Full-wave inversion (FWI), as a fundamental scientific approach to deducing unknown or unobservable subsurface properties, holds significant value in geophysics applications. Traditional FWI methods rely on physics-driven approaches that demand substantial computational resources. Recently, with the breakthroughs in machine learning (ML) and the prevalence of AI for science, data-driven approaches have been applied to FWI, showing promising results. However, as these applications often necessitate deployment in diverse regions with remote and extreme environments, localization of ML models on edge devices becomes imperative. A promising approach involves leveraging Generative AI models and governing wave equations to generate paired training data, including geophysical measurements (i.e., seismic waveform) as data and corresponding velocity maps as labels for model fine-tuning. However, the limited resources on edge devices pose significant challenges to achieving high software efficiency and low latency. In this article, we present a toolkit, namely DiGiT, a di ffusion-based modular g eophys i cal t oolkit platform. One key component is a library of decomposed modules from the widely used geophysical designs. Benefiting from the flexibility of combining modules, we composite a toolkit for the generation of on-device diffusion-based paired geophysical training data. The toolkit includes a 1-in-2-out network structure and diffusion model distillation, both of which can significantly reduce the computational time. Experiments on the OpenFWI dataset show that the DiGiT toolkit can generate paired seismic waveform and velocity map in seconds, which is over 100× speedup compared with the sequential execution of the diffusion model and the wave equation-based forward modeling.

Recently, the advent of generative AI technologies has made transformational impacts on our daily lives, yet its application in scientific applications remains in its early stages. Data scarcity is a major, well-known barrier in data-driven scientific computing, so physics-guided generative AI holds significant promise. In scientific computing, most tasks study the conversion of multiple data modalities to describe physical phenomena, for example, spatial and waveform in seismic imaging, time and frequency in signal processing, and temporal and spectral in climate modeling; as such, multi-modal pairwise data generation is highly required instead of single-modal data generation, which is usually used in natural images (e.g., faces, scenery). Moreover, in real-world applications, the unbalance of available data in terms of modalities commonly exists; for example, the spatial data (i.e., velocity maps) in seismic imaging can be easily simulated, but real-world seismic waveform is largely lacking. While the most recent efforts enable the powerful diffusion model to generate multi-modal data, how to leverage the unbalanced available data is still unclear. In this work, we use seismic imaging in subsurface geophysics as a vehicle to present "UB-Diff", a novel diffusion model for multi-modal paired scientific data generation. One major innovation is a one-in-two-out encoder-decoder network structure, which can ensure pairwise data is obtained from a co-latent representation. Then, the co-latent representation will be used by the diffusion process for pairwise data generation. Experimental results on the OpenFWI dataset show that UB-Diff significantly outperforms existing techniques in terms of Fréchet Inception Distance (FID) score and pairwise evaluation, indicating the generation of reliable and useful multi-modal pairwise data.

In subsurface imaging, learning the mapping from velocity maps to seismic waveforms (forward problem) and waveforms to velocity (inverse problem) is important for several applications. While traditional techniques for solving forward and inverse problems are computationally prohibitive, there is a growing interest to leverage recent advances in deep learning to learn the mapping between velocity maps and seismic waveform images directly from data. Despite the variety of architectures explored in previous works, several open questions still remain unanswered such as the effect of latent space sizes, the importance of manifold learning, the complexity of translation models, and the value of jointly solving forward and inverse problems. We propose a unified framework to systematically characterize prior research in this area termed the Generalized Forward-Inverse (GFI) framework, building on the assumption of manifolds and latent space translations. We show that GFI encompasses previous works in deep learning for subsurface imaging, which can be viewed as specific instantiations of GFI. We also propose two new model architectures within the framework of GFI: Latent U-Net and Invertible X-Net, leveraging the power of U-Nets for domain translation and the ability of IU-Nets to simultaneously learn forward and inverse translations, respectively. We show that our proposed models achieve state-of-the-art (SOTA) performance for forward and inverse problems on a wide range of synthetic datasets, and also investigate their zero-shot effectiveness on two real-world-like datasets. The code is available at https://github.com/KGML-lab/Generalized-Forward-Inverse-Framework-for-DL4SI

In this paper, we empirically demonstrate that natural images can be reconstructed with high fidelity from compressed representations using a simple first-order norm-plus-linear autoregressive (FINOLA) process—without relying on explicit positional information. Through systematic analysis, we observe that the learned coefficient matrices ($\mathbf{A}$ and $\mathbf{B}$) in FINOLA are typically invertible, and their product, $\mathbf{AB}^{-1}$, is diagonalizable across training runs. This structure enables a striking interpretation: FINOLA’s latent dynamics resemble a system of one-way wave equations evolving in a compressed latent space. Under this framework, each image corresponds to a unique solution of these equations. This offers a new perspective on image invariance, suggesting that the underlying structure of images may be governed by simple, invariant dynamic laws. Our findings shed light on a novel avenue for understanding and modeling visual data through the lens of latent-space dynamics and wave propagation.

Computational wave imaging (CWI) extracts hidden structure and physical properties of a volume of material by analyzing wave signals that traverse that volume. Applications include seismic exploration of the Earth's subsurface, acoustic imaging and non-destructive testing in material science, and ultrasound computed tomography in medicine. Current approaches for solving CWI problems can be divided into two categories: those rooted in traditional physics, and those based on deep learning. Physics-based methods stand out for their ability to provide high-resolution and quantitatively accurate estimates of acoustic properties within the medium. However, they can be computationally intensive and are susceptible to ill-posedness and nonconvexity typical of CWI problems. Machine learning-based computational methods have recently emerged, offering a different perspective to address these challenges. Diverse scientific communities have independently pursued the integration of deep learning in CWI. This review discusses how contemporary scientific machine-learning (ML) techniques, and deep neural networks in particular, have been developed to enhance and integrate with traditional physics-based methods for solving CWI problems. We present a structured framework that consolidates existing research spanning multiple domains, including computational imaging, wave physics, and data science. This study concludes with important lessons learned from existing ML-based methods and identifies technical hurdles and emerging trends through a systematic analysis of the extensive literature on this topic.

In CO2sequestration projects, multi-physics inversion has been widely used to reconstruct various geophysical properties (such as velocity and conductivity). However, the saturation of CO2is not feasible through partial differential equations (PDEs), which poses a challenge to traditional multi-physics inversion techniques in directly inverting CO2saturation from geophysical measurements. Typically, a rock physics model is constructed to tackle this challenge. Nevertheless, the construction of such a model is intricate due to the inherent complexities and uncertainties within subsurface geology and geophysical data. Data-driven inversion methods present an alternative solution, as they can connect CO2saturation to geophysical measurements and directly learn their relationships from labeled data. Nonetheless, the efficacy of these methods hinges on extensive data labeling, incurring considerable costs. To address this challenge, we propose a novel data-driven technique for the inversion of multi-physics data called Weakly Supervised Multi-Geophysical Inversion (WS-MGI), which reduces the need for labeling and promises to be a more cost-effective solution. In particular, we focus on the multi-physics inversion problem from two geophysical data (electromagnetic (EM) and seismic) to CO2saturation. By learning the local relationship between velocity and CO2saturation at a few well logs, we construct the pseudo labels for CO2saturation, thus enabling the data-driven inversion with few labels. We verify our method using synthetic data based on the Kimberlina storage reservoir in California. Experiments show that compared to the supervised counterpart, our method can achieve similar inversion results with only 2% labels.

Generative Adversarial Networks (GANs) are deep learning models that learn and generate new samples similar to existing ones. Traditionally, GANs are trained in centralized data centers, raising data privacy concerns due to the need for clients to upload their data. To address this, Federated Learning (FL) integrates with GANs, allowing collaborative training without sharing local data. However, this integration is complex because GANs involve two interdependent models—the generator and the discriminator—while FL typically handles a single model over distributed datasets. In this article, we propose a novel asynchronous FL framework for GANs, called AsyncFedGAN, designed to efficiently and distributively train both models tailored for molecule generation. AsyncFedGAN addresses the challenges of training interactive models, resolves the straggler issue in synchronous FL, reduces model staleness in asynchronous FL, and lowers client energy consumption. Our extensive simulations for molecular discovery show that AsyncFedGAN achieves convergence with proper settings, outperforms baseline methods, and balances model performance with client energy usage.

Full Waveform Inversion (FWI) is a technique used to visualize and analyze wave propagation through a medium in order to infer its physical properties. This method relies on computational models and algorithms to simulate and interpret the behavior of waves—such as sound, electromagnetic, or seismic waves—as they travel through different materials. By analyzing how these waves are reflected, refracted, or absorbed by the medium, FWI can provide detailed information about the medium’s internal structure, composition, and physical properties, such as density, elasticity, or internal defects. The traditional process typically involves: 1) Wave Simulation: Using physics-based models to simulate how waves propagate through a medium. This may involve solving complex differential equations that describe wave behavior in different contexts. 2) Data Acquisition: Collecting data on wave interactions with the medium using sensors or other measurement devices. This could include data on wave speed, direction, amplitude, and phase changes. 3) Image Reconstruction: Applying computational techniques, such as inverse problems or tomographic reconstruction, to create images or maps of the medium based on the acquired wave data. 4) Analysis: Interpreting the reconstructed images to deduce the physical properties of the medium. This can involve identifying features like boundaries, interfaces, or anomalies within the medium.

The rapid advancement of quantum computing has generated considerable anticipation for its transformative potential. However, harnessing its full potential relies on identifying "killer applications". In this regard, QuGeo emerges as a groundbreaking quantum learning framework, poised to become a key application in geoscience, particularly for Full-Waveform Inversion (FWI). This framework integrates variational quantum circuits with geoscience, representing a novel fusion of quantum computing and geophysical analysis. This synergy unlocks quantum computing's potential within geoscience. It addresses the critical need for physics-guided data scaling, ensuring high-performance geoscientific analyses aligned with core physical principles. Furthermore, QuGeo's introduction of a quantum circuit custom-designed for FWI highlights the critical importance of application-specific circuit design for quantum computing. In the OpenFWI's FlatVelA dataset experiments, the variational quantum circuit from QuGeo, with only 576 parameters, achieved significant improvement in performance. It reached a Structural Similarity Image Metric (SSIM) score of 0.905 between the ground truth and the output velocity map. This is a notable enhancement from the baseline design's SSIM score of 0.800, which was achieved without the incorporation of physics knowledge.

Full-waveform inversion (FWI) plays a vital role in geoscience to explore the subsurface. It utilizes the seismic wave to image the subsurface velocity map. As the machine learning (ML) technique evolves, the data-driven approaches using ML for FWI tasks have emerged, offering enhanced accuracy and reduced computational cost compared to traditional physics-based methods. However, a common challenge in geoscience --- the unprivileged data --- severely limits ML effectiveness. The issue becomes even worse during model pruning, a step essential in geoscience due to environmental complexities. To tackle this, we introduce the EdGeo toolkit, which employs a diffusion-based model guided by physics principles to generate high-fidelity velocity maps. The toolkit uses the acoustic wave equation to generate corresponding seismic waveform data, facilitating the fine-tuning of pruned ML models. Our results demonstrate significant improvements in SSIM scores and reduction in both MAE and MSE across various pruning ratios. Notably, the ML model fine-tuned using data generated by EdGeo yields superior quality of velocity maps, especially in representing unprivileged features, outperforming other existing methods.

Medical image reconstruction plays a pivotal role in early cancer detection, which can significantly enhance both the quality and longevity of a patient’s life through timely treatment. However, the extent to which current image reconstruction methods accurately represent all populations, and whether they underperform for certain groups, remains largely unexplored. In this work, we will examine the deep learning (DL)–based approach to image reconstruction and its associated fairness concerns. Initially, our experiments confirmed the unfairness’s presence. Subsequently, by addressing the issue from two perspectives, we gained valuable insights, which deepened our understanding of the problem. To assess a model’s fairness, it’s crucial to evaluate it from various perspectives, as relying on a single metric can often yield misleading results.

Ultrasound computed tomography (USCT) is an emerging imaging modality that holds great promise for breast imaging. Full-waveform inversion (FWI)-based image reconstruction methods leverage accurate wave physics to generate high spatial resolution quantitative images of the breast tissue’s acoustic properties, such as speed of sound, from USCT measurement data. However, the significant computational demand for FWI reconstruction poses a considerable challenge to its widespread adoption in clinical settings. Data-driven machine learning approaches offer a faster and more efficient means of translating waveform data into images. Yet, the effectiveness of machine learning methods is constrained by the diversity and quality of the training data. Given the heterogeneous distribution of breast tissue characteristics, such as fat content and size, the performance of machine learning varies across different sizes. This variability is problematic, particularly in medical diagnostics, where precision is crucial. In response to the limited data in certain categories, we propose utilizing generative AI to augment data samples, thereby enhancing FWI’s performance on limited-sample data and addressing issues of AI fairness.

Subsurface imaging involves solving full waveform inversion (FWI) to predict geophysical properties from measurements. This problem can be reframed as an image-to-image translation, with the usual approach being to train an encoder-decoder network using paired data from two domains: geophysical property and measurement. A recent seminal work (InvLINT) demonstrates there is only a linear mapping between the latent spaces of the two domains, and the decoder requires paired data for training. This paper extends this direction by demonstrating that only linear mapping necessitates paired data, while both the encoder and decoder can be learned from their respective domains through self-supervised learning. This unveils an intriguing phenomenon (named Auto-Linear) where the self-learned features of two separate domains are automatically linearly correlated. Compared with existing methods, our Auto-Linear has four advantages: (a) solving both forward and inverse modeling simultaneously, (b) reducing model size, (c) enhanced performance, especially when the paired data is limited, and (d) strong generalization ability of the trained encoder and decoder.

Recently, we have been witnessing the scale-up of superconducting quantum computers; however, the noise of quantum bits (qubits) is still an obstacle for real-world applications to leveraging the power of quantum computing. Although there exist error mitigation or error-aware designs for quantum applications, the inherent fluctuation of noise (a.k.a., instability) can easily collapse the performance of error-aware designs. What’s worse, users can even not be aware of the performance degradation caused by the change in noise. To address both issues, in this paper we use Quantum Neural Network (QNN) as a vehicle to present a novel compression-aided framework, namely QuCAD, which will adapt a trained QNN to fluctuating quantum noise. In addition, with the historical calibration (noise) data, our framework will build a model repository offline, which will significantly reduce the optimization time in the online adaption process. Emulation results on an earthquake detection dataset show that QuCAD can achieve 14.91% accuracy gain on average in 146 days over a noise-aware training approach. For the execution on a 7-qubit IBM quantum processor, ibm-jakarta, QuCAD can consistently achieve 12.52% accuracy gain on earthquake detection.

In the study of subsurface seismic imaging, solving the acoustic wave equation is a pivotal component in existing models. The advancement of deep learning enables solving partial differential equations, including wave equations, by applying neural networks to identify the mapping between the inputs and the solution. This approach can be faster than traditional numerical methods when numerous instances are to be solved. Previous works that concentrate on solving the wave equation by neural networks consider either a single velocity model or multiple simple velocity models, which is restricted in practice. Instead, inspired by the idea of operator learning, this work leverages the Fourier neural operator (FNO) to effectively learn thefrequency domainseismic wavefields under the context ofvariable velocity models. We also propose a new frameworkparalleled Fourier neural operator(PFNO) for efficiently training the FNO-based solver given multiple source locations and frequencies. Numerical experiments demonstrate the high accuracy of both FNO and PFNO with complicated velocity models in the OpenFWI datasets. Furthermore, the cross-dataset generalization test verifies that PFNO adapts to out-of-distribution velocity models. Finally, PFNO admits higher computational efficiency on large-scale testing datasets than the traditional finite-difference method. The aforementioned advantages endow the FNO-based solver with the potential to build powerful models for research on seismic waves.

The detection and picking of seismic waves is the first step toward earthquake catalog building, earthquake monitoring, and seismic hazard management. Recent advances in deep learning have leveraged the amount of labeled seismic data to improve the capability of detecting and picking earthquake signals. While these deep learning methods have shown great promise, their success remains hindered by low generalizability and poor performance in low signal-to-noise ratios (SNRs) data. Here, we propose a new processing workflow that integrates pretrained deep learning models, multi-frequency band predictions, and ensemble estimations to enhance the generalization of these algorithms. We test the performance of the ensemble model using three benchmark datasets, one of which is within-domain and has been used for training the deep learning models, the other two being cross-domain test datasets. We explore the performance given data and model characteristics. We also compare an ensemble approach with a transfer-learning approach and discuss the benefits and drawbacks of these two approaches when deploying on continuous data. Our experiments demonstrate that ensemble learning can drastically improve generalization ability and hence alleviate the need for transfer learning in the case where no labeled datasets exist.

Earth and planetary geosciences are essential for understanding and addressing many societal challenges and scientific questions. Increased availability of geoscience data creates an opportunity for deep learning to advance the methods and scientific understanding for tackling these challenges. However, the complex characteristics of geoscience problems and datasets necessitate the development of novel approaches and frameworks. This Special Issue aims at collecting new ideas and deep learning formulations to gain new earth and planetary insights. The contributions cover a wide range of topics, such as satellite and hyperspectral imaging, land monitoring, geophysical imaging, and subsurface analysis.

Model compression, such as pruning and quantization, has been widely applied to optimize neural networks on resource-limited classical devices. Recently, there are growing interest in variational quantum circuits (VQC), that is, a type of neural network on quantum computers (a.k.a., quantum neural networks). It is well known that the near-term quantum devices have high noise and limited resources (i.e., quantum bits, qubits); yet, how to compress quantum neural networks has not been thoroughly studied. One might think it is straightforward to apply the classical compression techniques to quantum scenarios. However, this paper reveals that there exist differences between the compression of quantum and classical neural networks. Based on our observations, we claim that the compilation/traspilation has to be involved in the compression process. On top of this, we propose the very first systematical framework, namely CompVQC, to compress quantum neural networks (QNNs). In CompVQC, the key component is a novel compression algorithm, which is based on the alternating direction method of multipliers (ADMM) approach. Experiments demonstrate the advantage of the CompVQC, reducing the circuit depth (almost over 2.5×) with a negligible accuracy drop (<1%), which outperforms other competitors. Another promising truth is our CompVQC can indeed promote the robustness of the QNN on the near-term noisy quantum devices.

Inversion techniques are widely used to reconstruct subsurface physical properties (e.g., velocity, conductivity) from surface-based geophysical measurements (e.g., seismic, electric/magnetic (EM) data). The problems are governed by partial differential equations (PDEs) like the wave or Maxwell’s equations. Solving geophysical inversion problems is challenging due to the ill-posedness and high computational cost. To alleviate those issues, recent studies leverage deep neural networks to learn the inversion mappings from measurements to the property directly. In this paper, we show that such a mapping can be well modeled by a very shallow (but not wide) network with only five layers. This is achieved based on our new finding of an intriguing property: a near-linear relationship between the input and output, after applying integral transform in high dimensional space. In particular, when dealing with the inversion from seismic data to subsurface velocity governed by a wave equation, the integral results of velocity with Gaussian kernels are linearly correlated to the integral of seismic data with sine kernels. Furthermore, this property can be easily turned into a light-weight encoder-decoder network for inversion. The encoder contains the integration of seismic data and the linear transformation without need for fine-tuning. The decoder only consists of a single transformer block to reverse the integral of velocity. Experiments show that this interesting property holds for two geophysics inversion problems over four different datasets. Compared to much deeper InversionNet, our method achieves comparable accuracy, but consumes significantly fewer parameters

Full waveform inversion (FWI) is widely used in geophysics to reconstruct high-resolution velocity maps from seismic data. The recent success of data-driven FWI methods results in a rapidly increasing demand for open datasets to serve the geophysics community. We present OpenFWI, a collection of large-scale multi-structural benchmark datasets, to facilitate diversified, rigorous, and reproducible research on FWI. In particular, OpenFWI consists of $12$ datasets ($2.1$TB in total) synthesized from multiple sources. It encompasses diverse domains in geophysics (interface, fault, CO$_2$ reservoir, etc.), covers different geological subsurface structures (flat, curve, etc.), and contain various amounts of data samples (2K - 67K). It also includes a dataset for 3D FWI. Moreover, we use OpenFWI to perform benchmarking over four deep learning methods, covering both supervised and unsupervised learning regimes. Along with the benchmarks, we implement additional experiments, including physics-driven methods, complexity analysis, generalization study, uncertainty quantification, and so on, to sharpen our understanding of datasets and methods. The studies either provide valuable insights into the datasets and the performance, or uncover their current limitations. We hope OpenFWI supports prospective research on FWI and inspires future open-source efforts on AI for science. All datasets and related information can be accessed through our website at https://openfwi-lanl.github.io/

Seismic full-waveform inversion (FWI) is a nonlinear computational imaging technique that can provide detailed estimates of subsurface geophysical properties. Solving the FWI problem can be challenging due to its ill-posedness and high computational cost. In this work, we develop a new hybrid computational approach to solve FWI that combines physics-based models with data-driven methodologies. In particular, we develop a data augmentation strategy that can not only improve the representativity of the training set but also incorporate important governing physics into the training process and, therefore, improve the inversion accuracy. To validate the performance, we apply our method to synthetic elastic seismic waveform data generated from a subsurface geologic model built on a carbon sequestration site at Kimberlina, California. We compare our physics-consistent data-driven inversion method to both purely physics-based and purely data-driven approaches and observe that our method yields higher accuracy and greater generalization ability.

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 nonconvex 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 (FCNs). 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 structures 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.

4-D seismic imaging has been widely used in CO2sequestration 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 and growing knowledge gap over time. The operator needs to understand the fluid flow throughout the project lifetime and the seismic data are only available at a limited number of times. This is insufficient for understanding reservoir behavior. To overcome those challenges, we have developed spatio-temporal neural-network-based models that can produce high-fidelity interpolated or extrapolated images effectively and efficiently. Specifically, our models are built on an autoencoder, and incorporate the long short-term memory (LSTM) structure with a new loss function regularized by optical flow. We validate the performance of our models using real 4-D post-stack seismic imaging data acquired at the Sleipner CO2sequestration field. We employ two different strategies in evaluating our models. Numerically, we compare our models with different baseline approaches using classic pixel-based metrics. We also conduct a blind survey and collect a total of 20 responses from domain experts to evaluate the quality of data generated by our models. Via both numerical and expert evaluation, we conclude that our models can produce high-quality 2-D/3-D seismic imaging data at a reasonable cost, offering the possibility of real-time monitoring or even near-future forecasting of the CO2storage reservoir.

Deep learning and data-driven approaches have shown great potential in scientific domains. The promise of data-driven techniques relies on the availability of a large volume of high-quality training datasets. Due to the high cost of obtaining data through expensive physical experiments, instruments, and simulations, data augmentation techniques for scientific applications have emerged as a new direction for obtaining scientific data recently. However, existing data augmentation techniques originating from computer vision yield physically unacceptable data samples that are not helpful for the domain problems that we are interested in. In this article, we develop new data augmentation techniques based on convolutional neural networks. Specifically, our generative models leverage different physics knowledge (such as governing equations, observable perception, and physics phenomena) to improve the quality of the synthetic data. To validate the effectiveness of our data augmentation techniques, we apply them to solve a subsurface seismic full-waveform inversion using simulated CO2leakage data. Our interest is to invert for subsurface velocity models associated with very small CO2leakage. We validate the performance of our methods using comprehensive numerical tests. Via comparison and analysis, we show that data-driven seismic imaging can be significantly enhanced by using our data augmentation techniques. Particularly, the imaging quality has been improved by 15% in test scenarios of general-sized leakage and 17% in small-sized leakage when using an augmented training set obtained with our techniques.

Seismic full-waveform inversion (FWI) techniques aim to find a high-resolution subsurface geophysical model provided with waveform data. Some recent effort in data-driven FWI has shown some encouraging results in obtaining 2-D velocity maps. However, due to high computational complexity and large memory consumption, the reconstruction of 3-D high-resolution velocity maps via deep networks is still a great challenge. In this article, we present InversionNet3D (InvNet3D), an efficient and scalable encoder–decoder network for 3-D FWI. The proposed method employs group convolution in the encoder to establish an effective hierarchy for learning information from multiple sources while cutting down unnecessary parameters and operations at the same time. The introduction of invertible layers further reduces the memory consumption of intermediate features during training and, thus, enables the development of deeper networks with more layers and higher capacity as required by different application scenarios. Experiments on the 3-D Kimberlina dataset demonstrate that InvNet3D achieves state-of-the-art reconstruction performance with lower computational cost and lower memory footprint compared to the baseline.

Full-waveform inversion is an important and widely used method to reconstruct subsurface velocity images. Waveform inversion is a typical nonlinear and ill-posed inverse problem. Existing physics-driven computational methods for solving waveform inversion suffer from the cycle-skipping and local-minima issues, and do not mention that solving waveform inversion is computationally expensive. In recent years, data-driven methods become a promising way to solve the waveform-inversion problem. However, most deep-learning frameworks suffer from the generalization and overfitting issue. In this article, we developed a real-time data-driven technique and we call it VelocityGAN, to reconstruct accurately the subsurface velocities. Our VelocityGAN is built on a generative adversarial network (GAN) and trained end to end to learn a mapping function from the raw seismic waveform data to the velocity image. Different from other encoder-decoder-based data-driven seismic waveform-inversion approaches, our VelocityGAN learns regularization from data and further imposes the regularization to the generator so that inversion accuracy is improved. We further develop a transfer-learning strategy based on VelocityGAN to alleviate the generalization issue. A series of experiments is conducted on the synthetic seismic reflection data to evaluate the effectiveness, efficiency, and generalization of VelocityGAN. We not only compare it with the existing physics-driven approaches and data-driven frameworks but also conduct several transfer-learning experiments. The experimental results show that VelocityGAN achieves the state-of-the-art performance among the baselines and can improve the generalization results to some extent.

Seismic event classification and detection have been important research topics because of their significance and wide applications on hazard assessment and global security. In the real world, seismic data acquisition are always impacted by unavoidable nature factors, which will introduce low-frequency noise to the seismic events of interests. Pre-processing of seismic signal using denoising techniques can be critical to the detection of the seismic events. In our work, we develop an end-to-end framework which can automatically learn the hyper-parameter in the denoising algorithm so that we do not need to manually set the hyper-parameter. Specifically, our network structure consists of two modules, an adaptive filtering module for signal denoising, and a classification module for signal classification. We further develop two mechanisms of the adaptive filtering module, namely, sample-specific mechanism and dataset-specific mechanism. We validate the performance of our detection method using a series of field seismic datasets. The classification results show that our framework can not only remove signal noise effectively but also improve the classification accuracy.

Acoustic-and elastic-waveform inversion is an important and widely used method to reconstruct subsurface velocity image. Waveform inversion is a typical non-linear and ill-posed inverse problem. Existing physics-driven computational methods for solving waveform inversion suffer from the cycle skipping and local minima issues, and not to mention solving waveform inversion is computationally expensive. In this paper, we developed a real-time datadriven technique, VelocityGAN, to accurately reconstruct subsurface velocities. Our VelocityGAN is an end-to-end framework which can generate high-quality velocity images directly from the raw seismic waveform data. A series of experiments are conducted on the synthetic seismic reflection data to evaluate the effectiveness and efficiency of VelocityGAN. We not only compare it with existing physics-driven approaches but also choose some deep learning frameworks as our data-driven baselines. The experiment results show that VelocityGAN outperforms the physics-driven waveform inversion methods and achieves the state-of-the-art performance among data-driven baselines.

Automatic event detection from time series signals has broad applications. Traditional detection methods detect events primarily by the use of similarity and correlation in data. Those methods can be inefficient and yield low accuracy. In recent years, machine learning techniques have revolutionized many sciences and engineering domains. In particular, the performance of object detection in a 2-D image data has significantly improved due to deep neural networks. In this paper, we develop a deep-learning-based detection method, called “DeepDetect,” to detect events from seismic signals. We find that the direct adaptation of similar ideas from 2-D object detection to our problem faces two challenges. The first challenge is that the duration of earthquake event varies significantly; the other is that the proposals generated are temporally correlated. To address these challenges, we propose a novel cascaded region-based convolutional neural network to capture earthquake events in different sizes while incorporating contextual information to enrich features for each proposal. To achieve a better generalization performance, we use densely connected blocks as the backbone of our network. Because some positive events are not correctly annotated, we further formulate the detection problem as a learning-from-noise problem. To verify the performance, we employ the seismic data generated from the Pennsylvania State University Rock and Sediment Mechanics Laboratory, and we acquire labels with the help of experts. We show that our techniques yield high accuracy. Therefore, our novel deep-learning-based detection methods can potentially be powerful tools for identifying events from the time series data in various applications.

Sparse representations are widely used in a broad variety of fields. A number of different methods have been proposed to solve the sparse coding problem, of which the alternating direction method of multipliers (ADMM) is one of the most popular. One of the disadvantages of this method, however, is the need to select an algorithm parameter, the penalty parameter, that has a significant effect on the rate of convergence of the algorithm. Although a number of heuristic methods have been proposed, as yet there is no general theory providing a good choice of this parameter for all problems. One obvious approach would be to try a number of different parameters at each iteration, proceeding further with the one that delivers the best reduction in functional value, but this would involve a substantial increase in computational cost. We show that, when solving the sparse coding problem for a dictionary corresponding to an operator with a fast transform, requiring iterative methods to solve the main linear system arising in the ADMM solution, it is possible to explore a large range of parameters at marginal additional cost, thus greatly improving the robustness of the method to the choice of penalty parameter.