Full-waveform inversion (FWI) is a critical technique for deriving high-resolution velocity models in geophysical studies. However, the lack of low-frequency components in seismic data can result in significant cycle-skipping issues, leading to inaccurate inversion outcomes. Fortunately, the envelope of seismic data contains abundant low-frequency information that can be utilized to improve the inversion of large-scale background velocity models. Within the FWI framework, current envelope inversion (EI) methods can be classified into two primary categories: (1) conventional envelope inversion, which employs the waveform Fréchet derivative and is optimally suited for weak scattering scenarios, and (2) direct envelope inversion, which utilizes the envelope Fréchet derivative and demonstrates effectiveness in inverting models characterized by strong contrasts. This review paper addresses the following key aspects: (1) an overview of the principles underlying conventional envelope inversion and direct envelope inversion methodologies, alongside a detailed comparative analysis; (2) an evaluation of the limitations and effectiveness of both conventional and direct envelope inversion techniques when applied to weak and strong scattering media, supported by comprehensive numerical test cases; and (3) a thorough review of the historical development of envelope inversion, exploring its critical challenges, current solutions, and future perspectives in the field.
Seismic data often face challenges in their utilization due to noise contamination, incomplete acquisition, and limited low-frequency information, which hinder accurate subsurface imaging and interpretation. Traditional processing methods rely heavily on task-specific designs to address these challenges and fail to account for the variability of data. To address these limitations, we present a generative seismic foundation model (GSFM), a unified framework based on generative diffusion models (GDMs), designed to tackle multi-task seismic processing challenges, including denoising, backscattered noise attenuation, interpolation, and low-frequency extrapolation. GSFM leverages a pre-training stage on synthetic data to capture the features of clean, complete, and broadband seismic data distributions and applies an iterative fine-tuning strategy to adapt the model to field data. By adopting a target-oriented diffusion process prediction, GSFM improves computational efficiency without compromising accuracy. Synthetic data tests demonstrate that GSFM surpasses benchmarks with equivalent architectures in all tasks and achieves performance comparable to traditional pre-training strategies, even after their fine-tuning. Also, field data tests suggest that our iterative fine-tuning approach addresses the generalization limitations of conventional pre-training and fine-tuning paradigms, delivering significantly enhanced performance across diverse tasks. Furthermore, GSFM’s inherent probabilistic nature enables effective uncertainty quantification, offering valuable insights into the reliability of processing results.
Recent studies of high-resolution seismic tomography of source zones of large crustal earthquakes, megathrust earthquakes, and intraslab earthquakes are reviewed, which shed new light on seismogenic structures and fluids in subduction zones. Large crustal earthquakes generally occurred in high-velocity (high-V) zones in the brittle upper crust, whereas low-velocity and high Poisson’s ratio anomalies exist in the lower crust and upper (or uppermost) mantle, which may reflect fluids released from dehydration of the subducting slab. The fluids may trigger large crustal earthquakes. The interplate megathrust zone exhibits prominent structural heterogeneities. Large megathrust earthquakes generally occurred in high-V areas, reflecting strongly coupled patches (or asperities) in the megathrust zone due to the subduction of seamounts or topographic plateaus in the incoming oceanic plate. The megathrust seismogenesis may be affected or controlled by structural anomalies in both the upper and lower plates, as well as hot upwelling flows in the subslab mantle. Lower-velocity anomalies are revealed in source zones of large intraslab earthquakes, which are attributed to the process of dehydration embrittlement resulting from dehydration of hydrous minerals in the slab, which may trigger the mainshock and aftershock sequences by enhancing pore pressures along preexisting faults and fractures in the slab. All these results indicate that fluids play an important role in the generation of most earthquakes in subduction zones.
Three-dimensional (3-D) magnetotelluric (MT) inversion outcomes are influenced by various user-defined configurations, yet comprehensive analyses and rigorous testing of them are rarely conducted, particularly for 3-D large-scale surveys. Additionally, different inversion frameworks will inevitably yield varying “preferred” models, highlighting the need to investigate the reasons behind these discrepancies, which can uncover model uncertainties linked to algorithm-specific choices. This study focuses on analyzing and comparing factors from the above two categories that contribute to uncertainties in inversions and interpretations. First, to explore the user-defined configurations that lead to differing results, we performed multiple tests using the USArray MT data. Specifically, we assessed the impact of regularization parameters, prior information, projection methods, regularization types, data types and frequencies, initial models, mesh settings, and distortion correction on inversion outcomes by the two most widely used inversion frameworks: ModEM and FEMTIC. After thoroughly analyzing these factors, we present a new electrical model for the Northwestern U.S. using FEMTIC code. The primary conductivity variation of this model aligns well with a previous one obtained by utilizing ModEM. However, large-scale differences between the two “preferred” solutions are still observed. We conclude that the discrepancies in geologically active high-conductivity zones are mainly due to different selection method for regularization parameter and mesh settings, and difference in average resistivities of the lower upper mantle primarily stem from differing degrees of dependence on the initial model, a distinction that fundamentally stems from differences in regularization assumptions and optimization algorithms.
Tsunami is the oceanic gravity waves produced by mass displacements in large shallow offshore thrust earthquakes. The January 1, 2024 (M_textrm{W})7.5 Noto Peninsula earthquake excited a tsunami to spread across the East Sea (Sea of Japan), arriving at the east coast of the Korean Peninsula. The influence of oceanic gravity waves on the coastal medium is investigated. The mass loading by tsunami induces ground tilting, producing transient long-period ground motions to be polarized in coastline-perpendicular directions. The tsunami-induced ground motions are well recorded in inland seismometers nearby the coast. The wavetrain durations and spectral contents of the tsunami-induced seismic signals in seismometers share with those of the tsunami waves in tide gauges, suggesting the same source of energy. The amplitudes of tsunami-induced ground motions are proportional to the tsunami heights, being modulated by the distance from the coast and medium properties. The discriminative tsunami-induced ground motions produce dynamic stress changes that are effective at shallow depths, reaching 0.81 kPa on the coast. A large runup height may induce dynamic stress changes effective to depths.
Gravitational fields are often modelled by the mathematical apparatus of integral transformations. A basic assumption of these integrals is the knowledge of relatively accurate data available globally. Practically, however, global data coverage is rarely achieved and data are always contaminated by measurement errors. Therefore, integral transformations are properly modified and practical integral estimators are formulated and further employed in numerical experiments. In addition, corresponding statistical characteristics are often desired to indicate the quality of calculated gravitational fields. In this article, we systematically formulate practical integral estimators and their respective errors. We present the practical integral estimators in the combined form (i.e. combining the restricted integrals for the near-zone effects and the truncated spherical harmonic series for the far-zone effects) and in the form of spherical harmonic series. The practical integral estimators form a theoretical basis for an accurate gravitational field modelling, e.g. when solving upward or downward continuation. By employing a unified notation, the mathematical formulas are derived to an unprecedented extent for a broad class of quantities. Namely, the theoretical formulations connect four types of boundary conditions with twenty computed quantities. The practical integral estimators are complemented by point-wise errors and global mean square counterparts. The point errors can be calculated from the errors of the near-zone and far-zone boundary values, the position of the computational point, the size of the integration radius, and the maximum spherical harmonic degree of the far-zone effects. The number of variables is reduced for the global mean square errors, as they are invariant from the horizontal position of computational points. Both statistical characteristics may also be employed in optimisation problems and experimental designs. The basic principles and formulations presented here may be employed in related problems of other potential fields, such as in electrostatics or magnetism.
Using geophysical inversion to determine the geometry of subsurface targets has a long-established history, tracing back to the early days of geophysical interpretation. These methods continue to gain considerable attention because of the growing demand for more precise and interpretable visual representations of subsurface bodies. A recent surge in interest has led to the development of numerous new strategies and algorithms that share the common primary goal of defining target geometries. A comprehensive review of these approaches is currently lacking, which has led to some overlap in research, where studies fail to acknowledge prior work or clarify how their methods compare with, or differ from, work by other researchers. In this paper, we present a thorough review of recent developments in the field, aiming: (1) to provide readers with a broader understanding of the various geometry-based inversion techniques currently being researched, (2) to help practitioners assess the practical applications of these inversion methods, and (3) to provide insight into promising directions for future research. We propose a standardized classification system and terminology to support the research community in formulating, discussing, and disseminating their findings within this rapidly expanding domain. We classify the approaches into five distinct categories. For each, we provide a broad literature search to discuss: the applications and types of geophysical data used, the parameters estimated by the inversion algorithms, the prior information and constraints applied, computational and numerical details, visualization and model evaluation approaches, and interpretation strategies. We finish with a forward looking discussion to summarize.
Over the past two decades, data science and machine learning (ML) techniques have attracted increasing attention within the electromagnetic (EM) community, opening up significant potential for applications while also presenting challenges. This review provides a comprehensive survey of the advancements ML has contributed to the EM field, exploring existing challenges and future development trends. We begin by introducing basic concepts and recent advances in ML, ranging from unsupervised learning algorithms such as clustering methods, to advanced neural networks, physics-guided and generative models. Then, practical applications are thoroughly investigated across a variety of EM techniques, including magnetotellurics (MT), transient EM (TEM), airborne EM (AEM), electrical resistivity tomography (ERT), ground penetrating radar (GPR), among others. For each technique, we offer a detailed review of ML applications through various data analysis processes, including denoising, signal detection, forward simulation, inversion, and joint interpretation with other geophysical data. Furthermore, we discuss extensive applications of ML in fields such as understanding Earth’s deep structure, mineral exploration, groundwater management and hazard monitoring. We also address the ongoing challenges, including model generalization, comparability and interpretability. Looking forward, we highlight emerging trends like the advancement of uncertainty evaluation, the development of physics-guided and generative models, enhancements in data management and accessibility and the integration of cloud computing technologies. This comprehensive overview aims to establish a clear scope for current achievements and future potential of integrating ML with EM, thus laying a foundation for continued research and practical applications within the EM community.

