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, we show that the traditionally defined Bouguer gravity anomaly needs a correction to become 'the no-topography gravity anomaly' and that the isostatic gravity anomaly is better defined ...by the latter anomaly plus a gravity anomaly compensation effect than by the Bouguer gravity anomaly plus a gravitational compensation effect. This is because only the new isostatic gravity anomaly completely removes and compensates for the topographic effect.
F. A. Vening Meinesz' inverse problem in isostasy deals with solving for the Moho depth from the known external gravity field and mean Moho depth (known, e.g. from seismic reflection data) by a regional isostatic compensation using a flat Earth approximation. H. Moritz generalized the problem to that of a global compensation with a spherical mean Earth approximation. The problem can be formulated mathematically as that of solving a non-linear Fredholm integral equation. The solutions to these problems are based on the condition of isostatic balance of the isostatic gravity anomaly, and, theoretically, this assumption cannot be met by the old definition of the isostatic gravity anomaly. We show how the Moho geometry can be solved for the gravity anomaly, gravity disturbance and disturbing potential, etc., and, from a theoretical point of view, all these solutions are the same.
Global Bathymetry and Topography at 15 Arc Sec: SRTM15 Tozer, B.; Sandwell, D. T.; Smith, W. H. F. ...
Earth and space science (Hoboken, N.J.),
October 2019, 2019-10-00, 20191001, 2019-10-01, Letnik:
6, Številka:
10
Journal Article
Recenzirano
Odprti dostop
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
The most comprehensive and precise gravity data for the sea region must be obtained for the Sub-Commission of gravity and geoid for Africa (The African Gravity and Geoid sub-commission (AGG) belongs ...to the Commission 2 of the International Association of Geodesy (IAG)). There are two gravity data sets available for the marine region. The first is the ship-borne gravity data set, which has large gaps but has good precision. The second is the regularly covered and less accurate gravity anomalies generated from satellite altimetry. The most effective fusion of the previous two gravity data sets is examined in this research. First, each data set has passed a gross-error detection scheme. Points with differences of more than 4.5 mGal between estimated and observed gravity anomalies were eliminated because they were deemed to have a blunder. The base has been entirely taken from the ship-borne gravity points since they are more precise (after the gross-error removal). At the altimetry data points, assessments have been made of the discrepancies between gravity anomalies generated by altimetry and ship-borne gravity anomalies. In most places, the employed ship-borne data and the used altimetry data exhibit an acceptable level of consistency. If altimetry-derived gravity anomalies deviate by more than 20 mGal from ship-borne gravity anomalies, they are disregarded. For the majority of nations, especially those with oceanic and maritime borders like Egypt, a mix of land gravity data and shipborne and altimetry data is necessary for exact regional geoid modelling. In nations where there are significant gaps in the terrestrial gravity anomalies, the shipborne and altimetry free-air anomalies are significant. Moreover, the smoothness of gravity database resulting from this investigation is used significantly in geophysical interpretation.
SUMMARY
We present a new global model for the Earth’s lithosphere and upper mantle (LithoRef18) obtained through a formal joint inversion of 3-D gravity anomalies, geoid height, satellite-derived ...gravity gradients and absolute elevation complemented with seismic, thermal and petrological prior information. The model includes crustal thickness, average crustal density, lithospheric thickness, depth-dependent density of the lithospheric mantle, lithospheric geotherms, and average density of the sublithospheric mantle down to 410 km depth with a surface discretization of 2° × 2°. Our results for lithospheric thickness and sublithospheric density structure are in excellent agreement with estimates from recent seismic tomography models. A comparison with higher resolution regional studies in a number of regions around the world indicates that our values of crustal thickness and density are an improvement over a number of previous global crustal models. Given the strong similarity with recent tomography models down to 410 km depth, LithoRef18 can be readily merged with these seismic models to include seismic velocities as part of the reference model. We include several analyses of robustness and reliability of input data, method and results. We also provide easy-to-use codes to interrogate the model and use its predictions for the development of higher-resolution models.
Considering the model‘s features and data fitting statistics, LithoRef18 will be useful in a wide range of geophysical and geochemical applications by serving as a reference or initial lithospheric model for (i) higher-resolution gravity, seismological and/or integrated geophysical studies of the lithosphere and upper mantle, (ii) including far-field effects in gravity-based regional studies, (iii) global circulation/convection models that link the lithosphere with the deep Earth, (iv) estimating residual, static and dynamic topography, (v) thermal modelling of sedimentary basins and (vi) studying the links between the lithosphere and the deep Earth, among others. Several avenues for improving the reliability of LithoRef18’s predictions are also discussed. Finally, the inversion methodology presented in this work can be applied in other planets for which potential field data sets are either the only or major constraints to their internal structures (e.g. Moon, Venus, etc.).
SUMMARY
Aegean Graben System is a significant member of the complex geology of western Turkey. The depths to the metamorphic basement reliefs in two major grabens have been reported by many ...geophysical studies. However, the sediment thicknesses of these graben basins still remain controversial due to the findings differing from each other. Thus, we have inverted the gravity data of the sedimentary cover–metamorphic basement using a stochastic derivative-free vector-based metaheuristic named differential evolution algorithm (DEA). This is the first application of DEA adapted to the basement relief depth problem. Model parametrizations have been achieved by discretizing the basins using a group of juxtaposed vertical blocks. Before the inversion studies, mathematical nature of the inverse problem has been investigated via prediction cost function/error energy maps for some block pairs using a hypothetical basin model. These maps have shown the resolvability characteristic of the block thicknesses on such inversion problem. Parameter tuning studies for the optimum mutation constant/weighting factor have been performed to increase the efficiency of the algorithm. The synthetic data have been successfully inverted via the tuned control parameter and some smoothing operators. Probability density function (PDF) analyses have shown that the best solutions are within the confidence interval limits without uncertainties. In the field data case, long-wavelength anomalies caused by both crustal and deeper effects have been removed from the complete Bouguer anomalies through 2-D finite element method using the element shape functions. Some profiles extracted from the residual gravity anomaly map have been used for the inversion and obtained results have shown that the maximum depths to the metamorphic basement reliefs in the grabens are shallower than the findings of the previous studies. Information obtained from the lithological logs drilled in the grabens has supported our results. Moreover, PDF analyses have indicated the reliability of the obtained solutions without uncertainties.
SUMMARY
Geophysical inverse problems are commonly ill-posed and require proper regularization to gain acceptable solutions. Adopting constraints on the smoothness and/or specified structures of an ...inverted geophysical model requires the implementation of regularization terms when either structured or unstructured meshes are used. Spatial gradients of the model parameters along axial or arbitrary directions are thus required. However, the calculation of spatial gradients on unstructured meshes is not straightforward since the interfaces between adjacent model cells (i.e. common edges or common faces) are orientated individually and usually are not perpendicular to the axial directions. Depending on the algorithm used, an uneven performance of the regularization is observed on unstructured meshes. To enforce effective and robust regularization terms for geophysical inversions on the unstructured meshes, we propose algorithms for constructing the smoothness and structural similarity operators that take advantage of the inherent merits of the unstructured meshes. Following a detailed introduction of the general inversion formula that we adopted, the smoothness and reference model constraints on triangular and tetrahedral meshes are proposed based on the neighbouring relationships between different model cells within the meshes. Particularly, a quasi-cross-gradient formulation is derived for triangular meshes suitable for the joint inversion of different kinds of geophysical data. Compared to existing algorithms, the new smoothness operator presents an equal or better performance for constraining the model roughness. In addition, the operator exploits the preferred elongation directions of the underground structures by performing varied constraints in different directions. Furthermore, the other new operator could effectively measure structural information of the inverted model even if the algorithms have incorporated sophisticated constraints from other geophysical or geological data. Demonstrated with the applications on synthetic examples, the new algorithms provide advanced regularization techniques for conducting geophysical inversions using unstructured meshes.
SUMMARY
We present a new global thermochemical model of the lithosphere and underlying upper mantle constrained by state of the art seismic waveform inversion, satellite gravity (geoid and gravity ...anomalies and gradiometric measurements from ESA's GOCE mission), surface elevation and heat flow data: WINTERC-G. The model is based upon an integrated geophysical–petrological approach where seismic velocities and density in the mantle are computed within a thermodynamically self-consistent framework, allowing for a direct parametrization in terms of the temperature and composition variables. The complementary sensitivities of the data sets allow us to constrain the geometry of the lithosphere–asthenosphere boundary, to separate thermal and compositional anomalies in the mantle, and to obtain a proxy for dynamic surface topography. At long spatial wavelengths, our model is generally consistent with previous seismic (or seismically derived) global models and earlier integrated studies incorporating surface wave data at lower lateral resolution. At finer scales, the temperature, composition and density distributions in WINTERC-G offer a new state of the art image at a high resolution globally (225 km average interknot spacing). Our model shows that the deepest lithosphere–asthenosphere boundary is associated with cratons and, also, some tectonically active areas (Andes, Persian Gulf). Among cratons we identify considerable differences in temperature and composition. The North American and Siberian Cratons are thick (>260 km) and compositionally refractory, whereas the Sino-Korean, Aldan and Tanzanian Cratons have a thinner, fertile lithosphere, similar to younger continental lithosphere elsewhere. WINTERC-G shows progressive thickening of oceanic lithosphere with age, but with significant regional differences: the lithospheric mantle beneath the Atlantic and Indian Oceans is, on average, colder, more fertile and denser than that beneath the Pacific Ocean. Our results suggest that the composition, temperature and density of the oceanic mantle lithosphere are related to the spreading rate for the rates up to 50–60 mm yr–1: the lower spreading rate, the higher the mantle fertility and density, and the lower the temperature. At greater spreading rates, the relationship disappears. The 1-D radial average of WINTERC-G displays a mantle geothermal gradient of 0.55–0.6 K km–1 and a potential temperature of 1300–1320 °C for depths >200 km. At the top of the mantle transition zone the amplitude of the maximum lateral temperature variations (cratons versus hotspots) is about 120 K. The isostatic residual topography values, a proxy for dynamic topography, are large (>1 km) mostly in active subduction settings. The residual isostatic bathymetry from WINTERC-G is remarkably similar to the pattern independently determined based on oceanic crustal data compilations. The amplitude of the continental residual topography is relatively large and positive (>600 m) in the East European Craton, Greenland, and the Andes and Himalayas. By contrast, central Asia, most of Antarctica, southern South America and, to a lesser extent, central Africa are characterized by negative residual topography values (>–400 m). Our results show that a substantial part of the topography signal previously identified as residual (or dynamic) is accounted for, isostatically, by lithospheric density variations.
SUMMARY
HY-2A is China's first satellite altimeter mission, launched in Aug. 2011. Its geodetic mission (GM) started from 2016 March 30 till present, collecting sea surface heights for about five ...168-d cycles. To test how the HY-2A altimeter performs in marine gravity derivation, we use the least-squares collocation method to determine marine gravity anomalies on 1′ × 1′ grids around the South China Sea (covering 0°–30°N, 105°E–125°E) from the HY-2A/GM-measured geoid gradients. We assess the qualities of the HY-2A/GM-derived gravity over different depths and areas using the bias and tilt-adjusted ship-borne gravity anomalies from the U.S. National Centers for Environmental Information (NCEI) and the Second Institute of Oceanography, Ministry of Natural Resources (MNR) of P. R. China. The RMS difference between the HY-2A/GM-derived and the NCEI ship-borne gravity is 5.91 mGal, and is 5.33 mGal when replacing the HY-2A value from the Scripps Institution of Oceanography (SIO) V23.1 value. The RMS difference between the HY-2A/GM-derived and the MNR ship-borne gravity is 2.90 mGal, and is 2.76 mGal when replacing the HY-2A value from the SIO V23.1 value. The RMS difference between the HY-2A and SIO V23.1 value is 3.57 mGal in open sea areas at least 20 km far away from the coast. In general, the difference between the HY-2A/GM-derived gravity and ship-borne gravity decreases with decreasing gravity field roughness and increasing depth. HY-2A results in the lowest gravity accuracy in areas with islands or reefs. Our assessment result suggests that HY-2A can compete with other Ku-band altimeter missions in marine gravity derivation.
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