East Antarctica magnetically linked to its ancient neighbours in Gondwana

We present a new magnetic compilation for Central Gondwana conformed to a recent satellite magnetic model (LCS-1) with the help of an equivalent layer approach, resulting in consistent levels, corrections that have not previously been applied. Additionally, we use the satellite data to its full spectral content, which helps to include India, where high resolution aeromagnetic data are not publically available. As India is located north of the magnetic equator, we also performed a variable reduction to the pole to the satellite data by applying an equivalent source method. The conformed aeromagnetic and satellite data are superimposed on a recent deformable Gondwana plate reconstruction that links the Kaapvaal Craton in Southern Africa with the Grunehogna Craton in East Antarctica in a tight fit. Aeromagnetic anomalies unveil, however, wider orogenic belts that preserve remnants of accreted Meso- to Neoproterozoic crust in interior East Antarctica, compared to adjacent sectors of Southern Africa and India. Satellite and aeromagnetic anomaly datasets help to portray the extent and architecture of older Precambrian cratons, re-enforcing their linkages in East Antarctica, Australia, India and Africa.

Convolutional equivalent layer for gravity data processing

We have developed an efficient and very fast equivalent-layer technique for gravity data processing by modifying an iterative method grounded on an excess mass constraint that does not require the solution of linear systems. Taking advantage of the symmetric block-Toeplitz Toeplitz-block (BTTB) structure of the sensitivity matrix that arises when regular grids of observation points and equivalent sources (point masses) are used to set up a fictitious equivalent layer, we develop an algorithm that greatly reduces the computational complexity and RAM memory necessary to estimate a 2D mass distribution over the equivalent layer. The structure of symmetric BTTB matrix consists of the elements of the first column of the sensitivity matrix, which, in turn, can be embedded into a symmetric block-circulant with circulant-block (BCCB) matrix. Likewise, only the first column of the BCCB matrix is needed to reconstruct the full sensitivity matrix completely. From the first column of the BCCB matrix, its eigenvalues can be calculated using the 2D fast Fourier transform (2D FFT), which can be used to readily compute the matrix-vector product of the forward modeling in the fast equivalent-layer technique. As a result, our method is efficient for processing very large data sets. Tests with synthetic data demonstrate the ability of our method to satisfactorily upward- and downward-continue gravity data. Our results show very small border effects and noise amplification compared to those produced by the classic approach in the Fourier domain. In addition, they show that, whereas the running time of our method is [Formula: see text] s for processing [Formula: see text] observations, the fast equivalent-layer technique used [Formula: see text] s with [Formula: see text]. A test with field data from the Carajás Province, Brazil, illustrates the low computational cost of our method to process a large data set composed of [Formula: see text] observations.

Generalized positivity constraint on magnetic equivalent layers

It is known from the potential theory that a continuous and planar layer of dipoles can exactly reproduce the total-field anomaly produced by arbitrary 3D sources. We have proven the existence of an equivalent layer having an all-positive magnetic-moment distribution for the case in which the magnetization direction of this layer is the same as that of the true sources, regardless of whether the magnetization of the true sources is purely induced or not. By using this generalized positivity constraint, we have developed a new iterative method for estimating the total magnetization direction of 3D magnetic sources based on the equivalent-layer technique. Our method does not impose a priori information about the shape or the depth of the sources, does not require regularly spaced data, and presumes that the sources have a uniform magnetization direction. At each iteration, our method performs two steps. The first step solves a constrained linear inverse problem to estimate a positive magnetic-moment distribution over a discrete equivalent layer of dipoles. We consider that the equivalent sources are located on a plane and have a uniform and fixed magnetization direction. In the second step, we use the estimated magnetic-moment distribution and solve a nonlinear inverse problem for estimating a new magnetization direction for the dipoles. The algorithm stops when the equivalent layer yields a total-field anomaly that fits the observed data. Tests with synthetic data simulating different geologic scenarios show that the final estimated magnetization direction is close to the true one. We apply our method to field data from the Goiás alkaline province, over the Montes Claros complex, in the center of Brazil. The results suggest the presence of intrusions with remarkable remanent magnetization, in agreement with the current literature for this region.

The SMOS-Derived Soil Water EXtent and equivalent layer thickness facilitate determination of soil water resources

The assessment of water resources in soil is important in understanding the water cycle in the natural environment and the processes of water exchange between the soil and the atmosphere. The main objective of the study was to assess water resources (in 2010–2013) in the topsoil from satellite (SMOS) and in situ (ground) measurements using the SWEX_PD approach (Soil Water EXtent at Penetration Depth). The SWEX_PD is a result of multiplying soil moisture (SM) and radiation penetration depth (PD) for each pixel derived from the SMOS satellite. The PD, being a manifold of the wavelength λ0 equal to 21 cm, was determined from the weekly SMOS L2 measurement data based on the real and imaginary part of complex dielectric constant. The SWEX_PD data were compared with soil water resources (WR) calculated from the sum of components derived from multiplication of soil moisture (SM) and layer thickness in nine agrometeorological stations located along the eastern border of Poland. Each study site consisted of seven neighbouring Discrete Global Grid pixels (nodes spaced at 15 km) including the central ones with agrometeorological stations. The study area included different types of soils and land covers. The agreement between the water resources obtained from the SWEX_PD and ground measurements (WR) was quantified using classical statistics and Bland–Altman's plots. Calibrated Layer Thickness (CLT = dbias) from 8 to 28 cm was obtained with a low values of bias (close to zero), limits of agreements, and confidence intervals for all the SWEX_PD, depending on the pixel location. The results revealed that the use of the SWEX_PD for assessing soil water resources is the most reliable approach in the study area. Additionally, the data from Bland–Altman plots and the equation proposed in these studies allowed calculation of the Equivalent Layer Thickness (ELT = $$d_{ei}^{SWEX}$$ d ei SWEX ), which corresponds to the water resources derived from the SMOS satellite at the same time as (SM) measurements performed in the agrometeorological stations. The ranges of the mean, standard deviation, minimum, maximum, and coefficient of variation (CV) of ELT among all pixels and stations were 8.28–28.7 cm, 3.27–12.66 cm, 3.03–10.87 cm, 19.23–94.97 cm, and 24.72–98.79%, respectively. The ranges of the characteristics depended on environmental conditions and their means were close to the values of the calibrated layer thickness. The impacts of soil texture, organic matter, vegetation, and their interactive effects on the differentiation and agreement of soil water resources obtained from SWEX_PD vs. data from ground measurements in the study area are discussed. Further studies are required to address the impact of the environmental factors to improve the assessment of soil water resources based on satellite SM products (retrievals).

RESEARCH OF INFLUENCE OF THE EARTH’S SUBSIDENCE OUTSIDE THE LOADS CONTOUR ON THE STABILITY OF THE HEIGHT POSITION OF THE POINTS OF LOCAL LEVELING NETWORKS

The influence of static loadings of the foundations of structures in the process of soil compaction of the base on the subsidence of the soil surface and the bench outside the loaded contour is considered in the work. The studies were performed on models of rectangular massive foundations using the method of equivalent soil layer, based on the theory of compaction of linear-deforming half-space. Using this method, the values of the average sedimentation of the models of rectangular foundations were calculated, taking into account all components of normal stresses and lateral soil extension. On the basis of the method of angular points of the equivalent layer, the values of subsidence of the soil surface outside the contour of the foundation models are calculated, depending on the distance from the contour of the foundation, the value of the average subsidence of the foundation and its parameters. To determine the areas of the soil surface most sensitive to the perception of static loads, lines of equal settlements of the soil surface outside the contour of the foundation models are constructed. On the basis of theoretical studies, probable magnitudes of sedimentation of soil benchmarks are calculated, depending on the subsidence of the soil surface and the distance from the contour of the foundation. The probable minimum distance from the contour of the structure to the places of laying of initial soil benchmarks is established to ensure the required accuracy of geodetic observations. The results of the conducted researches may find application in the design of geodetic observations of the settlements and deformations of the foundations of engineering structures and the choice of the locations of local level points.

Permeability Enhancement of Coal Seam by Lower Protective Layer Mining for Gas Outburst Prevention

Risk prediction of dynamic disasters such as rock burst, gas outburst, and water inrush is closely related to the permeability evolution of coal seam. According to the characteristics of the lower protective layer mining, the basic assumption of gas-solid coupling model of the coal was proposed in this paper. The permeability enhancement coefficient of equivalent layer spacing was first put forward. Based on the three-zone-shaped dynamic evolution of the permeability of the overlying protective layer during the lower protective layer mining, the theories of seepage mechanics and damage mechanics were applied to introduce the permeability enhancement coefficient of equivalent layer spacing. A mathematical model of permeability evolution of the protected coal seam in the lower protective layer mining was established. Based on the engineering background of the lower protective layer mining in Changping Coal Mine, the numerical simulation using the proposed mathematical model was performed. The results showed that the stress and permeability of the protected layer in #3 coal seam evolved dynamically with the advancement of the working face of the protective layer in #8 coal seam. When the working face of the protective layer in #8 coal seam advanced to 80 m, the stress reduction rate in the relief area tended to be stable, and the stress in the stress reduction area was about 50% of the original rock stress. When advanced to 80 m, the permeability of the protected layer of the #3 coal seam increased sharply, and the permeability increased by 873 times. With the continuous advancement, the permeability of the protected layer in #3 coal seam tended to increase steadily, and the permeability increased by 1100–1200 times. The calculated magnitude of permeability increment is consistent with that in the engineering practice, indicating that the permeability evolution model is basically reasonable. The research provides a theoretical guidance for the gas drainage field application in the lower protective layer mining for prevention of coal and gas outburst.

Subspace method for solving large-scale equivalent layer and density mapping problems

The equivalent layer technique explores an intrinsic property of potential fields that any observed field at the ground surface can be reconstituted from a fictitious continuous distribution at an arbitrary flat surface that is indistinguishable from the field of the true sources. This continuous distribution can be represented by a set of discrete cells of known position and size but unknown physical property by solving a linear system, with size proportional to the number of data points measured. The density distribution at the equivalent layer carries information about the true sources because it is a scaled and downward-continued version of the field generated by the true sources at the level that the geophysical survey was undertaken. The computation of this downward-continued field is unstable, and an equivalent source evaluation is constrained by the intense computational demand required to solve the associated large linear system. A new formulation is developed to directly solve large-scale gravity equivalent layer problems using a subspace representation for the unknown density distribution. This subspace basis is constructed by applying the singular value decomposition to the matrix containing the gridded data set. A procedure to diminish (by two orders of magnitude) the number of forward model evaluations is introduced by exploring the symmetry of the gravity kernel and its evaluation on a regular mesh. The density distribution at the equivalent layer is used to outline the spatial distribution of contrasting underlying sources, to discriminate regions with predominant positive or negative density contrast, and to estimate the mass excess or deficiency for sources with positive or negative density contrast. This technique is applied to determine density models for the Carajás airborne gravity survey and to analyze density distributions associated with banded iron formations and structures of the Carajás Mineral Province, Brazil, providing mass estimates for specific geologic unities.