Recovering Gravity from Satellite Altimetry Data Using Deep Learning Network

SUMMARYThe HaiYang-2A (HY-2A) satellite was launched in August 2011, filling a gap in the field of Chinese altimetry. The application of HY-2A-measured altimeter data in gravity research needs to be studied. CryoSat-2 altimetry data play an important role in constructing global marine gravity models. Based on HY-2A and CryoSat-2 altimetry data of Level-2 plus products from March 2016 to June 2020, marine gravity anomaly models on 1′ × 1′ grids were derived by the inverse Vening–Meinesz (IVM) method over the Gulf of Mexico (80–100°W, 17–32°N). The accuracy of the altimeter-derived gravity was assessed by ship-borne gravity anomalies and the SIO V30.1 global marine gravity model. Then, integrated gravity models on 1′ × 1′ grids were constructed from the altimeter-derived gravity anomaly models by the weighted modification method and the combined altimetry data by IVM method. The results show that the accuracy of altimeter-derived marine gravity anomalies is affected by the coastline and complicated submarine topography. The accuracy of gravity anomalies derived from HY-2A is slightly lower than that derived from CryoSat-2 in the offshore region and regions containing complicated submarine topography, and is consistent with that derived from CryoSat-2 in other regions. The HY-2A-measured altimetry data play a significant role in constructing integrated gravity models. To conclude, the gravity anomalies derived from HY-2A have similar accuracy to those derived from CryoSat-2 during the same period, and HY-2A altimetry data can be used to construct high-precision global/local marine gravity models.

In recent years, the satellite altimeter technology allows to enhance the marine investigation in any area. Up to now, many scientific studies have attempted to improve the accuracy and resolution of altimeter-derived gravity anomalies and have produced a gravity grid with interval of 1' × 1' for most the oceans all over the world. However, this gravity anomalies are not very high accuracy and have a large difference compared to shipboard gravity anomalies, especially in the coastal and islands areas. The purpose of this article is to improve the accuracy of altimeter-derived marine gravity anomalies for geological structure research in the Vietnam South-Central continental shelf and adjacent areas. The least squares collocation method is used to correct the altimeter-derived marine gravity data based on the shipboard gravity data in order to improve the accuracy of marine gravity anomalies. In this article, the altimeter-derived marine gravity anomalies are taken from Sandwell, D. T., et al., (V24.1) and the shipboard gravity anomalies are from the surveyed projects between Vietnam, Russia and other countries. Here, comparison of both those data has brought a mean-squared error is about ±9.358 mGal. After correcting, the mean-squared error between the corrected-altimeter-derived marine gravity and shipboard gravity anomalies are improved from ±9.358 to ±1.208 mGal (for the altimeter data coincided with shipboard track). Also, in this article, the Cenozoic sedimentary density and thickness are determined through the 3D interpretative methods of the above-corrected gravity anomalies in combination with seismic data. The achieved results realize how the efficiency and actuality of the corrected-altimeter-derived marine gravity anomalies for the detailed researches of geological structures. Especially, it is more meaningful in the remote or sparsely surveyed regions.

This paper presents for the first time the results of marine gravity recovery using the ocean observation data acquired by Tiangong-2 interferometric imaging radar altimeter (TG2 InIRA) which demonstrate not only the balanced accuracies of the north and east components of deflection of the vertical (DOV) as envisaged, but also the improved spatial resolutions of DOV compared with that by conventional altimeters (CAs). Moreover, much higher measurement efficiency owing to the wide-swath capability and the great potential in accuracy improvement of marine gravity field are also demonstrated. TG2 InIRA adopts the interferometry with short baseline and takes small incidence angles, by which wide-swath sea surface height (SSH) can be measured with high accuracy. Gravity recovery experiments in the Western Pacific area are conducted to demonstrate the performance, advantages and capability of TG2 InIRA. SSH data processing algorithms and DOV calculation have been designed by taking the wide-swath feature into account, based on which, the gravity anomalies are then calculated using the inverse Vening Meinesz formula. The derived gravity anomalies are compared with both the published gravity models and the shipborne gravity measurements. The results show that the accuracy of TG2 InIRA is equivalent to, or even a little better than, that of CAs. The fused gravity result using equal TG2 InIRA data and CAs data performs better than those using TG2 InIRA data alone or CAs data alone. Due to the signal bandwidth of TG2 InIRA is only 40 MHz which is much smaller than that of CAs, much higher accuracy can be hopefully achieved for future missions if larger signal bandwidth is used.

SARAL/AltiKA (SRL) is the first altimetry satellite with a Ka-band altimeter. To validate the advantages of the Ka-band altimeter over traditional Ku-band altimeters in marine geodetic applications, a comprehensive analysis is carried out over the South China Sea (SCS) (0–30° N, 105–125° E) from three aspects, namely the influence of load on waveforms, the precision of sea surface heights (SSHs), and the precision of altimeter-derived marine gravity field. Coastal waveforms of SRL, Jason-2, and CryoSat-2 are separately compared with corresponding ocean-type waveforms. The radius of coastal influence on SSHs of SRL/exact repeat mission (SRL/ERM) is the smallest, being about 3 km. Crossover discrepancies, global mean sea surface models, and tide gauge data are used to assess the precision of altimetric SSHs. Compared with the SSH precision of Ku-band Jason-2/ERM, the SSH precision of Ka-band SRL/ERM is 4.6% higher over the SCS and 10% higher in offshore areas. Gridded gravity anomalies are derived from measurements of SRL/drifting phase (SRL/DP) and CryoSat-2 through the inverse Vening-Meinesz formula, respectively. According to the assessment by shipborne gravity data and global marine gravity models, the precision of SRL/DP-derived gravity is higher than that of CryoSat-2-derived gravity over the SCS, especially in offshore areas. In some cycles, ground tracks of SRL/ERM have large drifting of more than 10 km from nominal tracks. The results show that the Ka-band altimeter of SRL has better precision in SSHs and marine gravity recovery than the Ku-band altimeter over the SCS, particularly in offshore areas.

With the advancements of satellite altimeter technology and data volume, the accuracy and spatial resolution of altimeter-derived marine gravity fields have been steadily improved. Ideally, a best marine gravity field from multi-altimeter missions is one that combines all data by optimally calibrating their relative weights. To this end, we use the minimum norm quadratic unbiased estimator theory to calibrate error variances of geoid gradients (GGs) from the Cryosat-2 mission and the Jason-1/2 geodetic missions and then use a scaling factor to modify the global covariance functions into local covariance functions. The calibrated error variances and the scaling factors are used in the least-squares collocation to estimate the gridded north and east components of GGs, which are used to compute gravity anomaly and vertical gravity gradient (VGG) by the methods of inverse Vening-Meinesz (IVM) and numerical differentiations. The assessment of the altimeter-derived gravity anomalies in the northern part of the South China Sea using the shipborne gravity data shows an average gravity accuracy improvement of 9.5% by calibrated and scaled covariances of GGs compared to the initial variances. The method for VGG computations is confirmed by examining the extinct ridges in the Gulf of Mexico.

Marine gravity anomalies are crucial parameters and elements for determining coastal and ocean geoid, tectonics and crustal structures, as well as offshore studies. This study aims to derive and develop a marine gravity anomaly model over Malaysian seas from multi-mission altimetry data. Universiti Teknologi Malaysia 2020 Mean Sea Surface Model is computed based on along-track data from nine satellite missions, incorporating TOPEX, Jason-1, Jason-2, ERS-2, Geosat Follow on (GFO), Envisat-1, CryoSat-2, SARAL/AltiKa, and Sentinel-3A. The data exploited are from 1993 to 2019 (27 years). Residual gravity anomaly is computed using Gravity Software, and two-dimensional planar Fast Fourier Transformation method is applied. The evaluation, selection, blunder detection, combination, and re-gridding of the altimetry-derived gravity anomalies and Global Geopotential Model data are demonstrated. Cross-validation procedure is employed for data cleaning and quality control using the Kriging interpolation method. Then, cross-validation procedure is applied to the tapering window width 200, which adopting the GECO model denotes the optimum gravity anomaly with root mean square errors in the range of ± 4.2472 mGal to ± 6.0202 mGal. The findings suggest that the estimated marine gravity anomaly is acceptable to be implemented in the marine geoid determination and bathymetry estimation over Malaysian seas. In addition, the results of this study are valuable for geodetic and geophysical applications in marine areas.

Using the spherical harmonic representations of the earth's disturbing potential and its functionals, we derive the inverse Vening Meinesz formula, which converts deflection of the vertical to gravity anomaly using the gradient of the H function. The deflection-geoid formula is also derived that converts deflection to geoidal undulation using the gradient of the C function. The two formulae are implemented by the 1D FFT and the 2D FFT methods. The innermost zone effect is derived. The inverse Vening Meinesz formula is employed to compute gravity anomalies and geoidal undulations over the South China Sea using deflections from Seasat, Geosat, ERS-1 and TOPEX//POSEIDON satellite altimetry. The 1D FFT yields the best result of 9.9-mgal rms difference with the shipborne gravity anomalies. Using the simulated deflections from EGM96, the deflection-geoid formula yields a 4-cm rms difference with the EGM96-generated geoid. The predicted gravity anomalies and geoidal undulations can be used to study the tectonic structure and the ocean circulations of the South China Sea.

During the 1980s satellite radar altimetry matured as a geophysical technique, quickly becoming the best way to map the gravity field of the world's oceans. Maps derived from SEASAT altimeter observations of sea surface topography (or geoid) revealed much that was previously unknown about the marine gravity field [Haxby, 1987] and underlying seafloor, particularly in the vast areas that are poorly charted by traditional shipboard observations.Seafloor topography, and to a lesser extent, crustal/upper mantle density variations, produce the short wavelength (<200 km) undulations in the marine gravity field. This is simply due to the gravitational attraction of the mass in the seamount or similar structure emplaced on the seafloor. For topographic structures beneath the sea that are 20‐200 km in spatial extent, this attraction causes the gravity anomalies at the sea surface to vary in proportion to the relative height of the underlying structures. (This ignores isostasy or internal deformation of the Earth's crust and mantle, which acts to reduce this gravitational effect particularly over long‐wavelength—greater than 200 km—topography.) The ratio between gravity anomalies and height variations is slightly less than 0.07 milligals per meter (1 mGal equals 10‐5 m/sec2). Therefore, the fine structure in these marine gravity fields reflects the tectonic fabric imprinted in the seafloor. This fabric includes the mid‐ocean ridge axes (where tectonic plates form), fracture zones, which record the directional history of seafloor spreading, seamount chains, rifted continental margins, and other features that chronicle the history of relative motion among the tectonic plates over the past 200 million years.

Construction of a high spatial resolution and high precision marine gravity field in coastal areas is constrained by the low quality and sparse coverage of altimetry data, except for limited shipborne and airborne gravity surveys. To address this problem, a mean sea surface height constraint factor (MSSHCF) method based on the ordinary kriging method and the remove-restore technique is proposed from the perspective of interpolation. In this method, the data is standardized during the interpolation process to reduce the error and mean sea surface as variables related to the marine gravity field are added to the semi-variance function in ordinary kriging to obtain a marine gravity field with a spatial resolution of 1′ × 1′. Validation experiments show that the MSSHCF method more closely agrees with the referenced SS V28, DTU17 global marine gravity models than the ordinary kriging method. Our results were further validated against shipborne data; the accuracy of the MSSHCF method is 0.13 and 0.33 mGal higher than that of the ordinary kriging method in two experimental areas. The effects of ocean depth and offshore distance on the results were also assessed. These results show that the proposed method is more accurate than the ordinary kriging method, when the distance and depth varied. Therefore, our study demonstrates that the MSSHCF method is an innovative and feasible tool for extracting gravity fields along coastal, beach, and island areas.

Mitigating errors in marine gravity recovery induced by sea level variability in SWOT observations

The Earth’s time-variable gravity field holds significant research and application value. However, satellite gravimetry missions such as GRACE and GRACE-FO face limitations in spatial resolution when detecting monthly gravity fields, while traditional radar altimeters lack the observational efficiency needed for monthly gravity anomaly inversion. These limitations hinder further exploration and application of the Earth’s time-variable gravity field. Leveraging its advantages, such as rapid global coverage, high revisit frequency, and low cost for constellation formation, spaceborne GNSS-R technology holds the potential to address the observational efficiency gaps of traditional radar altimeters. This study presents the first assessment of the capability of spaceborne GNSS-R interferometric altimetry for high spatial resolution monthly marine gravity anomaly inversion through simulations. The results indicate that under the PARIS Operational scenario of a single GNSS-R satellite (a spaceborne GNSS-R interferometric altimetry scenario proposed by Martin-Neira), a 30′ grid resolution marine gravity anomaly can be inverted with an accuracy of 4.93 mGal using one month of simulated data. For a dual-satellite constellation, the grid resolution improves to 20′, achieving an accuracy of 4.82 mGal. These findings underscore the promise of spaceborne GNSS-R interferometric altimetry technology for high spatial resolution monthly marine gravity anomaly inversion.

1. Summary DNSC07 is a new global ocean wide satellite altimetry derived gravity field computed at the Danish National Space Center (DTUDenmark) with a spatial resolution of 1 arc-minute by 1 arc-minute covering all marine regions of the world including the Arctic Ocean up to the North Pole. For more than a decade satellite altimetry has been used to determine the marine gravity field. All present satellite based global marine gravity fields are based on the GEOSAT and ERS-1 Geodetic Mission (GM) data combined with other satellite derived datasets. The most urgent outstanding problem with most existing marine gravity fields (i.e. KMS02, Sandwell and Smith V12, NTU 01, GSFC00) was to improve the coverage of the data and the quality of the satellite observations in order to gain higher accuracy of the derived marine gravity field in particularly high latitudes and in coastal regions where many sedimentary basins are found. By using a new double-retracking system for the entire ERS-1 GM mission using a highly advanced expert based system of multiple retrackers and subsequently repacking/retracking we have been able to obtain both higher quality data but also many more data than seen before. Especially in coastal and ice-covered regions the new DNSC07 global marine gravity field is superior to other satellite based global marine gravity fields. We will present the high resolution new global marine gravity field and comparison with existing marine gravity surveys in several regions of the world (Indonesia, Florida Keys and East Greenland) and demonstrate how much accuracy have been gained by retracking the satellite observations compared with existing global marine gravity fields.

The influencing factors of community risk are complex. For the low accuracy of traditional prediction model, a multichannel convolutional neural network community risk prediction model is proposed by improving convolutional neural network of deep learning. First of all, in the community risk prediction model, the structure of multichannel input convolutional neural network is selected. Then, add it into the full connection layer. Subsequently, the DenseNet layer is added to establish connections between different network layers. Finally, the receptive field is improved, and the gradient disappearance is solved. Thus, the prediction accuracy of model is improved. Compared with the traditional model, the proposed multichannel convolutional neural network model has better prediction accuracy. In addition, it performs better on the three indicators, namely, correlation coefficient R , coefficient of determination R 2 , and mean square root error RMSE. Compared with the commonly used LSTM model and logic regression model, the proposed model also has certain advantages, which is more suitable for community risk prediction.

SUMMARYHigh-precision and high-resolution satellite altimetry data from CryoSat-2 are widely utilized for marine gravity inversion. The vertical gravity gradient is a crucial parameter of the Earth's gravity field. To evaluate the performance of vertical gravity gradient determined from CryoSat-2 altimeter data, the pre-processed along-track sea surface heights (SSHs) are obtained through error correction. The study area focused on the Arabian Sea and its surrounding region, where the along-track geoid was derived by subtracting the mean dynamic topography of the ocean from the along-track SSH of CryoSat-2. The residual along-track geoidal gradients were obtained by adjusting the along-track geoid gradients calculated from CryoSat-2 altimeter data using the remove-restore method. This was done by subtracting the geoid gradients calculated by the gravity field model XGM2019e_2159. After obtaining the residual along-track geoidal gradients, the residual gridded deflections of the vertical (DOV) are calculated using the least-squares collocation (LSC) method. The residual gridded DOV are then used to compute the residual gridded gravity anomaly gradients in the study area using the finite-difference method. After restoring the gravity anomaly gradients computed by the XGM2019e_2159 model, a high-resolution gravity anomaly gradient model with a resolution of 1′ ×1′ is obtained for the Arabian Sea and its surrounding area. To evaluate the accuracy of the gravity anomaly gradient model derived from CryoSat-2, it was compared with the SIO V32.1 gravity anomaly gradient model released by the Scripps Institution of Oceanography. The comparison showed that the root mean square (RMS) of the differences between the two models is 7.69E, demonstrating the high accuracy and precision of the vertical gravity gradient determined from CryoSat-2 altimeter data.

Closely spaced satellite altimeter profiles collected during the Geosat Geodetic Mission (∼6 km) and the ERS 1 Geodetic Phase (8 km) are easily converted to grids of vertical gravity gradient and gravity anomaly. The long‐wavelength radial orbit error is suppressed below the noise level of the altimeter by taking the along‐track derivative of each profile. Ascending and descending slope profiles are then interpolated onto separate uniform grids. These four grids are combined to form comparable grids of east and north vertical deflection using an iteration scheme that interpolates data gaps with minimum curvature. The vertical gravity gradient is calculated directly from the derivatives of the vertical deflection grids, while Fourier analysis is required to construct gravity anomalies from the two vertical deflection grids. These techniques are applied to a combination of high‐density data from the dense mapping phases of Geosat and ERS 1 along with lower‐density but higher‐accuracy profiles from their repeat orbit phases. A comparison with shipboard gravity data shows the accuracy of the satellite‐derived gravity anomaly is about 4–7 mGal for random ship tracks. The accuracy improves to 3 mGal when the ship track follows a Geosat Exact Repeat Mission track line. These data provide the first view of the ocean floor structures in many remote areas of the Earth. Some applications include inertial navigation, prediction of seafloor depth, planning shipboard surveys, plate tectonics, isostasy of volcanoes and spreading ridges, and petroleum exploration.