The DNSC07 high resolution global marine gravity field

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.

In this contribution, we describe the global GOCE-only gravity field model ITG-Goce02 derived from 7.5 months of gradiometer and orbit data. This model represents an alternative to the official ESA products as it is computed completely independently, using a different processing strategy and a separate software package. Our model is derived using the short arc approach, which allows a very effective decorrelation of the highly correlated GOCE gradiometer and orbit data noise by introducing a full empirical covariance matrix for each arc, and gives the possibility to downweight ‘bad’ arcs. For the processing of the orbit data we rely on the integral equation approach instead of the energy integral method, which has been applied in several other GOCE models. An evaluation against high-resolution global gravity field models shows very similar differences of our model compared to the official GOCE results published by ESA (release 2), especially to the model derived by the time-wise approach. This conclusion is confirmed by comparison of the GOCE models to GPS/levelling and altimetry data.

To understand many geophysical phenomena, including ocean circulation, tectonic plate movement, and the Earth’s interior, it is important to study the Earth’s gravity field. During the past three decades, satellites have measured the Earth’s static gravity. As a result, high-resolution global gravity field models have been available. This paper aims to examine the appropriateness of the satellite derived gravity field models for the offshore and coastal regions of Sri Lanka.While these eight gravity field models with ID 155-EIGEN-6S4 V2, 168-Tongji-Grace 02K, 171-GO-CONS-GCF2-TIM-R6, 174-ITSG-GRACE 2018S, 178-Tongji-GMMG2021S, 148-EIGN-6C4, 152-GECO, 167-SGG-UGM-1, and 177-SGG-UGM2 were used for the study. The mean difference value, standard deviation value, and Root Mean Square values modeled by each of the model between the observed gravity data and the BGI observed gravity data. The results indicated that 171-GO-CONS-GCF2-TIM-R6 and 177-SGG-UGM2 is the more suited model for the coastal and offshore region of Sri Lanka. The study used the SARAL-Altika satellite Altimetry data to investigate the relationship between Mean see surface height and observed gravity. No significant relationship between Mean sea surface height and marine gravity is indicated by. In addition, the influence of gravity model type on each of the LEO satellite orbit predictions was also studied. The findings of the research demonstrate that the optimal type of gravity model applied for LEO satellite orbit prediction depends on a short-term or long-term predictions. The models JGM3, EGM2008, and GL04C are more appropriate for short-term predictions, while the models JGM3, EGM96, and EIGEN2 are the best for long-term predictions. The gravity order and permanent tides also have to be taken into account for the orbital prediction.In conclusion, this research provides valuable insights into the suitability of various satellite-derived gravity field models for Sri Lanka's coastal and offshore regions. The findings also emphasize the need to consider the impact of gravity models on LEO satellite orbit prediction, particularly for new applications such as LEO navigation, which require real-time precise orbits.

Global static gravity field models are used for various applications such as determination of geoid height (i.e., vertical datum), satellite orbits, and ocean circulation models. Such static gravity models are obtained by combination of various satellite gravimetry data such as GRACE and GOCE, altimetry measurements over the oceans and terrestrial gravity measurements. These datasets have different error characteristics as well as spatial and spectral contents, which makes the data combination in model production very challenging. Therefore, it is very important to validate the global static gravity field models using independent observations not used in those models. Laser ranging interferometer (LRI) measurements acquired by the GRACE-FO show extraordinary sensitivity to small-scale static gravity signals down to 100 km. We use one year of GRACE LRI observations in 2019 to validate six state-of-the-art global static gravity models: GGM05C, GGM05S, ITSG-Grace2018s, GOCO-TIM-R06e, EIGEN-6C4, and GOCO06s. Our comprehensive analysis leads to detection of the spectral (spherical harmonic) band and spatial regions where these models suffer from errors. We discuss inefficacies of each model as well as their potential causes. Our unique study helps inform the model developers about the spectral band and spatial regions where their models need improvement.

We present a method with which we determined the local lunar gravity field model over the South Pole‐Aitken (SPA) basin on the farside of the Moon by estimating adjustments to a global lunar gravity field model using SELENE tracking data. Our adjustments are expressed in localized functions concentrated over the SPA region in a spherical cap with a radius of 45° centered at (191.1°E, 53.2°S), and the resolution is equivalent to a 150th degree and order spherical harmonics expansion. The new solution over SPA was used in several applications of geophysical analysis. It shows an increased correlation with high‐resolution lunar topography in the frequency band l = 40–70, and admittance values are slightly different and more leveled when compared to other, global gravity field models using the same data. The adjustments expressed in free‐air anomalies and differences in Bouguer anomalies between the local solution and the a priori global solution correlate with topographic surface features. The Moho structure beneath the SPA basin is slightly modified in our solution, most notably at the southern rim of the Apollo basin and around the Zeeman crater.

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.

The satellite altimetry missions could measure high-accuracy sea surface heights (SSHs) that can be used to recover the marine gravity field. Traditional methods for estimating the marine gravity field from SSHs all rely on approximate physical correlations between SSHs and gravity, which may neglect nature’s complex nonlinearity. This work presents a new deep network-based method to recover the gravity anomaly. This new method uses a multi-channel convolutional neural network (MCCNN) architecture to capture the nolinear features between ship-borne gravity and a group of input parameters including deflections of the vertical (DOVs), submarine topography and the geo-locations. To validate the gravity, ship-borne gravity anomalies on the two independent cruises were not used in the deep learning process. For comparison, we also estimated the gravity using the traditional inverse Vening Meinesz (IVM) method. Our results indicate that the MCCNN method can derive high-quality marine gravity anomalies. The assessments using 1 mGal-accuracy ship-borne gravity anomalies show that the average accuracy for gravity from MCCNN method is higher than 3 mGal and this method achieves 0.05-0.50 mGal improvement over benchmark methods IVM. Assessed by marine gravity anomaly models with the accuracy of 1-2 mGal, the MCCNN method has shown to improve the accuracy of gravity by at least 4%. Comparisons with the IVM results show that improvements of the MCCNN method were mainly in wavelengths between 8 km and 100 km due to the using of bathymetry. The results show that our deep learning method maintains good performance and is promising for gravity recovering.

Summary The estimation of topographic gravity field models has attracted significant interest in recent years due to its growing relevance in Earth sciences. In this study, we present a robust methodology for the computation and comprehensive validation of global, complete spherical Bouguer and isostatic gravity anomalies that are essential for accurately interpreting subsurface mass distributions therefore geological structures. We synthesize these crucial gravitational functionals by leveraging spherical harmonic coefficients from high-resolution global gravity field models and various topographic/topographic-isostatic gravity field models. Our findings underscore the critical role of comprehensive terrain corrections in deriving physically meaningful, complete Bouguer gravity fields. The calculated global anomalies demonstrate strong coherence with established benchmark datasets, such as the World Gravity Map 2012. Residual differences are primarily attributed to variations in input Digital Terrain Models. Comparisons with regional Bouguer datasets reveal systematic biases that are largely explained by differing terrain correction methodologies. After removing this effect, there is a high level of consistency between the calculated global and published regional datasets, highlighting the utility of our global solutions, particularly in regions with sparse terrestrial data. Furthermore, the globally computed isostatic gravity anomalies exhibit significant agreement with both external global and diverse regional datasets, notably without the large systematic biases observed in Bouguer comparisons. This agreement reflects the effectiveness of the combined topographic and isostatic corrections in capturing Earth’s mass balance. This research provides valuable tools for new studies in the geoscience community by offering globally consistent and complete Bouguer and isostatic gravity field anomalies that have been rigorously validated for the ICGEM service.

: LONG-TERM GOALS: *Improve our understanding of the ocean basins for scientific research and Naval operations. OBJECTIVES: *Improve global marine gravity maps by a factor of 2 in deep ocean areas and a factor of 4 in the Arctic areas and on shallow continental margins. *Use these improved gravity maps along with a global compilation of soundings to refine a 30-arcsecond bathymetry model (SRTM30_PLUS). *Prepare the next generation of scientists for ocean research.

A new, detailed marine gravity field for the persistently ice‐covered Arctic Ocean, derived entirely from satellite data, reveals important new tectonic features in both the Amerasian and Eurasian basins. Reprocessed Geoscience Laser Altimeter System (GLAS) data collected by NASA's Ice Cloud and land Elevation Satellite (ICESat) between 2003 and 2005 have been combined with 8 years worth of retracked radar altimeter data from ESA's ERS‐2 satellite to produce the highest available resolution gravity mapping of the entire Arctic Ocean complete to 86°N. This ARCtic Satellite‐only (ARCS) marine gravity field uniformly and confidently resolves marine gravity to wavelengths as short as 35 km. ARCS relies on a Gravity Recovery and Climate Experiment (GRACE)‐only satellite gravity model at long (>580 km) wavelengths and plainly shows tectonic fabric and numerous details imprinted in the Arctic seafloor, in particular, in the enigmatic Amerasian Basin (AB). For example, in the Makarov Basin portion of the AB, two north‐south trending lineations are likely clues to the highly uncertain seafloor spreading history which formed the AB.

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.

Global static gravitational field determined by GOCE satellite data has become a hotspot in current research of geodesy. In this paper, a global static gravity field model entitled SWJTU-GO01S up to the degree and order 210 is recovered based on 12 months of GOCE orbit and gradient data from 2011-02-28 to 2012-03-05 with direct approach. GOCE gradient data are filtered by the zero phase finite impulse band-pass digital filter, and then a gradient observation equation is founded directly in gradiometer coordinates, which avoids high-accuracy gradient component loss in accuracy in the conversion process, while the orbit data is processed with short-arc integral approach. The optimal weight of combination result based on SST and SGG data is determined by variance component estimation and the polar gaps is dealt with the Kuala regularization method. Comparison of internal and external precision of SWJTU-GO01S with EGM2008 and with GPS leveling data of North America, shows that the geoid error and cumulative error of the SWJTU-GO01S model with the degree and order 210 are 2.1 cm and 13.7 cm respectively. Compared with the second generation models released by ESA and ITG-GRACE2010S, the accuracy of the model SWJTU-GO01S is higher than that of the model ITG-GRACE2010S and ESA official time-wise and space-wise model in the above degree and order 150. This study provides a reference to further joint multi-class satellite observation data to recover gravity field models.

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.

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.

<p>We proposed an alternative method to determine the height of Mount Everest (HME) based on the shallow layer method (SLM), which was put forward by Shen (2006). We use the precise external global Earth gravity field model (i.e., EGM2008 and EIGEN-6C4 models) as input information, and the digital topographic model (i.e., DTM2006.0) and crust models (i.e., CRUST2.0 and CRUST1.0 models) to construct the shallow layer model. There are four combined strategies：(1) EGM2008 and CRUST1.0 models, (2) EGM2008 and CRUST2.0 models, (3) EIGEN-6C4 and CRUST1.0 models, and (4) EIGEN-6C4 and CRUST2.0 models, respectively. We calculate the HME by two approaches: first approach, the HME is directly calculated by combining the geoid undulation (N) and geodetic height (h); second approach, we calculate the HME by the segment summation approach (SSA) using the gravity field inside the shallow layer determined by the SLM. Numerical results show that for four combined strategies, the differences between our results and the authoritatively released value 8848.86 m by the Chinese and Nepalese governments on December 8, 2020 are 0.448 m, -0.009 m, -0.295 m, and -0.741 m using first approach and 0.539 m, 0.083 m, -0.214 m, and -0.647 m using second approach. The combined calculation of the HME by the terrain model and gravity field model is more accurate than that by the gravity field model alone. This study is supported by the National Natural Science Foundations of China (NSFC) under Grants 42030105, 41721003, 41804012, 41631072, 41874023, Space Station Project (2020)228.</p>