaging of passive seismic sources with the cross-correlation imaging condition has potential for earthquake location with high accuracy and high resolution, but carries a large computational cost. Here we present an alternative deep-learning approach for earthquake location by combining the benefits of neural operators for wave propa…
The normalized raw data of the Earth's electric field, monitored at PYR, ATH, HIO monitoring sites in Greece, are studied as far as it concerns the presence of electric seismic precursors. Electric preseismic pulses, plateau-like anomalous electric field and Very Long Period (VLP) anomalies were detected prior to the occurrence of the July 1st, 2009 large (Ms = 6.3R) EQ in Greece. Further processing of the same data revealed the true form of the generated preseimic potential thus providing an indirect estimation of the time window of the occurrence of the large EQ. Finally, by correlating, at …
Ultra low frequency, kHz and MHz electromagnetic anomalies were recorded prior to the L'Aquila catastrophic earthquake that occurred on April 6, 2009. The main aims of this contribution are: (i) To suggest a procedure for the designation of detected EM anomalies as seismogenic ones. We do not expect to be possible to provide a succinct and solid definition of a pre-seismic EM emission. Instead, we attempt, through a multidisciplinary analysis, to provide elements of a definition. (ii) To link the detected MHz and kHz EM anomalies with equivalent last stages of the L'Aquila earthquake preparati…
Fault zones are associated with multi-scale heterogeneities of rock properties. Large scale variations may be imaged with conventional seismic reflection methods that detect offsets in geological units, and tomographic techniques that provide average seismic velocities in resolved volumes. However, characterizing elementary localized inhomogeneities of fault zones, such as cracks and fractures, constitutes a challenge for conventional techniques. Resolving these small-scale heterogeneities can provide detailed information for structural and mechanical models of fault zones. Recently, the refle…
GeoFWI3D: Large-scale 3D Velocity Model Dataset for Deep Learning-assisted Seismic Imaging
The University of Texas at Austin（德克萨斯大学奥斯汀分校）；Los Alamos National Laboratory（洛斯阿拉莫斯国家实验室）；Uppsala University（乌普萨拉大学）；The University of Texas at Permian Basin（德克萨斯大学佩米安盆地分校）；King Fahd University of Petroleum and Minerals（法赫德国王石油与矿产大学）
Phase maps, of the earth's electric field monitored at PYR and ATH monitoring sites in Greece, were compiled for two distinct oscillating earth's electric field components long before, during and after the Nafpactos EQs in Greece (January 18th and 22nd of 2010, Ms = 5.7 / 5.6R). The selected periods of the earth's oscillating electric field were the T = 1 day and T = 14 days. The specific components were selected due to the fact that they are highly depended from the corresponding same period tidal waves (M1, K1, P1). It was found that the "strange attractor like" electric seismic precursor pr…
Data interpolation is a fundamental step in any seismic processing workflow. Among machine learning techniques recently proposed to solve data interpolation as an inverse problem, Deep Prior paradigm aims at employing a convolutional neural network to capture priors on the data in order to regularize the inversion. However, this technique lacks of reconstruction precision when interpolating highly decimated data due to the presence of aliasing. In this work, we propose to improve Deep Prior inversion by adding a directional Laplacian as regularization term to the problem. This regularizer driv…
Los Alamos National Laboratory（洛斯阿拉莫斯国家实验室）；Michigan State University（密歇根州立大学）
4D seismic imaging has been widely used in CO$_2$ sequestration projects to monitor the fluid flow in the volumetric subsurface region that is not sampled by wells. Ideally, real-time monitoring and near-future forecasting would provide site operators with great insights to understand the dynamics of the subsurface reservoir and assess any potential risks. However, due to obstacles such as high deployment cost, availability of acquisition equipment, exclusion zones around surface structures, only very sparse seismic imaging data can be obtained during monitoring. That leads to an unavoidable a…
Ultra low frequency-ULF (1 Hz or lower), kHz and MHz electromagnetic (EM) anomalies were recorded prior to the L'Aquila catastrophic earthquake (EQ) that occurred on April 6, 2009. The detected anomalies followed this temporal scheme. (i) The MHZ EM anomalies were detected on March 26, 2009 and April 2, 2009. The kHz EM anomalies were emerged on April, 4 2009. The ULF EM anomaly was continuously recorded from March 29, 2009 up to April 2, 2009. "Are EQs predictable?" is a question hotly debated in the science community. Its answer begs for another question: "Are there credible EQ precursors?".…
The classical approach to solvability of a mathematical problem is to define a method which includes certain rules of operation or algorithms. Then using the defined method, one can show that some problems are solvable or not solvable or undecidable depending on the particular method. With numerical solutions implemented in a computer, it might be more practical to define solvability of a mathematical problem as a complex decomposition problem. The decomposition breaks the data into a simple part and a complex part. The simple part is the solvable part by the method prescribed in the problem d…
Seismic full-waveform inversion (FWI) uses full seismic records to estimate subsurface velocity structure. This requires a highly nonlinear and nonunique inverse problem to be solved, and Bayesian methods have been used to quantify uncertainties in the solution. Variational Bayesian inference uses optimization to provide solutions efficiently. The method has been applied to solve a transmission FWI problem using data generated by known earthquake-like sources, with strong prior information imposed on the velocity. Unfortunately such prior information about velocity structure and earthquake sou…
We present an application of deep generative models in the context of partial-differential equation (PDE) constrained inverse problems. We combine a generative adversarial network (GAN) representing an a priori model that creates subsurface geological structures and their petrophysical properties, with the numerical solution of the PDE governing the propagation of acoustic waves within the earth's interior. We perform Bayesian inversion using an approximate Metropolis-adjusted Langevin algorithm (MALA) to sample from the posterior given seismic observations. Gradients with respect to the model…
Using spectral-element and adjoint methods, we investigate body waves interacting with the Earth's most dramatic interface, the core-mantle boundary (CMB). Intermediate-to-high frequency seismograms are computed incorporating topography models. We analyse the sensitivity of many seismic phases interacting with the interface. The study aims at showing effects of CMB structure on synthetics and highlights difficulties of imaging this region due to strong trade-off between velocity variations and topography. Synthetic waveforms computed at dominant periods of 6-18 seconds are used in order to obs…
Incorporating wave physical priors into diffusion models: A novel approach to seismic resolution enhancement
King Abdullah University of Science and Technology（阿卜杜拉国王科技大学）；School of Petroleum, China University of Petroleum-Beijing at Karamay（中国石油大学（北京）克拉玛依校区石油学院）；School of Geography and Tourism, Zhengzhou Normal University（郑州师范学院地理与旅游学院）
Uncertainty quantification is essential when dealing with ill-conditioned inverse problems due to the inherent nonuniqueness of the solution. Bayesian approaches allow us to determine how likely an estimation of the unknown parameters is via formulating the posterior distribution. Unfortunately, it is often not possible to formulate a prior distribution that precisely encodes our prior knowledge about the unknown. Furthermore, adherence to handcrafted priors may greatly bias the outcome of the Bayesian analysis. To address this issue, we propose to use the functional form of a randomly initial…
Deep Earth imaging through neutrino and seismic tomography
Institute of Physics（印度物理研究所）；Homi Bhabha National Institute（霍米·巴巴国立学院）；Indian Institute of Science Education and Research, Pune（印度科学教育研究学院浦那分校）；Tata Institute of Fundamental Research（塔塔基础研究院）；CSIR Fourth Paradigm Institute（印度科学工业研究理事会第四范式研究所）；Department of Physics, Aligarh Muslim University（阿利加尔穆斯林大学物理系）
