Three gravity field models, parameterized in terms of spherical harmonic coefficients, have been computed from 71 days of GOCE (Gravity field and steady-state Ocean Circulation Explorer) orbit and gradiometer data by applying independent gravity field processing methods. These gravity models are one major output of the European Space Agency (ESA) project GOCE High-level Processing Facility (HPF). The processing philosophies and architectures of these three complementary methods are presented and discussed, emphasizing the specific features of the three approaches. The resulting GOCE gravity field models, representing the first models containing the novel measurement type of gravity gradiometry ever computed, are analysed and assessed in detail. Together with the coefficient estimates, full variance-covariance matrices provide error information about the coefficient solutions. A comparison with state-of-the-art GRACE and combined gravity field models reveals the additional contribution of GOCE based on only 71 days of data. Compared with combined gravity field models, large deviations appear in regions where the terrestrial gravity data are known to be of low accuracy. The GOCE performance, assessed against the GRACE-only model ITG-Grace2010s, becomes superior at degree 150, and beyond. GOCE provides significant additional information of the global Earth gravity field, with an accuracy of the 2-month GOCE gravity field models of 10 cm in terms of geoid heights, and 3 mGal in terms of gravity anomalies, globally at a resolution of 100 km (degree/order 200).

/pdf/first-goce-gravity-field-models-derived-by-three-different-55q4c3j26r.pdf

First GOCE gravity field models derived by three different approaches

SUMMARY Modelling the geoid has been a widely used and successful approach in constraining flow and viscosity in the Earth’s mantle. However, details of the viscosity structure cannot be tightly constrained with this approach. Here, radial viscosity variations in four to five mantle layers (lithosphere, upper mantle, one to two transition zone layers, lower mantle) are computed with the aid of independent mineral physics results. A density model is obtained by converting s-wave anomalies from seismic tomography to density anomalies. Assuming both are of thermal origin, conversion factors are computed based on mineral physics results. From the density and viscosity model, a model of mantle flow, and the resulting geoid and radial heat flux profile are computed. Absolute viscosity values in the mantle layers are treated as free parameters and determined by minimizing a misfit function, which considers fit to geoid, ‘Haskell average’ determined from post-glacial rebound and the radial heat flux profile and penalizes if at some depth computed heat flux exceeds the estimated mantle heat flux 33 TW. Typically, optimized models do not exceed this value by more than about 20 per cent and fit the Haskell average well. Viscosity profiles obtained show a characteristic hump in the lower mantle, with maximum viscosities of about 10 23 Pa s just above the D �� layer— several hundred to about 1000 times the lowest viscosities in the upper mantle. This viscosity contrast is several times higher than what is inferred when a constant lower mantle viscosity is assumed. The geoid variance reduction obtained is up to about 80 per cent—similar to previous results. However, because of the use of mineral physics constraints, a rather small number of free model parameters is required, and at the same time, a reasonable heat flux profile is obtained. Results are best when the lowest viscosities occur in the transition zone. When viscosity is lowest in the asthenosphere, variance reduction is about 70‐75 per cent. Best results were obtained with a viscous lithosphere with a few times 10 22 Pa s. The optimized models yield a core-mantle boundary excess ellipticity several times higher than observed, possibly indicating that radial stresses are partly compensated due to non-thermal lateral variations within the lowermost mantle.

/pdf/models-of-large-scale-viscous-flow-in-the-earth-s-mantle-w7kmy8io9c.pdf

Models of large‐scale viscous flow in the Earth's mantle with constraints from mineral physics and surface observations

[1] Satellite laser ranging (SLR) data were used to determine the variations in the Earth's principal figure axis represented by the degree 2 and order 1 geopotential coefficients: C21 and S21. Significant variations at the annual and Chandler wobble frequencies appear in the SLR time series when the rotational deformation or “pole tides” (i.e., the solid Earth and ocean pole tides) were not modeled. The contribution of the ocean pole tide is estimated to be only ∼8% of the total annual variations in the normalized coefficients: / based on the analysis of SLR data. The amplitude of the nontidal annual variation of is only ∼ 30% of from the SLR time series. The estimates of the annual variation in from SLR, the Gravity Recovery and Climate Experiment (GRACE) and polar motion excitation function, are in a good agreement. The nature of the linear trend for the Earth's figure axis determined by these techniques during the last several years is in general agreement but does not agree as well with results predicted from current glacial isostatic adjustment (GIA) models. The “fluid Love number” for the Earth is estimated to be ∼0.9 based on the position of the mean figure axis from the GRACE gravity model GGM03S and the mean pole defined by the IERS 2003 conventions. The estimate of / from GRACE and SLR provides an improved constraint on the relative rotation of the core. The results presented here indicate a possible tilt of the inner core figure axis of ∼2° and ∼3 arc sec displacement for the figure axis of the entire core.

https://agupubs.onlinelibrary.wiley.com/doi/pdf/10.1029/2010JB000850

Variations of the Earth's figure axis from satellite laser ranging and GRACE

[1] Densities in the 400–500 km height region inferred from accelerometer measurements on the CHAMP and GRACE satellites are utilized to study the response to the isolated and severe geomagnetic storm of 20–21 November 2003. The CHAMP and GRACE satellites provide data at approximate local times of 1110/2310 and 1430/0230 hours, respectively. In a global sense, density increases of order 300–800% occur during this storm, with relatively little time delay at high latitudes and with about 4-hour delay at the equator. Significant latitudinal asymmetries in the response are discussed in the context of neutral wind patterns and enhanced summer versus winter Joule heating rates at high latitudes. Comparisons with the NRLMSISE-00 empirical model densities during this period show marked differences in amplitude of the response, as well as latitudinal and temporal structures. Evidence for a tight coupling between solar wind and neutral density variability is found for the high-latitude summer hemisphere near noon, in that densities near 410 km are very responsive to increases in solar wind dynamic pressure, even during periods when both Bz and By are near zero or positive. Filtering of the data reveals regional-scale (∼1000–2000 km) density anomalies that are common between the CHAMP and GRACE measurements. During the geomagnetic disturbance, alternating regions of density enhancements (∼50%) and depressions (∼50%) exist between the pole and low to middle latitudes that have the appearance of a standing wave pattern. During magnetically quiet intervals before and after the storm, daytime density depressions (∼4–8%) are seen that track the magnetic equator, while density enhancements (∼10%) track the latitudes of the ionospheric Appleton anomaly peaks. Large-scale (≥1000 km) wave-like structures are also prevalent during both day and night during the magnetic disturbance and extend throughout both hemispheres, consistent with the concept that these are associated with the so-called “direct” gravity waves forced in the auroral regions and propagating far from the source. Substantial variability is also present at medium scales (∼300–500 km), but these structures are confined mainly to middle to high latitudes, in accord with theoretical expectations. GRACE-A and GRACE-B data are used in a feasibility study of the detection of small-scale wave activity by taking advantage of the 30-s separation of the satellites in the same orbital plane. Despite the large amount of maneuvers, which are not always recorded, this first analysis is promising. Amplitude variations of order 10–20% and wave speeds of 1000–1500 m s−1 are observed.

https://agupubs.onlinelibrary.wiley.com/doi/pdf/10.1029/2005JA011284

Thermosphere density response to the 20-21 November 2003 solar and geomagnetic storm from CHAMP and GRACE accelerometer data

Dedicated gravity field missions—principles and aims

The Global Isostatic Gravity Model of the Earth

CHAMP Phase B: Executive Summary

EIGEN-05C - A new global mean Gravity Field Model from Combination of Satellite Mission and Altimetry/Gravimetry Surface data

EIGEN-GL05C - A new global combined high-resolution GRACE-based gravity field model of the GFZ-GRGS cooperation

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The Global Isostatic Gravity Model of the Earth

CHAMP Phase B: Executive Summary

EIGEN-05C - A new global mean Gravity Field Model from Combination of Satellite Mission and Altimetry/Gravimetry Surface data

EIGEN-GL05C - A new global combined high-resolution GRACE-based gravity field model of the GFZ-GRGS cooperation