We present an improved mascon approach to transform monthly spherical harmonic solutions based on GRACE satellite data into mass anomaly estimates in Greenland. The GRACE-based spherical harmonic ...coefficients are used to synthesize gravity anomalies at satellite altitude, which are then inverted into mass anomalies per mascon. The limited spectral content of the gravity anomalies is properly accounted for by applying a low-pass filter as part of the inversion procedure to make the functional model spectrally consistent with the data. The full error covariance matrices of the monthly GRACE solutions are properly propagated using the law of covariance propagation. Using numerical experiments, we demonstrate the importance of a proper data weighting and of the spectral consistency between functional model and data. The developed methodology is applied to process real GRACE level-2 data (CSR RL05). The obtained mass anomaly estimates are integrated over five drainage systems, as well as over entire Greenland. We find that the statistically optimal data weighting reduces random noise by 35–69%, depending on the drainage system. The obtained mass anomaly time-series are de-trended to eliminate the contribution of ice discharge and are compared with de-trended surface mass balance (SMB) time-series computed with the Regional Atmospheric Climate Model (RACMO 2.3). We show that when using a statistically optimal data weighting in GRACE data processing, the discrepancies between GRACE-based estimates of SMB and modelled SMB are reduced by 24–47%.
On the boundaries of the states of Coahuila and Zacatecas in northern Mexico, scarce outcrops of a Triassic subduction complex have been used to infer in several positions a tectonostratigraphic ...terranes boundary. This crustal boundary is covered by a pile of Jurassic volcanosedimentary rocks and a thick, folded, and thrusted Mesozoic sedimentary marine succession. We carried out detailed mapping, geological cross-sections, and a geophysical survey using magnetic and gravity data to model the buried boundary between these crustal blocks. Qualitative analysis of the magnetic and gravity anomalies was performed in order to determine the crustal boundary. It was integrated with in situ rock magnetic susceptibility and density data obtained in the laboratory to restrict the inversion process. The calculated models helped us to better constrain a regional structural lineament, named Las Norias fault. This fault divides two cortical blocks, the Central terrane and Oaxaquia microcontinent, whose physical properties and styles of deformation in the Mesozoic cover are very contrasting.
•Analysis of geophysical and geological field information.•Modeling of gravity and magnetic anomalies by joint inversion techniques.•Estimation of the geophysical parameters density and magnetic susceptibility.•Recognizing the inferred boundary between the Oaxaquia microcontinent and Central terrane.
Gondwana breakup changed the global continental configuration, leading to opening of major oceanic gateways, shifts in the climate system and significant impacts on the biosphere, hydrosphere and ...cryosphere. Although of global importance, the earliest stages of the supercontinental fragmentation are poorly understood. Reconstructing the processes driving Gondwana breakup within the ice-covered Weddell Sea Rift System (WSRS) has proven particularly challenging. Paleomagnetic data and tectonic reconstructions of the WSRS region indicate that major Jurassic translation and rotation of microcontinental blocks were a key precursor to Gondwana breakup by seafloor spreading. However, geophysical interpretations have provided little support for major motion of crustal blocks during Jurassic extension in the WSRS. Here we present new compilations of airborne magnetic and airborne gravity data, together with digital enhancements and 2D models, enabling us to re-evaluate the crustal architecture of the WSRS and its tectonic and kinematic evolution. Two provinces are identified within the WSRS, a northern E/W trending province and a southern N/S trending province. A simple extensional or transtensional model including ~500km of crustal extension and Jurassic magmatism accounts for the observed geophysical patterns. Magmatism is linked with rifting between South Africa and East Antarctica in the north, and associated with back-arc extension in the south. Our tectonic model implies ~30° of Jurassic block rotation and juxtaposes the magnetically similar Haag Block and Shackleton Range, despite differences in both Precambrian and Pan African-age surface geology. Although geophysically favoured our new model cannot easily be reconciled with geological and paleomagnetic interpretations that require ~1500km of motion and 90° anticlockwise rotation of the Haag-Ellsworth Whitmore block from a pre-rift position adjacent to the Maud Belt. However, our model provides a simpler view of the WSRS as a broad Jurassic extensional/transtensional province within a distributed plate boundary between East and West Antarctica.
Display omitted
•Two distinct aeromagnetic provinces identified within the Weddell Sea Rift System•Approximately 500km continental extension suggested by 2D potential field models•Alternative simple model for tectonic evolution of Weddell Sea Rift System proposed
Abstract In gravity-anomaly-based prospecting, it is difficult to achieve large-scale and high-precision inversion imaging of complex geological models. To address this issue, this paper proposes a ...three-dimensional holographic numerical simulation method for gravity anomalies. This method transforms the 3D partial differential equation of gravity potential into many independent 1D differential equations with different wavenumbers by performing a 2D Fourier transform along the horizontal direction. It decomposes a large-scale 3D numerical modeling problem into many 1D numerical modeling problems, which greatly reduces the computation and memory requirements of modeling, and each 1D differential equation is independent, so it has high parallelism. The vertical direction is reserved as the spatial domain, which has strict upper and lower boundary conditions; The horizontal 2D Fourier transform uses a holographic Fourier transform (Holo-FT) with a full interval of integration, consistent with the physical boundary in the horizontal direction, thus the physical information of the gravity potential described by the three-dimensional partial differential equation is fully and accurately simulated. Using the high parallelism of the algorithm, the CPU is used for parallel solving ordinary differential equations, while the GPU is used for parallel computing of Holo-FT, which implements the CPU-GPU parallel acceleration scheme and further improves the efficiency of this algorithm.
SUMMARY
Point-mass inversion is widely employed in GRACE level-2 data processing. Conventionally, the spherical harmonic (SH) coefficients are used indirectly: a set of pseudo measurements is ...generated first using the SH coefficients through SH synthesis; then the point-mass inversion is done with these pseudo measurements. To be statistically optimal, the covariance matrix of pseudo measurements should be calculated and used to appropriately weigh the parameter estimation. In this work, we propose a statistically optimal point-mass inversion scheme by directly using the SH coefficients as measurements. We prove the equivalence between this direct approach and the conventional indirect approaches. We also demonstrated their comparable performance through both simulation and real GRACE data processing. Choosing and calculating pseudo measurements, propagating covariance matrix and potentially dealing with the singularity of the covariance matrix involved in the conventional indirect approaches are avoided in the proposed direct approach. This statistically optimal direct approach can readily be employed in mascon inversion of GRACE data and other radial basis functions-based approaches in regional gravity modeling.
Integral and differentiation are two mathematical operations in modern calculus and analysis which have been commonly applied in many fields of science. Integration and differentiation are associated ...and linked as inverse operation by the fundamental theorem of calculus. Both integral and differentiation are defined based on the concept of additive Lebesgue measure although various generations have been developed with different forms and notations. Fractals can be considered as geometry with fractal dimension (e.g., non-integer) which no longer possesses Lebesgue additive property. Accordingly, the ordinary integral and differentiation operations are no longer applicable to the fractal geometry with singularity. This paper introduces a recently developed concept of fractal differentiation and integral operations. These operations are expressed using the similar notations of the ordinary operations except the measures are defined in fractal space or measures with fractal dimension. The calculus operations can be used to describe the new concept of fractal density, the density with fractal dimension or density of matter with fractal dimension. The concept and methods are also applied to interpret the Bouguer anomaly over the mid-ocean ridges. The results show that the Bouguer gravity anomaly depicts singularity over the mid-ocean ridges. The development of new calculus operations can significantly improve the accuracy of geodynamic models.
The gravity method is one of the non-destructive geophysical methods, which aims to estimate the 3D subsurface density distribution of geological bodies from the observed 2D surface gravity ...anomalies. Recently, deep learning has achieved great success in solving ill-posed problems including gravity inversion. The limitation of the current deep learning methods for gravity inversion is the difference between synthetic and field data. Thus, we introduce a self-supervised estimation method for 3D gravity inversion (SSGI). SSGI learns the field data directly by closed-loop of the inversion model and forward model. The proposed inversion model contains an encoder, an expander, a decoder, and a 3D refiner. Since the forward model is built according to the law of universal gravitation, SSGI can optimize the inversion model by minimizing the mean absolute error of the original and reconstructed gravity anomalies. Besides, SSGI constrains the inversion model by a guide-line in the auxiliary loop. Since the guide-line corresponds to the sampling or average of the density matrix, minimizing the mean absolute error between the original guide-line and the generated guide-line can reduce the uncertainty of inversion. The experimental results demonstrate that the proposed SSGI achieves state-of-the-art performance in 3D gravity inversion.
SUMMARY
The separation of the effects of deep-seated sources of potential fields from those of shallower ones is a frequent requirement when interpreting magnetic or gravity fields. A common ...procedure is estimating the regional, long wavelength, component of the field by analysing the data over an area larger than that of the local feature of interest. The local components are found by subtracting the estimated regional from the observed data. These approaches may have difficulties in their application, as the dataset over large areas may not be available and other local anomalies, in the enlarged area, may prevent a reliable estimate of the regional field. We present an alternative and simple approach to the regional-residual separation problem not requiring the analysis over large areas and aiming at estimating the local, rather than the regional, component. Our method exploits the natural enhancement of short wavelengths obtainable by computing vertical derivatives of potential fields. An equivalent layer source is computed from the vertical derivative and is used to estimate the local field. The optimal differentiation order can be determined by inspecting the obtained results. This parameter may assume even fractional values, so that the method results a very versatile tool. The application to a complex synthetic case and two real data examples demonstrates the utility of this approach. In summary, our method has some peculiar characteristics making it an interesting alternative to currently used approaches to regional-residual separation: (i) it is a local method, so it can work well even when processing datasets relative to areas of limited extension; (ii) unlike most current methods, estimating a smooth regional component, our method directly produces an estimate of the local field and (iii) it is highly versatile, as the key parameter, that is the fractional differentiation order, can be finely adjusted up to obtain an optimal local field.
The Trans-Saharan Belt is one of the most important orogenic systems constitutive of the Pan-African cycle, which, at the end of the Neoproterozoic, led to the formation of the Gondwana ...Supercontinent. It is marked by the opening and closing of oceanic domains, collision of continental blocks and the deformation of thick synorogenic sedimentary basins. It extends from north to south over a distance of 3000 km in Africa, including the Nigerian Shield and the Tuareg Shield as well as their counterparts beneath the Phanerozoic oil-rich North- and South-Saharan sedimentary basins. In this study, we take advantage of potential field methods (magnetism and gravity) to analyze the crustal-scale structures of the Tuareg Shield terranes and to track these Pan-African structures below the sedimentary basins, offering a new, >1000 km extent. The map interpretations are based on the classical potential field transforms and two-dimensional forward modeling. We have identified geophysical units and first-order bounding lineaments essentially defined owing to magnetic and gravimetric anomaly signatures. In particular, we are able to highlight curved terminations, which in the Trans-Saharan context have been still poorly documented. We provide for the first time a rheological map showing a categorization of contrasted basement units from the south of the Tuareg Shield up to the Atlas Belt. These units highlight the contrasted rheological behavior of the Tuareg tectonostratigraphic terranes during (i) the northerly Pan-African tectonic escape characteristic of the Trans-Saharan Belt and (ii) the North Sahara basin development, especially during intraplate reworking tied to the Variscan event. The discovery of a relatively rigid E-W oriented unit to the south of the Atlas system, and on which the escaping Pan-African terranes were blocked, offers a new perspective on the structural framework of the north-Gondwana margin. It will help to understand how occurred the rendezvous of the N-S oriented Pan-African terranes and the E-W oriented Cadomian peri-Gondwanan terranes.
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•Geophysics compared to geology: delineation of cratons, metacratons and mobile zones•Another terrane compartmentalization for the Pan-African Trans-Saharan Belt•Northward preservation, extension and termination of Pan-African structures•Truncation of the Pan-African terranes and shear zones by the Cadomian orogen•Crustal rheology and the development of Phanerozoic North Sahara basins
We describe the computation of the first Australian quasigeoid model to include error estimates as a function of location that have been propagated from uncertainties in the EGM2008 global model, ...land and altimeter-derived gravity anomalies and terrain corrections. The model has been extended to include Australia’s offshore territories and maritime boundaries using newer datasets comprising an additional
∼
280,000 land gravity observations, a newer altimeter-derived marine gravity anomaly grid, and terrain corrections at
1
″
×
1
″
resolution. The error propagation uses a remove–restore approach, where the EGM2008 quasigeoid and gravity anomaly error grids are augmented by errors propagated through a modified Stokes integral from the errors in the altimeter gravity anomalies, land gravity observations and terrain corrections. The gravimetric quasigeoid errors (one sigma) are 50–60 mm across most of the Australian landmass, increasing to
∼
100
mm in regions of steep horizontal gravity gradients or the mountains, and are commensurate with external estimates.
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