Seismic full-waveform inversion (FWI), which uses iterative methods to estimate high-resolution subsurface models from seismograms, is a powerful imaging technique in exploration geophysics. In recent years, the computational cost of FWI has grown exponentially due to the increasing size and resolution of seismic data. Moreover, it is a non-convex problem and can encounter local minima due to the limited accuracy of the initial velocity models or the absence of low frequencies in the measurements. To overcome these computational issues, we develop a multiscale data-driven FWI method based on fully convolutional networks (FCN). In preparing the training data, we first develop a real-time style transform method to create a large set of synthetic subsurface velocity models from natural images. We then develop two convolutional neural networks with encoder-decoder structure to reconstruct the low- and high-frequency components of the subsurface velocity models, separately. To validate the performance of our data-driven inversion method and the effectiveness of the synthesized training set, we compare it with conventional physics-based waveform inversion approaches using both synthetic and field data. These numerical results demonstrate that, once our model is fully trained, it can significantly reduce the computation time, and yield more accurate subsurface velocity models in comparison with conventional FWI.
I train a Generative Adversarial Network to produce realistic seismic wave speed models. I integrate the generator network into seismic Full-Waveform Inversion to reduce the number of model parameters and restrict the inverted models to only those that are plausible. Applying the method to a 2D section of the SEAM model, I demonstrate that it can produce more plausible results than conventional Full-Waveform Inversion.
We have implemented an extension for the observational seismology obspy software package to provide a streamlined tool tailored to the processing of seismic signals from non-earthquake sources, in particular those from deforming systems such as glaciers and landslides. This seismic attributes library provides functionality to: (1) download and/or pre-process seismic waveform data; (2) detect and catalogue seismic events using multi-component signals from one or more seismometers; and (3) calculate characteristics ('attributes'/'features') of the identified events. The workflow is controlled by…
I demonstrate that the conventional seismic full-waveform inversion algorithm can be constructed as a recurrent neural network and so implemented using deep learning software such as TensorFlow. Applying another deep learning concept, the Adam optimizer with minibatches of data, produces quicker convergence toward the true wave speed model on a 2D dataset than Stochastic Gradient Descent and than the L-BFGS-B optimizer with the cost function and gradient computed using the entire training dataset. I also show that the cost function gradient calculation using reverse-mode automatic differentiat…
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…
In this abstract, we propose a multiscale fusion technique to enhance seismic geometric attributes, such as dip and curvature, which are very sensitive to noise present in seismic data. For a give seismic section, first, we construct a Gaussian pyramid that allows us to generate the seismic attribute at different resolutions (scales). Then, all attributes at the different scales are fused together to form the proposed multiscale enhanced attribute. Applications to the 3D seismic dataset over the Great South Basin in New Zealand demonstrate that the proposed method is capable of improving both …
The idea of curvature analysis has been widely used in subsurface structure interpretation from three-dimensional (3D) seismic data (e.g., fault/fracture detection and geomorphology delineation) by measuring the lateral changes in the geometry of seismic events. However, such geometric curvature utilizes only the kinematic information (two-way traveltime) of the available seismic signals. While analyzing the dynamic information (waveform), the traditional approaches (e.g., complex trace analysis) are often trace-wise and thereby fail to take into account the seismic reflector continuity and de…
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…
We present a technique for reconstructing subsurface velocity model changes from time-lapse seismic survey data using full-waveform inversion (FWI). The technique is based on simultaneously inverting multiple survey vintages, with model difference regularization using the total variation (TV) seminorm. We compare the new TV-regularized time-lapse FWI with the $L_2$-regularized joint inversion proposed in our earlier work, using synthetic data sets that exhibit survey repeatability issues. The results demonstrate clear advantages of the proposed TV-regularized joint inversion over alternatives …
Waveform-Based Probabilistic Seismic Hazard Analysis Using Ground-Motion Generative Models
National Research Institute for Resilience Engineering Research Center Earth Science and Disaster Resilience Graduate School of Engineering（国立研究开发法人防灾科学技术研究所地球科学与灾害韧性研究生院）；The University of Tokyo（东京大学）
University of Basel（巴塞尔大学）；Université Grenoble Alpes（格勒诺布尔阿尔卑斯大学）；Université Savoie Mont Blanc（萨瓦勃朗峰大学）；CNRS（法国国家科学研究中心）；Université Gustave Eiffel（埃菲尔大学）；Sapienza University of Rome（罗马大学）；Pennsylvania State University（宾夕法尼亚州立大学）；Rice University（莱斯大学）
Prediction of the Kamchatka July 29, 2025, earthquake by the evolution of low-magnitude seismicity recovered using waveform cross-correlation at IMS seismic arrays
Convergent representations of elastic-wave structure emerge across deliberately distinct seismic training routes
Institute of Geophysics, China Earthquake Administration（中国地震局地球物理研究所）；University of Chinese Academy of Sciences（中国科学院大学）；Laboratory of Seismology and Physics of Earth’s Interior, School of Earth and Space Sciences, University of Science and Technology of China（中国科学技术大学地球和空间科学学院地球内部地震学与物理学实验室）；Institute of Advanced Technology, University of Science and Technology of China（中国科学技术大学先进技术研究院）
$\bullet$ Multiscale model of inner-core anisotropy produced by hcp alloy deformation$\bullet$ 5 to 20% single-crystal elastic anisotropy and plastic deformation by pyramidal slip $\bullet$ Low-degree inner-core formation model with faster crystallization at the equatorThe Earth's solid inner-core exhibits a global seismic anisotropy of several percents. It results from a coherent alignment of anisotropic Fe-alloy crystals through the inner-core history that can be sampled by present-day seismic observations. By combining self-consistent polycrystal plasticity, inner-core formation models, Mon…
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…
A web application prototype is described, aimed at the generation of synthetic seismograms for user-defined earthquake models. The web application graphical user interface hides the complexity of the underlying computational engine, which is the outcome of the continuous evolution of sophisticated computer codes, some of which saw the light back in the middle '80s. With the web application, even the non-experts can produce ground shaking scenarios at the local or regional scale in very short times, depending on the complexity of the adopted source and medium models, without the need of a deep …
Derivatives of the displacement tensor with respect to the independent model parameters of the subsurface, also called Fréchet derivatives (or sensitivity kernels), are a key ingredient for seismic full-waveform inversion with a local-search optimization algorithm. They provide a quantitative measure of the expected changes in the seismograms due to perturbations of the subsurface model parameters for a given survey geometry. Since 2.5-D wavefield modeling involves a real point source in a 2-D geological model with 3D (spherical) wave properties, it yields synthetic data much closer to the act…
Seismic monitoring of the Comprehensive Nuclear-Test-Ban Treaty using waveform cross correlation requires a uniform coverage of the globe with master events well recorded at array stations of the International Monitoring System. The essence of cross correlation as a monitoring tool consists in a continuous comparison of digital waveforms at a given station with waveform templates from the global set of master events. At array stations, cross correlation demonstrates a higher resolution because the time delays at individual sensors from master and slave events are the same but they may differ f…
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…
Traditional seismic envelope inversion takes use of a nonlinear misfit functional which relates the envelope of seismogram to the observed wavefield records, and then derive the sensitivity kernel of envelope to velocity through the use of waveform Frechet derivative by linearizing the nonlinear functional. We know that the waveform Frechet derivative is based on the Born approximation of wave scattering and can only work for the case of weak scattering. Therefore, the traditional envelope inversion using waveform Frechet derivative has severe limitation in the case of strong-scattering for la…
Low-magnitude seismic activity between the Kamchatka July 20 and July 29, 2025, earthquakes. Spatio-temporal evolution recovered using waveform cross-correlation
This paper presents a novel numerical method for the Newton seismic full-waveform inversion (FWI). The method is based on the full-space approach, where the state, adjoint state, and control variables are optimized simultaneously. Each Newton step is formulated as a PDE-constrained optimization problem, which is cast in the form of the Karush-Kuhn-Tucker (KKT) system of linear algebraic equitations. The KKT system is solved inexactly with a preconditioned Krylov solver. We introduced two preconditioners: the one based on the block-triangular factorization and its variant with an inexact block …
Los Alamos National Laboratory（洛斯阿拉莫斯国家实验室）；The Pennsylvania State University（宾夕法尼亚州立大学）；Michigan State University（密歇根州立大学）；Microsoft Research（微软研究院）
This paper investigates unsupervised learning of Full-Waveform Inversion (FWI), which has been widely used in geophysics to estimate subsurface velocity maps from seismic data. This problem is mathematically formulated by a second order partial differential equation (PDE), but is hard to solve. Moreover, acquiring velocity map is extremely expensive, making it impractical to scale up a supervised approach to train the mapping from seismic data to velocity maps with convolutional neural networks (CNN). We address these difficulties by integrating PDE and CNN in a loop, thus shifting the paradig…
Recovery of low-magnitude seismic events before the July 29, 2025, Kamchatka megathrust earthquake using waveform cross-correlation enhanced by the addition of stochastic noise
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…
We propose and test the Direct Waveform Inversion (DWI) scheme to simultaneously invert for layered velocity and density profiles, using reflection seismic waveforms recorded on the surface. The recorded data include primary reflections and interbed multiples. DWI is implemented in the time-space domain. By explicitly enforcing the wavefield time-space causality, DWI can recursively determine the subsurface seismic structure in a local fashion for both sharp interfaces as well as the properties of the layers, from shallow to deep depths. DWI is different from the layer stripping methods in the…
Waveform cross correlation is an efficient tool for detection and characterization of seismic signals. The efficiency critically depends on the availability of master events. For the purposes of the Comprehensive Nuclear-Test-Ban Treaty, cross correlation can globally reduce the threshold monitoring by 0.3 to 0.4 magnitude units. In seismically active regions, the optimal choice of master events is straightforward. There are two approaches to populate the global grid in aseismic areas: the replication of real masters and synthetic seismograms calculated for seismic arrays of the International …
Active faults release tectonic stress imposed by plate motion through a spectrum of slip modes, from slow, aseismic slip, to dynamic, seismic events. Slow earthquakes are often associated with tectonic tremor, non-impulsive signals that can easily be buried in seismic noise and go undetected. We present a new methodology aimed at improving the detection and location of tremors hidden within seismic noise. After identifying tremors with a classic convolutional neural network, we rely on neural network attribution to extract core tremor signatures and denoise input waveforms. We then use these c…
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…
Detecting weak seismic events from noisy sensors is a difficult perceptual task. We formulate this task as Bayesian inference and propose a generative model of seismic events and signals across a network of spatially distributed stations. Our system, SIGVISA, is the first to directly model seismic waveforms, allowing it to incorporate a rich representation of the physics underlying the signal generation process. We use Gaussian processes over wavelet parameters to predict detailed waveform fluctuations based on historical events, while degrading smoothly to simple parametric envelopes in regio…
Full-waveform inversion (FWI) is a widely used technique in seismic processing to produce high resolution Earth models that fully explain the recorded seismic data. FWI is a local optimisation problem which aims to minimise in a least-squares sense the misfit between recorded and modelled data. The inversion process begins with a best-guess initial model which is iteratively improved using a sequence of linearised local inversions to solve a fully non-linear problem. Deep learning has gained widespread popularity in the new millennium. At the core of these tools are Neural Networks (NN), in pa…
In the last ten years, full-waveform inversion has emerged as a robust and efficient high-resolution velocity model-building tool for seismic imaging, with the unique ability to recover complex subsurface structures. Originally based on a data fitting process using a least-squares cost function, it suffered from high sensitivity to cycle-skipping and was therefore of poor efficiency in handling large time shifts between observed and modelled seismic events. To tackle this problem, a common practice is to start the inversion using the low temporal frequencies of the data and selecting diving wa…
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 …
Seismic-phase detection using multiple deep learning models for global and local representations of waveforms
Earthquake Research Institute, The University of Tokyo（东京大学地震研究所）；Graduate School of Information Science and Technology, The University of Tokyo（东京大学信息科学与技术研究生院）
We present a wave-equation inversion method that inverts skeletonized data for the subsurface velocity model. The skeletonized representation of the seismic traces consists of the low-rank latent-space variables predicted by a well-trained autoencoder neural network. The input to the autoencoder is the recorded common shot gathers, and the implicit function theorem is used to determine the perturbation of the skeletonized data with respect to the velocity perturbation. The final velocity model is the one that best predicts the observed latent-space parameters. Empirical results suggest that th…
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…
The multi-master method based on waveform cross-correlation has found several aftershocks of the third (DPRK3) and the fourth (DPRK4) announced underground nuclear tests conducted by the DPRK on 12.02.2013, and 06.01.2016, respectively. The second DPRK test had no reliable aftershock hypotheses at the level of the method sensitivity and resolution. The closest to the test site array station USRK was not operational before 20.12.2008 and the first DPRK test cannot be analyzed by the multi-master method based on waveform templates from two IMS stations - USRK and KSRS. The largest aftershocks of…
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…
Effects of stochastic and natural seismic noise on the performance of waveform cross-correlation used to recover low-magnitude seismicity prior to the July 29, 2025, Kamchatka earthquake
We investigate the possibility to extract information contained in seismic waveforms propagating in fluid-filled porous media by developing and using a full waveform inversion procedure valid for layered structures. To reach this objective, we first solve the forward problem by implementing the Biot theory in a reflectivity-type simulation program. We then study the sensitivity of the seismic response of stratified media to the poroelastic parameters. Our numerical tests indicate that the porosity and consolidation parameter are the most sensitive parameters in forward and inverse modeling, wh…
