Possibilities of inversion of satellite third-order gravitational tensor onto gravity anomalies: a case study for central Europe

Wed 04 Sep 2019 09:55:16 AEST

We investigate a numerical performance of four different schemes applied to a regional recovery of the gravity anomalies from the third-order gravitational tensor components (assumed to be observable in the future) synthetized at the satellite altitude of 200 km above the mean sphere. The first approach is based on applying a regional inversion without modelling the far-zone contribution or long-wavelength support. In the second approach we separate integral formulas into two parts, that is, the effects of the third-order disturbing tensor data within near and far zones. Whereas the far-zone contribution is evaluated by using existing global geopotential model (GGM) with spectral weights given by truncation error coefficients, the near-zone contribution is solved by applying a regional inversion. We then extend this approach for a smoothing procedure, in which we remove the gravitational contributions of the topographic-isostatic and atmospheric masses. Finally, we apply the remove-compute-restore (r-c-r) scheme in order to reduce the far-zone contribution by subtracting the reference (long-wavelength) gravity field, which is computed for maximum degree 80. We apply these four numerical schemes to a regional recovery of the gravity anomalies from individual components of the third-order gravitational tensor as well as from their combinations, while applying two different levels of a white noise. We validated our results with respect to gravity anomalies evaluated at the mean sphere from EGM2008 up to the degree 250. Not surprisingly, better fit in terms of standard deviation (STD) was attained using lower level of noise. The worst results were gained applying classical approach, STD values of our solution from T_zzz are 1.705 mGal (noise value with a standard deviation 0.01 × 10⁻¹⁵m⁻¹s⁻²) and 2.005 mGal (noise value with a standard deviation 0.05 × 10⁻¹⁵m⁻¹s⁻²), while the superior from r-c-r up to the degree 80, STD fit of gravity anomalies from T_zzz with respect to the same counterpart from EGM2008 is 0.510 mGal (noise value with a standard deviation 0.01 × 10⁻¹⁵m⁻¹s⁻²) and 1.190 mGal (noise value with a standard deviation 0.05 × 10⁻¹⁵m⁻¹s⁻²).

Spectral combination of spherical gravitational curvature boundary-value problems

Tue 02 Aug 2022 14:38:25 AEST

Four solutions of the spherical gravitational curvature boundary-value problems can be exploited for the determination of the Earth's gravitational potential. In this paper we discuss the combination of simulated satellite gravitational curvatures, that is, components of the thirdorder gravitational tensor, by merging these solutions using the spectral combination method. For this purpose, integral estimators of biased- and unbiased-types are derived. In numerical studies, we investigate the performance of the developed mathematical models for the gravitational fieldmodelling in the area of Central Europe based on simulated satellite measurements. First, we verify the correctness of the integral estimators for the spectral downward continuation by a closed-loop test. Estimated errors of the combined solution are about eight orders smaller than those from the individual solutions. Second, we perform a numerical experiment by considering the Gaussian noise with the standard deviation of 6.5 × 10-17m-1s-2in the input data at the satellite altitude of 250 km above the mean Earth sphere. This value of standard deviation is equivalent to a signal-to-noise ratio of 10. Superior results with respect to the global geopotential model TIM-r5 (Brockmann et al. 2014) are obtained by the spectral downward continuation of the vertical-vertical-vertical component with the standard deviation of 2.104 m2s-2, but the root mean square error is the largest and reaches 9.734 m2s-2. Using the spectral combination of all gravitational curvatures the root mean square error is more than 400 times smaller but the standard deviation reaches 17.234 m2s-2. The combination of more components decreases the root mean square error of the corresponding solutions while the standard deviations of the combined solutions do not improve as compared to the solution from the vertical-vertical-vertical component. The presented method represents a weight mean in the spectral domain that minimizes the root mean square error of the combined solutions and improves standard deviation of the solution based only on the least accurate components.

Comparison of spherical cap and rectangular harmonic analysis of airborne vector gravity data for high-resolution (1.5 km) local geopotential field models over Tanzania

Thu 13 Apr 2023 09:38:45 AEST

This study examines local geopotential field modeling over a mountainous region in Tanzania using vector airborne gravity data. We use the adjusted spherical cap and rectangular harmonic analyses. Both methods are based on expansion of gravitational potential into a series of orthogonal harmonic basis functions of local support in such a way that the expansion coefficients are determined by gravity observations. All three components of gravity vector are simultaneously inverted to derive the geopotential coefficients. In order to evaluate the accuracy of the local models, independent checkpoints are selected within the study region and around its boundary and the computed gravity vectors are compared with the independent gravity observations. The results show an excellent agreement with root mean square error (RMSE) of < 1.6 mGal over the study area. On the contrary, the RMSEs of global geopotential models against the checkpoints data are 7 mGal for the models up to the maximum degree of 2190 (a resolution of ∼9.1 km) and 5 mGal to 5399 (∼3.7 km). Our local models are significantly more accurate than the state-of-the-art global models and fully exploit the airborne vector data with the measurement error of ∼1 mGal. We also present the regional models constrained only by radial (vertical) or by lateral (horizontal) gravity observations. Those models are considerably less accurate than the one from 3D gravity data inversion. Lastly, the regional models are validated against topography data. It is found that the gravity-topography correlation is 0.8–0.9 at 100 km, 0.5 at 20 km, and higher than the correlations of the global models at all frequencies. The gravity-topography admittances estimated from our regional models indicate ∼130 mGal/km and imply the effective density of 2500 kg/m3 for topographical mass.

Determination of ellipsoidal surface mass change from GRACE time-variable gravity data

Fri 11 Nov 2022 19:54:47 AEDT

The problem of determining mass redistribution within the Earth system from time-variable gravity (TVG) data is non-unique. Over seasonal and decadal time-scales, mass redistribution likely takes place on the Earth’s surface. By approximating the Earth’s surface by a sphere, surface mass variation can be uniquely determined from TVG data. Recently, using the improved GRACE TVG data, Li et al. and Ditmar found that such spherical approximation is no longer tenable and suggested practical approaches to accommodate the elliptical shape of the Earth. In this study, we develop a rigorous method of determining surface mass change on the Earth’s reference ellipsoid. We derive a unique one-to-one relationship between ellipsoidal spectra of surface mass and gravitational potential for the ellipsoidal geometry. In conjunction with our ellipsoidal formulation, the linear transformation between spherical and ellipsoidal harmonic coefficients of the geopotential field enables us to determine mass redistribution on the ellipsoid from GRACE TVG data. Using the Release 6 of GRACE TVG data to degree 60, we show that the ellipsoidal approach reconciles surface mass change rate significantly better than the spherical computation by 3–4 cm yr⁻¹, equivalent to 10–15 per cent increase of total signal, in Greenland and West Antarctica. We quantify the spherical approximation error over the polar regions using GRACE Level-2 TVG data as well as mascon solutions, and demonstrate that the systematic error increases linearly with the maximum degree used for the synthesis. The terrestrial water storage computation is less affected by the spherical approximation because of geographic location of major river basins (lower latitude) and signal characteristics. The improvement of TVG data from GRACE and its Follow-On necessitates the ellipsoidal computation, particularly for quantifying mass change in polar regions.