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SUMMARY: Measurements of various physical properties of oceanic sediment and crustal structures provide insight into a number of geological and geophysical processes. In particular, knowledge of the shear wave velocity (VS) structure of marine sediments and oceanic crust has wide ranging implications from geotechnical engineering projects to seismic mantle tomography studies. In this study, we propose a novel approach to nonlinearly invert compliance signals recorded by colocated ocean-bottom seismometers and high-sample-rate pressure gauges for shallow oceanic shear wave velocity structure. The inversion method is based on a type of machine learning neural network known as a mixture density neural network (MDN). We demonstrate the effectiveness of the MDN method on synthetic models with a fixed deployment depth of 2015 m and show that among 30 000 test models, the inverted shear wave velocity profiles achieve an average error of 0.025 km s−1. We then apply the method to observed data recorded by a broad-band ocean-bottom station in the Lau basin, for which a VS profile was estimated using Monte Carlo sampling methods. Using the mixture density network approach, we validate the method by showing that our VS profile is in excellent agreement with the previous result. Finally, we argue that the mixture density network approach to compliance inversion is advantageous over other compliance inversion methods because it is faster and allows for standardized measurements.

An adjoint-based conjugate gradient algorithm provides an efficient means for imaging sources of deformation within the Earth, such as volume stresses associated with fluid flow in aquifers and reservoirs. For time intervals over which the overburden deforms elastically, one can calculate the gradient elements for a single model update using just two numerical simulations. The first is a forward run that is used to compute the residuals associated with the given iteration. The second simulation is to evaluate the application of the adjoint operator to the residuals. In this adjoint calculation, the residual displacements are applied as sources at the measurement locations, driving the deformation in the simulation. The volume stress on the source grid blocks, in response to the residual displacements, provide the gradient components. We apply this technique to satellite-based interferometric synthetic aperture radar (InSAR) line-of-sight displacements that were observed over an oil reservoir in California's Central Valley. We find that the adjoint-based gradient estimates, requiring 18 CPU seconds, agree with conventional numerical calculations that take over 3700 CPU seconds to compute. Conjugate gradient algorithms utilizing the conventional approach and adjoint-based gradient computations give roughly the same reductions in misfit and similar final estimates of reservoir volume change.

Our limited knowledge of the relationship between changes in the state of an aquifer or reservoir and the corresponding changes in the elastic moduli, that is the rock physics model, hampers the effective use of time-lapse seismic observations for estimating flow properties within the Earth. A central problem is the complicated dependence of the magnitude of time-lapse changes on the saturation, pressure, and temperature changes within an aquifer or reservoir. We describe an inversion methodology for reservoir characterization that uses onset times, the calendar time of the change in seismic attributes, rather than the magnitude of the changes. We find that onset times are much less sensitive than magnitudes to the rock physics model used to relate time-lapse observations to changes in saturation, temperature and fluid pressure. We apply the inversion scheme to observations from daily monitoring of enhanced oil recovery at the Peace River field in Canada. An array of 1492 buried hydrophones record seismic signals from 49 buried sources. Time-shifts for elastic waves traversing the reservoir are extracted from the daily time-lapse cubes. In our analysis 175 images of time-shifts are transformed into a single map of onset times, leading to a substantial reduction in the volume of data. These observations are used in conjunction with bottom hole pressure data to infer the initial conditions prior to the injection, and to update the reservoir permeability model. The combination of a global and local inversion scheme produces a collection of reservoir models that are best described by three clusters. The updated model leads to a nearly 70 percent reduction in seismic data misfit. The final set of solutions successfully predict the observed normalized pressure history during the soak and flow-back into the wells between 82 and 175 days into the cyclic steaming operation.

SUMMARY: With the increasing advances in the oil and gas industry, seismic imaging near or under salt structures has become an important point in deep-water exploration. Detailed velocity models of these areas are particularly interesting not only to characterize hydrocarbon reservoirs but also to identify potential sites for hydrogen and carbon dioxide storage in offshore salt caverns. Thus, we study the full-waveform inversion for the salt reconstruction in acoustic media with constant density considering the time-harmonic wave propagation in a finite element formulation using the topology optimization (TO) method. This problem is challenging due to the strong velocity contrast between salt bodies and the sedimentary background, in addition to the lack of low-frequency data and the inherent ill-posedness of the inverse problem. In this context, we incorporate techniques from the TO field, usually used in design applications, to overcome or reduce these known problems. We initially defined the squared slowness as a combination of two fields, one related to the salt shape and the other to the background. An interpolation rule based on the solid isotropic material with penalization method, combined with filtering and projection schemes, is used to find the shape of the salt bodies with increased sharpness interfaces. A Helmholtz-type filter is applied to modify the gradient aimed to regularize the problem and provide a more stable way for the salt shape to evolve during the inversion process. In particular, we demonstrate that the proposed approach may be relevant for reconstructing media with salt bodies when a suitable starting model is unavailable, and sharp interfaces are required. In addition, we present inversion results from synthetic data generated by a variable density model to demonstrate the approach capability when subjected to a reconstruction application. [ABSTRACT FROM AUTHOR]

SUMMARY: Seismic tomography is a cornerstone of geophysics and has led to a number of important discoveries about the interior of the Earth. However, seismic tomography remains plagued by the large number of unknown parameters in most tomographic applications. This leads to the inverse problem being underdetermined and requiring significant non-geologically motivated smoothing in order to achieve unique answers. Although this solution is acceptable when using tomography as an explorative tool in discovery mode, it presents a significant problem to use of tomography in distinguishing between acceptable geological models or in estimating geologically relevant parameters since typically none of the geological models considered are fit by the tomographic results, even when uncertainties are accounted for. To address this challenge, when seismic tomography is to be used for geological model selection or parameter estimation purposes, we advocate that the tomography can be explicitly parametrized in terms of the geological models being tested instead of using more mathematically convenient formulations like voxels, splines or spherical harmonics. Our proposition has a number of technical difficulties associated with it, with some of the most important ones being the move from a linear to a non-linear inverse problem, the need to choose a geological parametrization that fits each specific problem and is commensurate with the expected data quality and structure, and the need to use a supporting framework to identify which model is preferred by the tomographic data. In this contribution, we introduce geological parametrization of tomography with a few simple synthetic examples applied to imaging sedimentary basins and subduction zones, and one real-world example of inferring basin and crustal properties across the continental United States. We explain the challenges in moving towards more realistic examples, and discuss the main technical difficulties and how they may be overcome. Although it may take a number of years for the scientific program suggested here to reach maturity, it is necessary to take steps in this direction if seismic tomography is to develop from a tool for discovering plausible structures to one in which distinct scientific inferences can be made regarding the presence or absence of structures and their physical characteristics. [ABSTRACT FROM AUTHOR]

SUMMARY: A velocity model is generally an imperfect representation of the subsurface, which cannot precisely account for the 3-D inhomogeneities of Earth structure. We present a Bayesian moment tensor inversion framework for applications where reliable, tomography-based, velocity model reconstructions are not available. In particular, synthetic data generated using a 3-D model (SEG-EAGE Overthrust) are inverted using a layered medium model. We use a likelihood function derived from an optimal transport distance—specifically, the transport-Lagrangian distance introduced by Thorpe et al.—and show that this formulation yields inferences that are robust to misspecification of the velocity model. We establish several quantitative metrics to evaluate the performance of the proposed Bayesian framework, comparing it to Bayesian inversion with a standard Gaussian likelihood. We also show that the non-double-couple component of the recovered mechanisms drastically diminishes when the impact of velocity model misspecification is mitigated. [ABSTRACT FROM AUTHOR]

SUMMARY: Seismic data acquired from surface-deployed distributed acoustic sensing (DAS) fibre are broad band and typically dense spatially sampled. Corresponding to these features, compared with geophone data, the low-frequency components in DAS data show higher signal-to-noise ratio and multimode dispersion curves by broad-band DAS data exhibit a higher resolution, which increases the investigation depth of near-surface structures and enhances identification and picking of dispersion curves, respectively. Therefore, DAS data are ideal for the estimates of reliable and highly resolved near-surface velocity profiles. As surface-wave dispersion inversion (SWD) is a natural scheme for near-surface investigation, in this study we have formulated a DAS-SWD inversion in which multiple SWD modes are extracted from the DAS data, and are used as input to a trans-dimensional (TD) inversion procedure, in which the number of subsurface layers is treated as an unknown. Vibroseis data with a minimum frequency of 1 Hz were sensed along a horizontal surface trench as part of a baseline seismic survey carried out by the University of Calgary at the Containment and Monitoring Institute Field Research Station in Newell County, Alberta, Canada. These surface DAS data readily permit the picking of multimode dispersion curves, which are observed to enhance velocity profile resolution in both shallow and deep regions of the near-surface simultaneously, with the TD algorithm adapting the model to reflect this improved resolution. To avoid collecting abnormal model samples with thin-interleaved high- and low-velocity layers based on the known geological information of the field site, we employed constraints that preclude the structures that have velocity drops over 100 m s−1 along depth. Data errors are estimated via a non-parametric iterative process in terms of covariance matrices that include off-diagonal elements. Synthetic examples show that SWD with higher-order modes provides additional constraints on the structure and accurate noise estimation. Inversion of the field data resulted in high-resolution estimates of shear wave velocity as a function of depth throughout the top 120 m of the subsurface. The inferred structure is consistent with existing estimates of the regional lithology but resolves additional layers between 1- and 50-m depth. [ABSTRACT FROM AUTHOR]

SUMMARY: The elastic and anelastic structures of the Earth offer fundamental constraints for understanding its physical and chemical properties. Deciphering small variations in the velocity and amplitude of seismic waves can be challenging. Advanced approaches such as full-waveform inversion (FWI) can be useful. We rewrite the anelastic Fréchet kernel expression of Fichtner & van Driel using the displacement–stress formulation. We then derive the full Hessian kernel expression for viscoelastic properties. In these formulations, the anelastic Fréchet kernels are computed by the forward strain and a shift of the adjoint strain. This is complementary to the quality factor Q (i.e., inverse attenuation) Fréchet kernel expressions of Fichtner & van Driel that are explicit for the velocity–stress formulation. To reduce disk space and I/O requirements for computing the full Hessian kernels, the elastic full Hessian kernels are computed on the fly, while the full Hessian kernels for Q are computed by a combination of the on-the-fly approach with the parsimonious storage method. Applications of the Fréchet and full Hessian kernels for adjoint tomography are presented for two synthetic 2-D models, including an idealized model with rectangular anomalies and a model that approximates a subduction zone, and one synthetic 3-D model with an idealized geometry. The calculation of the full Hessian kernel approximately doubles the computationally cost per iteration of the inversion; however, the reduced number of iterations and fewer frequency stages required to achieve the same level of convergence make it overall computationally less expensive than the classical Limited-memory Broyden–Fletcher–Goldfarb–Shanno (L-BFGS) FWI for the 2-D elastic tested models. We find that the use of full Hessian kernels provides comparable results to the L-BFGS inversion using the improved anelastic Fréchet kernels for the 2-D anelastic models tested for the frequency stage up to 0.5 Hz. Given the computational expense of the Q full Hessian kernel calculation, it is not advantageous to use it in Q inversions at this time until further improvements are made. For the 3-D elastic inversion of the tested model, the full Hessian kernel provides similar image quality to the L-BFGS inversion for the frequency stage up to 0.1 Hz. We observe an improved convergence rate for the full Hessian kernel inversion in comparison to L-BFGS at a higher frequency stage, 0.1–0.2 Hz, and we speculate that at higher frequency stages the use of full Hessian kernels may be more computationally advantageous than the classical L-BFGS for the tested models. Finally, we perform 3-D elastic and Q L-BFGS inversions simultaneously using the rederived Q kernels, which can reduce the computational cost of the inversion by about 1/3 when compared to the classical anelastic adjoint tomography using the additionally defined adjoint source. The recovered Q model is smeared when compared to the recovered elastic model at the investigation frequencies up to 0.5 Hz. Q inversion remains challenging and requires further work. The 2-D and 3-D full Hessian kernels may be used for other purposes for instance resolution analysis in addition to the inversions. [ABSTRACT FROM AUTHOR]

SUMMARY: 3-D imaging of the lithosphere in the Mexican Ridges fold belt is important for understanding how the crustal deformations in this basin relate to deep tectonic processes and structures inherited from extinct Jurassic seafloor spreading. Here, we use broad-band (0.0001–0.4642 Hz) marine magnetotelluric data from the basin to reconstruct the 3-D anisotropic resistivities of the lithosphere and their spatial gradients. The resistivity gradients maxima enabled independent definition of important geological boundaries (seen on collocated seismic reflection data) and estimation of crustal thickness. We found anomalous layered zones of low resistivity and high electrical anisotropy at 5–8 km depth (coinciding with the regional detachment zone in Eocene shales in 3-D seismic data) and in the upper mantle which we interpret as indicating intense deformation and/or recent magmatic influence. We also found a banded crystalline basement structure across the fossil spreading centre comprising WSW–ENE trending, 6–10 km wide, electrically resistive subvertical sheets with conductive and anisotropic borders, which merge into a basal resistive stock-like body at 15–20 km depth. These are cut or bounded by later NNW trending major faults. These WSW and NNW structural trends correlate with the previously interpreted transform and normal faults that formed during the Late Jurassic opening of the Gulf of Mexico only if rotated clockwise by 25–30°. Surprisingly, the rugged thrust-related seabed is offset at the projected positions of the steep resistive-conductive basement sheets (which also have spatially coincident high magnetic intensity and seismicity) enabling us to infer they represent magmatic intrusions facilitated by pre-existing faults. Their conductive borders spatially coincide with possibly fluid-filled vertical fracture-sets in the overlying sediments seen in seismic data which we interpret as hydrothermal fluid pathways. We infer that a magmatic body recently intruded our study area, its ascent controlled by pre-existing basement structures, and influenced the deformation of the Neogene sequences and the seafloor topography. [ABSTRACT FROM AUTHOR]

SUMMARY: Gravity inversion is a process that obtains the spatial structure and physical properties of underground anomalies using surface collected gravity anomaly data. In recent years, the rapid development of deep learning (DL) has enabled the achievement of good results for gravity inversion methods based on DL. These methods aim to learn the mapping between geological models and gravity anomaly data by training a neural network with geological models as labels. However, using DL inversion requires generating a large amount of training data for each geological target and involves the forward calculation of the generated models, which inevitably consumes a large amount of time and storage space. To address this issue, we propose using a neural network to approximate the expensive forward computation with a fast evaluation alternative. After training, the network can reproduce gravity anomalies at any observation point. To evaluate the effectiveness of the forward model, we use the gravity anomalies predicted by the forward network for inversion network training. Additionally, to mitigate the problem of poor generalization of existing DL inversions, we propose using multitask learning. By learning multiple related tasks simultaneously, the generalization ability of the model improves, thus enhancing the performance of the main task. In this paper, a multitask UNet3+ network is proposed to realize anomaly bodies localization and density contrasts reconstruction simultaneously. Test results on the synthetic data set demonstrate that the gravity anomalies predicted by the forward network can be successfully inverted, and the multitask approach can predict subsurface geology more accurately than the single-task. To further illustrate the effectiveness of the algorithm, we apply this method to the inversion of the San Nicolas deposit in central Mexico. [ABSTRACT FROM AUTHOR]

SUMMARY: A test site containing 24 targets of various disarmed unexploded ordnance (UXO) and non-UXO items were placed on a beach on the island of Rømø (Denmark) in a 600 m × 100 m area. Scalar magnetic anomalies were measured at 3–5 m altitude using an uncrewed aerial vehicle (UAV), towing a bird with a three-sensor triangular configuration to achieve a dense coverage with flight lines of 2 m spacing. The triple-sensor data set is utilized in a probabilistic inversion setup to infer the magnetic moments of the 24 targets. The purpose of the study, is to try and distinguish between different types of ferromagnetic objects (UXO, non-UXO) using magnetic anomaly data. The inversion methodology uses different forward models (prolate spheroids, rectangular prisms) to infer target shape, size and orientation in an attempt to discriminate between UXO and non-UXO items. Stochastic inversions are carried out using different prior assumptions of remanent magnetization strength (10, 50 and 80 per cent) of the induced dipole moment. Among the three levels of remanent magnetization strength in the prior, only some cases of discrimination seem evident for the lowest strength of remanence. One item is correctly classified as a true-negative (i.e. non-UXO) when assuming low remanent magnetization strength (10 per cent of the induced moment). However, at low remanent strength, one false-negative classification emerges, making any discrimination unreliable when assuming such low remanent magnetization. In addition to the discrimination study, different covariance models are utilized to optimize the inversion by addressing correlated errors and noise in the triple-sensor data set. Three covariance models are tested to try and account for spatially correlated noise and potential errors among the three sensors of each overflight. In many cases, the covariance models presented show a potential increase in sampling efficiency and consistency between data and the noise model, suggesting a more robust approach to a noise model in magnetic anomaly inversions. If the noise model is poor, however, it may bias the results by addressing the anomaly signal as noise. The inversions with correlated noise models are compared with inversions using a simple uncorrelated noise model. For several cases of data anomalies, differences between the inversion estimates when using correlated and uncorrelated noise models were evident, indicating that some bias may appear when assuming uncorrelated noise. Due to the general high presence of correlated signals in magnetic survey data, correlated noise models can significantly improve the overall uncertainty estimate of the estimated dipole moment. The study demonstrates, in terms of the 24 targets considered, that discrimination between UXO and non-UXO using magnetics is difficult. However, when using scalar magnetic data of high quality and resolution, the estimated dipole moments are often well resolved and uniquely defined in magnitude and position. This could provide valuable posterior information for future inversion studies by building a library of inferred magnetic moments from targets that have been found and inspected. [ABSTRACT FROM AUTHOR]

Quantifying the contributions of distinct mineral populations in bulk magnetic experiments greatly enhances the analysis of environmental and rock magnetism studies. Here, we develop a new method of parametric unmixing of susceptibility components in hysteresis loops. Our approach is based on a modified Gamma‐Cauchy exponential model that accounts for variable skewness and kurtosis. The robustness of the model is tested with synthetic curves that examine the effects of noise, sampling, and proximity (similar coercivities) of susceptibility components. We provide a Python‐based script, the Hist‐unmix, which allows the user to adjust a forward model of up to three ferromagnetic components as well as a dia/paramagnetic contribution. Optimization of all the parameters is achieved through least squares fitting (Levenberg‐Marquardt method), with uncertainties of each inverted parameter calculated through a Monte Carlo error propagation approach. For each ferromagnetic component, it is possible to estimate the saturation magnetization (Ms), saturation remanent magnetization (Mrs) and the mean coercivity (Bc ${B}_{c}$). Finally, Hist‐unmix was applied to a set of weakly magnetic carbonate rocks from Brazil, which typically show distorted hysteresis loops (wasp‐waisted and potbellied). For these samples, we resolved two components with distinct coercivities. These results are corroborated by previous experimental data, showing that the lower branch of magnetic hysteresis can be modeled by the presented approach and might offer important mineralogical information for rock magnetic and paleomagnetic studies. Plain Language Summary: Rocks contain magnetic minerals that record Earth's varying magnetic field morphology and intensity and provide information on our planet's evolution, as well as the ancient environmental conditions where the rocks formed. To study these magnetic minerals, we need to identify and quantify them, but this is challenging because of the complex mixture of such minerals that a rock may contain. Magnetic hysteresis curves are a simple and quick measurement that provide information on the magnetic properties of a rock, reflecting the combined effects of different minerals. In this paper, we propose a mathematical model that can separate the individual contributions of each magnetic population. We also provide an open‐source Python script for users to apply our model to their own data. Key Points: A new method for the parametric unmixing of magnetic hysteresis data based on a modified Gamma‐Cauchy exponential model is presentedThe model accounts for curves with variable skewness/kurtosis, allowing the separation of dia/para and ferromagnetic contributionsAn open‐source Python script (Hist‐unmix) allows users to import, process and model their data via a friendly interface [ABSTRACT FROM AUTHOR]

Tong has proposed an adjoint-state traveltime tomography method to determine velocity heterogeneity and azimuthal anisotropy. This method, however, ignores the Earth's curvature when deriving the eikonal equation for azimuthally anisotropic media. Thus, further coordinate transformation or approximation is required to ensure the accuracy of traveltime prediction in large-scale tomography. To address this problem, we derive the eikonal equation for azimuthally anisotropic media in spherical coordinates, which naturally considers the Earth's curvature. Another key ingredient is the forward modelling algorithm, whose accuracy and efficiency dominate the numerical error and computational cost of the inversion. In this study, we apply a modified fast sweeping method to solve the eikonal equation in spherical coordinates. Two approaches, including the third-order weighted essentially non-oscillatory approximation and multiplicative factorization technique, are applied to improve the accuracy. According to the numerical experiments, this new eikonal solver achieves a second-order accuracy and is about two orders of magnitude more accurate than the commonly used first-order fast sweeping method with similar runtime. Taking advantage of the two improvements, we develop a novel eikonal equation-based adjoint-state traveltime tomography method for azimuthally anisotropic media in spherical coordinates. This method is applicable for large-scale tomography, and its performance is verified by a synthetic checkerboard test and a practical seismic tomographic inversion in central California near Parkfield. [ABSTRACT FROM AUTHOR]

Airborne electromagnetic (AEM) exploration produces large amounts of data due to its high sampling rate, so that the 3-D inversions take extremely big computation and time consumption. We present a fast 3-D inversion framework for large-scale AEM explorations using a pre-conditioned stochastic gradient descent combined with Gauss–Newton (PSG-GN) method. We adopt a compressed sensing (CS) in the 3-D forward modelling, in which a random undersampling is used to reduce the calculation, while the responses for all survey stations are obtained via a reconstruction technique. For our 3-D AEM inversions, a method of combining the stochastic gradient descent with Gauss–Newton (SG-GN) that requires only a small data set in each iteration instead of the conventional full-batch data (complete original data) inversion have been investigated. To further speed up the 3-D inversion, we develop a pre-conditioner considering the random sampling rate and gradient noise to achieve a fast convergence. We use two synthetic models to test the accuracy, convergence and efficiency of our algorithm. The results show that the conventional inversion with full-batch data and the PSG-GN method can both converge quickly, but our method can enhance the inversion efficiency up to 78 per cent. Finally, we invert a field data set acquired from a massive sulfide deposit in Ireland and obtain the results that agree well with the known geologies. [ABSTRACT FROM AUTHOR]

The analysis of controlled-source electromagnetic (EM) data recorded with semi-airborne exploration systems requires advanced simulation and inversion tools that are capable of handling realistic survey geometries. Semi-airborne EM setups with elongated transmitters deployed in mountainous terrain prohibit the exploitation of secondary-field formulations in numerical approximations without producing hardly quantifiable errors. Building upon the open-source software custEM for forward modeling and pyGIMLi for geophysical inversion, we present an inverse modeling procedure based on highly accurate second-order finite-element forward solutions on irregular grids and fast-converging Gauss–Newton minimization. Using the total-field formulation of the electric field approach in combination with a direct solver enables calculating explicit sensitivities with comparatively cheap back-substitutions for thousands of ground and airborne receiver stations in multiple flight areas. Second-order basis functions show general superiority over first-order basis-functions regarding the accuracy and performance of the forward problem. Beyond that, synthetic and real data inversion studies related to semi-airborne geometries indicate that second-order basis functions help particularly to avoid high modeling errors for the weakest field components and artifacts in the vicinity of transmitters or at the surface. This leads generally to a better convergence and final inversion results of higher robustness and quality. The presented tools are freely available such as the underlying software. [ABSTRACT FROM AUTHOR]

The inference of fluid motion below the core–mantle boundary from geomagnetic observations presents a highly non-unique inverse problem. We propose a new method that provides a unique local estimate of the velocity field, assuming quasi-geostrophic flow in the core interior (which implies equatorial mirror symmetry) and negligible magnetic diffusion. These assumptions remove the theoretical underdetermination, enabling us to invert for the flow at each point of a spherical grid representing the core surface. The unreliable reconstruction of small-scale flows, which arises because only large-scale observations are available, is mitigated by smoothing the locally estimated velocity field using a Gaussian process regression. Application of this method to synthetic data provided by a state-of-the-art geodynamo simulation suggests that using this approach, the large-scale flow pattern of the core surface flow can be well reconstructed, while the flow amplitude tends to be underestimated. We compare these results with a core flow inversion using a Bayesian framework that incorporates statistics from numerical geodynamo models as prior information. We find that whether the latter method provides a more accurate recovery of the reference flow than the local estimation depends heavily on how realistic/relevant the chosen prior information is. Application to real geomagnetic data shows that both methods are able to reproduce the main features found in previous core flow studies. [ABSTRACT FROM AUTHOR]

Subsurface fluid escape structures are geological features which are commonly observed in sedimentary basins worldwide. Their identification and description have implications for various subsurface fluid flow applications, such as assuring integrity of overburden rocks to geological CO2 storage sites. In this study, we applied 3-D first-arrival traveltime tomography to a densely sampled wide-azimuth and wide-angle ocean bottom seismometer (OBS) data set collected over the Scanner Pockmark complex, a site of active gas venting in the North Sea. Seismic reflection data show a chimney structure underlying the Scanner Pockmark. The objective of this study was to characterize this chimney as a representative fluid escape structure in the North Sea. An area of 6 |$\times $| 6 km2 down to a depth of 2 km below sea level was investigated using a regularized tomography algorithm. In total, 182   069 manually picked traveltimes from 24 OBS were used. Our final velocity model contains compressional wave velocity perturbations ranging from −125 to +110 ms−1 relative to its average 1-D model and compares favourably with a coincident seismic reflection data set. The tomographic velocity model reveals that the chimney as observed in seismic reflection data is part of a larger complex fluid escape structure, and discriminates the genuine chimney from seismic artefacts. We find that part of the seeping gas migrates from a deep source, accumulates beneath the Crenulate Reflector unconformity at ∼250 m below seafloor (mbsf) before reaching the porous sediments of the Ling Bank and Coal Pit formation at <100 mbsf. In addition, the model shows that the venting gas at Scanner Pockmark is also being fed laterally through a narrow NW–SE shallow channel. Quantitative velocity analysis suggests a patchy gas saturation within the gas-charged sediments of the Ling Bank and the Coal Pit formations. Confined to the well-resolved regions, we estimate a base case average gas saturation of ∼9 per cent and in-situ gas volume of ∼1.64 |$\times {10^6}\ {{\rm{m}}^3}$| across the Ling Bank and Coal Pit Fm. that can sustain the observed methane flux rate at the Scanner Pockmark for about 10 to 17 yr. [ABSTRACT FROM AUTHOR]

The spatio-temporal properties of seismicity give us incisive insight into the stress state evolution and fault structures of the crust. Empirical models based on self-exciting point processes continue to provide an important tool for analysing seismicity, given the epistemic uncertainty associated with physical models. In particular, the epidemic-type aftershock sequence (ETAS) model acts as a reference model for studying seismicity catalogues. The traditional ETAS model uses simple parametric definitions for the background rate of triggering-independent seismicity. This reduces the effectiveness of the basic ETAS model in modelling the temporally complex seismicity patterns seen in seismic swarms that are dominated by aseismic tectonic processes such as fluid injection rather than aftershock triggering. In order to robustly capture time-varying seismicity rates, we introduce a deep Gaussian process (GP) formulation for the background rate as an extension to ETAS. GPs are a robust non-parametric model for function spaces with covariance structure. By conditioning the length-scale structure of a GP with another GP, we have a deep-GP: a probabilistic, hierarchical model that automatically tunes its structure to match data constraints. We show how the deep-GP-ETAS model can be efficiently sampled by making use of a Metropolis-within-Gibbs scheme, taking advantage of the branching process formulation of ETAS and a stochastic partial differential equation (SPDE) approximation for Matérn GPs. We illustrate our method using synthetic examples, and show that the deep-GP-ETAS model successfully captures multiscale temporal behaviour in the background forcing rate of seismicity. We then apply the results to two real-data catalogues: the Ridgecrest, CA 2019 July 5 M w 7.1 event catalogue, showing that deep-GP-ETAS can successfully characterize a classical aftershock sequence; and the 2016–2019 Cahuilla, CA earthquake swarm, which shows two distinct phases of aseismic forcing concordant with a fluid injection-driven initial sequence, arrest of the fluid along a physical barrier and release following the largest M w 4.4 event of the sequence. [ABSTRACT FROM AUTHOR]

Full-waveform inversion (FWI) has been proven to be an effective tool for high-resolution multiparameter imaging of the shallow subsurface. It has been shown that the Gauss–Newton (GN) optimization method uses the off-diagonal information contained in the Hessian matrix and can increase resolution and mitigate crosstalk in multiparameter viscoelastic FWI. In this work, we demonstrate the advantages of GN viscoelastic FWI over the conventional FWI with a conjugate gradient optimization method by using synthetic examples. We also investigate the potential of shallow seismic-wave 2-D viscoelastic FWI as a method for high-resolution hydrogeological characterization. The GN viscoelastic FWI is applied to two orthogonal profiles acquired at the Krauthausen natural laboratory (Germany). The groundwater table is located at around 2 m, which nicely agrees with an abrupt increase of P -wave velocity in the inverted results. FWI also reveals a low S -wave velocity layer at the depth of 4–6 m with high Poisson's ratio values close to 0.5, which corresponds to a saturated sand layer known from previous studies. A K -mean cluster analysis is used to further analyse the multiparameter FWI results. By considering the derived Poisson's ratio, P - and S -wave velocities, we convert the complex relationship between the multivariate data into a lithological meaningful zonation of the shallow subsurface. By comparing the lithological units in the alluvial aquifer with the cone penetration tests clusters, we conclude that the divided facies describe valuable characterization information about the heterogeneity and connectivity of the aquifer. This experiment indicates that the multiparameter models derived by viscoelastic FWI contain useful information for high-resolution aquifer characterization, and the potential of multiparameter FWI combined with cluster analysis in shallow subsurface characterization is encouraging. [ABSTRACT FROM AUTHOR]

Full waveform inversion and least-squares reverse time migration are the leading technologies for imaging with seismic waves. Both of them usually rely (in one way or another) on a single-scattering approximation, i.e. the Born approximation, to compute gradients and obtain an updated model. This approximation linearises the relation between modelled data and model by ignoring multiple scattering. We propose to use the Marchenko integral, an equation originating from inverse scattering theory, to obtain an alternative linear equation. Using the Marchenko method we can retrieve Green's functions, including all orders of scattering, for virtual sources anywhere within the volume of interest – without prior knowledge of the high-wavelength model variations that induce scattering. Plugging these estimated Green's functions into the Lippmann–Schwinger integral delivers a Marchenko-linearised relation between the full waveform data and the model. We present this new linearisation strategy and illustrate its advantages and disadvantages by comparing numerical results for different inversion kernels. Our new linearisation is exact, i.e. it does not exclude any orders of scattering, however, it relies on the quality of the Marchenko-derived Green's functions. These Marchenko-based Green's functions require an estimate of the first arrivals of the Green's functions – commonly obtained by modelling in a background medium. Although these first arrival estimates strongly bias our results for inaccurate background models, we find the Marchenko-linearisation to deliver overall slightly better inverted models than the single-scattering approximation. [ABSTRACT FROM AUTHOR]

Seismic full-waveform inversion (FWI) provides high resolution images of the subsurface by exploiting information in the recorded seismic waveforms. This is achieved by solving a highly non-linear and non-unique inverse problem. Bayesian inference is therefore used to quantify uncertainties in the solution. Variational inference is a method that provides probabilistic, Bayesian solutions efficiently using optimization. The method has been applied to 2-D FWI problems to produce full Bayesian posterior distributions. However, due to higher dimensionality and more expensive computational cost, the performance of the method in 3-D FWI problems remains unknown. We apply three variational inference methods to 3-D FWI and analyse their performance. Specifically, we apply automatic differential variational inference (ADVI), Stein variational gradient descent (SVGD) and stochastic SVGD (sSVGD), to a 3-D FWI problem and compare their results and computational cost. The results show that ADVI is the most computationally efficient method but systematically underestimates the uncertainty. The method can therefore be used to provide relatively rapid but approximate insights into the subsurface together with a lower bound estimate of the uncertainty. SVGD demands the highest computational cost, and still produces biased results. In contrast, by including a randomized term in the SVGD dynamics, sSVGD becomes a Markov chain Monte Carlo method and provides the most accurate results at intermediate computational cost. We thus conclude that 3-D variational FWI is practically applicable, at least in small problems, and can be used to image the Earth's interior and to provide reasonable uncertainty estimates on those images. [ABSTRACT FROM AUTHOR]

Deep learning (DL) has achieved remarkable progress in geophysics. The most commonly used supervised learning (SL) framework requires massive labelled representative data to train artificial neural networks (ANNs) for good generalization. However, the labels are limited or unavailable for field seismic data applications. In addition, SL generally cannot take advantage of well-known physical laws and thus fails to generate physically consistent results. The weaknesses of standard SL are non-negligible. Therefore, we provide an open-source package for geophysics-steered self-supervised learning (SSL; taking application to seismic deconvolution as an example). With the wavelet given, we incorporate the convolution model into the loss function to measure the error between the synthetic trace generated by the ANN deconvolution result and the observed data, steering the ANN's learning process toward yielding accurate and physically consistent results. We utilize an enhanced U-Net as the ANN. We determine a hard threshold operator to impose a sparse constraint on the ANN deconvolution result, which is challenging for current DL platforms because no layer is available. 2-D/3-D ANNs can naturally introduce spatial regularization to the ANN deconvolution results. Tests on synthetic data and 3-D field data with available well logs verify the effectiveness of the proposed approach. The approach outperforms the traditional trace-by-trace method in terms of accuracy and spatial continuity. Experiments on synthetic data validate that sparsity promotion matters for sparse recovery problems. Field data results of the proposed approach precisely identify the layer interfaces and mostly match well with the log. All codes and data are publicly available at https://doi.org/10.5281/zenodo.7233751 (Xintao Chai). [ABSTRACT FROM AUTHOR]

Recent advances in magnetic microscopy have enabled studies of geological samples whose weak and spatially nonuniform magnetizations were previously inaccessible to standard magnetometry techniques. A quantity of central importance is the net magnetic moment, which reflects the mean direction and the intensity of the magnetization states of numerous ferromagnetic crystals within a certain volume. The planar arrangement of typical magnetic microscopy measurements, which originates from measuring the field immediately above the polished surface of a sample to maximize sensitivity and spatial resolution, makes estimating net moments considerably more challenging than with spherically distributed data. In particular, spatially extended and nonuniform magnetization distributions often cannot be adequately approximated by a single magnetic dipole. To address this limitation, we developed a multipole fitting technique that can accurately estimate net moment using spherical harmonic multipole expansions computed from planar data. Given that the optimal location for the origin of such expansions is unknown beforehand and generally unconstrained, regularization of this inverse problem is critical for obtaining accurate moment estimates from noisy experimental magnetic data. We characterized the performance of the technique using synthetic sources under different conditions (noiseless data, data corrupted with simulated white noise, and data corrupted with measured instrument noise). We then validated and demonstrated the technique using superconducting quantum interference device microscopy measurements of impact melt spherules from Lonar crater, India and dusty olivine chondrules from the CO chondrite meteorite Dominion Range 08006. Plain Language Summary: Rocks may acquire records of the ambient magnetic field that can be preserved over geological timescales. This occurs when ferromagnetic minerals in those rocks cool, crystallize, or experience a pressure pulse. Magnetic microscopes are very sensitive instruments that can measure weak magnetic fields produced by rock samples at close proximity. They enable the analysis of rocks that were previously inaccessible to traditional paleomagnetic instrumentation. However, special data analysis techniques are required for obtaining the magnetic record preserved in a rock from the measurements collected by a magnetic microscope. We developed a novel analytical technique that allows us to use those instruments to successfully study small rock samples with nonuniform magnetization. We validate and demonstrate the technique using magnetic microscopy measurements of impact spherules from Lonar crater, India and mineral grains extracted from the meteorite Dominion Range 08006. Key Points: A spherical harmonic multipole expansion model can be used to estimate net magnetic moment from magnetic microscopy dataPlanar geometry and indeterminacy of the origin location for the multipole expansion require regularization of an ill‐posed inverse problemAccurate moment estimates can be obtained for measurements of compact geological samples even with low signal‐to‐noise ratios [ABSTRACT FROM AUTHOR]

The traditional electrical resistivity tomography (ERT) inversion methods typically produce low-resolution imaging results due to the nonlinear and bulk effect of 2-D inversion. In this letter, we propose to directly establish the mapping from the geoelectric model of traditional inversion results (input) to the actual geoelectric models (output) through the fully convolutional networks (FCNs), inspired by the robust nonlinear mapping capabilities of deep learning methods. We designed an ERT resolution enhancement network (ERTReNet) based on the prevailing U-Net architecture, which can conduct end-to-end training and enhance the resolution of traditional inversion imaging results. This methodology has been tested on both synthetic and field measured data. Resolution has been improved, and the resistivity value of both target and geological background is closer to the synthetic model comparing to the tradition method. This work aids in improving the accuracy of subsurface target identification in ERT and serves as a guide for more precise ERT inversion in the future. [ABSTRACT FROM AUTHOR]

We consider marine controlled source electromagnetic (CSEM) data and demonstrate that a typical CSEM survey is associated with significant data redundancy. Thus, it should be possible to obtain a high-quality inversion result by using only a subset of the original data. Moreover, in survey design, effort should be made to optimize the placement of the receivers. This study therefore investigates the challenges of data decimation and survey design in the case of repeated surveys by use of the data resolution matrix and model resolution matrix. A framework of analysis has been developed to efficiently use these quantities. The feasibility of the proposed approach is demonstrated using both synthetic data computed from an interpreted model of the Wisting oil field in the Barents Sea, as well as actual field data from the same oil field. [ABSTRACT FROM AUTHOR]

Regularization methods improve the stability of ill-posed inverse problems by introducing some a priori characteristics for the solution such as smoothness or sharpness. In this contribution, we propose a multidimensional scale-dependent wavelet-based ℓ1-regularization term to cure the ill-posedness of the airborne (time-domain) electromagnetic induction inverse problem. The regularization term is flexible, as it can recover blocky, smooth and tunable in-between inversion models, based on a suitable wavelet basis function. For each orientation, a different wavelet basis function can be used, introducing an additional relative regularization parameter. We propose a calibration method to determine (an educated initial guess for) this relative regularization parameter, which reduces the need to optimize for this parameter and, consequently, the overall computation time is under control. We apply our novel scheme to a time-domain airborne electromagnetic data set in Belgian saltwater intrusion context, but the scheme could equally apply to any other 2D or 3D geophysical inverse problem. [ABSTRACT FROM AUTHOR]

Many geophysical inverse problems are known to be ill-posed and, thus, requiring some kind of regularization in order to provide a unique and stable solution. A possible approach to overcome the inversion ill-posedness consists in constraining the position of the model interfaces. For a grid-based parameterization, such a structurally constrained inversion can be implemented by adopting the usual smooth regularization scheme in which the local weight of the regularization is reduced where an interface is expected. By doing so, sharp contrasts are promoted at interface locations while standard smoothness constraints keep affecting the other regions of the model. In this work, we present a structurally constrained approach and test it on the inversion of frequency-domain electromagnetic induction (FD-EMI) data using a regularization approach based on the Minimum Gradient Support stabilizer, which is capable to promote sharp transitions everywhere in the model, i.e., also in areas where no structural a priori information is available. Using 1D and 2D synthetic data examples, we compare the proposed approach to a structurally constrained smooth inversion as well as to more standard (i.e., not structurally constrained) smooth and sharp inversions. Our results demonstrate that the proposed approach helps in finding a better and more reliable reconstruction of the subsurface electrical conductivity distribution, including its structural characteristics. Furthermore, we demonstrate that it allows to promote sharp parameter variations in areas where no structural information are available. Lastly, we apply our structurally constrained scheme to FD-EMI field data collected at a field site in Eastern Germany to image the thickness of peat deposits along two selected profiles. In this field example, we use collocated constant offset ground-penetrating radar (GPR) data to derive structural a priori information to constrain the inversion of the FD-EMI data. The results of this case study demonstrate the effectiveness and flexibility of the proposed approach. [ABSTRACT FROM AUTHOR]

We present an update of the geomagnetic data assimilation tool pygeodyn , use it to analyse ground and satellite-based geomagnetic data sets, and report new findings on the dynamics of the Earth's outer core on interannual to decadal timescales. Our results support the idea that quasi-geostrophic Magneto-Coriolis waves, recently discovered at a period of 7 yr, also operate on both shorter and longer timescales, specifically in period bands centred around 3.5 and 15 yr. We revisit the source of interannual variations in the length of day and argue that both geostrophic torsional Alfvén waves and quasi-geostrophic Magneto-Coriolis waves can possibly contribute to spectral lines that have been isolated around 8.5 and 6 yr. A significant improvement to our ensemble Kalman filter algorithm comes from accounting for cross-correlations between variables of the state vector forecast, using the 'Graphical lasso' method to help stabilize the correlation matrices. This allows us to avoid spurious shrinkage of the model uncertainties while (i) conserving important information contained in off-diagonal elements of the forecast covariance matrix, and (ii) considering a limited number of realizations, thus reducing the computational cost. Our updated scheme also permits us to use observations either in the form of Gauss coefficient data or more directly as ground-based and satellite-based virtual observatory series. It is thanks to these advances that we are able to place global constraints on core dynamics even at short periods. [ABSTRACT FROM AUTHOR]

Because the magnetotelluric (MT) method uses natural sources, the electric and magnetic fields recorded in the field acquisition are not directly used but usually converted into other MT response functions for interpretation such as inversion. Considering that inversion results are dependent on types of input data, it can be helpful to analyse different characteristics of MT response functions for inversion. In this study, we examine sensitivity patterns of MT response functions used commonly in MT inversion, which are the impedance tensor, apparent resistivity, phase, tipper, effective impedance and phase tensor; and investigate how their sensitivity patterns affect inversion results. We first describe overall tendencies of 3-D sensitivity patterns of the MT response functions, and then classify the MT response functions into six groups based on 2-D sensitivity patterns computed at the surface, which are briefly called 'surface-sensitivity patterns' in this study. The 'diagonal components of the impedance' and 'off-diagonal components of the phase tensor', which have four petals-shaped surface-sensitivity patterns along the diagonal directions, belong to Group 1, and contribute to imaging 3-D subsurface structures from receivers installed evenly at the surface. Group 2 contains the ' xy -components of the impedance, apparent resistivity and phase' and ' yy -component of the phase tensor' whose surface-sensitivity patterns are linear in the y -axis. The ' yx -components of the impedance, apparent resistivity and phase' and ' xx -component of the phase tensor' that have strong linear surface-sensitivity patterns along the x -axis are classified into Group 3. The MT response functions of Groups 2 and 3 are useful for inversion of structures close to 2-D, whose strike extends along the y - and x -axes, respectively. Groups 4 and 5 include the ' x - and y -components of tipper' that possess linearly aligned two petals-shaped surface-sensitivity patterns in the x - and y -axes, respectively. The tipper can be helpful in imaging both 2-D and 3-D structures. The 'effective impedance' belongs to Group 6, whose surface-sensitivity patterns appear as a small circle. The surface-sensitivity patterns allow the effective impedance to have an advantage in interpretation of 1-D structures. By using several MT response functions for specific cases of 1-D, 2-D and 3-D interpretation of MT data, we investigate whether characteristics of the sensitivity patterns are reflected in modelling (simulating field data) and inversion results, and then suggest optimal MT response functions for those cases. In doing so, we show how to utilize the characteristics of the sensitivity patterns in inversion, and recommend the input MT response functions for inversion according to MT exploration situations. Our study provides basic information on similarities and differences of major MT response functions for inversion and insights on which MT response functions are suitable to increase the feasibility of MT inversion for different field situations based on the sensitivity patterns. [ABSTRACT FROM AUTHOR]

Palaeomagnetic investigations often encounter multiple magnetization components, where secondary processes have obscured, partially overprinted or completely replaced the original (primary) remanent magnetization. Identification and separation of primary and secondary magnetizations are generally carried out with principal component analysis of stepwise demagnetization data. However, rocks may contain multiple generations of magnetic minerals with overlapping unblocking ranges that complicate the discrimination of components when applying best-fitting line procedures. Developing a method to differentiate and quantify contributions of overlapping magnetic components using directional data is therefore highly desirable. This paper presents a method to unmix stepwise demagnetization data using an inverse modelling approach. We show that the method is capable of accurately resolving two or three magnetic components with overlapping or superimposed unblocking spectra as well as quantifying absolute component contributions. The method depends on accurate identification and selection of end-member components prior to analysis; in doing so, the method can help palaeomagnetists understand how magnetization components combine to explain their data. We show that the dilution of one component by more than ca. 25 per cent from another component can result in linear demagnetization curves that decay to the origin on orthogonal plots, but whose best-fitting direction can significantly deviate from both end-members. The efficacy of the method is demonstrated through examples of demagnetization data from hematite and/or magnetite-bearing sandstones from China. This method can be broadly applied to all multicomponent magnetization problems in palaeomagnetism. [ABSTRACT FROM AUTHOR]

An adjoint-based conjugate gradient algorithm provides an efficient means for imaging sources of deformation within the Earth, such as volume stresses associated with fluid flow in aquifers and reservoirs. For time intervals over which the overburden deforms elastically, one can calculate the gradient elements for a single model update using just two numerical simulations. The first is a forward run that is used to compute the residuals associated with the given iteration. The second simulation is to evaluate the application of the adjoint operator to the residuals. In this adjoint calculation, the residual displacements are applied as sources at the measurement locations, driving the deformation in the simulation. The volume stress on the source grid blocks, in response to the residual displacements, provide the gradient components. We apply this technique to satellite-based interferometric synthetic aperture radar (InSAR) line-of-sight displacements that were observed over an oil reservoir in California's Central Valley. We find that the adjoint-based gradient estimates, requiring 18 CPU seconds, agree with conventional numerical calculations that take over 3700 CPU seconds to compute. Conjugate gradient algorithms utilizing the conventional approach and adjoint-based gradient computations give roughly the same reductions in misfit and similar final estimates of reservoir volume change.

In this study, seismic inversion is carried out using a genetic algorithm (GA) as well as a hybrid genetic algorithm (HGA) approach to optimize the objective function designed for the inversion. An HGA is a two steps coupled process, where a local optimization algorithm is applied to the best model obtained from each generation of the GA. The study aims to compare the qualitative as well as the quantitative performance of both methods to delineate the reservoir zone from the non-reservoir zone. Initially, the developed algorithm is tested on synthetic data followed by its application to real data. It is found that the HGA for synthetic data is providing more accurate and high-resolution subsurface information as compared with the conventional GA although the time taken later is less as compared with the former methods. The application to real data also shows very high-resolution subsurface acoustic impedance information. The interpretation of the impedance section shows a low impedance anomaly zone at (1055–1070) ms time interval with impedance ranging from (7500 to 9500) m s−1*g cc−1. The correlation between seismic and well data shows that the low impedance zone is characterized as a clastic glauconitic sand channel (reservoir zone). In seismic inversion using an HGA, one can delineate the areal extent of the reservoir zone from the non-reservoir zone more specifically as compared to the GA-derived impedance. The convergence time of HGA is 4.4 per cent more than GA and can be even more for larger seismic reflection data sets. Further, for a more detailed analysis of the reservoir zone and to cross-validate inverted results, an artificial neural network (ANN) is applied to data, and porosity volume is predicted. The analysis shows that the low impedance zone interpreted in inversion results are correlating with the high porosity zone found in ANN methods and confirm the presence of the glauconitic sand channel. This study is important in the aspect of qualitative as well as quantitative comparison of the performance of the GA and HGA to delineate sand channels. [ABSTRACT FROM AUTHOR]

The Gravity Recovery and Climate Experiment (GRACE) mass concentration (mascon) solutions provide enhanced signal and spatial resolution of surface mass changes by using regularization techniques to reduce striping errors. To further improve the computational efficiency and capture the same benefits as GRACE mascon solutions, we presented an estimation of regional mascon solutions from GRACE-based geopotential differences by using spatio-temporal constraints with the unconstrained spherical harmonic solutions as a priori information. As a case study, the changes in the basin-scale terrestrial water storage (TWS) over the Yangtze River Basin (YRB) on 2° × 2° grids at monthly intervals were estimated using GRACE-based geopotential differences, for the period of 2003 January—2013 December. The estimates were validated through official GRACE mascon solutions and in situ observations (i.e. time derivative of TWS change derived from precipitation, evapotranspiration and river run-off based on the water mass balance equation). The results demonstrate that the spatial and temporal patterns of TWS changes in the YRB inferred from geopotential differences adequately agree with the official mascon solutions; however, differences in amplitudes can be observed at the subbasin scale because of different regularizations applied in different solutions. In situ validations demonstrate that seasonal changes of mascon solutions and in situ observations agree well in the YRB; however, there are evident discrepancies in amplitudes over the subbasins owing to leakage biases in mascon solutions. For the entire YRB, the statistical evaluation and cross-wavelet transform demonstrate that our regional mascon solutions appear more consistent with in situ observations than the official mascon solutions. In addition, compared with the results estimated by spatial constraints, regional mascon solutions estimated by spatio-temporal constraints using observations from three consecutive months adjacent to the given month were improved. Our method provides an alternative option to use different regularization constraints, which is helpful for fine-tuning analysis of basin-scale TWS changes. [ABSTRACT FROM AUTHOR]

We present a fully finite-element based inversion methodology for imaging 3-D magnetotelluric impedance data on unstructured meshes. The inverse problem is formulated using a minimum-structure Gauss–Newton type optimization scheme that minimizes an objective function with respect to the model perturbation. By introducing a rigorous regularization scheme, we derived a Ritz-type variational formulation of the model objective function and designed a face-based finite-element basis function to discretize the model gradient across tetrahedron's inter-element boundaries. The forward modelling engine of our optimization scheme is based on a finite-element solution of the E-field Helmholtz equation that is enforced for the magnetotelluric simulation problem using the appropriate edge-based basis functions and 3D boundary conditions. The optimization algorithm developed here utilizes a message passing interface scheme and uses a direct solver to factorize and store both the regularization matrix and the forward modelling coefficient matrix on the processes working in parallel. Having to do this only once within each Gauss–Newton optimization cycle facilitates both the calculation of the dot product of the model regularization terms with the evolving model perturbation, and computing implicitly the sensitivity-vector products. We validated the methodology and the correctness of the developed algorithm for two test examples (COMMEMI 3Ds) from the literature. Also, by comparing the performance between classes of iterative solvers we demonstrated the superior performance of generalized minimum residual solver in reducing the residual norm of the iterative solver during model updates. Using the algorithm in a geologically realistic scenario, we imaged the anticipated geometry of the Lalor volcanogenic massive sulphide deposit in Canada. The feasibility of the imaging methodology is further evaluated with the survey data, for which, again the algorithm converged to the anticipated model solution reproducing the lithostratigraphic sequence of the ore deposit. [ABSTRACT FROM AUTHOR]

We explored the potential of fibre optics coupled with distributed acoustic sensing (DAS) to measure the thickness and Young's modulus of an ice layer, using the properties of guided seismic waves. During two winter seasons (2020 and 2021), an optical fibre was deployed over one of the frozen Roberts Mountain lakes (at 2400 m a.s.l) near Grenoble (France) and we measured both the continuous ambient seismic noise as well as signals generated by active sources (hammer), with a DAS interrogator. Following a Bayesian scheme, we inverted the dispersion curves of longitudinal and flexural guided waves retrieved from the analysis of active shot gathers and obtained Young's modulus E = 3.4 ± 0.1 GPa and ice thickness h = 47 ± 1 cm from the second-year data. The ice thickness was consistent with field measurements. Field observations of porous and/or fracture ice may explain the relatively low effective Young's modulus (relative to pure ice), which may also be affected by a snow layer not included in the model. The drastic improvements in the inversion results between the two years are related to better coupling conditions (drone deployment before early freezing), more appropriate acquisition parameters (2 m gauge length), and the upper snow layers (less thick and less heterogeneous in the second year). Moreover, we were able to use the non-dispersive low-frequency noise associated with gravity waves to estimate the lake depth H = 5 m which is compatible with independent observations. The use of DAS to record guided seismic waves could then appear as a relevant tool for monitoring environments like floating ice shelves and sea ice. [ABSTRACT FROM AUTHOR]

Periodic directional and temporal measurements are common in seismology, and necessitate specific statistical analyses that are appropriate for circular quantities. In this work, we explore the use of a von Mises distribution as a representation of errors on circular seismological observations. Specifically, we automate the estimation of surface-wave phase-velocity dispersion for the teleseismic two-station method, which generally suffers from a 2π phase ambiguity. The use of Bayesian inverse techniques, which aim to rigorously quantify model parameter uncertainty, have become widespread throughout seismology over the last decade. Here, we apply Bayesian inversion to measurements of surface-wave phase spectra in order to estimate 1-D, path-averaged Earth structure between station pairs. The dispersion curve and associated uncertainties are additional results of the inversion, which can then be used as input for subsequent analyses (e.g. tomography). We demonstrate this technique through application to surface-wave recordings from long-running seismic stations throughout western Canada. Our results for over 10 000 station pairs reveal first-order tectonic features consistent with previous studies, which provides confidence in our approach as well as an initial step towards resolving a full 3-D seismic velocity model for the region. This work also presents a foundation for the inversion of surface-wave phase spectra to estimate 3-D Earth structure directly. Finally, the ideas presented in this work are not limited to the inversion of surface-wave phase spectra, but can also be considered for Bayesian geophysical inversion of any circular quantities. [ABSTRACT FROM AUTHOR]

Correctly interpreting phase events thanks to data processing techniques based on correlation or deconvolution has been the focus of numerous studies in the field of high-resolution seismic imaging using full-waveform inversion. To mitigate the non-convexity of the misfit function and the risk to converge towards non-informative local minima, correlation and deconvolution techniques make it possible to focus on phase information instead of amplitude information and to design more convex misfit function, alleviating the dependency of the full-waveform inversion process on the accuracy of initial models. Such techniques however rely on the assumption that phase events can be compared one by one, or that all the phase events are shifted in time in a similar way. This assumption is not satisfied in practice, which limits the effectiveness of these correlation/deconvolution-based methods. To overcome this issue, we propose to account for the non-stationary relation between observed and predicted data through a local in-time deconvolution technique, based on time–frequency analysis of the signal using a Gabor transform. This makes it possible to estimate instantaneous time-shift between locally coherent phase events. This strategy generalizes the conventional normalized deconvolution technique, which has been popularized under the name of adaptive waveform inversion. To support the introduction of our novel method, we compare it with four misfit functions based respectively on classical cross-correlation, penalized cross-correlation, penalized deconvolution, and adaptive waveform inversion. We analyse the behaviour of these methods on specific scenarios, and then propose a comparison on 2-D synthetic benchmarks. We show how our 'localized' adaptive waveform inversion applies in these realistic tests and overcomes some of the limitations of the aforementioned techniques. [ABSTRACT FROM AUTHOR]

In some Earth materials, significant induced polarization (IP) phenomena are occurring when an electric perturbation is applied. These mechanisms are described by a frequency-dependent complex resistivity (CR). The study of the CR spectral signature allows to access indirectly to several properties of interest of the subsurface linked to the interaction between the pore space and fluids. CR is usually studied using the electrical method with a direct current approximation, neglecting by the way electromagnetic (EM) induction that can occur in the data. However, EM induction increases with frequency and offset, resulting in limitations at high frequencies or for the investigation of deep target. We implemented a frequency-dependent CR in a 3-D finite-differences (FD) modelling and inversion code for frequency domain controlled-source electromagnetic (CSEM) data to take into consideration IP information contained in EM data or reciprocally. The CSEM methods are resistivity imaging techniques using multifrequency EM fields that fully take into account EM induction with large investigation depth. Following a preliminary sensitivity study, a multistage inversion framework was designed to constrain the multiparameter inverse problem. Furthermore, to manage the increasing number of parameters, a second-order polynomial parametrization is used to describe independently frequency variation of CR norm and phase. We demonstrate the method through 1-D and 3-D synthetic data inversions for a deep-target model. We show that we were able to recover the CR and its frequency variation from CSEM data in the IP/EM coupling domain for 1-D targets. The problem of deep polarizable 3-D targets is more challenging and the resolution of the recovered CR spectrum was impacted. Nevertheless, we retrieved from a model containing several polarizable anomalies some crucial information allowing the discrimination of the targets from the non-polarizable background and from different spectral CR signatures. Our inversion strategy allows thus accessing to IP parameters of the medium in an extended frequency domain by fully taking EM induction information into account. [ABSTRACT FROM AUTHOR]

With the rise of the fourth industrial revolution, traditional methods of analyzing investment have been transformed into intelligent methods under big data and the Internet of Things. This has created a new approach to solving practical engineering problems. This paper examines the formation and evolution of the application of inversion theory in tunnel and underground engineering, summarizing research progress using traditional and intelligent inversion analysis methods to identify three types of target unknown quantities in tunnels and underground projects: initial ground stress, support structure load, and tunnel characteristic parameters. It also offers an outlook on how to optimize inversion analysis methods to solve more challenging and complex tunneling problems in the context of informatization, digitalization, and intelligence. In the current research process of tunnel and underground space engineering problems, the inversion theory system has been improved, but inversion analysis methods still face many challenges. These include the low reliability of initial ground stress inversion under complex geological conditions, the lack of indicators to objectively evaluate the accuracy of inversion analysis, and the high costs of intelligent inversion analysis means. Moving forward in the context of big data and the information era, the future development direction for inversion theory and inversion methods in tunnel and underground space engineering is to combine new monitoring technology, computer vision technology, and simulation analysis technology to establish multifaceted intelligent inversion analysis models. [ABSTRACT FROM AUTHOR]

Amplitude variation with incident angle and azimuth (AVAZ) inversion is usually used for estimating subsurface medium properties from azimuthal stacked seismic data for fracture prediction. And weak anisotropy parameters play an important role in the fracture prediction of shale reservoirs. However, the low contribution of the anisotropic parameters to the reflection coefficient and too many condition numbers of forward solver lead to insufficient inversion stability of the anisotropic parameters. Therefore, a new azimuthal-amplitude-difference inversion method with the azimuth-velocity-anisotropic constraints is proposed to improve the stability of inversion and obtain a reasonable estimation of anisotropic parameters. The azimuthal amplitude difference AVAZ forward solver in the anisotropic medium is initially established from a rewritten approximate reflectivity equation and variable substitution. Sensitivity analysis of estimated parameters of the rewritten approximate reflectivity indicates that our approach is sufficiently suitable for seismic inversion of anisotropic parameters. Furthermore, an azimuthal amplitude difference Bayesian AVAZ inversion approach with azimuth-velocity-anisotropic constraint is developed to improve the stability of the inversion. We add Gaussian noise to the synthetic seismic records and assume the Cauchy distributions as a prior constraint on the model parameters. The anisotropic information obtained from the azimuth-velocity-anisotropic inversion is utilized as a constraint for improving the stability of inversion. Synthetic data tests reveal that the anisotropic parameters can be estimated stably even with moderate noise. Field data tests illustrate the feasibility and reliability of the presented inversion method for estimating anisotropic parameters in a shale reservoir with vertical or near-vertical fractures. [ABSTRACT FROM AUTHOR]

Carbon capture and storage is an important technology for greenhouse gas mitigation. Monitoring of CO2 storage should, in addition to locating the plume, provide quantitative information on CO2 saturation. We propose a full waveform inversion (FWI) algorithm for the prediction of the spatial distribution of CO2 saturation from time-lapse seismic data. The methodology is based on the application of a rock-physics parametrized FWI scheme that allows for direct updating of reservoir properties. We derive porosity and lithology parameters from baseline data and use them as input to predict CO2 saturation from monitor data. The method is tested on synthetic time-lapse data generated for the Johansen formation model. Practical issues associated with field data applications, such as acquisition limitations, construction of the initial model, noise and uncertainty in the rock physics model, are taken into account in the simulation. The results demonstrate the robustness of our approach for reconstructing baseline and monitor models. We also illustrate the potential of the approach as compared to conventional two-step inversion algorithms, in which an elastic FWI prediction of velocities and density is followed by rock physics inversion. [ABSTRACT FROM AUTHOR]

Seismic inversion of amplitude versus offset (AVO) data in viscoelastic media can potentially provide high-resolution subsurface models of seismic velocities and attenuation from offset/angle seismic gathers. P - and S -wave quality factors (Q), whose inverse represent a measure of attenuation, depend on reservoir rock and pore fluid properties, in particular, saturation, permeability, porosity, fluid viscosity and lithology; however, these quality factors are rarely taken into account in seismic AVO inversion. For this reason, in this work, we aim to integrate quality factors derived from physically based models in AVO inversion by proposing a gradient descent optimization-based inversion technique to predict the unknown model properties (P - and S -wave velocities, the related quality factors and density). The proposed inversion minimizes the non-linear least-squares misfit with the observed data. The optimal solution is iteratively obtained by optimizing the data misfit using a second-order limited-memory quasi-Newton technique. The forward model is performed in the frequency–frequency-angle domain based on a convolution of broad-band signals and a linearized viscoelastic frequency-dependent AVO (FAVO) equation. The optimization includes the adjoint-state-based gradients with the Lagrangian formulation to improve the efficiency of the non-linear seismic FAVO inversion process. The inversion is tested on synthetic seismic data, in 1-D and 2-D, with and without noise. The sensitivity for seismic quality factors is evaluated using various rock physics models for seismic attenuation and quality factors. The results demonstrate that the proposed inversion method reliably retrieves the unknown elastic and an-elastic properties with good convergence and accuracy. The stability of the inverse solution especially seismic quality factors estimation relies on the noise level of the seismic data. We further investigate the uncertainty of the solution as a function of the variability of the initial models. [ABSTRACT FROM AUTHOR]

We present a basic algorithm for optimal experimental design in distributed fibre-optic sensing. It is based on the fast random generation of fibre-optic cable layouts that can be tested for their cost-benefit ratio. The algorithm accounts for the maximum available cable length, lets the cable pass through pre-defined points of interest, avoids obstacles that the cable must not traverse, permits the adaptation of geometric complexity of different cable segments and allows for the incorporation of topography. Furthermore, the algorithm can be combined with arbitrary measures of the cost-benefit ratio, and its simplicity enables easy adaptations to the needs of specific applications. In addition to a description of the basic concept, we provide examples that illustrate the circumnavigation of obstacles, the steering of geometric complexity and the cable layout optimization in the presence of topographic variations. [ABSTRACT FROM AUTHOR]

We have developed an inversion method for estimating 3-D tectonic stress fields from centroid moment tensor (CMT) data of seismic events. To obtain reliable inversion analysis results, we need to use as much data as possible, ranging over different periods. In this study, we improved the previously developed CMT data inversion method to incorporate preceding inversion analysis results into the present analysis as direct prior information about the stress field. The spatial distribution of seismic events and/or their focal mechanisms in a region would change from one period to another, reflecting temporal stress changes there. In the improved inversion method, in addition to the hyperparameter controlling the roughness of stress fields, we introduced another hyperparameter that controls the relative weight of direct prior information to the observed data to be analysed. The relative weights of direct and indirect prior information to the observed data are appropriately determined by using Akaike's Bayesian Information Criterion. We applied the improved inversion method to the observed CMT data of seismic events of 24 yr (1997−2020) in northeast Japan, where the Tohoku-oki megathrust event (M w 9.0) occurred on 11 March 2011 at the North American–Pacific Plate boundary. To investigate temporal changes in tectonic stress orientation, we divided the target period into the inter-, pre- and post-seismic periods of the megathrust event: P1 (January 1997−January 2007), P2 (February 2007−February 2011), and P3 (March 2011−December 2020). According to successive inversion analysis results for P1 and P2, we confirmed that the tectonic stress orientation was stable for 14 yr before the megathrust event. On the other hand, successive inversion analysis results for P2 and P3 indicated a possibility that the 2011 megathrust event caused significant changes in tectonic stress orientation in three regions. However, two of them were negative in the quantitative evaluation of the reliability of detected temporal changes. In conclusion, the stress orientation change in the region off Fukushima and Ibaraki, the southern margin of the main rupture area of the megathrust event, seems to be real. [ABSTRACT FROM AUTHOR]

Thunder-induced seismic waves recorded at dense seismic stations in Seoul, South Korea are analysed for inversion of thunder source spectra. Thunder-induced seismic waves from four local thunder events are analysed. A theory is introduced for the inversion of acoustic source spectra from thunder-induced seismic waves. In the course of source-spectral inversion, the propagation and acoustic-to-seismic coupling effects are counted. The thunder-induced seismic signals were well identified at distances of <∼20 km. Direct acoustic-to-seismic coupled seismic waves present apparent phase velocities of sound speed in atmosphere (340 m s−1). Thunder-induced seismic waves are dominant at high frequencies (>20 Hz). Vertical peak ground accelerations of thunder-induced seismic waves in local regions (0.024–0.110 m s−2 at distances of 2.4–3.7 km) are equivalent to the ground motion levels induced by a moderate-size (∼ M 5) earthquake at regional distances. The thunder-induced acoustic waves in the atmosphere are obtained by removing the acoustic-to-seismic coupling effect and site-response effect from the observed thunder-induced seismic waves. The quality factors for acoustic wave attenuation in the atmosphere are determined. Urban landscapes and atmospheric effects cause strong acoustic attenuation over atmospheric absorption. Acoustic thunder source spectra are determined by stacking the inverted acoustic spectra at all stations. The peak frequencies of acoustic thunder source spectra are around 34–36 Hz, suggesting the acoustic energy per unit length in lightning strikes to be ∼4 × 106 J m−1. Local seismic records are applicable for the investigation of thunder and lightning properties. [ABSTRACT FROM AUTHOR]

Reconstruction of the distribution of ground motion due to an earthquake is one of the key technologies for the prediction of seismic damage to infrastructure. Particularly, the immediate reconstruction of the spatially continuous wavefield is valuable for decision-making of disaster response decisions in the initial phase. For a fast and accurate reconstruction, utilization of prior information is essential. In fluid mechanics, full-state recovery, which recovers the full state from sparse observation using a data-driven model reduced-order model, is actively used. In this study, the framework developed in the field of fluid mechanics is applied to seismic wavefield reconstruction. A seismic wavefield reconstruction framework based on compressed sensing using the data-driven reduced-order model (ROM) is proposed and its characteristics are investigated through numerical experiments. The data-driven ROM is generated from the data set of the wavefield using the singular value decomposition. The spatially continuous seismic wavefield is reconstructed from the sparse and discrete observation and the data-driven ROM. The observation sites used for reconstruction are effectively selected by the sensor optimization method for linear inverse problems based on a greedy algorithm. The proposed framework was applied to simulation data of theoretical waveform with the subsurface structure of the horizontally stratified three layers. The validity of the proposed method was confirmed by the reconstruction based on the noise-free observation. Since the ROM of the wavefield is used as prior information, the reconstruction error is reduced to an approximately lower error bound of the present framework, even though the number of sensors used for reconstruction is limited and randomly selected. In addition, the reconstruction error obtained by the proposed framework is much smaller than that obtained by the Gaussian process regression. For the numerical experiment with noise-contaminated observation, the reconstructed wavefield is degraded due to the observation noise, but the reconstruction error obtained by the present framework with all available observation sites is close to a lower error bound, even though the reconstructed wavefield using the Gaussian process regression is fully collapsed. Although the reconstruction error is larger than that obtained using all observation sites, the number of observation sites used for reconstruction can be reduced while minimizing the deterioration and scatter of the reconstructed data by combining it with the sensor optimization method. Hence, a better and more stable reconstruction of the wavefield than randomly selected observation sites can be realized, even if the reconstruction is carried out with a smaller number of observations with observation noise, by combining it with the sensor optimization method. [ABSTRACT FROM AUTHOR]

Geophysicists have widely used least-squares reverse-time migration (LSRTM) to obtain high-resolution images of the subsurface. However, LSRTM is computationally expensive and it can suffer from multiple reflections. Recently, a target-oriented approach to LSRTM has been proposed, which focuses the wavefield above the target of interest. Remarkably, this approach can be helpful for imaging below complex overburdens and subsalt domains. Moreover, this approach can significantly reduce the computational burden of the problem by limiting the computational domain to a smaller area. Nevertheless, target-oriented LSRTM still needs an accurate velocity model of the overburden to focus the wavefield accurately and predict internal multiple reflections correctly. A viable alternative to an accurate velocity model for internal multiple prediction is Marchenko redatuming. This method is a novel data-driven method that can predict Green's functions at any arbitrary depth, including all orders of multiples. The only requirement for this method is a smooth background velocity model of the overburden. Moreover, with Marchenko double-focusing, one can make virtual sources and receivers at a boundary above the target and bypass the overburden. This paper proposes a new algorithm for target-oriented LSRTM, which fits the Marchenko double-focused data with predicted data. The predicted data of the proposed method is modelled by a virtual source term created by Marchenko double-focusing on a boundary above the target of interest. This virtual source term includes all the interactions between the target and the overburden. Moreover, the Marchenko double-focused data and the virtual source term are free of multiples generated in the overburden. Consequently, our target-oriented LSRTM algorithm suppresses the multiples purely generated inside the overburden. Our algorithm correctly accounts for all orders of multiples caused by the interactions between the target and the overburden, resulting in a significant reduction of the artefacts caused by the overburden internal multiple reflections and improves amplitude recovery in the target image compared to conventional LSRTM. [ABSTRACT FROM AUTHOR]

Drone-towed scalar field gradiometry surveys conducted in windy conditions or under self-excited oscillations generate attitude-induced responses that can hinder the geological interpretation. Here, we present a gradiometric equivalent source method (GESM) to remove these attitude-induced responses by interpolating and continuing the measured gradiometry data to new idealized pseudo-sensor positions free of any attitude deviations. In addition, we present transverse horizontal difference (THD) data from a precisely positioned drone-towed horizontal gradiometry survey collected in Nautanen, northern Sweden. Analysing the Nautanen survey's positional data revealed that the gradiometer system exhibited directional-dependent yaw deviations with periods of unpredictable attitude deviations. Based on synthetic THD data created using the Nautanen survey's positional data, these deviations manifest as line-to-line striping and short-wavelength oscillations in the THD maps. Applying GESM to the synthetic THD data removes these attitude-induced THD responses with satisfactory accuracy compared to the true THD values. Furthermore, on the actual THD data collected in Nautanen, applying GESM improved the continuity of anomalies, significantly improving the interpretation of the data. The results suggest that including GESM in the data processing of drone-towed gradiometry surveys, given precise positional information via an onboard GNSS-IMU system, ensures high-quality geological interpretation even in windy conditions or in high-gradient areas. [ABSTRACT FROM AUTHOR]

During tunnel construction, accurately ascertaining the adverse geological condition in front of the tunnel face is essential to ensure construction safety and decrease economic loss. As an accurate wave velocity modelling method, seismic full-waveform inversion (FWI) still faces many difficulties when applied in a tunnel observation environment because of fewer observation data and smaller offset than ground seismic detection. This paper analysed the FWI for tunnel active seismic forward prospecting with a single shot. We adopted the N -order time integral wavefield and normalized integration objective function method to improve the stability and reduce the dependence of FWI on the initial model. Based on two assumptions on the wave velocity distribution in the tunnel, we proposed a 1-D velocity structure correction method to reduce the multiplicity of inversion. Then the improved tunnel FWI method based on these two inversion strategies was applied to a synthetic model with a rectangular anomaly and a lithology interface, verifying the method's effectiveness. Based on typical adverse geological bodies during tunnelling, three additional adverse geological models were built and verified the reliability of the methods in tunnel detection environments. There are still some false anomalies interference in the inversion results of the synthetic models from the inversion results. However, these problems are acceptable in limited tunnel observation space. Then the method was applied in a field example in the Yinsong water supply project in Jilin Province, China, and verified the effect on field data. Finally, the influence of the shot number on the inversion effect and the method's robustness are discussed. [ABSTRACT FROM AUTHOR]

Abstract Quantifying the contributions of distinct mineral populations in bulk magnetic experiments greatly enhances the analysis of environmental and rock magnetism studies. Here, we develop a new method of parametric unmixing of susceptibility components in hysteresis loops. Our approach is based on a modified Gamma‐Cauchy exponential model that accounts for variable skewness and kurtosis. The robustness of the model is tested with synthetic curves that examine the effects of noise, sampling, and proximity (similar coercivities) of susceptibility components. We provide a Python‐based script, the Hist‐unmix, which allows the user to adjust a forward model of up to three ferromagnetic components as well as a dia/paramagnetic contribution. Optimization of all the parameters is achieved through least squares fitting (Levenberg‐Marquardt method), with uncertainties of each inverted parameter calculated through a Monte Carlo error propagation approach. For each ferromagnetic component, it is possible to estimate the saturation magnetization (Ms), saturation remanent magnetization (Mrs) and the mean coercivity (Bc). Finally, Hist‐unmix was applied to a set of weakly magnetic carbonate rocks from Brazil, which typically show distorted hysteresis loops (wasp‐waisted and potbellied). For these samples, we resolved two components with distinct coercivities. These results are corroborated by previous experimental data, showing that the lower branch of magnetic hysteresis can be modeled by the presented approach and might offer important mineralogical information for rock magnetic and paleomagnetic studies.