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Airborne gravity gradient dynamic measurement error compensation is a crucial aspect of data processing in gravity gradient dynamic measurements. This study introduces a deep learning approach based on a residual backpropagation (Res-BP) neural network for post-error compensation in airborne gravity gradient dynamic measurement. The network employs residual connections to facilitate identity mapping, thereby enabling gradient propagation across layers. This strategy preserves the original information while acquiring additional information through nonlinear operations, effectively mitigating the gradient vanishing issue and enhancing the neural network's fitting capability. The method proposed in this paper is applied to both simulation data from a gravity gradiometer and high-altitude dynamic measured data of an airborne gravity gradient. Compared to traditional neural network multilayer perceptron, the Res-BP method significantly improves compensation accuracy through its application in high flight experiment of the southern section of Zhangguangcai Ridge on the western side of Mudanjiang City, Heilongjiang Province. [ABSTRACT FROM AUTHOR]

In this paper, we augment airborne gravity anomaly data from Antarctica, expanding the coverage area by 10.4% based on the existing data set. These data are combined with a gravity field model to establish a more comprehensive gravity anomaly database for Antarctica. Utilizing the Integral of Stokes Kernels' Derivatives (ISKD) method, we create the first 10 km resolution gravity gradient map in the Antarctic region. According to measured data in the McFaulds Lake (located in the James Bay lowlands of northern Ontario, Canada), the proposed method achieves a calculation accuracy with a standard deviation (Std.) of 3–7 E ( 1 E = 1 × 10 - 9 s - 2 ) in Txx , Tyy , Txy , Txz , Tyz , and 12.9 E in Tzz . The calculated gravity gradient effectively reveals density boundaries in Antarctica. This research lays the groundwork for future studies exploring the gravitational characteristics of Antarctica on a broader scale. [ABSTRACT FROM AUTHOR]

As gravity exploration technology advances, gravity gradient measurement is becoming an increasingly important method for gravity detection. Airborne gravity gradient measurement is widely used in fields such as resource exploration, mineral detection, and oil and gas exploration. However, the motion and attitude changes of the aircraft can significantly affect the measurement results. To reduce the impact of the dynamic environment on the accuracy of gravity gradient measurements, compensation algorithms and techniques have become a research focus. This paper proposes a post-error compensation algorithm using convolutional and long short-term memory neural networks (CNN-LSTMs). By leveraging convolution feature extraction capabilities and considering the temporal dependencies of dynamic measurement parameters with LSTM, the model demonstrates a stronger ability to learn from severely coupled time series data, resulting in a significant improvement in the compensation performance. This method outperforms traditional neural networks' multi-layer perceptrons (MLPs) in terms of compensation accuracy on both simulated and measured airborne gravity gradient data from Heilongjiang Province. [ABSTRACT FROM AUTHOR]

Accurate Digital Elevation Models (DEMs) are essential for precise terrain gravity field calculations, which are critical in gravity field modeling, airborne gravimeter and gradiometer calibration, and geophysical inversion. This study evaluates the accuracy of various satellite DEMs by comparing them with a LiDAR DEM at the Wudalianchi test site, a location requiring ultra-accurate terrain gravity fields. Major DEM error sources, particularly those related to vegetation, were identified and corrected using a least squares method that integrates canopy height, vegetation cover, NDVI, and airborne LiDAR DEM data. The impact of DEM vegetation errors on terrain gravity anomalies and gravity gradients was quantified using a partitioned adaptive gravity forward-modeling method at different measurement heights. The results indicate that the TanDEM-X DEM and AW3D30 DEM exhibit the highest vertical accuracy among the satellite DEMs evaluated in the Wudalianchi area. Vegetation significantly affects DEM accuracy, with vegetation-related errors causing an impact of approximately 0.17 mGal (RMS) on surface gravity anomalies. This effect is more pronounced in densely vegetated and volcanic regions. At 100 m above the surface and at an altitude of 1 km, vegetation height affects gravity anomalies by approximately 0.12 mGal and 0.07 mGal, respectively. Additionally, vegetation height impacts the vertical gravity gradient at 100 m above the surface by approximately 4.20 E (RMS), with errors up to 48.84 E over vegetation covered areas. The findings underscore the critical importance of using DEMs with vegetation errors removed for high-precision terrain gravity and gravity gradient modeling, particularly in applications such as airborne gravimeter and gradiometer calibration. [ABSTRACT FROM AUTHOR]

Boundary recognition visually delineates the horizontal extent of subsurface anomalies, providing a foundational basis for interpreting gravity data. Compared to gravity observations, gravity gradient data offers the benefits of multiple components and the enhancement of shortwave information in graphical representations. In our study, we investigated the delineation of geological structure boundaries in the lunar Oceanus Procellarum region using gravity gradient techniques. First, based on the observations from the Gravity Recovery and Interior Laboratory (GRAIL) mission, we obtained high-precision synthetic full tensor values of the gravity gradient as our primary research data. Moreover, to reduce curvature errors during large-scale terrain forward modeling, we applied the spherical prism of tesseroid to eliminate the effects of near-surface topography. Grounded on the Bouguer anomalies of gravity gradient, four distinct boundary recognition methods have been employed to explore the geological structure of the lunar Oceanus Procellarum region. It includes the Theta map method, the directional Theta map method, the combination of total horizontal derivative and the modulus of full tensor gravity gradient, and the improved edge detection method based on the Theta map method.The common feature of these methods is the utilization of the multi-component data combination from gravity gradient tensors, which can enhance the accuracy of edge detection. From the investigation results presented in the paper, we have found the following: 1) The improved edge detection method, based on the Theta map principle, enables better identification of the center of subsurface anomaly bodies during boundary recognition, utilizing a consistent single color in graphic displays. 2) According to the results of boundary recognition, numerous strip anomalies exist in the Oceanus Procellarum area that show less correlation with topographic relief. One possible explanation for these graphical anomalies of gravity gradient is that they serve as channels for the upwelling of mantle material during lunar evolution. [ABSTRACT FROM AUTHOR]

Compared to gravity method, the gravity gradient has multi-component advantages and can emphasize short wavelength features. By providing more detailed features in the image display, it could present a more accurate determination of the spatial distribution of the underling anomaly body. In our study, based on the gravity gradient data that was synthesized from the high-precision gravity model from Gravity Recovery and Interior Laboratory mission, we analyzed the tectonic structure of the Moon's shallow layers in Oceanus Procellarum region. Bouguer anomalies of gravity gradient are used for geological boundary recognition and three-dimensional density inversion. Theta Map method is adopted for the edge identification of geological structures. It fully utilizes the characteristics of multi-components combination of gravity gradient to sharpen the boundaries identification of abnormal bodies. During the density inversion, in order to decrease the non-unique solution problem, the depth weight constraint is added to the inversion equation. Furthermore, the method of wavelet coefficient compression and Least Squares QR-decomposition is applied to accelerate the inverse calculation of large ill-conditioned equations. According to the result illustration, we found that: 1) The combination of gravity tensors has a strong boundary recognition ability in the horizontal direction. There is close consistency with the results of density inversion. 2) Our study supports the expansion and intrusion hypothesis of lunar magma in the research zone of Oceanus Procellarum, since the distribution of density tomography results at different depths is higher than the normal assumed crust density of the Moon in the majority of areas. Moreover, the intrusion source in our research area is concentrated at a direction depth of 30–45 km below the mean lunar radius surface approximately. [ABSTRACT FROM AUTHOR]

The gravity and gradient anomalies contain valuable information about the underground geological structures at various depths. Deep and shallow buried source bodies are able to be identified through multi-scale field separation processes, and visual comprehensions of geological structures can be obtained via 3D density inversion techniques. In this study, we propose an improved 3D imaging strategy based on gravitational field separation using the preferential continuation filter. This strategy incorporates the relationship between spectral features and buried depths of source bodies, allowing for a one-step transformation from planar gravity and full-tensor gradient field observations to a 3D density structure in the wave-number domain. Synthetic tests validate the effectiveness and robustness of the gravity and gradient imaging approaches, highlighting their advantages in high vertical resolution and low computational requirements. Nonetheless, it should be noted that the imaging effects of horizontal gradients Γ x x and Γ y y are unsatisfactory due to their weak noise resistance. Thus, they are not suitable for real data applications. The other imaging approaches are further applied to recover the subsurface 3D density structure beneath the Weishan cone in Wudalianchi Volcanic Field, Northeastern China. Our results provide insights into the possible location and shape of the low-density magma chamber. Also, the potential presence of partial melts is inferred and supported from a gravity perspective. The primary advantage of these approaches is their ability to generate a reasonable geological model in scenarios with limited prior information and physical property constraints. As a result, they have significant practical value in the field of applied geophysics, including mineral exploration and volcanology studies. [ABSTRACT FROM AUTHOR]

Copyright of Journal of Geodesy & Geodynamics (1671-5942) is the property of Editorial Board Journal of Geodesy & Geodynamics and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Local gravity and magnetic anomalies are employed to identify potential hydrocarbon reservoirs in the Middle Kura Depression (MKD) within the South Caspian basin in Azerbaijan. The MKD basin in Azerbaijan including the Yevlakh-Agjabedi trough covers a large part of the Kura intermountain basin between the Greater and Lesser Caucasus. In the study region, several local gravity and magnetic anomalies are discovered related to oil and gas deposits in the sedimentary depression whose thickness is 12–14 km. Gravity minima and maxima expressed by different wavelength anomalies are indicative of density variations within the basin. Local gravity minima with an intensity of 0.3–0.4 mGal identified in the study areas are related to the oil–gas deposits. While the local positive magnetic anomalies are associated with the volcanic formations, local negative magnetic anomalies appear over the productive parts of the buried structure within the sedimentary complex. Intense local magnetic minima anomalies with an intensity of 20–30 nT are evidence of oil and gas accumulations. The limitations of traditional methods for interpreting gravity and magnetic data to locate oil and gas fields have led to the use of gravity field gradients. This alternative approach has proven advantageous, as it confirms the results of gravity exploration and is useful for directly searching for hydrocarbons. [ABSTRACT FROM AUTHOR]

The Semangko Fault (SF) is a major active fault that extends across from Aceh (in northern part) to Lampung Province (in southern part) of Sumatra Island, contributing to much deformation and high seismicity along the fault. The fault affects a pattern in the density of surrounding rocks and can be identified by the gravity method. This research aimed to determine the fault structure using gravity gradient analysis in the Lampung area. Bouguer anomalies were analyzed from satellite gravity data and gravity gradient calculation, for fault structure identification around SF. Based on the Bouguer anomalies and gravity gradient analysis (first and second-order horizontal derivatives), SF trends NW-SE. The SF is divided into two sides at the Suoh area, West and East SF sides across to Semangko Bay. That trend is confirmed with geological and topographical data analysis. These findings suggest that gravity anomaly data and horizontal gravity gradient analysis can be used to determine and identify the presence of the SF. The seismic hazard assessments can mitigate hazards to all people in the vicinity of the SF area.

It is acknowledged that a classical definition of the geoid-to-quasigeoid separation as a function of the simple planar Bouguer gravity anomaly is compatible with Helmert's definition of orthometric heights. According to Helmert, the mean actual gravity along the plumbline between the geoid and the topographic surface in the definition of orthometric height is computed approximately from the measured surface gravity by applying the Poincaré-Prey gravity reduction. This study provides theoretical proof and numerical evidence that this assumption is valid. We demonstrate that differences between the normal and (Helmert) orthometric corrections are equivalent to the geoid-to-quasigeoid separation differences computed for individual levelling segments. According to our theoretical estimates, maximum differences between these 2 quantities should be less than ±1 mm. By analogy, differences between the Molodensky normal and Helmert orthometric heights at levelling benchmarks should be equivalent to the geoid-to-quasigeoid separation computed from the Bouguer gravity data. Both theoretical findings are inspected numerically by using levelling and gravity data along selected closed levelling loops of the vertical control network in Hong Kong. Results show that values of the geoid-to-quasigeoid separation at levelling benchmarks differ less than ±0.1 mm from differences between the normal and orthometric corrections. Relatively large differences (slightly exceeding 2 mm) between values of the geoid-to-quasigeoid separation and differences between the normal and (Helmert) orthometric heights at levelling benchmarks are explained by errors in levelling measurements rather than by inconsistencies in computed values of the geoid-to-quasigeoid separation and (Helmert) orthometric correction. [ABSTRACT FROM AUTHOR]

The space assembly of two flexible beams by a dual-arm space robot is a typical assembly scenario to construct ultra-large space structure. Yet, previous studies mainly focused on the assembly of small structures, neglecting the influences of space perturbations. Two models are developed in this research to investigate the effects of space perturbations on the space assembly process of ultra-large space structures. Firstly, a theoretical modelling method is proposed based on quasi-static hypothesis and linear structural mechanics. The theoretical model can be utilized for analytically estimating the transverse and axial distributed forces of the flexible beams, structural vibrations, and the control moments of the space robot. An orbit–attitude–structure coupled simulation model is then established to validate the theoretical model and study the dynamic behaviours more accurately, using absolute nodal coordinate formulation and natural coordinate formulation. Finally, the effects of the attitude angle, orbital radius, and lengths of beams on the dynamic responses during assembly are investigated. Theoretical and simulation results show that the control moments and structural vibration amplitude increase dramatically with the length of the beams. The effects of Coriolis force and gravity gradient must be considered for ultra-large space structures during assembly, otherwise the control moments and structural vibrations would be substantially underestimated. The results are instructive to the assembly strategy design as well as modular component design of ultra-large space structures. [ABSTRACT FROM AUTHOR]

Copyright of Journal of Geodesy & Geodynamics (1671-5942) is the property of Editorial Board Journal of Geodesy & Geodynamics and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Purpose: Large sun-facing deployable appendages are widely used in ultra-large spacecrafts. The effects of gravity gradient on the dynamic characteristics are always neglected due to the small size of traditional spacecrafts. Therefore, the dynamics of an axially deployable large flexible sun-facing spacecraft under gravity gradient are studied in this paper. Methods: Firstly, the extended Hamilton's principle is utilized to derive the transverse vibration equations of the deployable appendages under a floating coordinate frame. Two kinds of deployment strategies including constant-speed deployment and practical deployment are considered. Then, the assumed mode method and Galerkin's method are adopted to solve the governing equations. Finally, the numerical results of transverse vibration are obtained by using the symplectic Runge–Kutta method. Results: With the decrease of deploying time, the amplitude of flexible vibration decreases in the deploying process but increases in the long-time evolution for the two deploying strategies. Meanwhile, the higher orbital altitude leads to a lower vibration amplitude. In addition, the practical deploying strategy will lead to larger displacement than the constant deploying strategy even though it can avoid speed residual automatically. Conclusions: The results show that the gravity gradient force has a significant influence on the transverse vibration both in the deployment process and the long-time evolution. The results will provide constructive guidance for vibration control. [ABSTRACT FROM AUTHOR]

One of the main applications of the gravity field and steady-state Ocean Circulation Explorer (GOCE) satellite data is their combination with local gravity anomalies for geoid and gravity field modeling purposes. The aim of the present paper was the determination of an improved geoid model for the wider Hellenic area, using original GOCE SGG data filtered to retain only useful signals inside the measurement bandwidth (MBW) of the satellite. The filtered SGGs, originally at the satellite altitude, were projected to a mean orbit (MO) and then downward continued to the Earth's surface (ES) in order to be combined with local gravity anomalies. For the projection to an MO, grids of disturbing gravity gradients from a global geopotential model (GGM) were used, computed per 1 km from the maximum satellite altitude to that of the MO. The downward continuation process was then undertaken using an iterative Monte Carlo (MC) simulated annealing method with GGM gravity anomalies on the ES used as ground truth data. The final geoid model over the wider Hellenic area was estimated, employing the remove–compute–restore method and both Fast Fourier Transform (FFT) and Least Squares Collocation (LSC). Gravity-only, GOCE-only and combined models using local gravity and GOCE data were determined and evaluation of the results was carried out against available GNSS/levelling data in the study area. From the results achieved, it was concluded that even when FFT is used, so that a combined grid of local gravity and GOCE data is used, improvements to the differences regarding GNSS/levelling data by 14.53% to 27.78% can be achieved. The geoid determination with LSC was focused on three different areas over Greece, with different characteristics in the topography and gravity variability. From these results, improvements from 14.73%, for the well-surveyed local data of Thessaly, to 32.88%, over the mountainous area of Pindos, and 57.10% for the island of Crete for 57.10% were found. [ABSTRACT FROM AUTHOR]

In preparing gravity gradient reference maps for navigation purposes, researchers have tended to use a constant value for the density of seawater. However, the actual seawater density at a particular location may vary due to the effects of longitude, latitude and bathymetry. In this study, the right rectangular prism method was used to calculate the disturbing gravity gradient caused by the mass deficiency of seawater for three different seawater profiles in an area east of Taiwan. For this purpose, two seawater density models were used as alternatives to the constant seawater density model, and the alteration in the gravity gradient was calculated to quantify the error in the gravity gradient as a result of using a constant seawater density. The results demonstrated that the error in the gravity gradient can reach 1E for water at large depths. Moreover, the difference between the amplitude of the error of the corrected thermocline and that for the uncorrected seawater density model was found to be quite small. If a gravity gradient reference map with accuracy better than 1E is to be realized, the seawater density cannot be taken as constant during forward modeling. [ABSTRACT FROM AUTHOR]

Accurate and highly precise gravity gradient data are an important component of, for example, gravity field modeling, seabed topography inversion, and resource exploration. However, high-precision gravity gradient data are difficult to obtain. To address this difficulty, this work introduces the Fourier series expansion method to the modeling of gravity gradient fields. Based on gravity anomalies, the analytic expressions of the gravity gradient tensors have been deduced, which provides a new mathematical method for obtaining gravity gradient data. The expression's derivation and verification processes are as follows. First, these analytic expressions for inverting the gravity gradient based on gravity anomaly data are derived according to the Laplace equation, the boundary value conditions of spherical approximation, and the Fourier series expansion method. Then, global 1' × 1' gravity field data provided by UCSD are used to verify the accuracy of these formulas. Finally, the results are analyzed. The experimental results show that the results obtained based on this inversion formula can sufficiently show the details of gravity gradient changes. The formulas derived in this paper have good computational efficiency in the inversion of regional gravity gradients and provide a new mathematical method for gravity gradient data acquisition. [ABSTRACT FROM AUTHOR]

Copyright of Piezoelectrics & Acoustooptics is the property of Piezoelectric & Acoustooptic and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

The Semangko Fault (SF) is a major active fault that extends across from Aceh (in northern part) to Lampung Province (in southern part) of Sumatra Island, contributing to much deformation and high seismicity along the fault. The fault affects a pattern in the density of surrounding rocks and can be identified by the gravity method. This research aimed to determine the fault structure using gravity gradient analysis in the Lampung area. Bouguer anomalies were analyzed from satellite gravity data and gravity gradient calculation, for fault structure identification around SF. Based on the Bouguer anomalies and gravity gradient analysis (first and second-order horizontal derivatives), SF trends NW-SE. The SF is divided into two sides at the Suoh area, West and East SF sides across to Semangko Bay. That trend is confirmed with geological and topographical data analysis. These findings suggest that gravity anomaly data and horizontal gravity gradient analysis can be used to determine and identify the presence of the SF. The seismic hazard assessments can mitigate hazards to all people in the vicinity of the SF area. [ABSTRACT FROM AUTHOR]

The gravity gradient microsatellite applied to the exploration of space environment is subject to the problem of orbital transfer between two orbits. The contributions of this paper mainly include two aspects: (1) a segmented optimal trajectory and (2) the piecewise terminal tracking control method. In order to achieve orbital transfer between two coplanar orbits, an optimal controller is designed to obtain a segmented optimal trajectory and then it becomes a problem of attitude tracking in different segments. Compared with traditional finite‐time control methods, the adaptive sliding mode control method based on a finite‐time tracking error function is proposed, and the stability and robustness of the system can be guaranteed. A numerical case between two coplanar orbits is studied to validate the effectiveness of the control method. [ABSTRACT FROM AUTHOR]

The gravity gradient is a secondary derivative of gravity potential, containing more high-frequency information of Earth's gravity field. Gravity gradient observation data require deducting its prior and intrinsic parts to obtain more variational information. A model generated from a topographic surface database is more appropriate to represent gradiometric effects derived from near-surface mass, as other kinds of data can hardly reach the spatial resolution requirement. The rectangle prism method, namely an analytic integration of Newtonian potential integrals, is a reliable and commonly used approach to modeling gravity gradient, whereas its computing efficiency is extremely low. A modified rectangle prism method and a graphical processing unit (GPU) parallel algorithm were proposed to speed up the modeling process. The modified method avoided massive redundant computations by deforming formulas according to the symmetries of prisms' integral regions, and the proposed algorithm parallelized this method's computing process. The parallel algorithm was compared with a conventional serial algorithm using 1″ elevation data in two topographic areas (rough and moderate terrain). Modeling differences between the two algorithms were less than 0.1 E, which is attributed to precision differences between single-precision and double-precision float numbers. The parallel algorithm showed computational efficiency approximately 200 times higher than the serial algorithm in experiments, demonstrating its effective speeding up in the modeling process. Further analysis indicates that both the modified method and computational parallelism through GPU contributed to the proposed algorithm's performances in experiments.

Gravity survey is an effective method for determining density variations and geological structure features. In most cases, techniques for transforming gravity data into other gravity components and their gradients, such as the equivalent-source method, are widely used to accurately delineate subsurface geological objects. Nevertheless, the traditional single-layer equivalent-source technique generates large transform errors at altitudes far from the observation surface, due to the discrete observation stations and their limited regions. We present an equivalent-source method in which the equivalent-source system consists of two layers rather than one layer. The first layer is placed near the surface of the Earth, which is similar to that in the traditional equivalent-source method, and the second layer is placed at a certain depth and used for the simulation of the long-wavelength gravity anomaly of deep sources. The depth of the deep layer can be estimated by the spectrum analysis of the observed data. The verification of the proposed method on the synthetic data demonstrates that the dual-layer model can generate three gravity components and six gradients with high accuracy and can rebuild the regional field better than the single-layer method in transformation and upward continuation. Furthermore, the proposed method can predict the gravity vector and full gradient tensors with high precision on their observed points. Real data from the Barkol Basin, Xinjiang, China, are used to transform the gravity gradients from observed gravity anomaly data to provide abundant gravity field information for further research in geology. [ABSTRACT FROM AUTHOR]

Airborne gravity gradient data contain additional short-wavelength information about the buried geological bodies. This study develops a fast interpretation method based on the gravity gradient data for the sources' spatial location and physical property parameters. This study analyzes the advantages of the source parameter inversion method based on tensor invariants. It proposes a normalized fast-imaging method based on tensor invariants to quickly estimate the spatial location parameters of sources through the local maximum value position of the imaging results. First, the tensor invariant characteristics and the imaging method's effect in a simple model are analyzed using a theoretical model. Second, to analyze the imaging method's application eff ect in complex model conditions, the method's applicability is quantitatively analyzed using the data added with noise, superimposed anomalies of adjacent sources, and anomalies of deep and shallow geological bodies. The theoretical model's simulation results show that the model's imaging results in this study have satisfactory performance on the spatial position estimation of the sources. Finally, the method is applied to the gravity anomaly data corresponding to the Humble salt dome. The imaging results can effectively estimate the distribution of the salt dome's horizontal and depths, verifying the practicability of the method. [ABSTRACT FROM AUTHOR]

Combined Global Gravitational Models (GGMs) are being used in numerous geoscience applications, most notably for gravimetric geoid modeling (in geodesy) and for geological mapping and geophysical explorations (in the Earth’s sciences). The aim of this study is to evaluate the suitability of different combined GGMs that could be used for the geological mapping of middle belt region and Southeastern Nigeria. For this purpose, we digitized geological maps of Afikpo and Anambra Basins to evaluate geological signatures implied by gravity field quantities (Bouguer gravity anomalies and vertical gravity gradient) derived from the EGM2008, EIGEN-6C4, GECO, SGG-UGM-1 and XGM2019e_2159 gravitational models. We also stochastically evaluated the performance of these GGMs by computing their Root-Mean-Square (RMS) fit with ground-based gravity measurements. The results show that the EIGEN-6C4 and XGM2019e_2159 models have the best RMS fit with the ground-based gravity data. A spatial pattern in Bouguer gravity maps (compiled using these two models) generally closely agrees with a geological configuration of the basins, while also exhibiting some more detailed geological features. Interestingly, however, despite the XGM2019e has the best fit and better mimics major geological features, the gravity image from this model does not exhibit a sediment signature in a portion of the Afikpo basin. A possible reason is that the topographic information used to recover a higher-frequency gravity spectrum of this model might suppress a gravitational signature of subsurface density structures. A comprehensive interpretation of geological features thus requires a careful analysis of existing GGMs, terrestrial gravity data as well as all other reliable geological and geophysical information.

Combined Global Gravitational Models (GGMs) are being used in numerous geoscience applications, most notably for gravimetric geoid modeling (in geodesy) and for geological mapping and geophysical explorations (in the Earth's sciences). The aim of this study is to evaluate the suitability of different combined GGMs that could be used for the geological mapping of middle belt region and Southeastern Nigeria. For this purpose, we digitized geological maps of Afikpo and Anambra Basins to evaluate geological signatures implied by gravity field quantities (Bouguer gravity anomalies and vertical gravity gradient) derived from the EGM2008, EIGEN-6C4, GECO, SGG-UGM-1 and XGM2019e_2159 gravitational models. We also stochastically evaluated the performance of these GGMs by computing their Root-Mean-Square (RMS) fit with ground-based gravity measurements. The results show that the EIGEN-6C4 and XGM2019e_2159 models have the best RMS fit with the ground-based gravity data. A spatial pattern in Bouguer gravity maps (compiled using these two models) generally closely agrees with a geological configuration of the basins, while also exhibiting some more detailed geological features. Interestingly, however, despite the XGM2019e has the best fit and better mimics major geological features, the gravity image from this model does not exhibit a sediment signature in a portion of the Afikpo basin. A possible reason is that the topographic information used to recover a higher-frequency gravity spectrum of this model might suppress a gravitational signature of subsurface density structures. A comprehensive interpretation of geological features thus requires a careful analysis of existing GGMs, terrestrial gravity data as well as all other reliable geological and geophysical information. [ABSTRACT FROM AUTHOR]

In this study, a new approach for the computation of coseismic gravity gradient changes in a spherically symmetric Earth model is presented. We derived the mathematical expressions of gravity gradient changes based on the Green's functions for four independent seismic sources. The results obtained from numerical computations and those calculated using the flat‐Earth model are in good agreement within a near field, verifying that our computing scheme is valid, while the differences in the far field show the advantages of the spherical model. Furthermore, the proposed method was applied to analyze the coseismic gravity gradient changes caused by the 2011 Tohoku‐Oki earthquake. The theoretical gravity gradient changes agree well with the Gravity Recovery and Climate Experiment observations, indicating that the proposed dislocation theory is important and can be used to efficiently interpret seismic deformations. In addition, the contribution of seawater was discussed. Plain Language Summary: Earthquakes are accompanied by surface displacements, gravity, and strain changes which can be calculated by solving a set of fundamental equations based on a specific Earth model. This theoretical method to calculate the seismic deformation is called dislocation theory. Mass redistributions inside the Earth caused by subduction zone earthquakes can be detected by the gravity satellite in the form of gravity changes or gravity gradient changes. For precisely calculating gravity gradient changes due to an earthquake, we proposed a method to compute such changes in a spherical symmetric Earth model based on the Green's functions for four types of seismic source models. Comparison of the results calculated by our approach to the results calculated based on flat‐space model indicates the validity of our method. Besides, we applied the theoretical calculation to the 2011 Tohoku‐Oki earthquake to interpret the observation results of gravity satellite. Our study provides a new perspective on the studies of the Earth deformations and for effectively verifying and interpreting the results of geodetic observations. Furthermore, its use will enable more accurate inversions of seismic fault slip models. Key Points: The dislocation theory for gravity gradient changes based on a spherical Earth model is proposed in this studyThe gravity gradient changes due to solid Earth deformation and seawater redistribution are almost equivalentGravity Recovery and Climate Experiment‐observed gravity gradient changes for the 2011 Tohoku‐Oki earthquake can be explained well with our method [ABSTRACT FROM AUTHOR]

The determination of the calibration parameters of the gravity gradiometer play an important role in the GOCE gravity gradient data processing. In this paper, the temporal signals and outliers in the GOCE gravity gradient observations are analyzed. Based on the different global gravity field models, the scale factors and biases are determined in all the components of GOCE gravity gradients. And then the accuracy of the calibration results is validated. The results indicated that the effect of the ocean tide is at mE magnitude in the measurement band, which is equivalent to the precision of the gravity gradiometer, while the effect of the non-tide temporal signals, such as terrestrial water is in the order of 10 -4E, is slightly less than that of the ocean tide. The outliers in all the gravity gradient components are larger than 0.2%. And after the calibration using global gravity field models except EGM96, the stability of scale factors in the Vxx、Vyy、Vzz、Vyz components reaches 10 -4 magnitude, and the Vxz component reaches 10 -5 while that of the Vxy component is about 10 -2, which are in accordance with the accuracy differences of the gradient components.

Swarm intelligence method is an effective way to improve the particle degradation and sample depletion of the traditional particle filter. This paper proposes a particle filer based on the gravitation field algorithm (GF-PF), and the gravitation field algorithm is introduced into the resampling process to improve particle degradation and sample depletion. The gravitation field algorithm simulates the solar nebular disk model, and introduces the virtual central attractive force and virtual rotation repulsion force between particles. The particles are moves rapidly to the high-likelihood region under action of the virtual central attractive force. The virtual rotation repulsion force makes the particles keep a certain distance from each other. These operations improve estimation performance, avoid overlapping of particles and maintain the diversity of particles. The proposed method is applied into INS/gravity gradient aided navigation, by combining the sea experimental data of an inertial navigation system. Compared with the particle swarm optimization particle filter(PSO-PF) and artificial physics optimized particle filter (APO-PF), the GF-PF has higher position estimate accuracy and faster convergence speed with the same experimental conditions.

The continuous uplift and evolution of the Qinghai‐Tibet Plateau region (TPR) represents one of the most important Cenozoic geological events on Earth. The deformation mechanism of the lithosphere in the TPR is still under debate. Relevant viewpoints can be informed by investigations of the lithospheric density structure in the Qinghai‐Tibet Plateau and surrounding regions (TP‐SRs). Considering investigating the fine‐scale lithospheric density structure of the large‐scale areas, the GOCE satellite data covering entire TP‐SRs are used in this study. GOCE gravity gradient data are first subjected to several corrections. Then, based on gravity gradient curvature (SI) calculation complemented with the preconditioned conjugate gradient algorithm, the distribution of SI and the lithospheric density structure at depths of 0–80 km in TP‐SRs are obtained. The effects of temperature differences and material composition on the lithospheric density distribution are further distinguished. The results show that in the crust, the density anomalies in the TPR are blocked by the surrounding hard blocks. In the upper mantle, the distribution of the density anomalies in the TPR is predominantly affected by the northward subduction of the Indian Plate and the high heat flux environment. The Longmen Shan Thrust Belt is found to have penetrated the lower crust but has not reached the depth of the upper mantle. The density anomalies in the basins on the northern side of the TPR exhibit features indicative of independent stable blocks. Key Points: Gravity gradient inversion coupled with curvature calculation are used to investigate the fine‐scale density structure of the lithosphereThe effects of temperature differences and material composition on the lithospheric density distribution are further distinguishedThe anomalous gravity gradient effect resulting from the uncertainty of the Moho layer depth is considered and assessed [ABSTRACT FROM AUTHOR]

In this paper, relative orbit and attitude adaptive controllers are integrated to perform roto-translational maneuvers for CubeSats equipped with a Drag Maneuvering Device (DMD). The DMD enables the host CubeSat with modulation of aerodynamic forces/torques and gravity gradient torque. Adaptive controllers for independent orbital and attitude maneuvers are revisited to account for traslational-attitude coupling while compensating for uncertainty in parameters such as atmospheric density, drag/lift coefficients, location of the Center of Mass (CoM) and inertia matrix. Uniformly ultimately bounded convergence of the attitude error and relative orbit states is guaranteed by Lyapunov-based stability analysis for the integrated roto-translational maneuver. A simulation example of an along-track formation maneuver between two CubeSats with simultaneous attitude control using only environmental forces and torques is presented to validate the controller. [ABSTRACT FROM AUTHOR]

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The article considers a new design option of a vertical gravity gradiometer. The main idea is to use a height-separated test mass and float, stiffly connected to each other and placed in a fluid, and the weight of the system is balanced by the buoyance force. Changing the gravity gradient results in small movement of the system, which is connected to the body by a soft spring. When measured by a sensor, this movement contains information about the gradient value. Despite the external simplicity of the idea, its implementation is quite difficult due to the influence of temperature variations. We discuss four options for creating the device, which demonstrate the fundamental possibility of implementing a measuring device with a resolution of hundredths to tenths of an eotvos. [ABSTRACT FROM AUTHOR]

Abstract Areas with sharp spatial changes in crustal structure are usually considered prone to strong earthquakes, especially late Cenozoic structural zones. However, quantitative relationships have not been established between the occurrence of earthquakes and the extent to which the crustal structure changes. The crustal structure can be reflected by gravity anomalies. In this study, we investigate the crustal structure variation in the eastern Tibetan Plateau based on the gravity data acquired by the Gravity field and steady‐state Ocean Circulation Explorer satellite. The multiscales wavelet decomposition and power spectrum methods are used to analyze the spatial variation of crustal structure at different depths. Based on a fourth‐order wavelet map, four variable factors are constructed to represent the spatial variations of the crustal structure, and their statistical relationship with earthquakes is studied. The results show that the changing rate of the gravity anomalies is significantly positively correlated with the occurrence of earthquakes. Areas of high earthquake hazards are places where the gravity field changes dramatically, usually with a value of 11°–18° for the SLP (slope) index. The assessment efficiency of the SLP increases with the earthquake magnitude. According to the SLP index, several regions are assessed to have a high level of risk for strong earthquakes in the eastern Tibetan Plateau, including the Longmenshan Fault belt, where a Ms8.0 earthquake occurred in 2008, thus demonstrating the promising implications of our method in the earthquake susceptibility assessment.

Gravity gradient plays an important role in many fields of science, and many methods are used to achieve the measurement of it. To improve measurement accuracy, various error analyses have been conducted in previous studies about positioning and orientation errors and system noise, among others. However, knowledge on the influence of omission errors from the theoretical models of gravity gradient measurement is limited. In this paper, we investigated omission errors in gravity gradient measurement, which was accomplished with the principle of differential acceleration. First, we determined the source of the omission errors to be the omission of high-order terms. Second, we calculated these terms on the basis of the Earth Gravitational Model 2008. Specifically, the expression of the partial derivative of the high order for the gravity potential in the spherical coordinates and the recursive equations for the high-order partial derivatives of the Legendre function were derived. Moreover, we transformed these high-order terms from the spherical coordinate system to the local north-oriented frame. The analysis led to three findings. First, a positive correlation was found between the omission errors and the distance between two measuring points. Second, the influences of the omission errors varied across different regions. Third, $\Gamma _{zz} $ was the least affected by the omission errors among the components $\Gamma _{xz} $ , $\Gamma _{yz} $ , and $\Gamma _{zz} $ . In conclusion, our study demonstrates that omission errors affect gravity gradient measurement.

We compile the GOCE-only satellite model GOSG01S complete to spherical harmonic degree of 220 using Satellite Gravity Gradiometry (SGG) data and the Satellite-to-Satellite Tracking (SST) observations along the GOCE orbit based on applying a least-squares analysis. The diagonal components (Vxx, Vyy, Vzz) of the gravitational gradient tensor are used to form the system of observation equations with the band-pass ARMA filter. The point-wise acceleration observations (ax, ay, az) along the orbit are used to form the system of observation equations up to the maximum spherical harmonic degree/order 130. The analysis of spectral accuracy characteristics of the newly derived gravitational model GOSG01S and the existing models GOTIM04S, GODIR04S, GOSPW04S and JYY_GOCE02S based on their comparison with the ultra-high degree model EIGEN-6C2 reveals a significant consistency at the spectral window approximately between 80 and 190 due to the same period SGG data used to compile these models. The GOCE related satellite gravity models GOSG01S, GOTIM05S, GODIR05S, GOTIM04S, GODIR04S, GOSPW04S, JYY_GOCE02S, EIGEN-6C2 and EGM2008 are also validated by using GPS-leveling data in China and USA. According to the truncation at degree 200, the statistic results show that all GGMs have very similar differences at GPS-leveling points in USA, and all GOCE related gravity models have better performance than EGM2008 in China. This suggests that all these models provide much more information on the gravity field than EGM2008 in areas with low terrestrial gravity coverage. And STDs of height anomaly differences in China for the selected truncation degrees show that GOCE has improved the accuracy of the global models beyond degree 90 and the accuracies of the models improve from 24 cm to 16 cm. STDs of geoid height differences in USA show that GOSG01S model has best consistency comparing with GPS-leveling data for the frequency band of the degree between 20 and 160.

The problem of the magnetic attitude tracking control is studied for a gravity gradient microsatellite in orbital transfer. The contributions of the work are mainly shown in two aspects: (1) the design of an expected attitude trajectory; (2) a method of the magnetic attitude tracking control. In orbital transfer, the gravity gradient microsatellite under a constant thrust shows complicated dynamic behaviours. In order to damp out the pendular motion, the gravity gradient microsatellite is subject to the the attitude tracking problem. An expected attitude trajectory is designed based on dynamic characteristics revealed in the paper, which not only ensures the flight safety of the system, but also reduces the energy consumption of the controller. Besides, the control torque produced by a magnetorquer is constrained to lie in a two-dimensional plane orthogonal to the magnetic field, so an auxiliary compensator is proposed to improve the control performance, which is different from existing magnetic control methods. In addition, a sliding mode control based on the compensator is presented, and the Lyapunov stability analysis is performed to show the global convergence of the tracking error. Finally, a numerical case of the gravity gradient microsatellite is studied to demonstrate the effectiveness of the proposed tracking control. [ABSTRACT FROM AUTHOR]

This article analyzes and controls the quasi-periodic attitude motion of a gravity-gradient stabilized spacecraft in eccentric orbit by way of system states augmentation, Lyapunov-Floquet transformation and normal forms simplification. Perturbing torques in the ambient space environment can be shown to engender spacecraft attitude motion represented by nonlinear dynamics coupled in the roll-yaw axes; and, uncoupled planar dynamics in the pitch axis. The non-planar dynamics equations are homogeneous and analytically solvable. However, the pitch attitude motion is nonlinear, possesses parameter-varying coefficients and is subjected to external periodic excitations. Consequently, we transform the unwieldy attitude dynamics into relatively more amenable schemes for analysis and control law synthesis. Subsequently, we demonstrate the implementation of linear and nonlinear control laws (i.e. bifurcation and sliding mode control laws) on the relatively acquiescent transformed attitude dynamics. By employing a two-pronged approach, the quasi-periodic planar motion is independently shown to be stabilizable via the nonlinear control approaches. [ABSTRACT FROM AUTHOR]

Copyright of Hydrographic Surveying & Charting / Haiyang Cehui is the property of Hydrographic Surveying & Charting Editorial Board and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Natural density variations in the near surface soil (i.e. the top 5 m) cause variations in the values recorded by geophysical surveys undertaken with gravity instruments. Whilst this 'soil noise' is too small to be noticeable with current instruments (e.g. Scintrex CG-5 and CG-6), the future use of more accurate instruments such as quantum technology gravity sensors, especially if used in a gradiometer configuration makes this noise source more significant and in need of characterisation and quantification. This paper reviews the magnitude and distribution of density variations in the near surface using data from the British Geological Survey (BGS) national geotechnical properties database which is then used to quantify the effect on practical gravity measurements in computer simulations. The desk study identified that the scale of density variation in the near surface was typically within a range of 600–900 kg/m3, and showed no obvious relationship with underlying geology, superficial deposits or depth below the surface. The distribution of density varied, from normally distributed to between normal and uniform or bimodal distributions. The forward modelled computer simulations showed a significant impact on the measurements of gravity if new instruments can reach greater levels of accuracy, especially for gravity gradient instruments. Analysing possible methods of suppressing this noise source through the design of gravity gradient instruments showed that, although increasing the height of the instrument above the ground is almost twice as effective at decreasing the scale of the soil noise, increasing the sensor vertical spacing may be the preferred option. This is due to relaxed sensitivity requirements on the new sensors and the preservation of the noise in shorter signal wavelength bands than the targets of interest, which not only reduces the cases of mistaken features of interest but also provides the possibility of spatial filtering to be used in order to enhance the signals from targets of interest. • Natural soil density variation which creates noise on gravity and gravity gradient readings is quantified • Desk study showed density variation follows a random normal distribution and varies on a scale of less than a few meters • Computer simulations showed the noise is significant, especially for gravity gradient instruments • Investigation of noise reduction found the preferred solution is to increase the spacing between the top and bottom sensors [ABSTRACT FROM AUTHOR]