Improving the accuracy of the marine gravity field requires both improved altimeter range precision and dense track coverage. After a hiatus of more than 15 yr, a wealth of suitable data is now ...available from the CryoSat-2, Envisat and Jason-1 satellites. The range precision of these data is significantly improved with respect to the conventional techniques used in operational oceanography by retracking the altimeter waveforms using an algorithm that is optimized for the recovery of the short-wavelength geodetic signal. We caution that this new approach, which provides optimal range precision, may introduce large-scale errors that would be unacceptable for other applications. In addition, CryoSat-2 has a new synthetic aperture radar (SAR) mode that should result in higher range precision. For this new mode we derived a simple, but approximate, analytic model for the shape of the SAR waveform that could be used in an iterative least-squares algorithm for estimating range. For the conventional waveforms, we demonstrate that a two-step retracking algorithm that was originally designed for data from prior missions (ERS-1 and Geosat) also improves precision on all three of the new satellites by about a factor of 1.5. The improved range precision and dense coverage from CryoSat-2, Envisat and Jason-1 should lead to a significant increase in the accuracy of the marine gravity field.
Summary
We present a 3-D joint inversion framework for seismic, magnetotelluric (MT) and scalar and tensorial gravity data. Using large-scale optimization methods, parallel forward solvers and a ...flexible implementation in terms of model parametrization allows us to investigate different coupling approaches for the various physical parameters involved in the joint inversion. Here we compare two different coupling approaches, direct parameter coupling where we calculate conductivities and densities from seismic slownesses and cross-gradient coupling, where each model cell has an independent value for each physical property and a structural similarity is enforced through a term in the objective function.
For both types of approaches we see an improvement of the inversion results over single inversions when the inverted data sets are generated from compatible models. As expected the direct coupling approach results in a stronger interaction between the data sets and in this case better results compared to the cross-gradient coupling. In contrast, when the inverted MT data is generated from a model that violates the parameter relationship in some regions but conforms with the cross-gradient assumptions, we obtain good results with the cross-gradient approach, while the direct coupling approach results in spurious features. This makes the cross-gradient approach the first choice for regions were a direct relationship between the physical parameters is unclear.
We discuss the connection between the integer moments of the Fermi distribution function that occur in the Sommerfeld expansion and the coefficients that occur in anomalous conservation laws for ...chiral fermions. For an illustration, we extract the chiral magnetothermal energy current from the mixed gauge-gravity anomaly in the 3+1-dimensional energy-momentum conservation law. We then use a similar method to confirm the conjecture that the T2/12 thermal contribution to the chiral vortical effect current arises from the gravitational Pontryagin term in the 3+1-dimensional chiral anomaly.
SUMMARY
A gravity inversion procedure using the success-history-based adaptive differential evolution (SHADE) algorithm is presented to reconstruct the 3-D basement relief geometry in sedimentary ...basins. We introduced exponential population size (number) reduction (EPSR) to reduce the computational cost and used self-adaptive control parameters to solve this highly nonlinear inverse problem. Model parametrization was carried out by discretizing the sedimentary cover via juxtaposed right prisms, each placed below each observation point. Resolvability characteristics of the 3-D inverse problem were revealed through some cost function topography landscapes. The fine-tuned control parameter namely, population number allowed us to get best benefit from the algorithm. Additionally, a stabilizing function as a relative constraint was used to avoid undesired effects originated from the ill-posedness of the problem. In the synthetic data cases, the strategy we propose outperformed the linear population number reduction strategy which has won various IEEE–CEC competitions so far. Thorough uncertainty assessments via probability density function and principal component analysis demonstrated the solidity of the obtained inverse models. In the real data case, residual gravity anomalies of two well-known major grabens of Aegean Graben System (Türkiye), calculated thanks to the finite element method, were inverted. It was determined that the inverse solutions obtained for these basement reliefs, whose depths are still controversial, are statistically reliable. Moreover, these depths were found to be less than the depths reported in most previous studies. We conclude that the SHADE using EPSR strategy that we propose is a powerful alternative inversion tool for highly nonlinear geophysical problems.
SUMMARY
The Marvin Spur is a 450-km-long east–west trending escarpment along the northernmost periphery of the Alpha Ridge, starting about 500 km from the coasts of Ellesmere Island and Greenland off ...the Arctic Ocean margin of North America and running subparallel to the Amerasian margin of the continental Lomonosov Ridge. This region was investigated as part of the Canada–Sweden Polar Expedition in 2016, from which two seismic profiles are presented. The first is a 165-km-long line along the crest of the Marvin Spur. The second is a 221-km-long line extending southwestward from the spur to the northern flank of the Alpha Ridge within the Cretaceous High Arctic Large Igneous Province (HALIP). Multichannel seismic reflection data were acquired along both lines using a 100-m-long streamer, and the airgun shots were also recorded using 16 sonobuoys and 5 stations on the sea ice to calculate a velocity model for the crust from forward modelling of seismic traveltimes. The Marvin Spur profile reveals up to 1100 m of sedimentary rocks on top of a 1-km-thick series of basalts (4.5–5.1 km s−1). Upper and lower crust have velocities of 5.8–5.9 km s−1 and 6.2–6.3 km s−1, respectively, with the upper crust being 1–2 km thick compared to around 13 km for the lower crust. A wide-angle double seismic reflection manifests the top and base of a 6-km-thick lower crustal layer that we interpret as magmatic underplating beneath the continental crust of the Marvin Spur. We correlate a high-amplitude magnetic anomaly on Marvin Spur with a comparable anomaly on Lomonosov Ridge by invoking 110 km of dextral strike-slip motion. Assuming that HALIP-related magmatic deposits generate these anomalies, the strike-slip motion pre-dates the main phase of magmatism (latest Cretaceous, 78 Ma). On the northern Alpha Ridge, sediments are around 1-km-thick and cover a 700 to 1700-m-thick series of basalts with velocities of 4.4–4.8 km s−1. Below is a 3-km-thick layer with intermediate velocities of 5.6 km s−1 and a lower crust with a velocity of 6.8 km s−1. Moho depth is not resolved seismically, but gravity modelling indicates a total thickness of 13 or 18 km for the igneous crust except for the Fedotov Seamount where Moho deepens by about 5 km. Construction of the seamount occurred in multiple magmatic phases, including flow eruptions during deposition of the Cenozoic sedimentary succession post-dating the main HALIP magmatism.
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.
The Himalaya is the result of the on-going convergence and collision of India and Asia. The internal configuration and processes that govern the rise of the Himalayan Mountains and Tibetan Plateau ...are crucial to understand continental collision zones. However, knowledge of the prior configuration of the colliding plates is equally important, since inherited (pre-orogenic/basement) structures can undeniably influence the development of the orogenic architecture throughout the orogen's cycle of collision and eventual collapse. Three northeast-trending palaeotopographic ridges of faulted Precambrian Indian basement underlie the Ganga basin south of the Himalaya. Our paper illustrates a crustal-scale fault origin for these ridges and succeeds in determining how far north beneath the Himalayan system they extend and how they ultimately govern the location of upper crustal faults in southern Tibet. Spectrally filtered EGM2008 Bouguer gravity data and edges in its horizontal gradient at different source depths (‘gravity worms’) over northern Peninsular India, the Himalaya and southern Tibet reveal several continuous Himalayan cross-strike discontinuities interpreted to represent crustal faults. Gravity lineaments in Peninsular India coincide with edges of the Precambrian basement ridges and megakinks up to 100 km wide develop in foreland cover sequences between the interpreted basement faults. The interpreted basement faults project northward beneath the Himalayan system and southern Tibet. Our results suggest that several active Himalayan cross-strike faults, such as the ones related to many graben in southern Tibet, are rooted in the underplated Indian lower crust or step en échelon along interpreted basement faults. Our interpretation thus suggests that south Tibet graben are spatially related to deep-seated crustal-scale faults rooted in the underplated Indian crust. These major discontinuities partition the Himalayan range into distinct zones, and could ultimately contribute to lateral variability in tectonic evolution along the orogen's strike.
SUMMARY
A fast algorithm for the large-scale joint inversion of gravity and magnetic data is developed. The algorithm uses a non-linear Gramian constraint to impose correlation between the density ...and susceptibility of the reconstructed models. The global objective function is formulated in the space of the weighted parameters, but the Gramian constraint is implemented in the original space, and the non-linear constraint is imposed using two separate Lagrange parameters, one for each model domain. It is significant that this combined approach, using the two spaces provides more similarity between the reconstructed models. Moreover, it is shown theoretically that the gradient for the use of the unweighted space is not a scalar multiple of that used for the weighted space, and hence cannot be accounted for by adjusting the Lagrange parameters. It is assumed that the measured data are obtained on a uniform grid and that a consistent regular discretization of the volume domain is imposed. Then, the sensitivity matrices exhibit a block-Toeplitz-Toeplitz-block structure for each depth layer of the model domain, and both forward and transpose operations with the matrices can be implemented efficiently using two dimensional fast Fourier transforms. This makes it feasible to solve for large scale problems with respect to both computational costs and memory demands, and to solve the non-linear problem by applying iterative methods that rely only on matrix–vector multiplications. As such, the use of the regularized reweighted conjugate gradient algorithm, in conjunction with the structure of the sensitivity matrices, leads to a fast methodology for large-scale joint inversion of geophysical data sets. Numerical simulations demonstrate that it is possible to apply a non-linear joint inversion algorithm, with Lp-norm stabilisers, for the reconstruction of large model domains on a standard laptop computer. It is demonstrated, that while the p = 1 choice provides sparse reconstructed solutions with sharp boundaries, it is also possible to use p = 2 in order to provide smooth and blurred models. The methodology is used for inverting gravity and magnetic data obtained over an area in northwest of Mesoproterozoic St Francois Terrane, southeast of Missouri, USA.
SUMMARY
The use of the probabilistic approach to solve inverse problems is becoming more popular in the geophysical community, thanks to its ability to address nonlinear forward problems and to ...provide uncertainty quantification. However, such strategy is often tailored to specific applications and therefore there is a need for common platforms to solve different geophysical inverse problems and showing potential and pitfalls of the methodology. In this work, we demonstrate a common framework within which it is possible to solve such inverse problems ranging from, for example, earthquake source location to potential field data inversion and seismic tomography. This allows us to fully address nonlinear problems and to derive useful information about the subsurface, including uncertainty estimation. This approach can, in fact, provide probabilities related to certain properties or structures of the subsurface, such as histograms of the value of some physical property, the expected volume of buried geological bodies or the probability of having boundaries defining different layers. Thanks to its ability to address high-dimensional problems, the Hamiltonian Monte Carlo (HMC) algorithm has emerged as the state-of-the-art tool for solving geophysical inverse problems within the probabilistic framework. HMC requires the computation of gradients, which can be obtained by adjoint methods. This unique combination of HMC and adjoint methods is what makes the solution of tomographic problems ultimately feasible. These results can be obtained with ‘HMCLab’, a numerical laboratory for solving a range of different geophysical inverse problems using sampling methods, focusing in particular on the HMC algorithm. HMCLab consists of a set of samplers (HMC and others) and a set of geophysical forward problems. For each problem its misfit function and gradient computation are provided and, in addition, a set of prior models can be combined to inject additional information into the inverse problem. This allows users to experiment with probabilistic inverse problems and also address real-world studies. We show how to solve a selected set of problems within this framework using variants of the HMC algorithm and analyse the results. HMCLab is provided as an open source package written both in Python and Julia, welcoming contributions from the community.
Large-scale topography may be due to several causes, including (1) variations in crustal thickness and density structure, (2) oceanic lithosphere age differences, (3) subcrustal density variations in ...the continental lithosphere and (4) convective flow in the mantle beneath the lithosphere. The last contribution in particular may change with time and be responsible for continental inundations; distinguishing between these contributions is therefore important for linking Earth's history to its observed geological record. As a step towards this goal, this paper aims at such distinction for the present-day topography: the approach taken is deriving a ‘model’ topography due to contributions (3) and (4), along with a model geoid, using a geodynamic mantle flow model. Both lithosphere thickness and density anomalies beneath the lithosphere are inferred from seismic tomography. Density anomalies within the continental lithosphere are uncertain, because they are probably due to variations in composition and temperature, making a simple scaling from seismic to density anomalies inappropriate. Therefore, we test a number of different assumptions regarding these. As a reality check, model topography is compared, in terms of both correlation and amplitude ratio, to ‘residual’ topography, which follows from observed topography after subtracting contributions (1) and (2). The model geoid is compared to observations as well. Comparatively good agreement is found if there is either an excess density of ≈0.2 per cent in the lithosphere above ≈150 km depth, with anomalies below as inferred from tomography, or if the excess density is ≈0.4 per cent in the entire lithosphere. Further, a good fit is found for viscosity ≈1020 Pa s in the asthenosphere, increasing to ≈1023 Pa s in the lower mantle above D′. Results are quite dependent on which tomography models they are based on; for some recent ones, topography correlation is ≈0.6, many smaller scale features are matched, topography amplitude is less than ≈30 per cent too large, while geoid variance reduction exceeds 70 per cent—overall a considerable improvement compared to previous models. Correlation becomes less if smaller scale features (corresponding to spherical harmonic degrees 15 and higher), which are probably largely due to anomalies in the lithosphere, are also considered. Comparison of results with different viscosity structures, and a regional comparison of amplitude ratios, indicates that lateral viscosity variations can be quite strong, but only leading to moderate variations in model topography of a factor probably less than two.
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