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Keywords = vertical gravity gradient anomaly

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18 pages, 10026 KiB  
Article
Marine Gravity Field Modeling Using SWOT Altimetry Data in South China Sea
by Zejie Tu, Tao Jiang and Fuxi Zhao
J. Mar. Sci. Eng. 2025, 13(5), 827; https://doi.org/10.3390/jmse13050827 - 22 Apr 2025
Viewed by 731
Abstract
The Surface Water and Ocean Topography (SWOT) satellite delivers an unprecedented spatial resolution, offering new opportunities for advanced marine gravity field modeling. This study investigates the application of SWOT observational data by computing deflections of the vertical (DOVs) using the eight-directional geoid gradient [...] Read more.
The Surface Water and Ocean Topography (SWOT) satellite delivers an unprecedented spatial resolution, offering new opportunities for advanced marine gravity field modeling. This study investigates the application of SWOT observational data by computing deflections of the vertical (DOVs) using the eight-directional geoid gradient method, followed by gravity field inversion through the inverse Vening–Meinesz (IVM) formula. Experimental results in the South China Sea region demonstrate that SWOT DOVs, based on 19 observation cycles, achieved accuracies of 0.86 arcseconds for the east–west component η and 0.77 arcseconds for the north–south component ξ. The marine gravity field inversion accuracy reached 4.97 mGal, comparable to the multi-source altimetry-derived model SIO_v32.1. Further analysis reveals that the primary contributions of SWOT DOVs are observed within the 3.5–20 km wavelength band, with cross-track systematic errors identified as the key factor influencing both DOV calculations and gravity anomaly inversion. Additionally, extending the SWOT observation period enhances DOV accuracy, particularly for the η. These findings highlight the potential of SWOT data in advancing high-resolution marine gravity field modeling. Full article
(This article belongs to the Section Physical Oceanography)
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18 pages, 3055 KiB  
Article
Efficiency of Optimized Approaches for Gravity Operator Modeling
by David Fuseau, Lucia Seoane, Guillaume Ramillien, José Darrozes, Bastien Plazolles, Didier Rouxel, Thierry Schmitt and Corinne Salaün
Remote Sens. 2024, 16(21), 4031; https://doi.org/10.3390/rs16214031 - 30 Oct 2024
Viewed by 949
Abstract
Numerical tesseroid and radial-type approaches are presented and compared in terms of their efficiency for deriving the regional geoid height, vertical gravity, and gradiometric anomalies from sea floor topography grids. The vertical gradient function is particularly suitable for representing shorter wavelengths of gravity, [...] Read more.
Numerical tesseroid and radial-type approaches are presented and compared in terms of their efficiency for deriving the regional geoid height, vertical gravity, and gradiometric anomalies from sea floor topography grids. The vertical gradient function is particularly suitable for representing shorter wavelengths of gravity, typically less than 10 km. These two modeling methods were applied to the Great Meteor guyot in the Atlantic Ocean using its bathymetry. To optimize the computation of high-resolution gravity anomalies, the Armadillo, GSL, and OpenMP libraries were used to provide an environment for fast vector implementation, numerical integration for tesseroid calculation, and parallelization for loop iterations, resulting in a computation speed increase. The tesseroid and radial methods remain equivalent up to a resolution of about 1 min, with the radial method being faster when dealing with a large number of model points for the geoid. Aside from optimization enabling high-resolution gravity simulations, these fast modeling data can be used as the main operators in gravimetric inversion or to reduce the terrain effects in gravity observations, revealing gravity and sedimentary layers. Full article
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18 pages, 3251 KiB  
Article
Impacts of Digital Elevation Model Elevation Error on Terrain Gravity Field Calculations: A Case Study in the Wudalianchi Airborne Gravity Gradiometer Test Site, China
by Lehan Wang, Meng Yang, Zhiyong Huang, Wei Feng, Xingyuan Yan and Min Zhong
Remote Sens. 2024, 16(21), 3948; https://doi.org/10.3390/rs16213948 - 23 Oct 2024
Cited by 1 | Viewed by 1900
Abstract
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 [...] Read more.
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. Full article
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16 pages, 2025 KiB  
Article
A G-Modified Helmholtz Equation with New Expansions for the Earth’s Disturbing Gravitational Potential, Its Functionals and the Study of Isogravitational Surfaces
by Gerassimos Manoussakis
AppliedMath 2024, 4(2), 580-595; https://doi.org/10.3390/appliedmath4020032 - 4 May 2024
Viewed by 1705
Abstract
The G-modified Helmholtz equation is a partial differential equation that enables us to express gravity intensity g as a series of spherical harmonics having radial distance r in irrational powers. The Laplace equation in three-dimensional space (in Cartesian coordinates, is the sum of [...] Read more.
The G-modified Helmholtz equation is a partial differential equation that enables us to express gravity intensity g as a series of spherical harmonics having radial distance r in irrational powers. The Laplace equation in three-dimensional space (in Cartesian coordinates, is the sum of the second-order partial derivatives of the unknown quantity equal to zero) is used to express the Earth’s gravity potential (disturbing and normal potential) in order to represent other useful quantities—which are also known as functionals of the disturbing potential—such as gravity disturbance, gravity anomaly, and geoid undulation as a series of spherical harmonics. We demonstrate that by using the G-modified Helmholtz equation, not only gravity intensity but also disturbing potential and its functionals can be expressed as a series of spherical harmonics. Having gravity intensity represented as a series of spherical harmonics allows us to create new Global Gravity Models. Furthermore, a more detailed examination of the Earth’s isogravitational surfaces is conducted. Finally, we tabulate our results, which makes it clear that new Global Gravity Models for gravity intensity g will be very useful for many geophysical and geodetic applications. Full article
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18 pages, 3415 KiB  
Article
Improved Approaches for 3D Gravity and Gradient Imaging Based on Potential Field Separation: Application to the Magma Chamber in Wudalianchi Volcanic Field, Northeastern China
by Weikai Li, Meng Yang, Wei Feng and Min Zhong
Remote Sens. 2024, 16(7), 1187; https://doi.org/10.3390/rs16071187 - 28 Mar 2024
Cited by 2 | Viewed by 1776
Abstract
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 [...] Read more.
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 Γxx and Γyy 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. Full article
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21 pages, 15023 KiB  
Article
Expected Precision of Gravity Gradient Recovered from Ka-Band Radar Interferometer Observations and Impact of Instrument Errors
by Hengyang Guo, Xiaoyun Wan, Fei Wang and Song Tian
Remote Sens. 2024, 16(3), 576; https://doi.org/10.3390/rs16030576 - 2 Feb 2024
Cited by 1 | Viewed by 1874
Abstract
Full tensor of gravity gradients contains extremely large amounts of information, which is one of the most important sources for research on recovery seafloor topography and underwater matching navigation. The calculation and accuracy of the full tensor of gravity gradients are worth studying. [...] Read more.
Full tensor of gravity gradients contains extremely large amounts of information, which is one of the most important sources for research on recovery seafloor topography and underwater matching navigation. The calculation and accuracy of the full tensor of gravity gradients are worth studying. The Ka-band interferometric radar altimeter (KaRIn) of surface water and ocean topography (SWOT) mission enables high spatial resolution of sea surface height (SSH), which would be beneficial for the calculation of gravity gradients. However, there are no clear accuracy results for the gravity gradients (the gravity gradient tensor represents the second-order derivative of the gravity potential) recovered based on SWOT data. This study evaluated the possible precision of gravity gradients using the discretization method based on simulated SWOT wide-swath data and investigated the impact of instrument errors. The data are simulated based on the sea level anomaly data provided by the European Space Agency. The instrument errors are simulated based on the power spectrum data provided in the SWOT error budget document. Firstly, the full tensor of gravity gradients (SWOT_GGT) is calculated based on deflections of the vertical and gravity anomaly. The distinctions of instrument errors on the ascending and descending orbits are also taken into account in the calculation. The precision of the Tzz component is evaluated by the vertical gravity gradient model provided by the Scripps Institution of Oceanography. All components of SWOT_GGT are validated by the gravity gradients model, which is calculated by the open-source software GrafLab based on spherical harmonic. The Tzz component has the poorest precision among all the components. The reason for the worst accuracy of the Tzz component may be that it is derived by Txx and Tyy, Tzz would have a larger error than Txx and Tyy. The precision of all components is better than 6 E. Among the various errors, the effect of phase error and KaRIn error (random error caused by interferometric radar) on the results is greater than 2 E. The effect of the other four errors on the results is about 0.5 E. Utilizing multi-cycle data for the full tensor of gravity gradients recovery can suppress the effect of errors. Full article
(This article belongs to the Special Issue Remote Sensing in Space Geodesy and Cartography Methods II)
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24 pages, 5399 KiB  
Article
Comparative Study on Predicting Topography from Gravity Anomaly and Gravity Gradient Anomaly
by Huan Xu, Yuwei Tian, Jinhai Yu, Ole Baltazar Anderson, Qiuyu Wang and Zhongmiao Sun
Remote Sens. 2024, 16(1), 166; https://doi.org/10.3390/rs16010166 - 30 Dec 2023
Cited by 4 | Viewed by 2141
Abstract
Owing to the dependence of algorithms on the measurement of ship soundings and geophysical parameters, the accuracy and coverage of topography still need to be improved. Previous studies have mostly predicted topography using gravity or gravity gradient, However, there is a relative lack [...] Read more.
Owing to the dependence of algorithms on the measurement of ship soundings and geophysical parameters, the accuracy and coverage of topography still need to be improved. Previous studies have mostly predicted topography using gravity or gravity gradient, However, there is a relative lack of integrated research combining or comparing gravity and gravity gradient. In this study, we develop observation equations to predict topography based on vertical gravity anomalies (VG; also called gravity anomalies) and vertical gravity gradient (VGG) anomalies generated by a rectangular prism. The sources of interference are divided into medium- to high-frequency errors and low-frequency errors, and these new methods reduce these errors through regularization and error equations. We also use numerical simulations to test the efficiency of the algorithm and error-reduction method. Statistics show that VGG anomalies are more sensitive to topographic fluctuations; however, the linear correlation between VG anomalies and topography is stronger. Additionally, we use the EIGEN-6C4 model of VG and VGG anomalies to predict topography in shallow and deep-sea areas, with maximum depths of 2 km and 5 km, respectively. In the shallow and deep-sea areas, the root mean square (RMS) errors of VGG anomalies prediction are 93.8 m and 233.8 m, and the corresponding accuracies improved by 7.3% and 2.3% compared with those of VG anomaly prediction, respectively. Furthermore, we use cubic spline interpolation to fuse ship soundings and improve the accuracy of the final topography results. We develop a novel analytical algorithm by constructing an observation equation system applicable to VG and VGG anomalies. This will provide new insights and directions to refine topography prediction based on VG and VGG anomalies. Full article
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14 pages, 3707 KiB  
Article
Improved Bathymetry in the South China Sea from Multisource Gravity Field Elements Using Fully Connected Neural Network
by Qianqian Li, Zhenhe Zhai, Qi Li, Lin Wu, Lifeng Bao and Heping Sun
J. Mar. Sci. Eng. 2023, 11(7), 1345; https://doi.org/10.3390/jmse11071345 - 30 Jun 2023
Cited by 12 | Viewed by 2555
Abstract
Traditional bathymetry inversion methods that rely on an altimetry-derived gravity anomaly (GA) and/or a vertical gravity gradient anomaly (VGG) have been widely used for bathymetry prediction in the South China Sea. However, few studies attempt new methods to combine multisource gravity data to [...] Read more.
Traditional bathymetry inversion methods that rely on an altimetry-derived gravity anomaly (GA) and/or a vertical gravity gradient anomaly (VGG) have been widely used for bathymetry prediction in the South China Sea. However, few studies attempt new methods to combine multisource gravity data to improve the accuracy of the bathymetry. In this study, we introduce a fully connected deep neural network (FC-DNN) to merge GA, VGG, and the deflection of vertical (DOV) to predict the bathymetry in the South China Sea. Single beam sounding depths were used as sample data for neural network training. Independent shipboard depths and GEBCO2023, topo_25.1, and ETOPO2022 models were applied as validation data. The assessment results showed that the FC-DNN model reached a high precision level with an STD of 49.20 m. More than 70% of the differences between the FC-DNN bathymetric model and other depth models were less than 100 m. Furthermore, the spectral analysis results showed that the FC-DNN bathymetry model has stronger energy in medium and short wavelengths than other models, which indicates that additional gravity field element DOVs can recover richer topographic signals in those particular bands. Full article
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21 pages, 15414 KiB  
Article
A New Global Bathymetry Model: STO_IEU2020
by Diao Fan, Shanshan Li, Jinkai Feng, Yongqi Sun, Zhenbang Xu and Zhiyong Huang
Remote Sens. 2022, 14(22), 5744; https://doi.org/10.3390/rs14225744 - 13 Nov 2022
Cited by 12 | Viewed by 2337
Abstract
To address the limitations in global seafloor topography model construction, a scheme is proposed that takes into account the efficiency of seafloor topography prediction, the applicability of inversion methods, the heterogeneity of seafloor environments, and the inversion advantages of sea surface gravity field [...] Read more.
To address the limitations in global seafloor topography model construction, a scheme is proposed that takes into account the efficiency of seafloor topography prediction, the applicability of inversion methods, the heterogeneity of seafloor environments, and the inversion advantages of sea surface gravity field element. Using the South China Sea as a study area, we analyzed and developed the methodology in modeling the seafloor topography, and then evaluated the feasibility and effectiveness of the modeling strategy. Based on the proposed modeling approach, the STO_IEU2020 global bathymetry model was constructed using various input data, including the SIO V29.1 gravity anomaly (GA) and vertical gravity gradient anomaly (VGG), as well as bathymetric data from multiple sources (single beam, multi-beam, seismic, Electronic Navigation Chart, and radar sensor). Five evaluation areas located in the Atlantic and Indian Oceans were used to assess the performance of the generated model. The results showed that 79%, 89%, 72%, 92% and 93% of the checkpoints were within the ±100 m range for the five evaluation areas, and with average relative accuracy better than 6%. The generated STO_IEU2020 model correlates well with the SIO V20.1 model, indicating that the proposed construction strategy for global seafloor topography is feasible. Full article
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17 pages, 17021 KiB  
Technical Note
A New 1′ × 1′ Global Seafloor Topography Model Predicted from Satellite Altimetric Vertical Gravity Gradient Anomaly and Ship Soundings BAT_VGG2021
by Minzhang Hu, Li Li, Taoyong Jin, Weiping Jiang, Hanjiang Wen and Jiancheng Li
Remote Sens. 2021, 13(17), 3515; https://doi.org/10.3390/rs13173515 - 4 Sep 2021
Cited by 21 | Viewed by 3344
Abstract
In this paper, we construct a new 1′ × 1′ global seafloor topography model, BAT_VGG2021, using the satellite altimetric vertical gravity gradient anomaly model (VGG), SIO curv_30.1.nc, and ship soundings. Approximately 74.66 million single-beam depths and more than 180 GB of multibeam grids [...] Read more.
In this paper, we construct a new 1′ × 1′ global seafloor topography model, BAT_VGG2021, using the satellite altimetric vertical gravity gradient anomaly model (VGG), SIO curv_30.1.nc, and ship soundings. Approximately 74.66 million single-beam depths and more than 180 GB of multibeam grids were downloaded and adopted from the National Centers for Environmental Information (NCEI), Japan Agency for Marine-Earth Science and Technology (JAMSTEC), and Geosciences Australia (GA). The SIO curv_30.1.nc model was used to predict seafloor topography at 15~160 km wavelengths, and ship soundings were used to calibrate topography to VGG ratios. The accuracy of the new BAT_VGG2021 model was assessed by comparing it with ship soundings and existing models. The results indicate that the standard deviation of differences between the predicted model and ship soundings is about 40~80 m, and ~93% of the differences are within 100 m, similar to that of the SIO topo_20.1.nc model. The new BAT_VGG2021 model shows better accuracy than the DTU18BAT, ETOPO1, and GEBCO_08 models, and has been improved significantly from our last model, BAT_VGG2014. Full article
(This article belongs to the Section Satellite Missions for Earth and Planetary Exploration)
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19 pages, 8509 KiB  
Article
Seafloor Topography Estimation from Gravity Anomaly and Vertical Gravity Gradient Using Nonlinear Iterative Least Square Method
by Diao Fan, Shanshan Li, Xinxing Li, Junjun Yang and Xiaoyun Wan
Remote Sens. 2021, 13(1), 64; https://doi.org/10.3390/rs13010064 - 26 Dec 2020
Cited by 38 | Viewed by 4387
Abstract
Currently, seafloor topography inversion based on satellite altimetry gravity data provides the principal means to predict the global seafloor topography. Researchers often use sea surface geoid height or gravity anomaly to predict sea depth in the space domain. In this paper, a comprehensive [...] Read more.
Currently, seafloor topography inversion based on satellite altimetry gravity data provides the principal means to predict the global seafloor topography. Researchers often use sea surface geoid height or gravity anomaly to predict sea depth in the space domain. In this paper, a comprehensive discussion on seafloor topography inversion formulas in the space domain is presented using sea surface geoid height, gravity anomaly and introduces an approach that uses vertical gravity gradient. This would be the first study to estimate seafloor topography by vertical gravity gradient in the space domain. Further, a nonlinear iterative least-square inversion process is discussed. Using the search area for the Malaysia Airlines Flight MH370 as study site, we used the DTU17 gravity anomaly model and SIO V29.1 vertical gravity gradient to generate the seafloor topography. The results of the proposed bathymetric models were analyzed and compared with the DTU18 and SIO V20.1 bathymetric models. The experimental results show that the gravity anomaly and vertical gravity gradient in the study area are strongly correlated with the seafloor topography in the 20–200 km wavelength range. The optimal initial iteration values for seafloor topography variance and correlation length are 0.6365 km2 and 10.5′, respectively. Shipborne measurements from SONAR data were used as external checkpoints to evaluate the bathymetric models. The results show that the RMS for BAT_VGG_ILS (inversion model constructed by vertical gravity gradient) is smaller than for BAT_GA_ILS (inversion model constructed by gravity anomaly) and BAT_GA_VGG_ILS (inversion model constructed by gravity anomaly and vertical gravity gradient). The relative accuracy of the DTU18 bathymetry model was 9.27%, while the relative accuracy of the proposed seafloor models was higher than 4%. Within the 200 m difference range, the proportion of checkpoints for BAT_VGG_ILS was close to 95%, about 80% for BAT_GA_ILS and BAT_GA_VGG_ILS, and less than 50% for the DTU18. The results show that the nonlinear iterative least square method in the space domain is feasible. Full article
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