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We present a method for inverting total-field anomaly data to estimate the geometry of a uniformly magnetized 3-D geological source in the subsurface. The method assumes the total-magnetization direction is known. We approximate the source by an ensemble of vertically juxtaposed right prisms, all of them with the same total-magnetization vector and depth extent. The horizontal cross-section of each prism is a polygon defined by a given number of equi-angularly spaced vertices from 0° to 360°, whose polygon vertices are described by polar coordinates with an origin defined by a horizontal location over the top of each prism. Because our method estimates the radii of each polygon vertex we refer to it as radial inversion. The position of these vertices, the horizontal location of each prism and the depth extent of all prisms are the parameters to be estimated by solving a constrained non-linear inverse problem of minimizing a goal function. We run successive inversions for a range of tentative total-magnetization intensities and depths to the top of the shallowest prism. The estimated models producing the lowest values of the goal function form the set of candidate solutions. To obtain stabilized solutions, we impose the zeroth- and first-order Tikhonov regularizations on the shape of the prisms. The method allows estimating the geometry of both vertical and inclined sources, with a constant direction of magnetization, by using the Tikhonov regularization. Tests with synthetic data show that the method can be of utility in estimating the shape of the magnetic source even in the presence of a strong regional field. Results obtained by inverting airborne total-field anomaly data over the Anitápolis alkaline–carbonatitic complex, in southern Brazil, suggest that the emplacement of the magnetic sources was controlled by NW–SE-trending faults at depth, in accordance with known structural features at the study area. [ABSTRACT FROM AUTHOR]

The multichannel transient electromagnetic method (MTEM), sensitive to both near-surface and deeply buried geoelectric structures, is a useful geophysical tool to map resistive targets. A typical MTEM survey consists of a large number of receiver and transmitter positions. The produced data volume is much larger than a traditional transient electromagnetic method survey, posing computational difficulties for its data inversion and interpretation. We proposed a 3-D parallel inversion algorithm for MTEM data based on nonlinear conjugate gradient method and the moving footprint technique. The electromagnetic response and Fréchet derivative are first calculated in the frequency domain with integral equation method and then cosine transformed into time domain. We not only fully parallelize the forward modelling and Fréchet derivative calculation but also use a moving footprint to speed up the inversion. The footprints for different offsets are carefully evaluated through synthetic models. The effectiveness of the developed algorithm has been demonstrated through synthetic and case studies. [ABSTRACT FROM AUTHOR]

The inversion of electromagnetic induction data to a conductivity profile is an ill-posed problem. Regularization improves the stability of the inversion and a smoothing constraint is typically used. However, the conductivity profiles are not always expected to be smooth. Here, we develop a new inversion scheme in which we transform the model to the wavelet space and impose a sparsity constraint. This sparsity constrained inversion scheme will minimize an objective function with a least-squares data misfit and a sparsity measure of the model in the wavelet domain. A model transform to the wavelet domain allows to investigate the temporal resolution (periodicities at different frequencies) and spatial resolution (location of the peaks) characteristics of the model, and penalizing small-scale coefficients effectively reduces the complexity of the model. The novel scale-dependent regularization term can be used to favour either blocky or smooth structures, as well as high-amplitude models in globally smooth structures in the inversion. Depending on the expected conductivity profile, a suitable wavelet basis function can be chosen. The scheme supports multiple types of regularization with the same algorithm and is thus flexible. Finally, we apply this new scheme on a frequency domain electromagnetic sounding data set, but the scheme could equally apply to any other 1-D geophysical method. [ABSTRACT FROM AUTHOR]

Time-lapse resistivity tomography bring valuable information on the physical changes occurring inside a geological reservoir. In this study, resistivity monitoring from controlled source electromagnetics (CSEM) data is investigated through synthetic and real data. We present three different schemes currently used to perform time-lapse inversions and compare these three methods: parallel, sequential and double difference. We demonstrate on synthetic tests that double difference scheme is the best way to perform time-lapse inversion when the survey parameters are fixed between the different time-lapse acquisitions. We show that double difference inversion allows to remove the imprint of correlated noise distortions, static shifts and most of the non-linearity of the inversion process including numerical noise and acquisition footprint. It also appears that this approach is robust against the baseline resistivity model quality, and even a rough starting resistivity model built from borehole logs or basic geological knowledge can be sufficient to map the time-lapse changes at their right positions. We perform these comparisons with real land time-lapse CSEM data acquired one year apart over the Reykjanes geothermal field. [ABSTRACT FROM AUTHOR]

The classical Backus–Gilbert method seeks localized Earth-structure averages at the shortest length scales possible, given a data set, data errors, and a threshold for acceptable model errors. The resolving length at a point is the width of the local averaging kernel, and the optimal averaging kernel is the narrowest one such that the model error is below a specified level. This approach is well suited for seismic tomography, which maps 3-D Earth structure using large sets of seismic measurements. The continual measurement-error decreases and data-redundancy increases have reduced the impact of random errors on tomographic models. Systematic errors, however, are resistant to data redundancy and their effect on the model is difficult to predict. Here, we develop a method for finding the optimal resolving length at every point, implementing it for surface-wave tomography. As in the Backus–Gilbert method, every solution at a point results from an entire-system inversion, and the model error is reduced by increasing the model-parameter averaging. The key advantage of our method stems from its direct, empirical evaluation of the posterior model error at a point. We first measure inter-station phase velocities at simultaneously recording station pairs and compute phase-velocity maps at densely, logarithmically spaced periods. Numerous versions of the maps with varying smoothness are then computed, ranging from very rough to very smooth. Phase-velocity curves extracted from the maps at every point can be inverted for shear-velocity (V S) profiles. As we show, errors in these phase-velocity curves increase nearly monotonically with the map roughness. We evaluate the error by isolating the roughness of the phase-velocity curve that cannot be explained by any Earth structure and determine the optimal resolving length at a point such that the error of the local phase-velocity curve is below a threshold. A 3-D V S model is then computed by the inversion of the composite phase-velocity maps with an optimal resolution at every point. The estimated optimal resolution shows smooth lateral variations, confirming the robustness of the procedure. Importantly, the optimal resolving length does not scale with the density of the data coverage: some of the best-sampled locations display relatively low lateral resolution, probably due to systematic errors in the data. We apply the method to image the lithosphere and underlying mantle beneath Ireland and Britain. Our very large data set was created using new data from Ireland Array, the Irish National Seismic Network, the UK Seismograph Network and other deployments. A total of 11 238 inter-station dispersion curves, spanning a very broad total period range (4–500 s), yield unprecedented data coverage of the area and provide fine regional resolution from the crust to the deep asthenosphere. The lateral resolution of the 3-D model is computed explicitly and varies from 39 km in central Ireland to over 800 km at the edges of the area, where the data coverage declines. Our tomography reveals pronounced, previously unknown variations in the lithospheric thickness beneath Ireland and Britain, with implications for their Caledonian assembly and for the mechanisms of the British Tertiary Igneous Province magmatism. [ABSTRACT FROM AUTHOR]

The northeastern Indian region is characterized by complex lithospheric structure that developed due to collision between the Indian and Eurasian tectonic plates, in the north, and to subduction beneath the Burmese arc, in the east. We report results from joint modelling of Ps and Sp receiver functions and Rayleigh wave group velocity dispersion curves in which a broad search for acceptable models is performed via simulated annealing. We identify three tectonic domains, the Shillong plateau, Brahmaputra valley and Indo-Burma convergence zone (IBCZ), sampled by teleseismic earthquake data recorded by nine broad-band seismic stations. Our results reveal that the region's thinnest crust lies beneath the Shillong plateau, where it increases slightly from the plateau's eastern edge to its centre and reaches a maximum at the western edge of the plateau. Crustal Vp / Vs ratios range between 1.69 and 1.75 for the Shillong plateau, which is consistent with a felsic composition. Deeper Moho depths beneath the Brahmaputra valley, adjacent to the northern front of the Shillong plateau, may be due to the flexure of Indian lithosphere subducting beneath Asia. Low velocity zones are indicated at ∼5–10 km depth beneath the Brahmaputra valley, which may have been developed by NE–SW trending compressional stresses from the collision at the Himalayan arc and subduction at the Burmese arc. The crust is thickest in Kohima, beneath the Naga thrust in the IBCZ, where a high velocity zone is observed for both Vp and Vs at a depth of 25–40 km. This anomaly may be associated with a high velocity slab, trending N–NE to S–SW, that comprises the subducting Indian lithosphere in the IBCZ. [ABSTRACT FROM AUTHOR]

The ongoing InSight mission has recently deployed very broad band seismometers to record the Martian seismic activity. These recordings constitute the first seismic data set collected at the surface of Mars. This unique but sparse record compels for the development of new techniques tailored to make the best use of the specific context of single station-multiple events with several possible ranges of uncertainties on the event location. To this end, we conducted sets of Markov chain Monte Carlo inversions for the 1-D seismic structure of Mars. We compared two inversion techniques that differ from the nature of the parametrization on which they rely. A first classical approach based on a parametrization of the 1-D seismic profile using Bézier curves. A second, less conventional approach that relies on a parametrization in terms of quantities that influence the thermochemical evolution of the planet (mantle rheology, initial thermal state and composition), which accounts for 4.5 Gyr of planetary evolution. We considered several combinations of true model parameters to retrieve, and explored the influence of the type of seismic data (body waves with or without surface waves), the number of events and their associated epicentral distances and uncertainties, and the presence of potential constraints on Moho depth inferred from independent measurements/considerations (receiver functions and gravity data). We show that due to its inherent tighter constraints the coupled approach allows a considerably better retrieval of Moho depth and the seismic structure underneath it than the classical inversion, under the condition that the physical assumptions made in the coupled approach are valid for Mars. In addition, our tests indicate that in order to constrain the seismic structure of Mars with InSight data, the following independent conditions must be met: (1) The presence of surface waves triggered by an internal source to constrain the epicentral distance. (2) The presence of just a few well-localized impact sources, with at least one located at close epicentral distance (<5°) to illuminate independently the crust and the mantle. In addition to providing tighter constraints of Mars seismic structure, geodynamically constrained inversions allow one to reconstruct the thermochemical and rheological history of Mars until present. Therefore, even with a relatively small amount of large events and in absence of surface waves, constraining the present-day structure and long-term evolution of the red planet remains possible through the use of tailored hybrid inversion schemes. [ABSTRACT FROM AUTHOR]

Several seismic techniques, both passive and active, exist for estimating the shear‐wave velocity VS structure of shallow sedimentary structures. In particular, passive compliance signals recorded by broadband ocean‐bottom seismometers (OBSs) can be used to invert for VS structure. While compliance‐based imaging studies have been carried out at several locations across the Cascadia Subduction Zone, such an approach has not been extensively applied to OBSs deployed on the continental shelf and slope. In this study, we measure compliance and coherence signals at 13 broadband OBSs deployed along Cascadia's continental shelf and upper slope. We then use a recently developed technique to probabilistically invert compliance signals for shallow VS structure that makes use of mixture density neural networks. Finally, we compare and contrast our inverted VS profiles and derived properties obtained using this method with previous studies focused on the properties of basin sediments. Plain Language Summary: Long‐period water waves on the open ocean are capable of deforming the seafloor above which they propagate. The physical phenomenon, whereby the seafloor deforms in response to the loading caused by these waves, is known as compliance. The characteristics of compliance depend on the elastic properties beneath the seafloor. Consequently, material properties can be inferred from compliance measurements. In this study, we measure compliance signals recorded by 13 broadband ocean‐bottom seismometers deployed along the continental shelf of the Cascadia Subduction Zone. We then use a technique from the field of machine learning, known as a mixture density network, to determine the most probable range of structures that gave rise to the compliance signals observed by each station. Finally, we compare and contrast our results with other studies on the properties of Cascadia basin sediments. Key Points: We measure compliance signals at 13 broadband ocean‐bottom seismometers deployed along Cascadia's continental marginWe train neural networks to invert compliance data for shear‐wave velocity structure at each stationWe compare and contrast our findings to similar results obtained from Cascadia basin sediments [ABSTRACT FROM AUTHOR]

A strategy is presented to incorporate prior information from conceptual geological models in probabilistic inversion of geophysical data. The conceptual geological models are represented by multiple-point statistics training images (TIs) featuring the expected lithological units and structural patterns. Information from an ensemble of TI realizations is used in two different ways. First, dominant modes are identified by analysis of the frequency content in the realizations, which drastically reduces the model parameter space in the frequency-amplitude domain. Second, the distributions of global, summary metrics (e.g. model roughness) are used to formulate a prior probability density function. The inverse problem is formulated in a Bayesian framework and the posterior pdf is sampled using Markov chain Monte Carlo simulation. The usefulness and applicability of this method is demonstrated on two case studies in which synthetic crosshole ground-penetrating radar traveltime data are inverted to recover 2-D porosity fields. The use of prior information from TIs significantly enhances the reliability of the posterior models by removing inversion artefacts and improving individual parameter estimates. The proposed methodology reduces the ambiguity inherent in the inversion of high-dimensional parameter spaces, accommodates a wide range of summary statistics and geophysical forward problems.

Abstract Several seismic techniques, both passive and active, exist for estimating the shear‐wave velocity VS structure of shallow sedimentary structures. In particular, passive compliance signals recorded by broadband ocean‐bottom seismometers (OBSs) can be used to invert for VS structure. While compliance‐based imaging studies have been carried out at several locations across the Cascadia Subduction Zone, such an approach has not been extensively applied to OBSs deployed on the continental shelf and slope. In this study, we measure compliance and coherence signals at 13 broadband OBSs deployed along Cascadia's continental shelf and upper slope. We then use a recently developed technique to probabilistically invert compliance signals for shallow VS structure that makes use of mixture density neural networks. Finally, we compare and contrast our inverted VS profiles and derived properties obtained using this method with previous studies focused on the properties of basin sediments.

The current work makes use of the geometrical configuration of the two lower-altitude Swarm satellites (Swarm A and C), moving side by side with a longitudinal distance of 1.4°, to estimate a two-dimensional (2D) model of the lithospheric magnetic anomaly field over Egypt using gradient data. The gradient in both the north–south and the east–west directions have been inverted using the weighted damping least-squares fit technique to estimate the best model coefficients of the 2D model. The best model coefficients have been obtained under the expansion of the Legendre polynomial from degree n = 7 to n = 56. Results showed that the gradient of the field in the north–south direction is always much smoother than that in the east–west direction. The noise in the east–west direction is attributed to the different environmental conditions surrounding both satellites. The modeled field always showed smoother variations than the observed data, even for the horizontal components (Bx and By).

Kinematic finite‐fault source inversions aim at resolving the spatio‐temporal evolution of slip on a fault given ground motion recorded on the Earth's surface. This type of inverse problem is inherently ill posed due to two main factors. First, the number of model parameters is typically greater than the number of independent observed data. Second, small singular values are generated by the discretization of the physical rupture process and amplify the effect of noise in the inversion. As a result, one can find different slip distributions that fit the data equally well. This ill posedness can be mitigated by decreasing the number of model parameters, hence improving their relationship to the observed data. In this study, we propose a fuzzy function approximation approach to describe the spatial slip function. In particular, we use an Adaptive Network‐based Fuzzy Inference System (ANFIS) to find the most adequate discretization for the spatial variation of slip on the fault. The fuzzy basis functions and their respective amplitudes are optimized through hybrid learning. We solve this earthquake source problem in the frequency domain, searching for optimal spatial slip distribution independently for each frequency. The approximated frequency‐dependent spatial slip functions are then used to compute the forward relationship between slip on the fault and ground motion. The method is constrained through Tikhonov regularization, requiring a smooth spatial slip variation. We discuss how the number of model parameters can be decreased, while keeping the inversion stable and achieving an adequate resolution. The proposed inversion method is tested using the SIV1‐benchmark exercise. Plain Language Summary: Earthquake kinematic source inversions help seismologists infer key features of fault ruptures from the available recorded data. The technique faces inherent ill posedness from the viewpoint of its mathematical formulation. Furthermore, the limited available datasets render the problem even more challenging. In this study, we use an adaptive function approximation methodology that describes slip on the fault using a reduced number of model parameters. This innovative formulation helps us to achieve a good balance between available data (information) and model parameters (unknowns). The proposed technique decreases the degree of ill posedness of the inverse problem by adaptively improving the slip discretization and the slip amplitude using neural network learning. Key Points: We present a new method to kinematically image finite‐fault rupture which reduces the number of basis to spatially discretize the slipThe inversion employs a neural‐network based evolutionary method that improves model estimationWe discretize the fault using fuzzy basis functions that stabilizes the inversion and reduces the number of small singular values [ABSTRACT FROM AUTHOR]

In this article, we validate the neuro‐fuzzy kinematic finite‐fault inversion method by studying the rupture process of the Mw6.2, Aug/24/2016, Amatrice, central Italy, earthquake. We jointly invert three different datasets to infer the spatio‐temporal slip distribution, namely static and high‐rate GNSS data (<=0.06 Hz) and strong‐motion data (0.06−0.5 Hz). Each data set is used to constrain a different frequency range of the source model, depending on the sensitivity of the data set. The inferred slip shows a slow nucleation phase at shallow depths of 3–4 km, followed by a bilateral rupture that forms two asperities, one to the NW (Norcia) and another to the SE (Amatrice) of the hypocenter. Our inferred slip is compared with those previously obtained using well‐established methods. In order to select an adequate number of fuzzy basis functions, we propose two alternative procedures, which yield the same general slip features. The first approach consists of ensuring that the inverse problem is formally over‐determined and uses the same number of basis functions at all frequencies. The second approach is based on a maximum‐likelihood analysis of the model misfit and selects a different number of basis functions for each frequency. The maximum‐likelihood approach allows for more basis functions at high frequencies, where more detail in the spatial slip distribution is needed. The solution obtained with the maximum‐likelihood approach provides a more physically plausible source time function, which shows less back slip artifacts. The accurate prediction of high‐rate GNSS traces not used in the inversion attests the robustness of the inferred slip model. Plain Language Summary: The accuracy of the earthquake's slip imaging method proposed in the companion article by Kheirdast et al. (2021), is tested using data recorded during the 2016 Mw6.2, Amatrice, earthquake. Many previously well‐understood features of the rupture process of this earthquake are well retrieved by the proposed method, including a slow nucleation phase, a bilateral rupture and a high‐amplitude slip patch to the NW of the hypocenter. We present a new strategy to spatially discretize the fault plane, which maximizes the inversion power by taking into account the uncertainty at different frequencies. Key Points: The neuro‐fuzzy kinematic finite‐fault inversion is used to study the Amatrice earthquake and the inferred slip model is compared with previous studiesWe present a new maximum‐likelihood strategy to select an adequate, problem‐specific number of fuzzy basis functionsThe inferred source model is able to correctly predict high‐rate GNSS waveforms not used in the inversion [ABSTRACT FROM AUTHOR]

In the context of seismic imaging, full waveform inversion (FWI) is increasingly popular. Because of its lower numerical cost, the acoustic approximation is often used, especially at the exploration geophysics scale, both for tests and for real data. Moreover, some research domains such as helioseismology face true acoustic media for which FWI can be useful. In this work, an argument that combines particle relabelling and homogenization is used to show that the general acoustic inverse problem based on band-limited data is intrinsically non-unique. It follows that the results of such inversions should be interpreted with caution. To illustrate these ideas, we consider 2-D numerical FWI examples based on a Gauss–Newton iterative inversion scheme and demonstrate effects of this non-uniqueness in the local optimization context. [ABSTRACT FROM AUTHOR]

Magnetic surveys conducted in complex conditions, such as low magnetic latitudes, uneven observation surfaces, or above high-susceptibility sources, pose significant challenges for obtaining stable solutions for reduction-to-the-pole (RTP) and upward-continuation processing on arbitrary surfaces. To tackle these challenges, in this study, we propose constructing an equivalent-susceptibility model based on the partial differential equation (PDE) framework in the space domain. A multilayer equivalent-susceptibility method was used for RTP and upward-continuation operations, thus allowing for application on undulating observation surfaces and strong self-demagnetization effect in a non-uniform mesh. A novel positivity constraint is introduced to improve the accuracy and efficiency of the inversion. We analysed the effect of the depth-weighting function in the inversion of equivalent susceptibility for RTP and upward-continuation reproduction. Iterative and direct solvers were utilized and compared in solving the large, sparse, non-symmetric and ill-conditioned system of linear equations produced by PDE-based equivalent-source construction. Two synthetic models were used to illustrate the efficiency and accuracy of the proposed method in processing both ground and airborne magnetic data. Aeromagnetic and ground data collected in Brazil at a low magnetic latitude region were used to validate the proposed method for processing RTP and upward-continuation operations on magnetic data sets with strong self-demagnetization. [ABSTRACT FROM AUTHOR]

To understand earth processes, geoscientists infer subsurface earth properties such as electromagnetic resistivity or seismic velocity from surface observations of electromagnetic or seismic data. These properties are used to populate an earth model vector, and the spatial variation of properties across this vector sheds light on the underlying earth structure or physical phenomenon of interest, from groundwater aquifers to plate tectonics. However, to infer these properties the spatial characteristics of these properties need to be known in advance. Typically, assumptions are made about the length scales of earth properties, which are encoded a priori in a Bayesian probabilistic setting. In an optimization setting, appeals are made to promote model simplicity together with constraints which keep models close to a preferred model. All of these approaches are valid, though they can lead to unintended features in the resulting inferred geophysical models owing to inappropriate prior assumptions, constraints or even the nature of the solution basis functions. In this work it will be shown that in order to make accurate inferences about earth properties, inferences can first be made about the underlying length scales of these properties in a very general solution basis. From a mathematical point of view, these spatial characteristics of earth properties can be conveniently thought of as 'properties' of the earth properties. Thus, the same machinery used to infer earth properties can be used to infer their length scales. This can be thought of as an 'infer to infer' paradigm analogous to the 'learning to learn' paradigm which is now commonplace in the machine learning literature. However, it must be noted that (geophysical) inference is not the same as (machine) learning, though there are many common elements which allow for cross-pollination of useful ideas from one field to the other, as is shown here. A non-stationary trans-dimensional Gaussian Process (TDGP) is used to parametrize earth properties, and a multichannel stationary TDGP is used to parametrize the length scales associated with the earth property in question. Using non-stationary kernels, that is kernels with spatially variable length scales, models with sharp discontinuities can be represented within this framework. As GPs are multidimensional interpolators, the same theory and computer code can be used to solve geophysical problems in 1-D, 2-D and 3-D. This is demonstrated through a combination of 1-D and 2-D non-linear regression examples and a controlled source electromagnetic field example. The key difference between this and previous work using TDGP is generalized nested inference and the marginalization of prior length scales for better posterior subsurface property characterization. [ABSTRACT FROM AUTHOR]

An underground nuclear explosion (UNE) couples mechanical energy into crustal rock, which propagates as seismic and acoustic waves. These different physical phenomena transport, by different pathways, to standoff detectors at varying distances. The transport pathways attenuate the original signal but in different ways. Enabled by correct statistical weighting, signal attenuation models can be used to combine these disparate sensor data to estimate the yield of an UNE. Contemporaneous statistical models, used in yield estimation, can be improved with an advanced partition of error for these physical signal propagation models. We present an advanced multivariate approach to error modelling of multiphenomenology physical signatures. In addition to measurement error, our error model represents physical model biases as random with a physics-based covariance structure. To illustrate this proposed framework, we demonstrate the estimation of explosion yield using openly available seismic and acoustic data from chemical single-point explosions. [ABSTRACT FROM AUTHOR]

Interfaces are important part of Earth's layering structure. Here, we developed a new model parametrization and iterative linearized inversion method that determines 1-D crustal velocity structure using surface wave dispersion, teleseismic P -wave receiver functions and Ps and PmP traveltimes. Unlike previous joint inversion methods, the new model parametrization includes interface depths and layer Vp / Vs ratios so that smoothness constraint can be conveniently applied to velocities of individual layers without affecting the velocity discontinuity across the interfaces. It also allows adding interface-related observation such as traveltimes of Ps and PmP in the joint inversion to eliminate the trade-off between interface depth and Vp / Vs ratio and therefore to reduce the uncertainties of results. Numerical tests show that the method is computationally efficient and the inversion results are robust and independent of the initial model. Application of the method to a dense linear array across the Wabash Valley Seismic Zone (WVSZ) produced a high-resolution crustal image in this seismically active region. The results show a 51–55-km-thick crust with a mid-crustal interface at 14–17 km. The crustal Vp / Vs ratio varies from 1.69 to 1.90. There are three pillow-like, ∼100 km apart high-velocity bodies sitting at the base of the crust and directly above each of them are a low-velocity anomaly in the middle crust and a high-velocity anomaly in the upper crust. They are interpreted to be produced by mantle magmatic intrusions and remelting during rifting events in the end of the Precambrian. The current diffuse seismicity in the WVSZ might be rooted in this ancient distributed rifting structure. [ABSTRACT FROM AUTHOR]

The Mexican subduction zone is a complex convergent margin characterized by a slab with an unusual morphology, an abnormal location of the volcanic arc, and the existence of slow earthquakes (slow slip events and tectonic tremors). The number of seismic imaging studies of the Mexican subduction zone has increased over the past decade. These studies have revealed the seismic wave velocity structure beneath Central and Southern Mexico. However, the existing tomographic models are either confined to specific areas or have coarse resolution. As a consequence, they do not capture the lateral and finer‐scale variations in the mantle and the crust structure. Here, we fit frequency‐dependent traveltime differences between observed and synthetic seismograms in a three‐dimensional model of Central and Southern Mexico to constrain crustal and upper mantle seismic velocity structures jointly. We use ∼3,300 seismic records, filtered between 5 and 50 s, from 74 regional earthquakes. We perform point spread function tests to assess the resolution and trade‐offs between model parameters. Our tomographic model reveals several seismic wave velocity features. These features include the geometry of the Cocos slab, the partial melting zone beneath the Trans‐Mexican Volcanic Belt, and the Yucatan slab diving below Los Tuxtlas Volcanic Field that are consistent with previous studies. We also identify horizontal structures in the lower crust and the shallow upper mantle that were not previously identified. These structures include slow seismic wave velocity anomalies that may be correlated with ultraslow seismic velocity zones and high conductivity regions, where slow earthquakes have been identified. Plain Language Summary: The Trans‐Mexican Volcanic Belt is one of the most enigmatic geological regions in Mexican territory because it is the superficial expression of volcanism associated with the subduction system in Mexico. The Mexican subduction has received significant attention from the scientific community due to the diversity of earthquakes produced in the region (large earthquakes, tectonic tremors, and silent earthquakes). Previous studies have investigated the velocity structure of the Mexican subduction zone. However, the existing velocity models are confined to specific areas or have a low resolution. In this work, we present a new model of the velocity structure of the crust and shallow upper mantle of central and southern Mexico. Our velocity model reveals several seismic wave velocity features consistent with previous studies and new low‐velocity anomalies correlated with tectonic tremors and silent earthquake regions, which increase the understanding of the Mexican subduction zone's complexity. Key Points: A three‐dimensional full seismic waveform model of Central and Southern Mexico for 5–50 s periods was constructed via adjoint methodsThe shear wave velocity model indicated two continuous anomalies in the shallow upper mantle and the lower crustThese anomalies were associated with the ultraslow seismic velocity zones and the high conductivity regions where slow earthquakes have been identified [ABSTRACT FROM AUTHOR]

The analysis of surface wave dispersion curves is a way to infer the vertical distribution of shear wave velocity. The range of applicability is extremely wide: going, for example, from seismological studies to geotechnical characterizations and exploration geophysics. However, the inversion of the dispersion curves is severely ill-posed and only limited efforts have been put in the development of effective regularization strategies. In particular, relatively simple smoothing regularization terms are commonly used, even when this is in contrast with the expected features of the investigated targets. To tackle this problem, stochastic approaches can be utilized, but they are too computationally expensive to be practical, at least, in case of large surveys. Instead, within a deterministic framework, we evaluate the applicability of a regularizer capable of providing reconstructions characterized by tunable levels of sparsity. This adjustable stabilizer is based on the minimum support regularization, applied before on other kinds of geophysical measurements, but never on surface wave data. We demonstrate the effectiveness of this stabilizer on (i) two benchmark—publicly available—data sets at crustal and near-surface scales and (ii) an experimental data set collected on a well-characterized site. In addition, we discuss a possible strategy for the estimation of the depth of investigation. This strategy relies on the integrated sensitivity kernel used for the inversion and calculated for each individual propagation mode. Moreover, we discuss the reliability, and possible caveats, of the direct interpretation of this particular estimation of the depth of investigation, especially in the presence of sharp boundary reconstructions. [ABSTRACT FROM AUTHOR]

Seismic inversion is one of the most commonly used methods in the oil and gas industry for reservoir characterization from observed seismic data. Deep learning (DL) is emerging as a data-driven approach that can effectively solve the inverse problem. However, existing DL-based methods for seismic inversion utilize only seismic data as input, which often leads to poor stability of the inversion results. Besides, it has always been challenging to train a robust network since the real survey has limited labelled data pairs. To partially overcome these issues, we develop a neural network framework with a priori initial model constraint to perform seismic inversion. Our network uses two parts as one input for training. One is the seismic data, and the other is the subsurface background model. The labels for each input are the actual model. The proposed method is performed by log-to-log strategy. The training data set is first generated based on forward modelling. The network is then pre-trained using the synthetic training data set, which is further validated using synthetic data that have not been used in the training step. After obtaining the pre-trained network, we introduce the transfer learning strategy to fine-tune the pre-trained network using labelled data pairs from a real survey to acquire better inversion results in the real survey. The validity of the proposed framework is demonstrated using synthetic 2-D data including both post-stack and pre-stack examples, as well as a real 3-D post-stack seismic data set from the western Canadian sedimentary basin. [ABSTRACT FROM AUTHOR]

We develop and apply a method to constrain the space- and frequency-dependent location of ambient noise sources. This is based on ambient noise cross-correlation inversion using numerical wavefield simulations, which honour 3-D crustal and mantle structure, ocean loading and finite-frequency effects. In the frequency range from 3 to 20 mHz, our results constrain the global source distribution of the Earth's hum, averaged over the Southern Hemisphere winter season of 9 yr. During Southern Hemisphere winter, the dominant sources are largely confined to the Southern Hemisphere, the most prominent exception being the Izu-Bonin-Mariana arc, which is the most active source region between 12 and 20 mHz. Generally, strong hum sources seem to be associated with either coastlines or bathymetric highs. In contrast, deep ocean basins are devoid of hum sources. While being based on the relatively small number of STS-1 broad-band stations that have been recording continuously from 2004 to 2013, our results demonstrate the practical feasibility of a frequency-dependent noise source inversion that accounts for the complexities of 3-D wave propagation. It may thereby improve full-waveform ambient noise inversions and our understanding of the physics of noise generation. [ABSTRACT FROM AUTHOR]

Scattered seismic coda waves are frequently used to characterize small scale medium heterogeneities, intrinsic attenuation or temporal changes of wave velocity. Spatial variability of these properties raises questions about the spatial sensitivity of seismic coda waves. Especially the continuous monitoring of medium perturbations using ambient seismic noise led to a demand for approaches to image perturbations observed with coda waves. An efficient approach to localize spatial and temporal variations of medium properties is to invert the observations from different source–receiver combinations and different lapse times in the coda for the location of the perturbations. For such an inversion, it is key to calculate the coda-wave sensitivity kernels which describe the connection between observations and the perturbation. Most discussions of sensitivity kernels use the acoustic approximation in a spatially uniform medium and often assume wave propagation in the diffusion regime. We model 2-D multiple non-isotropic scattering in a random elastic medium with spatially variable heterogeneity and attenuation using the radiative transfer equations which we solve with the Monte Carlo method. Recording of the specific energy density of the wavefield that contains the complete information about the energy density at a given position, time and propagation direction allows us to calculate sensitivity kernels according to rigorous theoretical derivations. The practical calculation of the kernels involves the solution of the adjoint radiative transport equations. We investigate sensitivity kernels that describe the relationships between changes of the model in P - and S -wave velocity, P - and S -wave attenuation and the strength of fluctuation on the one hand and seismogram envelope, traveltime changes and waveform decorrelation as observables on the other hand. These sensitivity kernels reflect the effect of the spatial variations of medium properties on the wavefield and constitute the first step in the development of a tomographic inversion approach for the distribution of small-scale heterogeneity based on scattered waves. [ABSTRACT FROM AUTHOR]

Time-lapse monitoring is useful for imaging changes in geophysical attributes due to fluid flow. In trying to use time-lapse data for reservoir characterization, difficulties often arise when relating changes in geophysical observations to changes in fluid saturation and pressure. As an alternative approach for reservoir monitoring and characterization, we introduce the idea of an onset time, the time at which a measured quantity, such as a seismic traveltime or a reflection amplitude, begins to deviate from its background value. We illustrate the idea and demonstrate its utility through the consideration of traveltimes recorded by the continuous active source seismic monitoring system at the Frio pilot site near Houston, Texas. The system, which transmits an elastic wave every 15 min, is used to monitor the movement of carbon dioxide injected into a permeable sand formation. From these data we can estimate the onset of changes in seismic traveltimes to six receivers in an adjacent borehole. Numerical simulation and synthetic tests indicate that the onset times are not very sensitive to the method used to compute the effective fluid bulk modulus and, correspondingly, the seismic compressional velocity. Rather, the onset times are strongly influenced by saturation changes within the formation, specifically by the break-through time of the injected fluid phase. By means of an iterative inversion algorithm we use the onset times to estimate permeability variations between the boreholes at the Frio pilot site. © The Authors 2014. Published by Oxford University Press on behalf of The Royal Astronomical Society.

Geodetic imaging data and seismicwaveformdata have complementary strengthswhen considering the modelling of earthquakes. The former, particularly modern space geodetic techniques such as Interferometric Synthetic Aperture Radar (InSAR), permit high spatial density of observation and thus fine resolution of the spatial pattern of fault slip; the latter provide precise and accurate timing information, and thus the ability to resolve how that fault slip varies over time. In order to harness these complementary strengths, we propose a method through which the two data types can be combined in a joint inverse model for the evolution of slip on a specified fault geometry. We present here a derivation of Akaike's Bayesian Information Criterion (ABIC) for the joint inversion of multiple data sets that explicitly deals with the problem of objectively estimating the relative weighting between data sets, as well as the optimal influence of model smoothness constraints in space and time. We demonstrate our ABIC inversion scheme by inverting InSAR displacements and teleseismic waveform data for the 1997 Manyi, Tibet, earthquake.We test, using a simplified fault geometry, three cases-InSAR data inverted alone, vertical component teleseismic broad-band waveform data inverted alone and a joint inversion of both data sets. The InSAR-only model and seismic-only model differ significantly in the distribution of slip on the fault plane that they predict. The joint-inversion model, however, has not only a similar distribution of slip and fit to the InSAR data in the InSAR-only model, suggesting that those data provide the stronger control on the pattern of slip, but is also able to fit the seismic data at a minimal degradation of fit when compared with the seismic-only model. The rupture history of the preferred, joint-inversion model, indicates bilateral rupture for the first 20 s of the earthquake, followed by a further 25 s of westward unilateral rupture afterwards, with slip peaking at 7m in the upper 6 km of the fault. This joint-inversion approach is thus shown to be a viable method for the study of large shallow continental earthquakes, and may be of particular benefit in cases where near-field seismic observations are not available. © The Authors 2014. Published by Oxford University Press on behalf of The Royal Astronomical Society.

Probabilistic inversion methods based on Markov chain Monte Carlo (MCMC) simulation are well suited to quantify parameter and model uncertainty of nonlinear inverse problems. Yet, application of such methods to CPU-intensive forward models can be a daunting task, particularly if the parameter space is high dimensional. Here, we present a 2-D pixel-based MCMC inversion of plane-wave electromagnetic (EM) data. Using synthetic data, we investigate how model parameter uncertainty depends on model structure constraints using different norms of the likelihood function and the model constraints, and study the added benefits of joint inversion of EM and electrical resistivity tomography (ERT) data. Our results demonstrate that model structure constraints are necessary to stabilize the MCMC inversion results of a highly discretized model. These constraints decrease model parameter uncertainty and facilitate model interpretation. A drawback is that these constraints may lead to posterior distributions that do not fully include the true underlying model, because some of its features exhibit a low sensitivity to the EM data, and hence are difficult to resolve. This problem can be partly mitigated if the plane-wave EM data is augmented with ERT observations. The hierarchical Bayesian inverse formulation introduced and used herein is able to successfully recover the probabilistic properties of the measurement data errors and a model regularization weight. Application of the proposed inversion methodology to field data from an aquifer demonstrates that the posterior mean model realization is very similar to that derived from a deterministic inversion with similar model constraints. © The Authors 2013.

We review Gaussian process regression (GPR) and analyze it in the context of Inverse Theory—the collection of techniques used in geophysics (among other fields) to understand the structure of data analysis problems and the quality of their solutions. By viewing GPR as a special case of generalized least squares (least squares with prior information), we derive expressions for a variety of standard Inverse Theory quantities, including the data and model resolution matrices, the importance (influence) vector, and the gradient of the solution with respect to a parameter. We study the impulse response in the one-dimensional continuum limit and provide formulas for its area and width. Finally, we demonstrate how the importance vector can be used to design an optimum GPR experiment, through a process we call importance winnowing. [ABSTRACT FROM AUTHOR]

The model prediction errors that originate from the uncertainty of underground structure are often a major contributor of the errors between the data and the model predictions in fault slip estimation using geodetic or seismic waveform data. However, most studies on slip inversions either neglect the model prediction errors or do not distinguish them from observation errors. Several methods that explicitly incorporated the model prediction errors in slip estimation, which has been proposed in the past decade, commonly assumed a Gaussian distribution for the stochastic property of the model prediction errors to simplify the formulation. Moreover, the information on both the slip distribution and the underground structure is expected to be successfully extracted from the data by incorporating the stochastic property of the model prediction errors. In this study, we propose a novel flexible Bayesian inference framework for estimating fault slips that can accurately incorporate non-Gaussian model prediction errors. This method considers the uncertainty of the underground structure, including fault geometry, based on the ensemble modelling of the uncertainty of Green's functions. Furthermore, the framework allows the estimation of the posterior probability density function (PDF) of the parameters of the underground structure by calculating the likelihood of each sample in the ensemble. We performed numerical experiments for estimating the slip deficit rate (SDR) distribution on a 2-D thrust fault using synthetic data of surface displacement rates, which is the simplest problem setting that can essentially demonstrate the fundamental idea and validate the advantage of the proposed method. In the experiments, the dip angle of the fault plane was the parameter used to characterize the underground structure. The proposed method succeeded in estimating a posterior PDF of SDR that is consistent with the true one, despite the uncertain and inaccurate information of the dip angle. In addition, the method could estimate a posterior PDF of the dip angle that has a strong peak near the true angle. In contrast, the estimation results obtained using a conventional approach, which introduces regularization based on smoothing constraints and does not explicitly distinguish the prediction and observation errors, included a significant amount of bias, which was not noted in the results obtained using the proposed method. The estimation results obtained using different settings of the parameters suggested that inaccurate prior information of the underground structure with a small variance possibly results in significant bias in the estimated PDFs, particularly the posterior PDFs for SDR, those for the underground structure, and the posterior predicted PDF of the displacement rates. The distribution shapes of the model prediction errors for the representative model parameters in certain observation points are significantly asymmetric with large absolute values of the sample skewness, suggesting that they would not be well-modelled by Gaussian approximations. [ABSTRACT FROM AUTHOR]

Centroid moment tensor (CMT) parameters can be estimated from seismic waveforms. Since these data indirectly observe the deformation process, CMTs are inferred as solutions to inverse problems which are generally underdetermined and require significant assumptions, including assumptions about data noise. Broadly speaking, we consider noise to include both theory and measurement errors, where theory errors are due to assumptions in the inverse problem and measurement errors are caused by the measurement process. While data errors are routinely included in parameter estimation for full CMTs, less attention has been paid to theory errors related to velocity-model uncertainties and how these affect the resulting moment-tensor (MT) uncertainties. Therefore, rigorous uncertainty quantification for CMTs may require theory-error estimation which becomes a problem of specifying noise models. Various noise models have been proposed, and these rely on several assumptions. All approaches quantify theory errors by estimating the covariance matrix of data residuals. However, this estimation can be based on explicit modelling, empirical estimation and/or ignore or include covariances. We quantitatively compare several approaches by presenting parameter and uncertainty estimates in nonlinear full CMT estimation for several simulated data sets and regional field data of the M l 4.4, 2015 June 13 Fox Creek, Canada, event. While our main focus is at regional distances, the tested approaches are general and implemented for arbitrary source model choice. These include known or unknown centroid locations, full MTs, deviatoric MTs and double-couple MTs. We demonstrate that velocity-model uncertainties can profoundly affect parameter estimation and that their inclusion leads to more realistic parameter uncertainty quantification. However, not all approaches perform equally well. Including theory errors by estimating non-stationary (non-Toeplitz) error covariance matrices via iterative schemes during Monte Carlo sampling performs best and is computationally most efficient. In general, including velocity-model uncertainties is most important in cases where velocity structure is poorly known. [ABSTRACT FROM AUTHOR]

A non-iterative first-arrival traveltime inversion method (NFTI) is proposed for building smooth velocity models using seismic diving waves observed on irregular surface. The new ray and traveltime equations of diving waves propagating in smooth media with undulant observation surface are deduced. According to the proposed ray and traveltime equations, an analytical formula for determining the location of the diving-wave turning points is then derived. Taking the influence of rough topography on first-arrival traveltimes into account, the new equations for calculating the velocities at turning points are established. Based on these equations, a method is proposed to construct subsurface velocity models from the observation surface downward to the bottom using the first-arrival traveltimes in common offset gathers. Tests on smooth velocity models with rugged topography verify the validity of the established equations, and the superiority of the proposed NFTI. The limitation of the proposed method is shown by an abruptly-varying velocity model example. Finally, the NFTI is applied to solve the static correction problem of the field seismic data acquired in a mountain area in the western China. The results confirm the effectivity of the proposed NFTI. [ABSTRACT FROM AUTHOR]

In general, the inverse problem of electrical resistivity tomography (ERT) is treated using a deterministic algorithm to find a model of subsurface resistivity that can numerically match the apparent resistivity data acquired at the ground surface and has a smooth distribution that has been introduced as prior information. In this paper, we propose a new deep learning algorithm for processing the 3-D reconstruction of ERT. This approach relies on the approximation of the inverse operator considered as a nonlinear function linking the section of apparent resistivity as input and the underground distribution of electrical resistivity as output. This approximation is performed with a large amount of known data to obtain an accurate generalization of the inverse operator by identifying during the learning process a set of parameters assigned to the neural networks. To train the network, the subsurface resistivity models are theoretically generated by a geostatistical anisotropic Gaussian generator, and their corresponding apparent resistivity by solving numerically 3-D Poisson's equation. These data are formed in a way to have the same size and trained on the convolutional neural networks with SegNet architecture containing a three-level encoder and decoder network ending with a regression layer. The encoders including the convolutional, max-pooling and nonlinear activation operations are sequentially performed to extract the main features of input data in lower resolution maps. On the other side, the decoders are dedicated to upsampling operations in concatenating with feature maps transferred from encoders to compensate the loss of resolution. The tool has been successfully validated on different synthetic cases and with particular attention to how data quality in terms of resolution and noise affects the effectiveness of the approach. [ABSTRACT FROM AUTHOR]

Electrical resistivity tomography (ERT) is widely used to image the Earth's subsurface and has proven to be an extremely useful tool in application to hydrological problems. Conventional smoothness-constrained inversion of ERT data is efficient and robust, and consequently very popular. However, it does not resolve well sharp interfaces of a resistivity field and tends to reduce and smooth resistivity variations. These issues can be problematic in a range of hydrological or near-surface studies, for example mapping regolith-bedrock interfaces. While fully Bayesian approaches, such as those using Markov chain Monte Carlo sampling, can address the above issues, their very high computation cost makes them impractical for many applications. Ensemble Kalman inversion (EKI) offers a computationally efficient alternative by approximating the Bayesian posterior distribution in a derivative-free manner, which means only a relatively small number of 'black-box' model runs are required. Although common limitations for ensemble Kalman filter-type methods apply to EKI, it is both efficient and generally captures uncertainty patterns correctly. We propose the use of a new EKI-based framework for ERT which estimates a resistivity model and its uncertainty at a modest computational cost. Our EKI framework uses a level-set parametrization of the unknown resistivity to allow efficient estimation of discontinuous resistivity fields. Instead of estimating level-set parameters directly, we introduce a second step to characterize the spatial variability of the resistivity field and infer length scale hyperparameters directly. We demonstrate these features by applying the method to a series of synthetic and field examples. We also benchmark our results by comparing them to those obtained from standard smoothness-constrained inversion. Resultant resistivity images from EKI successfully capture arbitrarily shaped interfaces between resistivity zones and the inverted resistivities are close to the true values in synthetic cases. We highlight its readiness and applicability to similar problems in geophysics. [ABSTRACT FROM AUTHOR]

The largest earthquake recorded in South Korea occurred in Gyeongju on 2016 September 12. Since then, understanding the geological structures near the Gyeongju earthquake's epicentre has been demanded. As a preliminary step to understand the geological structures around the epicentre, a 3-D audio-magnetotelluric (AMT) survey was conducted. These 3-D AMT data were imaged through data processing and inversion. However, because the AMT data acquired in Gyeongju were very noisy, conventional imaging procedures did not yield reliable results. To obtain a reliable model inverted from such noisy data, we propose various imaging strategies: an additional data processing technique using the Nyquist diagram after conventional data processing and several inversion strategies related to the selection of data, the weighting of the data, the constraints on the model parameter vector and the Lagrange multiplier used for the regularization. By applying the additional data processing step and several inversion strategies, we were able to successfully invert the noisy field data. The inversion results verify that the data-screening procedure applying the Nyquist diagram remarkably improves the results compared with those obtained using only conventional data processing. The imaging strategies proposed in this case study can be used to image noisy MT/AMT field data for other regions. [ABSTRACT FROM AUTHOR]

Ambient noise tomography (ANT) has been considerably used in the last decade in both academic and industrial research. In this work, we propose an innovative technique for ANT based on nonlinear multiscale inversions. Our method relies on a progressive increase in the model parametrization to reduce the nonlinearity of the inverse problem. The developed method is compared with conventional inversion schemes (linear and nonlinear), using different regularization techniques and two different network configurations. The inversion is tested on 22 different synthetic models including classical checkerboard tests. Furthermore, we performed the inversion using real data from a campaign in 2018 at Cumbre Vieja volcano (Canary Islands). The results obtained on both network configurations show an improvement compared to conventional linear and nonlinear inversion schemes, especially when the ray path density is low. This technique does not require expensive computational resources, making it convenient for small-scale industrial applications, especially in the framework of geothermal exploration. [ABSTRACT FROM AUTHOR]

We explore here the benefits of using constraints from seismic tomography in gravity data inversion and how inverted density distributions can be improved by doing so. The methodology is applied to a real field case in which we reconstruct the density structure of the Pyrenees along a southwest–northeast transect going from the Ebro basin in Spain to the Arzacq basin in France. We recover the distribution of densities by inverting gravity anomalies under constraints coming from seismic tomography. We initiate the inversion from a prior density model obtained by scaling a pre-existing compressional seismic velocity Vp model using a Nafe–Drake relationship: the Vp model resulting from a full-waveform inversion of teleseismic data. Gravity data inversions enforce structural similarities between Vp and density by minimizing the norm of the cross-gradient between the density and Vp models. We also compare models obtained from 2.5-D and 3-D inversions. Our results demonstrate that structural constraints allow us to better recover the density contrasts close to the surface and at depth, without degrading the gravity data misfit. The final density model provides valuable information on the geological structures and on the thermal state and composition of the western region of the Pyrenean lithosphere. [ABSTRACT FROM AUTHOR]

Earthquake location is one of the oldest problems in seismology, yet remains an active research topic. With dense seismic monitoring networks, it is possible to obtain reliable locations for microearthquakes; however, in many cases dense networks are lacking, limiting the location accuracy, or preventing location when there are too few observations. For small events in all settings, recording may be sparse and location may be difficult due to low signal-to-noise ratio. In this work, we introduce a new, distance-geometry-based method to locate seismicity clusters using only one or two seismic stations. A distance geometry problem consists in determining the location of sets of points based only on the distances between member pairs. Applied to seismology, our approach allows earthquake location using the interevent distance between earthquake pairs, which can be estimated using only one or two seismic stations. We first validate the method with synthetic data that resemble common cluster shapes, and then test the method with two seismic sequences in California: the August 2014    M w 6.0 Napa earthquake and the July 2019  M w 6.4 Ridgecrest earthquake sequence. We demonstrate that our approach provides robust and reliable results even for a single station. When using two seismic stations, the results capture the same structures recovered with high-resolution double-difference locations based on multiple stations. The proposed method is particularly useful for poorly monitored areas, where only a limited number of stations are available. [ABSTRACT FROM AUTHOR]

Full-waveform inversion (FWI) is a procedure based on the minimization of a misfit (or cost) function applied to the difference between synthetic waveforms and real seismic traces that derives high-resolution velocity models. This is achieved through the iterative adjustment of the velocity model and/or some other physical parameters of the Earth's subsurface, which generally implies large computational effort. In order to minimize this cost function, we explore the use of adaptive gradient optimization (AGO), a variant of stochastic gradient descent (SGD) methods, combining them with a dynamic simultaneous sources strategy that allow us to reduce the computational cost involved in this process. AGO methods are computationally efficient, have little memory requirements and have the capability of adapting the step length according to the optimization process' evolution. Since a precise calibration of the step length is needed to ensure efficiency, the AGOs are well suited for this task because they are able to adapt the step length according to the optimization's development. In this work, we propose a simple nonlinear relationship that allows an adjustment of the step length with respect to the frequencies used in the multiscale FWI, avoiding the line-search strategy's high computational burden. Additionally, the application of this new step length rule into the AGO methods with a dynamic simultaneous sources strategy, allow us to concurrently accelerate and significantly improve the FWI's numerical performance and results. We compare the performance and final results of seven AGO methods, using two different FWI misfit functionals (based on L 1 and L 2 norms) applied to estimate the final velocity models of two benchmark acoustic models: the Marmousi and the Canadian overthrust BP velocity models. [ABSTRACT FROM AUTHOR]

Wave-equation migration velocity analysis (WEMVA) is an image-domain inversion method for velocity model building. Automatic plane-wave WEMVA (PWEMVA) calculates the moveouts of plane-wave common-image gathers (CIGs) by searching a best-fitting parabola with semblance analysis and backprojects residual CIG moveouts into wavefield wave paths with a reflection tomographic kernel. However, 3-D PWEMVA is very computationally expensive because 3-D reflection tomographic inversion requires at least five 3-D reverse-time migrations per iteration and stores two types of source wavefields at model boundaries. We develop a joint inline and crossline PWEMVA method for efficient 3-D velocity model building. We alternatively implement the inline and crossline PWEMVAs with a constraint for each other, in which we iteratively construct the 3-D velocity model update through 1-D spline interpolation of 2-D gradients. The inline and crossline joint inversion is practical since PWEMVA only inverts for low-wavenumber velocity perturbations along wave paths, and the method can take less than 1 per cent of the computational cost of full 3-D PWEMVA. To construct unaliased plane waves for our joint inline and crossline PWEMVA, we develop a 3-D data interpolation method in the frequency–wavenumber (FK) domain to recover regularly and randomly missing traces. The method minimizes the misfit on sufficiently localized data subsets with iterative optimal step lengths and a gradient preconditioner that iteratively selects dominant dips along different azimuths. In numerical experiments, we use a 3-D synthetic seismic data set and a land 3-D field seismic data set acquired at the Farnsworth CO2-EOR (enhanced oil recovery) field to demonstrate the efficacy of our velocity model building and data interpolation methods. [ABSTRACT FROM AUTHOR]

We propose a new procedure for obtaining thermal properties (thermal conductivity, diffusivity, and capacity) of marine sediments from the heat-pulse Lister-type probe method. Established methods suffered from ill-posed inversion when aiming for the determination of sediment thermal diffusivities. Our new approach is based on the first-order Taylor expansion of the temperature decay function as before, but including important modifications/extensions: (1) we introduce the thermal contact resistance into the formulation of the temperature decay function, (2) we improve numerical properties of the inversion procedure itself by introducing a regularization method including constraints, and (3) we use an adaptive choice of time frames for thermal decay inversion. Here, we demonstrate that integrating the thermal contact resistance into the procedure improves inversion results for the thermal diffusivity considerably. Moreover, we show that including regularization and constraints based on a-priori knowledge of the admissible range of the corresponding parameter values leads to stable inversion results. [ABSTRACT FROM AUTHOR]

In the Earth's upper mantle, seismic anisotropy mainly originates from the crystallographic preferred orientation (CPO) of olivine due to mantle deformation. Large-scale observation of anisotropy in surface wave tomography models provides unique constraints on present-day mantle flow. However, surface waves are not sensitive to the 21 coefficients of the elastic tensor, and therefore the complete anisotropic tensor cannot be resolved independently at every location. This large number of parameters may be reduced by imposing spatial smoothness and symmetry constraints to the elastic tensor. In this work, we propose to regularize the tomographic problem by using constraints from geodynamic modelling to reduce the number of model parameters. Instead of inverting for seismic velocities, we parametrize our inverse problem directly in terms of physical quantities governing mantle flow: a temperature field, and a temperature-dependent viscosity. The forward problem consists of three steps: (1) calculation of mantle flow induced by thermal anomalies, (2) calculation of the induced CPO and elastic properties using a micromechanical model, and (3) computation of azimuthally varying surface wave dispersion curves. We demonstrate how a fully nonlinear Bayesian inversion of surface wave dispersion curves can retrieve the temperature and viscosity fields, without having to explicitly parametrize the elastic tensor. Here, we consider simple flow models generated by spherical temperature anomalies. The results show that incorporating geodynamic constraints in surface wave inversion help to retrieve patterns of mantle deformation. The solution to our inversion problem is an ensemble of models (i.e. thermal structures) representing a posterior probability, therefore providing uncertainties for each model parameter. [ABSTRACT FROM AUTHOR]

Under favourable circumstances, seismic waveforms corresponding to an ensemble of events related by a common, spatially distributed process collectively exhibit a regular, signal-space geometry. When events in the ensemble have a common, or nearly common, source mechanism, this geometry is a distorted image of the distribution of events in the source region. The signal-space image can be visualized using a relatively simple waveform alignment and projection operation. Ensemble waveform correlation measurements can be inverted to estimate the distribution of the events in the source region, up to an arbitrary rotation, reflection and scaling, with residual distortion. We demonstrate these concepts with synthetic waveforms and with observations of long-wall mining induced seismicity for which substantial ground truth information is available. Our experience with these data has implications for location, correlation detection and machine learning and possible application to studies of repeating events in induced, volcanic and glacial seismicity. Our results place limits on the widely held assumption that waveform correlation is a useful measure of event separation. We suggest that the constraints on event separation need to be evaluated in the context of a population of related events, whose waveforms sample the signal space image of the source region. A better indicator of event separation is the length of the shortest path in signal space along the image. [ABSTRACT FROM AUTHOR]

Surface wave tomography is a valuable tool for constraining azimuthal anisotropy at regional scales. However, sparse and uneven coverage of dispersion measurements make meaningful uncertainty estimation challenging, especially when applying subjective model regularization. This paper considers azimuthal anisotropy constrained by measurements of surface wave dispersion data within a Bayesian trans-dimensional (trans-d) tomographic inversion. A recently proposed alternative model parametrization for trans-d inversion is implemented in order to produce more realistic models than previous studies considering trans-d surface wave tomography. The reversible-jump Markov chain Monte Carlo sampling technique is used to numerically estimate the posterior probability density of the model parameters. Isotropic and azimuthally anisotropic components of surface wave group velocity maps (and their associated uncertainties) are estimated while avoiding model regularization and allowing model complexity to be determined by the data information content. Furthermore, data errors are treated as unknown, and solved for within the inversion. The inversion method is applied to measurements of surface wave dispersion from regional earthquakes recorded over northern Cascadia and Haida Gwaii, a region of complex active tectonics but highly heterogeneous station coverage. Results for isotropic group velocity are consistent with previous studies that considered the southern part of the study region over Cascadia. Azimuthal anisotropic fast-axis directions are generally margin-parallel between Vancouver Island and Haida Gwaii, with a small change in direction and magnitude along the margin which may be attributed to the changing tectonic regime (from subduction to transform tectonics). Estimated errors on the dispersion data (solved for within the inversion) reveal a correlation between surface wave period and the dependence of data errors on travel path length. This paper demonstrates the value of considering azimuthal anisotropy within Bayesian tomographic inversions. Furthermore, this work provides structural context for future studies of tectonic structure and dynamics of northern Cascadia and Haida Gwaii, with the aim of improving our understanding of seismic and tsunami hazards. [ABSTRACT FROM AUTHOR]

Due to a too sparse permanent seismic coverage during the last decades, the crustal structure of western France and the surrounding regions is poorly known. In this study, we present a 3-D seismic tomographic model of this area obtained from the analysis of 2-yr continuous data recorded from 55 broad-band seismometers. An unconventional approach is used to convert Rayleigh wave dispersion diagrams obtained from ambient noise cross-correlations into posterior distributions of 1-D VS models integrated along each station pair. It allows to avoid the group velocity map construction step (which means dispersion curve extraction) while providing meaningful VS posterior uncertainties. VS models are described by a self-adapting and parsimonious parametrization using cubic Bézier splines. 1268 separately inverted 1-D VS profiles are combined together using a regionalization scheme, to build the 3-D VS model with a lateral resolution of 75 km over western France. The shallower part of the model (horizontal cross-section at 4 km depth) correlates well with the known main geological features. The crystalline Variscan basement is clearly associated with positive VS perturbations while negative heterogeneities match the Mesocenozoic sedimentary basins. At greater depths, the Bay of Biscay exhibits positive VS perturbations,which eastern and southern boundaries can be interpreted as the ocean−continent transition. The overall crustal structure below the Armorican Massif appears to be heterogenous at the subregional scale, and tends to support that both the South-Armorican Shear Zone and the Paris Basin Magnetic Anomaly are major crustal discontinuities that separate distinct domains. [ABSTRACT FROM AUTHOR]

We define a two-step procedure to obtain reliable inverse models of the distribution of electrical conductivity at depth from apparent conductivities estimated by electromagnetic instruments such as GEONICS EM38, EM31 or EM 34-3. The first step of our procedure consists in the correction of the apparent conductivities to make them consistent with a low induction number condition, for which these data are very similar to the true conductivity. Then, we use a linear inversion approach to obtain a conductivity model. To improve the conductivity estimation at depth we introduced a depth-weighting function in our regularized weighted minimum length solution algorithm. We test the whole procedure on two synthetic data sets generated by the COMSOL Multiphysics for both the vertical magnetic dipole and horizontal magnetic dipole configurations of the loops. Our technique was also tested on a real data set, and the inversion result has been compared with the one obtained using the dipole-dipole DC electrical resistivity (ER) method. Our model not only reproduces all shallow conductive areas similar to the ER model, but also succeeds in replicating its deeper conductivity structures. On the contrary, inversion of uncorrected data provides a biased model underestimating the true conductivity. [ABSTRACT FROM AUTHOR]

We present new regional models, denoted CLAS, of the Chinese lithospheric field, combining the long-wavelength information provided by satellite-derived models: CHAOS-6, MF7, LCS-1 and NGDC720, and an extremely high-quality compilation of 97 994 aeromagnetic survey data with 10 km × 10 km resolution for shorter wavelength. The models are estimated using a depleted basis of global spherical harmonic functions centred on China. CLAS models are determined include harmonic degrees up to 400. Although some accuracy of aeromagnetic data is lost in order to balance the consistent of two data sets, the results show that CLAS models have a high correlation with the satellite models at low-degree terms (degree correlation > 0.9) but with more power at high-degree terms, reflecting more features of the lithospheric field in continental China. Examples of improvement include Changbai mountains, Sichuan Basin and Qinghai–Tibet Plateau. CLAS models have good agreement (coherence > 0.9) with Chinese aeromagnetic data at wavelength down to about 100 km (corresponding to spherical harmonic degree n  = 400), filling the usual gap between satellite models and aeromagnetic data. Comparison with aeromagnetic data filtered at 100 km gives good agreement (correlation > 0.95). The residuals between CLAS models and aeromagnetic data are still large (rms > 70 nT), but with most of misfits arising from shorter wavelength fields that the model cannot fit at degree up to 400; such misfit could be reduced by increasing the model degree. We provide a geological example of how the inclusion of satellite data can change the geological conclusions that can be drawn from the magnetic information. However, the two data sets are not completely consistent, future models should start from a reanalysis of the aeromagnetic data and its line levelling to ensure consistency with the satellite model. [ABSTRACT FROM AUTHOR]

This paper describes the design of a candidate secular variation model for the 13th generation of the International Geomagnetic Reference Field. This candidate is based upon the integration of an ensemble of 100 numerical models of the geodynamo between epochs 2019.0 and 2025.0. The only difference between each ensemble member lies in the initial condition that is used for the numerical integration, all other control parameters being fixed. An initial condition is defined as follows: an estimate of the magnetic field and its rate-of-change at the core surface for 2019.0 is obtained from a year (2018.5–2019.5) of vector Swarm data. This estimate (common to all ensemble members) is subject to prior constraints: the statistical properties of the numerical dynamo model for the main geomagnetic field and its secular variation, and prescribed covariances for the other sources. One next considers 100 three-dimensional core states (in terms of flow, buoyancy and magnetic fields) extracted at different discrete times from a dynamo simulation that is not constrained by observations, with the time distance between each state exceeding the dynamo decorrelation time. Each state is adjusted (in three dimensions) in order to take the estimate of the geomagnetic field and its rate-of-change for 2019.0 into account. This methodology provides 100 different initial conditions for subsequent numerical integration of the dynamo model up to epoch 2025.0. Focussing on the 2020.0–2025.0 time window, we use the median average rate-of-change of each Gauss coefficient of the ensemble and its statistics to define the geomagnetic secular variation over that time frame and its uncertainties. [ABSTRACT FROM AUTHOR]

Earthquake source estimates are affected by many types of uncertainties, deriving from observational errors, modelling choices and our simplified description of the Earth's interior. While observational errors are often accounted for, epistemic uncertainties, which stem from our imperfect description of the forward model, are usually neglected. In particular, 3-D variations in crustal properties are rarely considered. 3-D crustal heterogeneity is known to largely affect estimates of the seismic source, using either geodetic or seismic data. Here, we use a perturbation approach to investigate, and account for, the impact of epistemic uncertainties related to 3-D variations of the mechanical properties of the crust. We validate our approach using a Bayesian sampling procedure applied to synthetic geodetic data generated from 2-D and 3-D finite-fault models. We show that accounting for uncertainties in crustal structure systematically increases the reliability of source estimates. [ABSTRACT FROM AUTHOR]

We propose a new surface wave tomography approach that benefits from densely sampled active-source arrays and brings together elements from active-source seismic-wave interferometry, full waveform inversion and dense-array processing. In analogy with optical interferometry, seismic Michelson interferometer (SMI) uses seismic interference patterns given by the data-based diffraction kernels in an iterative inversion scheme to image a medium. SMI requires no traveltime measurements and no spatial regularization, and it accounts for bent rays. Furthermore, the method does not need computation of complex synthetic models, as it works as a data-driven inversion technique that makes it computationally very fast. In an automatic way, it provides high-resolution phase-velocity maps and their error estimation. SMI can complete traditional surface wave tomography studies, as its use can be easily extended from land active seismic data to the virtual source gathers of ambient-noise-based studies with dense arrays. [ABSTRACT FROM AUTHOR]