Explore the vast range of titles available.

The availability of high-resolution global digital elevation data sets has raised a growing interest in the feasibility of obtaining their spherical harmonic representation at matching resolution, and from there in the modelling of induced gravity perturbations. We have therefore estimated spherical Bouguer and Airy isostatic anomalies whose spherical harmonic models are derived from the Earth’s topography harmonic expansion. These spherical anomalies differ from the classical planar ones and may be used in the context of new applications. We succeeded in meeting a number of challenges to build spherical harmonic models with no theoretical limitation on the resolution. A specific algorithm was developed to enable the computation of associated Legendre functions to any degree and order. It was successfully tested up to degree 32,400. All analyses and syntheses were performed, in 64 bits arithmetic and with semi-empirical control of the significant terms to prevent from calculus underflows and overflows, according to IEEE limitations, also in preserving the speed of a specific regular grid processing scheme. Finally, the continuation from the reference ellipsoid’s surface to the Earth’s surface was performed by high-order Taylor expansion with all grids of required partial derivatives being computed in parallel. The main application was the production of a 1′ × 1′ equiangular global Bouguer anomaly grid which was computed by spherical harmonic analysis of the Earth’s topography–bathymetry ETOPO1 data set up to degree and order 10,800, taking into account the precise boundaries and densities of major lakes and inner seas, with their own altitude, polar caps with bedrock information, and land areas below sea level. The harmonic coefficients for each entity were derived by analyzing the corresponding ETOPO1 part, and free surface data when required, at one arc minute resolution. The following approximations were made: the land, ocean and ice cap gravity spherical harmonic coefficients were computed up to the third degree of the altitude, and the harmonics of the other, smaller parts up to the second degree. Their sum constitutes what we call ETOPG1, the Earth’s TOPography derived Gravity model at 1′ resolution (half-wavelength). The EGM2008 gravity field model and ETOPG1 were then used to rigorously compute 1′ × 1′ point values of surface gravity anomalies and disturbances, respectively, worldwide, at the real Earth’s surface, i.e. at the lower limit of the atmosphere. The disturbance grid is the most interesting product of this study and can be used in various contexts. The surface gravity anomaly grid is an accurate product associated with EGM2008 and ETOPO1, but its gravity information contents are those of EGM2008. Our method was validated by comparison with a direct numerical integration approach applied to a test area in Morocco–South of Spain (Kuhn, private communication 2011) and the agreement was satisfactory. Finally isostatic corrections according to the Airy model, but in spherical geometry, with harmonic coefficients derived from the sets of the ETOPO1 different parts, were computed with a uniform depth of compensation of 30 km. The new world Bouguer and isostatic gravity maps and grids here produced will be made available through the Commission for the Geological Map of the World. Since gravity values are those of the EGM2008 model, geophysical interpretation from these products should not be done for spatial scales below 5 arc minutes (half-wavelength).

In this study, solutions were derived to calculate the two horizontal components of gravity anomaly vectors using a horizontal polygonal thin plate. Although analytical solutions for the three components of the gravity anomaly vector for a rectangular prism model have been derived, it is sometimes difficult or inefficient to approximate subsurface structures by assembling rectangular prisms. An alternative to these models is to approximate an arbitrary three-dimensional subsurface structure by stacking several polygonal thin plates. As the solutions presented here are approximate, comparative analyses with analytical solutions and higher-accuracy numerical solutions were conducted for the rectangular prism Δ g x and Δ g y , and for the model assuming practical field modeling. The results showed that by setting a small thickness Δ z for the horizontal polygonal thin plate, a solution comparable to the analytical or correct solution can be obtained. For a realistic analysis, setting Δ z to match the measurement accuracy of Δ g x and Δ g y , or the conversion accuracy from Δ g z to Δ g x and Δ g y , will enable practical numerical solutions to be obtained. Graphical Abstract

An updated global bathymetry and topography grid is presented using a spatial sampling interval of 15 arc sec. The bathymetry is produced using a combination of shipboard soundings and depths predicted using satellite altimetry. New data consists of >33.6 million multibeam and singlebeam measurements collated by several institutions, namely, the National Geospatial‐Intelligence Agency, Japan Agency for Marine‐Earth Science and Technology, Geoscience Australia, Center for Coastal and Ocean Mapping, and Scripps Institution of Oceanography. New altimetry data consists of 48, 14, and 12 months of retracked range measurements from Cryosat‐2, SARAL/AltiKa, and Jason‐2, respectively. With respect to SRTM15_PLUS (Olson et al.,), the inclusion of these new data results in a ∼1.4‐km improvement in the minimum wavelength recovered for sea surface free‐air gravity anomalies, a small increase in the accuracy of altimetrically derived predicted depths, and a 1.24% increase, from 9.60% to 10.84%, in the total area of ocean floor that is constrained by shipboard soundings at 15‐arc sec resolution. Bathymetric grid cells constrained by satellite altimetry have estimated uncertainties of ±150 m in the deep oceans and ±180 m between coastlines and the continental rise. Onshore, topography data are sourced from previously published digital elevation models, predominately SRTM‐CGIAR V4.1 between 60°N and 60°S. ArcticDEM is used above 60°N, while Reference Elevation Model of Antarctica is used below 62°S. Auxiliary grids illustrating shipboard data coverage, marine free‐air gravity anomalies, and vertical gradient gradients are also provided in common data formats. Key Points An updated global elevation grid is presented using a spatial sampling interval of 15 arc sec New bathymetry data include more than 33.6 million ship soundings and more than 6 years of non‐repeat altimetry measurements The percentage of seafloor mapped by echo soundings remains low; our current compilation covers only 10.84% at 15‐arc sec resolution

High-precision and high-resolution gravity fields can be derived from multi-source satellite altimeter data. A gravity anomaly model around the South China Sea (SCSGA) V1.0 on a 1′ × 1′ grid is established from sea surface heights (SSHs) of several geodetic missions (GMs) and exact repeat missions. Gridded deflections of the vertical are first calculated from SSHs by the least squares collocation (LSC) method and then used to derive gravity anomalies by the inverse Vening Meinesz formula. In gravity derivation processing, we establish an approximate relationship among the precision of altimetric gravity, precision of geoid gradients, and density of geoid gradients (the average number of geoid gradients per 1′ × 1′ region). The weights of geoid gradients from the Ka-band altimeter for the LSC are innovatively determined by an iterative method. Finally, SCSGA V1.0 is assessed by ship-borne gravity anomalies and marine gravity models. The performance of GMs in gravity derivation is evaluated. In general, the altimetric gravity precision in regions with many islands and reefs increases more obviously than those in other regions when the geoid gradient density increases. The standard deviation of SCSGA V1.0 is 2.78 mGal, which is slightly better than those of four recognized global marine gravity models around the SCS. CryoSat-2 is the most important dataset for SCSGA V1.0. Ka-band SARAL/AltiKa plays a major role in gravity derivation, and the contribution of Haiyang-2A is greater than those of other Ku-band satellites, except CryoSat-2. SCSGA V1.0 is concluded to reach an international advanced level for marine gravity from altimeter data around the SCS.

There are two dominating approaches of modeling the marine gravity field based on satellite altimetry observations. In this study, the marine gravity field is determined in four selected areas (Northwestern Atlantic, Hawaii ocean area, Mariana Trench area, and Aegean Sea) by using exact same input datasets but different methods which are based on sea surface height (SSH) and sea surface slope (SSS), respectively. The impact of the methodology is evaluated by conducting validations with shipborne gravity observation. The CryoSat-2, Jason-1/2, and SARAL/Altika geodetic mission data (similarly 3-year-long time series) are firstly retracked by the two-pass retracker. After that, the obtained SSHs are used for the derivation of geoid undulations and vertical deflections, and then for the resulting marine gravity field separately. The validation results indicate that the SSH-based method has advantages in robustly estimating marine gravity anomalies near the coastal zone. The SSS-based method has advantages over regions with intermedium ocean depths (2000–4000 m) where seamounts and ridges are found, but obvious disadvantages when the ocean currents flow along the north–south direction (e.g., western boundary currents) or the topography features north–south directional trenches. In the deep ocean where the seafloor topography is plain and smooth, the two methods have similar accuracy.

The “non-harmonicity” problem in residual terrain modelling (RTM) is a challenging issue, causing errors exceeding 200 mGal in the RTM gravity anomaly in rugged areas. Although various methods have been proposed to address this problem, including the condensation method, regularized downward continuation methods with Taylor series expansions (TS) and spherical harmonics (SH), complete harmonic correction (HC) method, closed-form complete HC method, and Kadlec's method, their performances in gravity field determination have not been directly validated. In this study, we reviewed and evaluated these methods, especially for their performance in regional geoid determination. We found that the HC's expression for the closed-form complete method is identical to that under the unlimited Bouguer plate approximation, and Kadlec’s method is equivalent to the condensation method with the same approximation for Bouguer masses. However, the HC associated with the complete HC method shows large differences compared to other methods. This is because the upward and downward continuations in the complete HC method consider an Earth with changing total mass. To address it, we propose a new three-step approach, proved to be equivalent to the HC using the TS method. Then the performance of various HC methods is evaluated in gravity anomaly synthesis and geoid determination over a select region in Colorado, USA. The best result is achieved when using the SH method to compute RTM gravity anomalies, resulting in a geoid accuracy of ~ 1.62 cm. Involving the HC for the height anomaly in the restore procedure slightly improves the accuracy to ~ 1.56 cm.

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.

Gravity forward modeling provides important high-resolution information for the development of global gravity models, and can also be applied in many studies, e.g., topographic/isostatic effects computation and Bouguer anomaly maps compilation. In this paper, we present efficient spectral forward modeling approaches in the spheroidal harmonic domain, based on a single layer with constant density or volumetric layers with laterally varying density. With the binomial series expansion applied in spheroidal harmonic gravity forward modeling, the computational cost of these approaches is much lower than similar approaches. In both layering cases, we derive topographic potential models up to degree and order (d/o) 2190 by applying the approaches proposed here. Our methodology is evaluated by comparing these outcome models with other similar topographic potential models derived from spherical harmonic solutions. We find that topographic potentials from spheroidal and spherical harmonic approaches are in great agreement. Finally, the model named EHFM_Earth_7200 with a maximum degree of 7200 was derived by a layer-based approach. The evaluations by ground-truth data show that EHFM_Earth_7200 improves GO_CONS_GCF_2_DIR_R6 by 4% over Antarctica, and improves EGM2008 by ~ 34% over northern Canada. A global map of Bouguer gravity anomaly was also compiled with EHFM_Earth_7200 and EGM2008. As the main conclusion of this work, the new model EHFM_Earth_7200 is beneficial for investigating and modeling the Earth’s external gravity field, the new approaches have comparable accuracy to spherical harmonic approaches and are more suitable for practical use with guaranteed convergence regions because they are performed in the spheroidal harmonic domain.

Advancements in satellite altimetry have significantly enhanced high-resolution mean sea surface (MSS) models, enabling the computation of high-resolution vertical gravity anomaly gradient (VGAG) models. This study focused on the methodology for computing VGAG models using MSS models, introducing innovative improvements to established techniques. Using the SDUST2020 MSS model within the Arabian Sea research area, the DTU22 and CNES-CLS22 mean dynamic topography (MDT) models, and the XGM2019e_2159 Earth gravity field model for the remove–restore process, the short-wavelength geoid was derived. To harness the extensive marine gravity field information within the MSS model, the study considered the complex marine environment and calculated the second-order derivatives of the geoid in multiple directions. These derivatives were then used to determine their north–south and east–west components through the least squares method, resulting in the computation of the short-wavelength VGAG. By restoring the long-wavelength VGAG, a VGAG model for the study area was established. Finally, the results were analyzed using the SIO V32.1 VGAG model (named curv). Experimental results demonstrated that this approach effectively extracted marine gravity field information from the MSS model using multidirectional data, mitigating the amplification of geoid uncertainties caused by second-order derivatives. Graphical Abstract

Palu is one of the cities that is a residential center in carrying out socio-political and economic activities located in the Palu valley. The existence of the Palu-Koro fault makes this city very vulnerable to earthquake shocks. Earthquake activity causes strong rock deformation that allows the formation of local faults in the Palu Valley. One of the mitigation steps that can be taken is to map the geological structure in this city. This study aims to map the geological structure using horizontal gradients on gravity anomaly data. Gravity measurements were carried out in Palu City and its surroundings with a research area of approximately 11 km x 6 km. Furthermore, data processing and analysis were carried out using horizontal gradient techniques on residual gravity anomaly data. The study produced several local faults that were mapped and spread across the western and eastern regions of the Palu Valley in varying directions. In the western region of the Palu Valley, a fault was identified that extends from north to south. This fault is estimated to be the Palu-Koro fault plane formed by an earthquake.