GOCE Gradients Research Articles

Lithosphere density structure beneath the eastern margin of the Tibetan Plateau and its surrounding areas derived from GOCE gradients data

A three-dimensional density model of the crust and uppermost mantle is determined by the inversion of a set of GOCE gravity and gradients residual anomalies beneath the eastern margin of the Tibetan Plateau and its surrounding areas. In our work, we choose five independent gravity gradients (Txx, Tzz, Txy, Txz, Tyz) to perform density inversion. Objective function is given based on Tikhonov regularization theory. Seismic S-wave velocities play the role of initial constraint for the inversion based on a relationship between density and S-wave velocity. Damped Least Square method is used during the inversion. The final density results offer some insights into understanding the underlying geodynamic processes: (1) Low densities in the margin of the Tibet, along with low wave velocity and resistivity results, yield conversions from soft and weak Tibet to the hard and rigid cratons. (2)The lowest densities are found in the boundary of the plateau, instead of the whole Tibet indicates that the effects of extrusion stress environment in the margin affect the changes of the substance there. The substances and environments conditioning for the earthquake preparations and strong deformation in this transitional zone. (3) Evident low-D anomaly in the upper and middle crust in the Lasha terrane and Songpan-Ganzi terrane illustrated the eastward sub-ducted of southeastern Tibet, which could be accounts for the frequent volcano and earthquakes there.

Upward continuation of Dome-C airborne gravity and comparison with GOCE gradients at orbit altitude in east Antarctica

An airborne gravity campaign was carried out at the Dome-C survey area in East Antarctica between the 17th and 22nd of January 2013, in order to provide data for an experiment to validate GOCE satellite gravity gradients. After typical filtering for airborne gravity data, the cross-over error statistics for the few crossing points are 11.3 mGal root mean square (rms) error, corresponding to an rms line error of 8.0 mGal. This number is relatively large due to the rough flight conditions, short lines and field handling procedures used. Comparison of the airborne gravity data with GOCE RL4 spherical harmonic models confirmed the quality of the airborne data and that they contain more high-frequency signal than the global models. First, the airborne gravity data were upward continued to GOCE altitude to predict gravity gradients in the local North-East-Up reference frame. In this step, the least squares collocation using the ITGGRACE2010S field to degree and order 90 as reference field, which is subtracted from both the airborne gravity and GOCE gravity gradients, was applied. Then, the predicted gradients were rotated to the gradiometer reference frame using level 1 attitude quaternion data. The validation with the airborne gravity data was limited to the accurate gradient anomalies (TXX, TYY, TZZ and TXZ) where the long-wavelength information of the GOCE gradients has been replaced with GOCO03s signal to avoid contamination with GOCE gradient errors at these wavelengths. The comparison shows standard deviations between the predicted and GOCE gradient anomalies TXX, TYY, TZZ and TXZ of 9.9, 11.5, 11.6 and 10.4 mE, respectively. A more precise airborne gravity survey of the southern polar gap which is not observed by GOCE would thus provide gradient predictions at a better accuracy, complementing the GOCE coverage in this region.

An iterative Wiener filtering method based on the gravity gradient invariants

How to deal with colored noises of GOCE (Gravity field and steady – state Ocean Circulation Explorer) satellite has been the key to data processing. This paper focused on colored noises of GOCE gradient data and the frequency spectrum analysis. According to the analysis results, gravity field model of the optimal degrees 90–240 is given, which is recovered by GOCE gradient data. This paper presents an iterative Wiener filtering method based on the gravity gradient invariants. By this method a degree-220 model was calculated from GOCE SGG (Satellite Gravity Gradient) data. The degrees above 90 of ITG2010 were taken as the prior gravity field model, replacing the low degree gravity field model calculated by GOCE orbit data. GOCE gradient colored noises was processed by Wiener filtering. Finally by Wiener filtering iterative calculation, the gravity field model was restored by space-wise harmonic analysis method. The results show that the model's accuracy matched well with the ESA's (European Space Agency) results by using the same data.

A refined model of sedimentary rock cover in the southeastern part of the Congo basin from GOCE gravity and vertical gravity gradient observations

We aim to interpret the vertical gravity and vertical gravity gradient of the GOCE-GRACE combined gravity model over the southeastern part of the Congo basin to refine the published model of sedimentary rock cover. We use the GOCO03S gravity model and evaluate its spherical harmonic representation at or near the Earth's surface. In this case, the gradiometry signals are enhanced as compared to the original measured GOCE gradients at satellite height and better emphasize the spatial pattern of sedimentary geology.To avoid aliasing, the omission error of the modelled gravity induced by the sedimentary rocks is adjusted to that of the GOCO03S gravity model. The mass-density Green's functions derived for the a priori structure of the sediments show a slightly greater sensitivity to the GOCO03S vertical gravity gradient than to the vertical gravity. Hence, the refinement of the sedimentary model is carried out for the vertical gravity gradient over the basin, such that a few anomalous values of the GOCO03S-derived vertical gravity gradient are adjusted by refining the model. We apply the 5-parameter Helmert's transformation, defined by 2 translations, 1 rotation and 2 scale parameters that are searched for by the steepest descent method.The refined sedimentary model is only slightly changed with respect to the original map, but it significantly improves the fit of the vertical gravity and vertical gravity gradient over the basin. However, there are still spatial features in the gravity and gradiometric data that remain unfitted by the refined model. These may be due to lateral density variation that is not contained in the model, a density contrast at the Moho discontinuity, lithospheric density stratifications or mantle convection.In a second step, the refined sedimentary model is used to find the vertical density stratification of sedimentary rocks. Although the gravity data can be interpreted by a constant sedimentary density, such a model does not correspond to the gravitational compaction of sedimentary rocks. Therefore, the density model is extended by including a linear increase in density with depth. Subsequent L2 and L∞ norm minimization procedures are applied to find the density parameters by adjusting both the vertical gravity and the vertical gravity gradient.We found that including the vertical gravity gradient in the interpretation of the GOCO03S-derived data reduces the non-uniqueness of the inverse gradiometric problem for density determination. The density structure of the sedimentary formations that provide the optimum predictions of the GOCO03S-derived gravity and vertical gradient of gravity consists of a surface density contrast with respect to surrounding rocks of 0.24–0.28g/cm3 and its decrease with depth of 0.05–0.25g/cm3 per 10km. Moreover, the case where the sedimentary rocks are gravitationally completely compacted in the deepest parts of the basin is supported by L∞ norm minimization. However, this minimization also allows a remaining density contrast at the deepest parts of the sedimentary basin of about 0.1g/cm3.

Sensitivity of Goce Gradients on Greenland Mass Variation And Changes in Ice Topography

Abstract The Gravity field and steady state Ocean Circulation Explorer (GOCE) maps variations in the gravity field by observing second order derivatives (gradients) of the Earth gravitational potential. Flying in the low altitude of 255 km and having a spatially dense data distribution of short wavelengths of the gravity field, GOCE may be used to enhance the time varying gravity signal coming fromthe GRACE satellites. The GOCE gradients may potentially be used for the determination of residual masses in local regions. This can be done using Least-Squares Collocation (LSC) or the Reduced Point Mass (RPM) method. In this study, different gravity field solutions are calculated by the use of RPM, LSC and GOCE gradients, respectively. Gravity field time series are created and presented for the six consecutive months of GOCE gradient observations, data being acquired between November 2009 and June 2010. Corresponding gravity anomaly results are used for the calculation of ice mass changes by the use of theRPMmethod. The results are then compared with the computed topographic effect of the ice by the use of a modified topographic correction and the Gravsoft TC program. The maximal gravity changes at the ground predicted from GOCE gradients are between 2 and 4 mGal for the period considered. The gravity anomaly estimation error arising from the GOCE gradient data using only Tzz with an associated error of 20 mE is 11 mGal. This analysis shows the potential of using GOCE data for observations of ice mass changes although the GOCE dataset is limited to only six months. We expect four years of GOCE gradient observations to be available by mid-2014. This will increase the accuracy and spatial resolution of the GOCE measurements, which may lead to an accuracy necessary for observing ice mass changes.

Gravity field model calculated by using the GOCE data

Global static gravitational field determined by GOCE satellite data has become a hotspot in current research of geodesy. In this paper, a global static gravity field model entitled SWJTU-GO01S up to the degree and order 210 is recovered based on 12 months of GOCE orbit and gradient data from 2011-02-28 to 2012-03-05 with direct approach. GOCE gradient data are filtered by the zero phase finite impulse band-pass digital filter, and then a gradient observation equation is founded directly in gradiometer coordinates, which avoids high-accuracy gradient component loss in accuracy in the conversion process, while the orbit data is processed with short-arc integral approach. The optimal weight of combination result based on SST and SGG data is determined by variance component estimation and the polar gaps is dealt with the Kuala regularization method. Comparison of internal and external precision of SWJTU-GO01S with EGM2008 and with GPS leveling data of North America, shows that the geoid error and cumulative error of the SWJTU-GO01S model with the degree and order 210 are 2.1 cm and 13.7 cm respectively. Compared with the second generation models released by ESA and ITG-GRACE2010S, the accuracy of the model SWJTU-GO01S is higher than that of the model ITG-GRACE2010S and ESA official time-wise and space-wise model in the above degree and order 150. This study provides a reference to further joint multi-class satellite observation data to recover gravity field models.

Reference frame transformation of satellite gravity gradients and topographic mass reduction

The Gravity field and steady state Ocean Circulation Explorer (GOCE) is the European Space Agency's mission that combines GPS tracking and gravity gradiometry to determine the Earth's mean gravity field with unprecedented, global accuracy with a spatial resolution down to 80 km. This resolution makes GOCE gravity gradient data in particular useful for lithospheric scale modeling. However, the relation between coordinates in a model frame and at satellite altitude is not straightforward, and most geophysical modeling programs require a planar approximation, which may not be appropriate for satellite data. We derive the exact relation between the model reference frame, in which gradients from lithospheric modeling are given, and the local north‐oriented frame in which GOCE gradients at 255 km altitude are given. We generated gradients from a GOCE gravity field model and assessed whether the orientation differences between local north‐oriented frame and model reference frame are relevant. In addition, we assessed the same for airborne gradiometry at an altitude of 5 km because these data are complementary to GOCE. We find that if the regional area has a longitude extension of 5°, the errors stay below 10%. For larger areas the standard deviation of the systematic errors may be 40% of the signal standard deviation. Comparing topographic mass reduction in planar and spherical approximation, one sees significant long wavelength differences in terms of gravity gradients or gradient‐tensor invariants. The maximum error is up to 1 E at satellite altitude compared with maximum signal amplitude of 3 E. Planar approximation is therefore not accurate enough for topographic mass reduction of GOCE gravity gradients.

GOCE gravity gradients versus global gravity field models

The GOCE mission, a part of ESA′s Living Planet Programme, aims at improved gravity field modelling at high spatial resolution. On-board GOCE a gradiometer, in combination with a scientific on-board GPS receiver, measures the earth′s gravity field with unprecedented accuracy. These measurements have been used to compute GOCE gravity field solutions and combined GOCE/GRACE solutions. The main difference between the solutions is how they incorporate the required a priori information, which consists either of existing gravity field models or Kaula′s rule for the signal variances of the gravity field. We assessed four series of models by comparing the gravity gradients they predict with the measured GOCE gradients. The analysis of the gravity gradients fits may reveal differences between the different solutions that can be attributed to the solution strategy, assuming that the measurement errors are homogeneous. We compared the GOCE gradients with existing state-of-the-art global gravity field models and conclude that the gradient errors are indeed globally homogeneous, with the exception of the cross-track gradient especially south of Australia. Furthermore, we find that the use of existing global gravity field models as a priori information should be avoided because this may increase the gradient residuals in spatial and spectral domain. Finally, we may conclude that the GOCE and GRACE data are compatible and complementary.

Combined satellite gravity field model GOCO01S derived from GOCE and GRACE

The satellite‐only gravity field model GOCO01S is a combination solution based on 61 days of GOCE gravity gradient data, and 7 years of GRACE GPS and K‐band range rate data, resolved up to degree/order 224 of a harmonic series expansion. The combination was performed consistently by addition of full normal equations and stochastic modeling of GOCE and GRACE observations. The model has been validated against external global gravity models and regional GPS/leveling observations. While low to medium degrees are mainly determined by GRACE, significant contributions by the new measurement type of GOCE gradients can already be observed at degree 100. Beyond degree 150, GOCE becomes the dominant contributor. Correspondingly, with GOCO01S a global gravity field model with high performance for the complete spectral range up to degree/order 224 is now available. This new gravity model will be beneficial for many applications in geophysics, oceanography, and geodesy.

Calibration of GOCE SGG data using high?low SST, terrestrial gravity data and global gravity field models

It is the aim of the GOCE mission to determine a model of the Earth’s gravity field with high accuracy and resolution. For this purpose, gravity gradients will be measured in combination with high–low satellite-to-satellite tracking. The gravity gradients are derived from pair-wise differenced accelerations as determined by the six three-axes accelerometers that form the GOCE gradiometer. Since the measured accelerations suffer from errors of a random and systematic nature, the gravity gradients may suffer from random and systematic errors as well. Systematic errors are, for example, a scale factor and a bias. The common accelerations of the paired accelerometers also are contaminated with such errors. The common accelerations are used in the drag-free control of the satellite and are important for the separation of the gravitational and non-gravitational forces in the gravity field determination. The checking of the gravity gradients and the common accelerations against independent data (i.e. external to the GOCE satellite) in order to free the observations as well as is possible from systematic errors is called external calibration. The possibilities and limitations of using terrestrial gravity data and global gravity models for external calibration of the gravity gradients are reviewed. It turns out that the determination of a gravity gradient scale factor and bias using just the accurate knowledge of the central term and the flattening (J2) of the Earth’s gravity field is not good enough. When global gravity field models are used for the calibration, higher degrees and orders should be taken into account as well. With today’s existing global models it seems to be possible to remove the greater part of the systematic errors of the GOCE gradients. A gravity gradient bias can accurately be recovered using terrestrial gravity data in a regional approach with least squares collocation. However, since regional data are used it may not be possible to determine calibration parameters valid for the whole (global) gravity gradient data set. Nevertheless, regional terrestrial gravity data could be used to validate the measured and calibrated gravity gradients. In addition, a possible use of GOCE high–low satellite-to-satellite tracking data to calibrate the common accelerations is explored; it is shown that this approach fails. If more accurate gravity field information becomes available then such a calibration may become feasible.