Gradio: Project proposal for satellite gradiometry

A gradiometric approach, rather than the more complicated satellite to satellite tracking, is proposed for studying anomalies in the gravitational fields of the Earth and, possibly, other telluric bodies. The first analyses of a gradiometer based on four of ONERA's CACTUS or SUPERCACTUS accelerometers are summarized. it is shown that the obstacles to achieving the required accuracy are not insuperable. The device will be carried in a 1000 kg lens shaped satellite in a heliosynchronous orbit 200 to 300 km in altitude. The first launching is planned for the end of 1987

Analytical and numerical study of the ground-track resonances of Dawn orbiting Vesta

The aim of Dawn mission is the acquisition of data from orbits around two bodies, (4)Vesta and (1)Ceres, the two most massive asteroids. Due to the low thrust propulsion, Dawn will slowly cross and transit through ground-track resonances, where the perturbations on Dawn orbit may be significant. In this context, to safety go the Dawn mission from the approach orbit to the lowest science orbit, it is essential to know the properties of the crossed resonances. This paper analytically investigates the properties of the major ground-track resonances (1:1, 1:2, 2:3 and 3:2) appearing for Vesta orbiters: location of the equilibria, aperture of the resonances and period at the stable equilibria. We develop a general method using an averaged Hamiltonian formulation with a spherical harmonic approximation of the gravity field. If the values of the gravity field coefficient change, our method stays correct and applicable. We also discuss the effect of one uncertainty on the C20 and C22 coefficients on the properties of the 1:1 resonance. These results are checked by numerical tests. We determine that the increase of the eccentricity appearing in the 2:3 resonance is due to the C22 and S22 coefficients. Our method can be easily adapted to missions similar to Dawn because, contrarily to the numerical results, the analytical formalism stays the same and is valid for a wide range of physical parameters of the asteroid (namely the shape and the mass) as well as for different spacecraft orbits. Finally we numerically study the probability of the capture in resonance 1:1. Our paper reproduces, explains and supplements the results of Tricarico and Sykes (2010).Comment: 34 pages, 9 figures, 10 Table

Evaluation of high-degree series expansions of the topographic potential to higher-order powers

Mass associated with surface topography makes a significant contribution to the Earth’s gravitational potential at all spectral scales. Accurate computation in spherical harmonics to high degree requires calculations of multiple integer powers of the global topography. The purpose of this paper is to analyse the contributions of Earth’s topography to its potential to the tenth power of the topography, and quantify truncation errors resulting from neglecting higher-order powers. To account for the effect of gravity attenuation with height, we use series expansions for gravity upward-continuation to the Earth’s surface. With degree-2160 expansions, limitation to the first three powers of the topography, as often done in practice, may give rise to maximum truncation errors exceeding 100 mGal at a reference sphere, and ~25 mGal at the topography. Aiming for a maximum truncation error of 1 mGal we found that higher-order terms to the seventh power are required over the Himalaya Mountains as example of Earth’s most rugged land region. Upward-continuation of topographic gravity effects with mGal-precision from the sphere to the Earth’s surface is accomplished with a series expansion of fifth order. As a key finding, the accurate conversion of topography to gravity effects at the Earth’s surface is governed by two similar yet not identical series expansions. For degree-2160 expansions, we recommend that the powers of Earth’s topography be used up to seventh order to accurately evaluate the topographic potential to the mGal-level, as required, e.g., for the construction of high-resolution Bouguer gravity anomaly maps in spherical harmonics

How well can we measure the ocean’s mean dynamic topography from space?

Recent gravity missions have produced a dramatic improvement in our ability to measure the ocean’s mean dynamic topography (MDT) from space. To fully exploit this oceanic observation, however, we must quantify its error. To establish a baseline, we first assess the error budget for an MDT calculated using a 3rd generation GOCE geoid and the CLS01 mean sea surface (MSS). With these products, we can resolve MDT spatial scales down to 250 km with an accuracy of 1.7 cm, with the MSS and geoid making similar contributions to the total error. For spatial scales within the range 133–250 km the error is 3.0 cm, with the geoid making the greatest contribution. For the smallest resolvable spatial scales (80–133 km) the total error is 16.4 cm, with geoid error accounting for almost all of this. Relative to this baseline, the most recent versions of the geoid and MSS fields reduce the long and short-wavelength errors by 0.9 and 3.2 cm, respectively, but they have little impact in the medium-wavelength band. The newer MSS is responsible for most of the long-wavelength improvement, while for the short-wavelength component it is the geoid. We find that while the formal geoid errors have reasonable global mean values they fail capture the regional variations in error magnitude, which depend on the steepness of the sea floor topography

GOCE’s view below the ice of Antarctica: Satellite gravimetry confirms improvements in Bedmap2 bedrock knowledge

Accurate knowledge of Antarctica's topography, bedrock, and ice sheet thickness is pivotal for climate change and geoscience research. Building on recent significant progress made in satellite gravity mapping with European Space Agency's Gravity field and Ocean Circulation Explorer (GOCE) mission, we here reverse the widely used approach of validating satellite gravity with topography and instead utilize the new GOCE gravity maps for novel evaluation of Bedmap1/2. Space-collected GOCE gravity reveals clear improvements in the Bedmap2 ice and bedrock data over Bedmap1 via forward modeled topographic mass and gravity effects at spatial scales of 400 to 80 km. Our study demonstrates GOCE's sensitivity for the subsurface mass distribution in the lithosphere and delivers independent evidence for Bedmap2's improved quality, reflecting new radar-derived ice thickness data. GOCE and Bedmap2 are combined to produce improved Bouguer gravity maps over Antarctica. We recommend incorporation of Bedmap2 in future high-resolution global topography and geopotential models and its use for detailed geoid modeling over Antarctica

A comparison of GOCE and drifter-based estimates of the North Atlantic steady-state surface circulation

Over the last decade, due to the Gravity Recovery And Climate Experiment (GRACE) mission and, more recently, the Gravity and steady state Ocean Circulation Explorer (GOCE) mission, our ability to measure the ocean’s mean dynamic topography (MDT) from space has improved dramatically. Here we use GOCE to measure surface current speeds in the North Atlantic and compare our results with a range of independent estimates that use drifter data to improve small scales. We find that, with filtering, GOCE can recover 70% of the Gulf Steam strength relative to the best drifter-based estimates. In the subpolar gyre the boundary currents obtained from GOCE are close to the drifter-based estimates. Crucial to this result is careful filtering which is required to remove small-scale errors, or noise, in the computed surface. We show that our heuristic noise metric, used to determine the degree of filtering, compares well with the quadratic sum of mean sea surface and formal geoid errors obtained from the error variance–covariance matrix associated with the GOCE gravity model. At a resolution of 100 km the North Atlantic mean GOCE MDT error before filtering is 5 cm with almost all of this coming from the GOCE gravity model

New ultrahigh-resolution picture of Earth's gravity field

We provide an unprecedented ultrahigh resolution picture of Earth’s gravity over all continents and numerous islands within ±60° latitude. This is achieved through augmentation of new satellite and terrestrial gravity with topography data and use of massive parallel computation techniques, delivering local detail at ~200 m spatial resolution. As such, our work is the first-of-its-kind to model gravity at unprecedented fine scales yet with near-global coverage. The new picture of Earth’s gravity encompasses a suite of gridded estimates of gravity accelerations, radial and horizontal field components, and quasi-geoid heights at over 3 billion points covering 80% of Earth’s land masses. We identify new candidate locations of extreme gravity signals, suggesting that the Committee on Data for Science and Technology standard for peak-to-peak variations in free-fall gravity is too low by about 40%. The new models are beneficial for a wide range of scientific and engineering applications and freely available to the public

Constraints from GPS measurements on the dynamics of deformation in Anatolia and the Aegean

We estimate the strength of the lithosphere in Anatolia and the Aegean, and the boundary forces acting upon it, using a dynamical model that treats the lithosphere as a thin fluid sheet deforming in response to variations in gravitational potential energy. This model has one free material parameter, the power law exponent, n, of the vertically averaged rheology of the lithosphere, and two parameters that specify the forces per unit length applied to its edges. Solutions to this model that best fit the velocities of 346 reliable GPS sites require an effective viscosity of the lithosphere of 1022 to 1021 Pa s at strain rates of 10 to 100 nanostrain per year. The best-fitting force at the Arabia-Anatolia boundary is consistent with the lithostatic pressure due to the high topography there, and the force at the Nubia-Aegean boundary is consistent with the contrast in lithostatic pressure across that boundary. No additional force, from “slab rollback” or basal tractions due to convection in the mantle, is required to explain the observations. These results are supported by scaling relations derived from approximate analytical solutions. The inverse relationship between the viscosity of the lithosphere and deviatoric stress produces strong slowly deforming regions in the Southern Aegean and Central Anatolia whose motions resemble those of microplates. The distribution of geodetic strain rates within the region, and the partitioning between normal and strike-slip faulting, are explained by the interplay between boundary conditions, internal variations in gravitational potential energy, and the power law rheology of the lithosphere

Radio Science Investigation on a Mercury Orbiter Mission

We review the results from {\it Mariner 10} regarding Mercury's gravity field and the results from radar ranging regarding topography. We discuss the implications of improving these results, including a determination of the polar component, as well as the opportunity to perform relativistic gravity tests with a future {\it Mercury Orbiter}. With a spacecraft placed in orbit with periherm at 400 km altitude, apherm at 16,800 km, period 13.45 hr and latitude of periherm at +30 deg, one can expect a significant improvement in our knowledge of Mercury's gravity field and geophysical properties. The 2000 Plus mission that evolved during the European Space Agency (ESA) {\it Mercury Orbiter} assessment study can provide a global gravity field complete through the 25th degree and order in spherical harmonics. If after completion of the main mission, the periherm could be lowered to 200 km altitude, the gravity field could be extended to 50th degree and order. We discuss the possibility that a search for a Hermean ionosphere could be performed during the mission phases featuring Earth occultations. Because of its relatively large eccentricity and close proximity to the Sun, Mercury's orbital motion provides one of the best solar-system tests of general relativity. Consequently, we emphasize the number of feasible relativistic gravity tests that can be performed within the context of the parameterized post-Newtonian formalism - a useful framework for testing modern gravitational theories. We pointed out that current results on relativistic precession of Mercury's perihelion are uncertain by 0.5 %, and we discuss the expected improvement using {\it Mercury Orbiter}. We discuss the importance of {\it Mercury Orbiter} for setting limits on a possible time variation in theComment: 23 pages, LaTeX, no figure

USArray Imaging of Continental Crust in the Conterminous United States

The thickness and bulk composition of continental crust provide important constraints on the evolution and dynamics of continents. Crustal mineralogy and thickness both may influence gravity anomalies, topographic elevation, and lithospheric strength, but prior to the inception of EarthScope’s USArray, seismic measurements of crustal thickness and properties useful for inferring lithology are sparse. Here we improve upon a previously published methodology for joint inversion of Bouguer gravity anomalies and seismic receiver functions by using parameter space stacking of cross correlations of modeled synthetic and observed receiver functions instead of standard H-κ amplitude stacking. The new method is applied to estimation of thickness and bulk seismic velocity ratio, vP/vS, of continental crust in the conterminous United States using USArray and other broadband network data. Crustal thickness variations are reasonably consistent with those found in other studies and show interesting relationships to the history of North American continental formation. Seismic velocity ratios derived in this study are more robust than in other analyses and hint at large-scale variations in composition of continental crust. To interpret the results, we model the pressure-/temperature-dependent thermodynamics of mineral formation for various crustal chemistries, with and without volatile constituents. Our results suggest that hydration lowers bulk crustal vP/vS and density and releases heat in the shallow crust but absorbs heat in the lowermost crust (where plagioclase breaks down to pyroxene and garnet resulting in higher seismic velocity). Hence, vP/vS variations may provide a useful proxy for hydration state in the crust