Surveys in Geophysics

In this study, we investigate the representation of the global mean energy balance components in 10 atmospheric reanalyses, and compare their magnitudes with recent reference estimates as well as the ones simulated by the latest generation of climate models from the 6th phase of the coupled model intercomparison project (CMIP6). Despite the assimilation of comprehensive observational data in reanalyses, the spread amongst the magnitudes of their global energy balance components generally remains substantial, up to more than 20 Wm−2 in some quantities, and their consistency is typically not higher than amongst the much less observationally constrained CMIP6 models. Relative spreads are particularly large in the reanalysis global mean latent heat fluxes (exceeding 20%) and associated intensity of the global water cycle, as well as in the energy imbalances at the top-of-atmosphere and surface. A comparison of reanalysis runs in full assimilation mode with corresponding runs constrained only by sea surface temperatures reveals marginal differences in their global mean energy balance components. This indicates that discrepancies in the global energy balance components caused by the different model formulations amongst the reanalyses are hardly alleviated by the imposed observational constraints from the assimilation process. Similar to climate models, reanalyses overestimate the global mean surface downward shortwave radiation and underestimate the surface downward longwave radiation by 3–7 Wm−2. While reanalyses are of tremendous value as references for many atmospheric parameters, they currently may not be suited to serve as references for the magnitudes of the global mean energy balance components.

Electromagnetic (EM) imaging aims to produce large-scale, high-resolution soil conductivity maps that provide essential information for Earth subsurface exploration. To rigorously generate EM subsurface models, one must address both the forward problem and the inverse problem. From these subsurface resistivity maps, also referred to as volumes of resistivity distribution, it is possible to extract useful information (lithology, temperature, porosity, permeability, among others) to improve our knowledge about geo-resources on which modern society depends (e.g., energy, groundwater, and raw materials, among others). However, this ability to detect electrical resistivity contrasts also makes EM imaging techniques sensitive to metallic structures whose EM footprint often exceeds their diminutive stature compared to surrounding materials. Depending on target applications, this behavior can be advantageous or disadvantageous. In this work, we review EM modeling and inverse solutions in the presence of metallic structures, emphasizing how these structures affect EM data acquisition and interpretation. By addressing the challenges posed by metallic structures, our aim is to enhance the accuracy and reliability of subsurface EM characterization, ultimately leading to improved management of geo-resources and environmental monitoring. Here, we consider the latter through the lens of a triple helix approach: physics behind metallic structures in EM modeling and imaging, development of computational tools (conventional strategies and artificial intelligence schemes), and configurations and applications. The literature review shows that, despite recent scientific advancements, EM imaging techniques are still being developed, as are software-based data processing and interpretation tools. Such progress must address geological complexities and metallic casing measurements integrity in increasing detail setups. We hope this review will provide inspiration for researchers to study the fascinating EM problem, as well as establishing a robust technological ecosystem to those interested in studying EM fields affected by metallic artifacts.

The adjoint method is a popular method used for seismic (full-waveform) inversion today. The method is considered to give more realistic and detailed images of the interior of the Earth by the use of more realistic physics. It relies on the definition of an adjoint wavefield (hence its name) that is the time-reversed synthetics that satisfy the original equations of motion. The physical justification of the nature of the adjoint wavefield is, however, commonly done by brute force with ad hoc assumptions and/or relying on the existence of Green’s functions, the representation theorem and/or the Born approximation. Using variational principles only, and without these mentioned assumptions and/or additional mathematical tools, we show that the time-reversed adjoint wavefield should be defined as a premise that leads to the correct adjoint equations. This allows us to clarify mathematical inconsistencies found in previous seminal works when dealing with viscoelastic attenuation and/or odd-order derivative terms in the equation of motion. We then discuss some methodologies for the numerical implementation of the method in the time domain and to present a variational formulation for the construction of different misfit functions. We here define a new misfit travel-time function that allows us to find consensus for the longstanding debate on the zero sensitivity along the ray path that cross-correlation travel-time measurements show. In fact, we prove that the zero sensitivity along the ray path appears as a consequence of the assumption on the similarity between data and synthetics required to perform cross-correlation travel-time measurements. When no assumption between data and synthetics is preconceived, travel-time Fréchet kernels show an extremum along the ray path as one intuitively would expect.

Geophysical logging series are valuable geological data that record the physical and chemical information of borehole walls and in-situ formations, and are widely used by geologists for interpreting geological problems due to their continuity, high resolution, and ease of access. Recently, machine learning methods are gradually bringing data science and geoscience closer together, and Intelligent Recognition using Logging Data (IRLD) is increasingly becoming an important interpretation task. However, due to the specificity of geological information, relatively low data quality makes the direct application of machine learning models to IRLD often not optimal. And to the best of our knowledge, IRLDs are not highly generalizable and technical surveys are still lacking. Therefore, this paper presents a comprehensive review of IRLD. Specifically, after systematically reviewing geophysical well logging and machine learning techniques, the main applications and general processes for the cross-discipline task of IRLD are summarized. More importantly, the key challenges of IRLD in the four stages of data acquisition, feature engineering, model building, and practical application are discussed in this review. The potential risks of these challenges are visualized by using real logging data from a study area in the South China Sea and the example of a lithology identification task. For these challenges, we give the current state-of-the-art methods and feasible strategies in conjunction with published research. This comprehensive review is expected to provide insights for practitioners to construct more robust models and achieve more effective application results in IRLD.

The Earth exhibits an equatorial flattening specified by the ellipticity and the east longitude (or orientation) of the equatorial major axis, which is uniquely determined by the degree 2 and order 2 gravitational coefficients, C22 and S22. The 31-year SLR (satellite laser ranging) and 22-year GRACE/GRACE-FO (gravity recovery and climate experiment) data are analyzed to study the climate-related secular and 5.7 years to decadal variations in C22 and S22, in turn, the drift and decadal variation in the Earth’s equatorial ellipticity and orientation of the principal axis of the least moment of inertia. The effects of the surface floating mass changes (including atmosphere, ocean and surface water redistribution and the melting of the mountain and polar glaciers) and the interior fluid convective (Earth’s core flows) were evaluated. Results reveal that the equatorial ellipticity of the Earth is linearly increasing along with a remarkable decadal variation and the Earth’s equator is flattening by ~ 0.16 mm/yr.

Blended acquisition offers significant cost and period reduction in seismic data acquisition. However, fired blended sources are usually deployed at off-the-grid (OffG) samples due to obstacle limitation and economic cost considerations. The irregular distribution of coordinates, along with the blending noise, has a detrimental effect on the performance of subsequent seismic processing and imaging. The interpolated multichannel singular spectrum analysis (I-MSSA) algorithm effectively provides on-the-grid deblended results by employing an interpolator, in conjunction with a projected gradient descent strategy. However, the deblending accuracy and computational efficiency of the I-MSSA are still a concern due to the limitations of the traditional singular value decomposition (SVD). To address these limitations, we propose an interpolated fast damped multichannel singular spectrum analysis (I-FDMSSA) rank-reduction algorithm. The proposed algorithm incorporates the damping operator, the randomized SVD (RSVD) and the fast Fourier transform (FFT) strategy. The damping operator can further attenuate the remaining noise in the estimated signal obtained from the truncated SVD, resulting in an improved deblending performance. The RSVD accelerates the rank-reduction process by shrinking the size of the Hankel matrix. To expedite the rank-reduction and anti-diagonal averaging stages without explicitly constructing large-scale block Hankel matrices, the FFT strategy is employed. By incorporating a 2D separable sinc interpolator, the I-FDMSSA enables an efficient and accurate deblending of 3D OffG blended data. The deblending performance and operational efficiency improvements of the proposed I-FDMSSA algorithm over the traditional I-MSSA algorithm are demonstrated through OffG synthetic and field blended data examples.

Prior model construction is a fundamental component in geophysical inversion, especially Bayesian inversion. The prior model, usually derived from available geological information, can reduce the uncertainty of model characteristics during the inversion. However, the prior geological data for inferring a prior distribution model are often limited in real cases. Our work presents a novel framework to create 3D geophysical prior models using soil geochemistry and borehole rock sample measurements. We focus on the Bayesian inversion, which enables encoding of knowledge and multiple non-geophysical data into the prior. The new framework developed in our research comprises three main parts, namely correlation analysis, prior model reconstruction, and Bayesian inversion. We investigate the correlations between surface and subsurface geochemical features, as well as the correlation between geochemistry and geophysics, using canonical correlation analysis for the surface and borehole geochemistry. Based on the resulting correlations, we construct the prior susceptibility model. The informed prior model is then tested using geophysical forward modeling and outlier detection methods. In this test, we aim to falsify the prior model, which happens when the model cannot predict the field geophysical observation. To obtain the posterior models, the reliable prior models are incorporated into a Bayesian inversion framework. Using a real case of exploration in the Central African Copperbelt, we illustrate the workflow of constructing the high-resolution 3D stratigraphic model conditioned on soil geochemistry, borehole data, and airborne geophysics.

The subsurface in situ stress fields significantly influence the elastic and anisotropic properties of rocks, yet traditional linear elastic theories often overlook the impact of stress on seismic response characteristics. Nonlinear acoustoelastic theory integrates third-order elastic constants (TOECs) to elucidate the influence of stress on changes in elastic and anisotropic properties of stressed rocks. A comprehensive examination of recent scholarly investigations on nonlinear acoustoelastic phenomena precedes the introduction of an innovative stress-dependent equation for the PP-wave reflection coefficient. This equation delineates the dependence of azimuthal seismic response on horizontal uniaxial stress in inherently vertical transversely isotropic (VTI) media, or those VTI formations induced by a single set of horizontal aligned fractures. Emphasis is placed on delineating stress-induced anisotropy and elucidating azimuthal PP-wave reflection characteristics in horizontally uniaxially stressed VTI media. Additionally, this discourse extends to more intricate scenarios involving horizontally biaxially and triaxially stressed VTI media, as delineated by nonlinear acoustoelastic theory. Subsequently, the reflection coefficient of horizontally uniaxially stressed VTI media is expressed in terms of azimuthal Fourier coefficients (FCs), revealing that the unstressed VTI background exhibits heightened sensitivity to zeroth-order FC, while the stress-induced anisotropy manifests greater sensitivity to second-order FC. Through the application of azimuthal FCs-based amplitude versus offset and azimuth (AVOAz) inversion method to both synthetic and field datasets, the proposed model and approach offer promising avenues for reservoir characterization in VTI media subject to horizontal uniaxial stress conditions.

Integration of different kinds of data is an important issue in archaeological prospection. However, the current methodological approaches are underdeveloped and rarely use the data to their maximum potential. Common approaches to integration in the geophysical sciences are mostly just various forms of comparison. We argue that true integration should involve the mathematical manipulation of input data such that the original values of the input data are changed, or that new variables are produced. To address this important research gap, we present an innovative approach to the analysis of geochemical and geophysical datasets in prospection-focused disciplines. Our approach, which we refer to as “multiscalar integration” to differentiate it from simpler methods, involves the application of mathematical methods and tools to process the data in a unified way. To demonstrate our approach, we focus on integrating geophysical data (magnetometry) with geochemical data (elemental content). Our approach comprises three main stages: Quantification of the data deviation from random distributions, linear modelling of geophysical and geochemical data and integration based on weighting of the different elements derived in previous steps. All the steps of the workflow can be also applied separately and independently as needed or preferred. Our approach is implemented in the R environment for statistical computing. All data, functions and scripts used in the work are available from open access repositories (Zenodo.org and Github.com) so that others can test, modify and apply our proposed methods to new cases and problems. Our approach has the following advantages: (1) It allows the rapid exploration of multiple data sources in an unified way; (2) it can increase the utility of geochemical data across diverse prospection disciplines; (3) it facilitates the identification of links between geochemical and geophysical data (or generally, between point-based and raster data); (4) it innovatively integrates various datasets by weighting the information provided by each; (5) it is simple to apply following a step-by-step framework; (6) the code and workflow is fully open to allow for customization, improvements and additions.

Machine learning-based seismic processing models are typically trained separately to perform seismic processing tasks (SPTs) and, as a result, require plenty of high-quality training data. However, preparing training data sets is not trivial, especially for supervised learning (SL). Despite the variability in seismic data across different types and regions, some general characteristics are shared, such as their sinusoidal nature and geometric texture. To learn the shared features and thus, quickly adapt to various SPTs, we develop a unified paradigm for neural network-based seismic processing, called Meta-Processing, that uses limited training data for meta learning a common network initialization, which offers universal adaptability features. The proposed Meta-Processing framework consists of two stages: meta-training and meta-testing. In the former, each SPT is treated as a separate task and the training dataset is divided into support and query sets. Unlike conventional SL methods, here, the neural network (NN) parameters are updated by a bilevel gradient descent from the support set to the query set, iterating through all tasks. In the meta-testing stage, we also utilize limited data to fine-tune the optimized NN parameters in an SL fashion to conduct various SPTs, such as denoising, interpolation, ground-roll attenuation, image enhancement, and velocity estimation, aiming to converge quickly to ideal performance. Extensive numerical experiments are conducted to assess the effectiveness of Meta-Processing on both synthetic and real-world data. The findings reveal that our approach leads to a substantial improvement in the convergence speed and predictive performance of the NN.

Seamount eruptions alter the bathymetry and can occur undetected due to lack of explosive character. We review documented eruptions to define whether they could be detected by a future satellite gravity mission. We adopt the noise level in acquisitions of multi-satellite constellations as in the MOCAST+ study, with a proposed payload of a quantum technology gradiometer and clock. The review of underwater volcanoes includes the Hunga Tonga Hunga Ha’apai (HTHH) islands for which the exposed surface changed during volcanic unrests of 2014/2015 and 2021/2022. The Fani Maoré submarine volcanic eruption of 2018–2021 produced a new seamount 800 m high, emerging from a depth of 3500 m, and therefore not seen above sea surface. We review further documented submarine eruptions and estimate the upper limit of the expected gravity changes. We find that a MOCAST+ type mission should allow us to detect the subsurface mass changes generated by deep ocean submarine volcanic activity for volume changes of 6.5 km3 upwards, with latency of 1 year. This change is met by the HTHH and Fani Maoré volcanoes.

The wave reflection and transmission (R/T) coefficients in fluid-saturated porous media with the effect of effective pressure are rarely studied, despite the ubiquitous presence of in situ pressure in the subsurface Earth. To fill this knowledge gap, we derive exact R/T coefficient equations for a plane wave incident obliquely at the interface between the dissimilar pressured fluid-saturated porous half-spaces described by the theory of poro-acoustoelasticity (PAE). The central result of the classic PAE theory is first reviewed, and then a dual-porosity model is employed to generalize this theory by incorporating the impact of nonlinear crack deformation. The new velocity equations of generalized PAE theory can describe the nonlinear pressure dependence of fast P-, S- and slow P-wave velocities and have a reasonable agreement with the laboratory measurements. The general boundary conditions associated with membrane stiffness are used to yield the exact pressure-dependent wave R/T coefficient equations. We then model the impacts of effective pressure on the angle and frequency dependence of wave R/T coefficients and synthetic seismic responses in detail and compare our equations to the previously reported equations in zero-pressure case. It is inferred that the existing R/T coefficient equations for porous media may be misleading, since they lack consideration for inevitable in situ pressure effects. Modeling results also indicate that effective pressure and membrane stiffness significantly affect the amplitude variation with offset characteristics of reflected seismic signatures, which emphasizes the significance of considering the effects of both in practical applications related to the observed seismic data. By comparing the modeled R/T coefficients to the results computed with laboratory measured velocities, we preliminarily confirm the validity of our equations. Our equations and results are relevant to hydrocarbon exploration, in situ pressure detection and geofluid discrimination in high-pressure fields.

Different observation data are utilized to obtain a unified geophysical model based on the correlations of underground geological bodies in joint inversions. By specifying a type of Gramian constraints, Gramian as a coupling term can link geophysical models through relationships of physical properties or structural similarities. Considering the complex relationships of physical properties of underground geological bodies, we proposed an adaptive zoning method to automatically divide the whole inversion area into subregions with different relationships of physical properties and to determine the number and range of subregions that utilized correlation between geophysical data before joint inversions. On this basis, we considered the use of a combination of Gramian coupling terms rather than one term to link petrophysical and structural domains during joint inversions. Synthetic tests showed that the algorithm is capable of having a robust estimate of the spatial distribution and relationships between density and magnetization intensity of geological bodies. The idea was also applied to the ore concentration area in the middle and lower reaches of the Yangtze River to obtain the three-dimensional (3-D) distribution model of magnetite-bearing rocks within 5 km underground, which corresponds well with the existing shallow ore sites and demonstrates the existence of available deep resources in the study area.

This paper delivers an in-depth bibliometric analysis of distributed acoustic sensing (DAS) research within the realm of geophysics, covering the period from 2012 to 2023 and drawing on data from the Web of Science. By employing bibliographic and structured network analysis methods, including the use of Bibliometrix and VOSviewer®, the study highlights the most influential scholars, leading institutions, and pivotal research contributions that have significantly shaped the field of DAS in geophysics. The research delves into key collaborative dynamics, unraveling them through co-authorship network analysis, and delves into thematic developments and trajectories via comprehensive co-citation and keyword co-occurrence network analyses. These analyses elucidate the most robust and prominent areas within DAS research. A critical insight gained from this study is the rise of ‘photonic seismology’ as an emerging interdisciplinary domain, exemplifying the fusion of photonic sensing techniques with seismic science. This paper also discusses certain limitations inherent in the study and concludes with implications for future research.

As an emerging seismic acquisition technology, distributed acoustic sensing (DAS) has drawn significant attention in earth science for long-term and cost-effective monitoring of underground activities. Field seismic experiments with optical fibers in a vertical seismic profile (VSP) configuration were conducted at the Newell County Facility of Carbon Management Canada in Alberta, Canada, for \({\text{CO}}_2\) injection and storage monitoring. Seismic full-waveform inversion (FWI) represents one promising approach for high-resolution imaging of subsurface model properties. In this study, anisotropic FWI with variable density is applied to the DAS-recorded walk-away VSP data for characterizing the subsurface velocity, anisotropy, and density structures, serving as baseline models for future time-lapse studies at the pilot site. Synthetic inversion experiments suggest that, without accounting for anisotropy, the inverted density structures by isotropic FWI are damaged by strong trade-off artifacts. Anisotropic FWI can provide more accurate P-wave velocity, density, and valuable anisotropy models. Field data applications are then performed to validate the effectiveness and superiority of the proposed methods. Compared to the inversion outputs of isotropic FWI, the inverted P-wave velocity by anisotropic FWI matches trend variation of the well log more closely. In the inverted density model, the \({\text{CO}}_2\) injection formation can be clearly resolved. The inverted anisotropy parameters provide informative references to interpret the structures and lithology around the target \({\text{CO}}_2\) injection zone.

Earth’s energy imbalance (EEI) is a fundamental metric of global Earth system change, quantifying the cumulative impact of natural and anthropogenic radiative forcings and feedback. To date, the most precise measurements of EEI change are obtained through radiometric observations at the top of the atmosphere (TOA), while the quantification of EEI absolute magnitude is facilitated through heat inventory analysis, where ~ 90% of heat uptake manifests as an increase in ocean heat content (OHC). Various international groups provide OHC datasets derived from in situ and satellite observations, as well as from reanalyses ingesting many available observations. The WCRP formed the GEWEX-EEI Assessment Working Group to better understand discrepancies, uncertainties and reconcile current knowledge of EEI magnitude, variability and trends. Here, 21 OHC datasets and ocean heat uptake (OHU) rates are intercompared, providing OHU estimates ranging between 0.40 ± 0.12 and 0.96 ± 0.08 W m−2 (2005–2019), a spread that is slightly reduced when unequal ocean sampling is accounted for, and that is largely attributable to differing source data, mapping methods and quality control procedures. The rate of increase in OHU varies substantially between − 0.03 ± 0.13 (reanalysis product) and 1.1 ± 0.6 W m−2 dec−1 (satellite product). Products that either more regularly observe (satellites) or fill in situ data-sparse regions based on additional physical knowledge (some reanalysis and hybrid products) tend to track radiometric EEI variability better than purely in situ-based OHC products. This paper also examines zonal trends in TOA radiative fluxes and the impact of data gaps on trend estimates. The GEWEX-EEI community aims to refine their assessment studies, to forge a path toward best practices, e.g., in uncertainty quantification, and to formulate recommendations for future activities.

Low-rank approximation has emerged as a promising technique for recovering five-dimensional (5D) seismic data, yet the quest for higher accuracy and stronger rank robustness remains a critical pursuit. We introduce a low-rank approximation method by leveraging the complete graph tensor network (CGTN) decomposition and the learnable transform (LT), referred to as the LRA-LTCGTN method, to simultaneously denoise and reconstruct 5D seismic data. In the LRA-LTCGTN framework, the LT is employed to project the frequency tensor of the original 5D data onto a small-scale latent space. Subsequently, the CGTN decomposition is executed on this latent space. We adopt the proximal alternating minimization algorithm to optimize each variable. Both 5D synthetic data and field data examples indicate that the LRA-LTCGTN method exhibits notable advantages and superior efficiency compared to the damped rank-reduction (DRR), parallel matrix factorization (PMF), and LRA-CGTN methods. Moreover, a sensitivity analysis underscores the remarkably stronger robustness of the LRA-LTCGTN method in terms of rank without any optimization procedure with respect to rank, compared to the LRA-CGTN method.

The quality factor Q is a dimensionless measure of the energy loss per cycle of a wave field, and a proper understanding of this factor is important in a variety of fields, from seismology, geophysical prospecting to electrical science. Here, the focus is on viscoelasticity. When interpreting experimental values, several factors must be taken into account, in particular the shape of the medium (rods, bars or unbounded media) and the fact that the measurements are made on stationary or propagating modes. From a theoretical point of view, the expressions of Q may differ due to different definitions, the spatial dimension and the inhomogeneity of the wave, i.e. the fact that the vectors of propagation (or wavenumber) and attenuation do not point in the same direction. We show the difference between temporal and spatial Q, the relationships between compressional and shear Q, the dependence on frequency, the case of poro-viscoelasticity and anisotropy, the effect of inhomogeneous waves and various loss mechanisms, and consider the analogy between elastic and electromagnetic waves. We discuss physical theories describing relaxation peaks, bounds on Q and experiments showing the behaviour of Q as a function of frequency, saturation and pore pressure. Finally, we propose an application example where Q can be used to estimate porosity and saturation.

Lacustrine shale oil resources are essential for the maintenance of energy supply. Fluid types and contents play important roles in estimating resource potential and oil recovery from organic-rich shales. Precise identification of fluid types hosted in shale oil reservoir successions that are characterized by marked lithological heterogeneity from only a single well is a significant challenge. Although previous research has proposed a large number of methods for determining both porosity and fluid saturation, many can only be applied in limited situations, and several have limited accuracy. In this study, an advanced logging technique, combinable magnetic resonance logging (CMR-NG), is used to evaluate fluid types. Two-dimensional nuclear magnetic resonance (2D-NMR) experiments on reservoir rocks subject to different conditions (as received, after being dried at 105 ℃, and kerosene imbibed) were carried out to define the fluid types and classification criteria. Then, with the corresponding Rock–Eval pyrolysis parameters and various mineral contents from X-ray diffraction, the contribution of organic matter and mineral compositions was investigated. Subsequently, the content of different fluid types is calculated by CMR-NG (combinable magnetic resonance logging, viz. 2D NMR logging). According to the fluid classification criteria under experimental conditions and the production data, the most favorable model and optimal solution for logging evaluation was selected. Finally, fluid saturations of the Cretaceous Qingshankou Formation in the Gulong Sag were calculated for a single well. Results show that six fluid types (kerogen-bitumen-group OH, irreducible oil, movable oil, clay-bound water, irreducible water, and movable water) can be recognized through the applied 2D NMR test. The kerogen-bitumen-group OH was mostly affected by pyrolysis hydrocarbon (S2) and irreducible oil by soluble hydrocarbon (S1). However, kerogen-bitumen-group OH and clay-bound water cannot be detected by CMR-NG due to the effects of underground environmental conditions on the instruments. Strata Q8–Q9 of the Qing 2 member of the cretaceous Qingshankou Formation are the most favorable layers of shale oil. This research provides insights into the factors controlling fluid types and contents; it provides guidance in the exploration and development of unconventional resources, for example, for geothermal and carbon capture, utilization, and storage reservoirs.