地震层析成像是一种对地球地下属性进行成像的方法。为了更好地解释成像结果，评估结果的不确定性十分重要。混合密度网络（Mixture density networks, MDNs）为估计描述层析成像不确定性的贝叶斯后验概率密度函数（probability density functions, pdfs）提供了一种高效途径。但该方法仅适用于数据数量固定的场景，因此无法解决大量数据规模可变的实际应用问题。为解决这一问题，我们引入图神经网络（graph neural networks, GNNs）来求解地震层析成像问题。图是一种能灵活表示复杂可变系统的数据结构，GNNs是处理图数据的神经网络，可与MDNs结合（称为图MDNs），为图数据提供后验概率密度函数的高效估计。本研究通过用图表示走时数据，将图MDNs应用于地震层析成像。我们使用合成数据和实际数据验证了该方法，并将结果与马尔可夫链蒙特卡洛（Markov chain Monte Carlo, McMC）方法的结果进行对比。结果表明，图MDNs能以显著更低的计算成本得到与McMC方法相当的后验概率密度函数。因此我们得出结论：图MDNs可应用于一系列需要求解大量数据数量不同的同类地震层析成像问题的实际场景。
英文摘要：
Seismic tomography is a methodology to image subsurface properties of the Earth. In order to better interpret the resulting images, it is important to assess uncertainty in the results. Mixture density networks (MDNs) provide an efficient way to estimate Bayesian posterior probability density functions (pdfs) that describe the uncertainty of tomographic images. However, the method can only be applied in cases where the number of data is fixed, and consequently a large number of practical applications that have variable data sizes cannot be solved. To resolve this issue, we introduce graph neural networks (GNNs) to solve seismic tomographic problems. Graphs are data structure which provides flexible representation of complex, variable systems. GNNs are neural networks that manipulates graph data, and can be combined with MDNs (called graph MDNs) to provide efficient estimates of posterior pdfs for graph data. In this study we apply graph MDNs to seismic tomography by representing travel time data with a graph. We demonstrate the method using both synthetic and real data, and compare the results with those obtained using Markov chain Monte Carlo (McMC). The results show that graph MDNs can provide comparable posterior pdfs to those obtained using McMC at significantly lower cost. We thus conclude that graph MDNs can be used in a range of practical applications that require many similar seismic tomographic problems with different number of data to be solved.
Seismotectonics and Slip Behavior of a Submarine Plate Boundary Fault from Seismicity Repeaters and Tomography using a high-resolution earthquake catalog from machine learning
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. …
The effects of several nonlinear regularization techniques are discussed in the framework of 3D seismic tomography. Traditional, linear, $\ell_2$ penalties are compared to so-called sparsity promoting $\ell_1$ and $\ell_0$ penalties, and a total variation penalty. Which of these algorithms is judged optimal depends on the specific requirements of the scientific experiment. If the correct reproduction of model amplitudes is important, classical damping towards a smooth model using an $\ell_2$ norm works almost as well as minimizing the total variation but is much more efficient. If gradients (e…
Seismic tomography is a methodology to image the interior of solid or fluid media, and is often used to map properties in the subsurface of the Earth. In order to better interpret the resulting images it is important to assess imaging uncertainties. Since tomography is significantly nonlinear, Monte Carlo sampling methods are often used for this purpose, but they are generally computationally intractable for large datasets and high-dimensional parameter spaces. To extend uncertainty analysis to larger systems we use variational inference methods to conduct seismic tomography. In contrast to Mo…
The purpose of this work is to generalize the frozen Gaussian approximation (FGA) theory to solve the 3-D elastic wave equation and use it as the forward modeling tool for seismic tomography with high-frequency data. FGA has been previously developed and verified as an efficient solver for high-frequency acoustic wave propagation (P-wave). The main contribution of this paper consists of three aspects: 1. We derive the FGA formulation for the 3-D elastic wave equation. Rather than standard ray-based methods (e.g. geometric optics and Gaussian beam method), the derivation requires to do asymptot…
This paper introduces novel deep recurrent neural network architectures for Velocity Model Building (VMB), which is beyond what Araya-Polo et al 2018 pioneered with the Machine Learning-based seismic tomography built with convolutional non-recurrent neural network. Our investigation includes the utilization of basic recurrent neural network (RNN) cells, as well as Long Short Term Memory (LSTM) and Gated Recurrent Unit (GRU) cells. Performance evaluation reveals that salt bodies are consistently predicted more accurately by GRU and LSTM-based architectures, as compared to non-recurrent architec…
We introduce a `double-difference' method for the inversion for seismic wavespeed structure based on adjoint tomography. Differences between seismic observations and model predictions at individual stations may arise from factors other than structural heterogeneity, such as errors in the assumed source-time function, inaccurate timings, and systematic uncertainties. To alleviate the corresponding nonuniqueness in the inverse problem, we construct differential measurements between stations, thereby reducing the influence of the source signature and systematic errors. We minimize the discrepancy…
In this article, we develop a 1-D traveltime tomography method to calculate the seismic P-wave velocity of a medium. We use the results of 1-D tomography to obtain linear inhomogeneity parameters in a specific layer. To get the trustworthiness of the method, we perform several synthetic experiments. We show that the inverted model parameters are reasonably accurate and stable. To examine the results of linear inhomogeneity parameters using a different method, we also develop an inversion method based on a two-parameter velocity model. Finally, we apply both the methods to Vertical Seismic Prof…
We propose a local earthquake tomography method that applies a structured regularization technique to determine sharp changes in Earth's seismic velocity structure using arrival time data of direct waves. Our approach focuses on the ability to better image two common features that are observed in Earth's seismic velocity structure: sharp changes in velocities that correspond to material boundaries, such as the Conrad and Moho discontinuities; and gradual changes in velocity that are associated with pressure and temperature distributions in the crust and mantle. We employ different penalty term…
Seismic Traveltime Tomography with Label-free Learning
College of Big Data and Software Engineering, Zhejiang Wanli University（浙江万里学院大数据与软件工程学院）；Key Laboratory of Geoscience Big Data and Deep Resource of Zhejiang Province, School of Earth Sciences, Zhejiang University（浙江大学地球科学学院浙江省地球科学大数据与深部资源重点实验室）
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）
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…
Imperial College London（帝国理工学院）；Open Energi Ltd.（Open Energi有限公司）；Technical University of Denmark（丹麦技术大学）；Euclidity SL（Euclidity SL公司）；Skolkovo Institute of Science and Technology（斯科尔科沃科学技术研究所）；Expero Inc.（Expero公司）
Traditional physics-based approaches to infer sub-surface properties such as full-waveform inversion or reflectivity inversion are time-consuming and computationally expensive. We present a deep-learning technique that eliminates the need for these computationally complex methods by posing the problem as one of domain transfer. Our solution is based on a deep convolutional generative adversarial network and dramatically reduces computation time. Training based on two different types of synthetic data produced a neural network that generates realistic velocity models when applied to a real data…
The purpose of marine seismic experiments is to provide information of the structure and physical properties of the subsurface. The P-wave velocity distribution is the most commonly modelled property, usually by inversion of arrival times or waveform attributes. The most widely used tool to extract refractions as first arrivals from MCS recordings is the so-called downward continuation technique, which is designed for redatuming streamer field data to the seafloor. In this new virtual configuration, the early refractions transform to seismic phases that are becoming visible as first arrivals f…
Enhanced Seismicity Monitoring in the Rapid Scientific Response to the 2025 Santorini Crisis
The Lyell Centre, British Geological Survey（英国地质调查局利尔中心）；School of GeoSciences, The University of Edinburgh（爱丁堡大学地球科学学院）；Department of Geophysics, Stanford University（斯坦福大学地球物理学系）；GFZ Helmholtz Centre for Geosciences（GFZ德国地学研究中心赫尔姆霍茨）；RWTH Aachen University（亚琛工业大学）；Dipartimento di Fisica Ettore Pancini, Università degli Studi di Napoli Federico II（那不勒斯费德里科二世大学埃托雷·潘奇尼物理系）；Istituto Nazionale di Geofisica e Vulcanologia (INGV)（意大利国家地球物理学和火山学研究所）；U.S. Geological Survey, Volcano Disaster Assistance Program（美国地质调查局火山灾害援助计划）；Department of Earth Sciences, University of Oxford（牛津大学地球科学系）；Department of Civil and Environmental Engineering, University of Southern California（南加州大学土木与环境工程系）；Division of Natural Sciences, Academy of Athens（雅典科学院自然科学部）；U.S. Geological Survey, Pacific Coastal and Marine Science Center（美国地质调查局太平洋沿海与海洋科学中心）；Institute of Geodynamics, National Observatory of Athens（雅典国立天文台地球动力学研究所）；Dipartimento di Geoscienze, Università degli Studi di Padova（帕多瓦大学地球科学系）；Dipartimento di Scienze della Terra, dell’ Ambiente e delle Risorse, Università degli Studi di Napoli Federico II（那不勒斯费德里科二世大学地球、环境与资源科学系）
Travel time tomography is used to infer the underlying three-dimensional wavespeed structure of the Earth by fitting seismic travel time data collected at surface stations. Data interpolation and denoising techniques are important pre-processing steps that use prior knowledge about the data, including parsimony in the frequency and wavelet domains, low-rank structure of matricizations, and local smoothness. We show how local smoothness structure can be combined with low rank constraints using level-set optimization formulations, and develop a new relaxation algorithm that can efficiently solve…
Solving or resolving global tomographic models with spherical wavelets, and the scale and sparsity of seismic heterogeneity
Princeton University（普林斯顿大学）；Université Libre de Bruxelles（布鲁塞尔自由大学）；GéoAzur Université de Nice（尼斯大学地理与地球物理实验室）；Program in Applied and Computational Mathematics Princeton University（普林斯顿大学应用与计算数学项目）
We present a technique to automatically classify the wave type of seismic phases that are recorded on a single six-component recording station (measuring both three components of translational and rotational ground motion) at the earth's surface. We make use of the fact that each wave type leaves a unique 'fingerprint' in the six-component motion of the sensor. This fingerprint can be extracted by performing an eigenanalysis of the data covariance matrix, similar to conventional three-component polarization analysis. To assign a wave type to the fingerprint extracted from the data, we compare …
We propose the use of $\ell_1$ regularization in a wavelet basis for the solution of linearized seismic tomography problems $Am=d$, allowing for the possibility of sharp discontinuities superimposed on a smoothly varying background. An iterative method is used to find a sparse solution $m$ that contains no more fine-scale structure than is necessary to fit the data $d$ to within its assigned errors.
Seismic velocity is one of the most important parameters used in seismic exploration. Accurate velocity models are key prerequisites for reverse-time migration and other high-resolution seismic imaging techniques. Such velocity information has traditionally been derived by tomography or full-waveform inversion (FWI), which are time consuming and computationally expensive, and they rely heavily on human interaction and quality control. We investigate a novel method based on the supervised deep fully convolutional neural network (FCN) for velocity-model building (VMB) directly from raw seismogra…
Precise real time estimates of earthquake magnitude and location are essential for early warning and rapid response. While recently multiple deep learning approaches for fast assessment of earthquakes have been proposed, they usually rely on either seismic records from a single station or from a fixed set of seismic stations. Here we introduce a new model for real-time magnitude and location estimation using the attention based transformer networks. Our approach incorporates waveforms from a dynamically varying set of stations and outperforms deep learning baselines in both magnitude and locat…
In Earthquake Early Warning (EEW), every sufficiently impulsive signal is potentially the first evidence for an unfolding large earthquake. More often than not, however, impulsive signals are mere nuisance signals. One of the most fundamental - and difficult - tasks in EEW is to rapidly and reliably discriminate real local earthquake signals from all other signals. This discrimination is necessarily based on very little information, typically a few seconds worth of seismic waveforms from a small number of stations. As a result, current EEW systems struggle to avoid discrimination errors, and s…
As the number of seismic sensors grows, it is becoming increasingly difficult for analysts to pick seismic phases manually and comprehensively, yet such efforts are fundamental to earthquake monitoring. Despite years of improvements in automatic phase picking, it is difficult to match the performance of experienced analysts. A more subtle issue is that different seismic analysts may pick phases differently, which can introduce bias into earthquake locations. We present a deep-neural-network-based arrival-time picking method called "PhaseNet" that picks the arrival times of both P and S waves. …
This paper presents several strategies for spectral de-noising of hyperspectral images and hypercube reconstruction from a limited number of tomographic measurements. In particular we show that the non-noisy spectral data, when stacked across the spectral dimension, exhibits low-rank. On the other hand, under the same representation, the spectral noise exhibits a banded structure. Motivated by this we show that the de-noised spectral data and the unknown spectral noise and the respective bands can be simultaneously estimated through the use of a low-rank and simultaneous sparse minimization op…
Parameter-Efficient Adaptation of Pre-Trained Vision Foundation Models for Active and Passive Seismic Data Denoising
Computation-based Science and Technology Research Center, The Cyprus Institute（计算科学与技术研究中心，塞浦路斯研究所）；Department of Geosciences, College of Petroleum Engineering and Geosciences, King Fahd University of Petroleum & Minerals（地质学系，石油工程与地质学院，国王法赫德石油与矿物大学）；Department of Intelligent Systems, Faculty of Electrical Engineering, Mathematics and Computer Science, Delft University of Technology（智能系统系，电气工程、数学与计算机科学学院，代尔夫特理工大学）；Department of Mathematics and Statistics, Faculty of Pure and Applied Sciences, University of Cyprus（数学与统计学系，纯应用科学学院，塞浦路斯大学）；Department of Geoscience and Engineering, Faculty of Civil Engineering and Geosciences, Delft University of Technology（地质科学与工程系，土木工程与地质科学学院，代尔夫特理工大学）
