Evaluation of the latest GOCE GGMs in support of regional geoid modeling over Greece

<p>In the frame of the GeoGravGOCE project, funded by the Hellenic Foundation for Research Innovation, GOCE Satellite Gravity Gradiometry (SGG) data are to be used for regional geoid and gravity field refinement as well as for potential determination in the frame of the International Height Reference Frame (IHRF). An inherent step in the geoid computation with either stochastic or spectral methods is the reduction of the related disturbing potential functionals within the well-known Remove-Compute-Restore (RCR) procedure. In this work we evaluate the latest, Release 6 (R6), satellite only and combined Global Geopotential Models (GGMs) which rely solely on GOCE and on land gravity data. The evaluation is performed over the established network of 1542 GPS/Levelling benchmarks over Greece mainland (BMs), which have been used in the past for the evaluation of GOCE GGMs. We employ the spectral enhancement approach, during which the GOCE-based GGMs are evaluated every one degree to the maximum degree of expansion coupled by EGM2008 and high-frequency RTM effects. This synthesis resolves wavelengths corresponding to maximum degree 216,000, hence the omission error is at the few mm-level. TIM-R6, DIR-R6, GOCO06s and XGM2019e are evaluated using EGM2008 residuals to the GPS/Levelling as the ground truth. From the results achieved, the optimal combination degree of a GOCE-only GGM augmented with EGM2008 is selected to be used in the sequel as reference field for the practical determination of the gravimetric geoid over Greece.</p>

GOCE SGG filtering with FIR, IIR and wavelet MRA

<p>GOCE Satellite Gravity Gradiometry (SGG) data have been widely used in gravity field research in order to provide improved representations of the gravity field spectrum either in the form of Global Geopotential Models (GGMs) or grids at satellite altitude. One of the key points in utilizing SGG observations is their proper filtering, in order to remove noise and long-wavelength correlated error, while the signals in the GOCE measurement bandwidth (MBW) should be preserved. Due to the gradiometer’s design, the GOCE satellite can achieve high accuracy and stable measurements in the MBW of 0.005 Hz to 0.1 Hz. The gravity gradient in MBW are at an equivalent accuracy level, while   are of lower accuracy. Outside of the MBW, systematic errors, colored noise, and noise with sharp peaks are observed, especially in the frequencies lower than 0.005 Hz. With that in mind, the present work focuses on the investigation of various filtering options ranging from Finite Impulse Response (FIR) filters, Infinite Impulse Response (IIR) filters, and filtering based on Wavelets. The latter are employed given their inherent characteristic of being localized both in frequency and space, meaning that the signal can be decomposed at different levels, thus allowing multi-resolution approximation (MRA). The analysis is performed with one month of GOCE SGG data in order to conclude on the method that provides the overall best results. SGG observations are reduced to a GGM in order to account for the long- and medium-wavelengths of the gravity field spectrum. Then, various filter orders are investigated for the FIR and IIR filters, while selective reconstruction is employed for the WL-MRA. Evaluation of the results is performed in terms of the smoothness of the filtered fields and the Power Spectral Density (PSD) functions of the entire GOCE tensor.</p>

An Improved Model of the Earth’s Static Gravity Field Solely Derived from Reprocessed GOCE Data

After it was found that the gravity gradients observed by the Gravity field and steady-state Ocean Circulation Explorer (GOCE) satellite could be significantly improved by an advanced calibration, a reprocessing project for the entire mission data set was initiated by ESA and performed by the GOCE High-level processing facility (GOCE HPF). One part of the activity was delivering the gravity field solutions, where the improved level 1b and level 2 data serve as an input for global gravity field recovery. One well-established approach for the analysis of GOCE observations is the so-called time-wise approach. Basic characteristics of the GOCE time-wise solutions is that only GOCE observations are included to remain independent of any other gravity field observables and that emphasis is put on the stochastic modeling of the observations’ uncertainties. As a consequence, the time-wise solutions provide a GOCE-only model and a realistic uncertainty description of the model in terms of the full covariance matrix of the model coefficients. Within this contribution, we review the GOCE time-wise approach and discuss the impact of the improved data and modeling applied in the computation of the new GO_CONS_EGM_TIM_RL06 solution. The model reflects the Earth’s static gravity field as observed by the GOCE satellite during its operation. As nearly all global gravity field models, it is represented as a spherical harmonic expansion, with maximum degree 300. The characteristics of the model and the contributing data are presented, and the internal consistency is demonstrated. The updated solution nicely meets the official GOCE mission requirements with a global mean accuracy of about 2 cm in terms of geoid height and 0.6 mGal in terms of gravity anomalies at ESA’s target spatial resolution of 100 km. Compared to its RL05 predecessor, three kinds of improvements are shown, i.e., (1) the mean global accuracy increases by 10–25%, (2) a more realistic uncertainty description and (3) a local reduction of systematic errors in the order of centimeters.

Sequential inversion of GOCE satellite gravity gradient data and terrestrial gravity data for the lithospheric density structure in the North China Craton

The North China Craton (NCC) is one of the oldest cratons in the world. Currently, the destruction mechanism and geodynamics of the NCC remain controversial. All of the proposed views regarding the issues involve studying the internal density structure of the NCC lithosphere. Gravity field data are among the most important data in regard to investigating the lithospheric density structure, and gravity gradient data and gravity data each possess their own advantages. Given the different observational plane heights between the on-orbit GOCE (Gravity Field and Steady-State Ocean Circulation Explorer) satellite gravity gradient and terrestrial gravity and the effects of the initial density model on the inversion results, sequential inversion of the gravity gradient and gravity are divided into two integrated processes. By using the preconditioned conjugate gradient (PCG) inversion algorithm, the density data are calculated using the preprocessed corrected gravity anomaly data. Then, the newly obtained high-resolution density data are used as the initial density model, which can serve as constraints for the subsequent gravity gradient inversion. Several essential corrections are applied to the four gravity gradient tensors (Txx, Txz, Tyy, Tzz) of the GOCE satellite, after which the corrected gravity gradient anomalies (T′xx, T′xz, T′yy, T′zz) are used as observations. The lithospheric density distribution result within the depth range of 0–180 km in the NCC is obtained. This study clearly illustrates that GOCE data are helpful in understanding the geological settings and tectonic structures in the NCC with regional scale. The inversion results show that in the crust the eastern NCC is affected by lithospheric thinning with obvious local features. In the mantle, the presented obvious negative-density areas are mainly affected by the high-heat-flux environment. In the eastern NCC, the density anomaly in the Bohai Bay area is mostly attributed to the extension of the Tancheng–Lujiang major fault at the eastern boundary. In the western NCC, the crustal density anomaly distribution of the Qilian block is consistent with the northwest–southeast strike of the surface fault belt, whereas such an anomaly distribution experiences a clockwise rotation to a nearly north–south direction upon entering the mantle.

High-resolution numerical modelling of the altimetry-derived gravity disturbances and disturbing gradients

<p>Recent high-resolution mean sea surface models obtained from satellite altimetry in a combination with the GRACE/GOCE-based global geopotential models provide valuable information for detailed modelling of the altimetry-derived gravity data. Our approach is based on a numerical solution of the altimetry-gravimetry boundary-value problem using the finite volume method (FVM). FVM discretizes the 3D computational domain between an ellipsoidal approximation of the Earth's surface and an upper boundary chosen at a mean altitude of the GOCE satellite orbits. A parallel implementation of the finite volume numerical scheme and large-scale parallel computations on clusters with distributed memory allow to get a high-resolution numerical solution in the whole 3D computational domain. Our numerical experiment presents the altimetry-derived gravity disturbances and disturbing gradients determined with the high-resolution 1 x 1 arc min at two altitude levels; on the reference ellipsoid and at the altitude of 10 km above the ellipsoid. As input data, the Dirichlet boundary conditions over oceans/seas are considered in the form of the disturbing potential. It is obtained from the geopotential evaluated on the DTU18 mean sea surface model from the GO_CONS_GCF_2_TIM_R5 geopotential model and then filtered using the nonlinear diffusion filtering. On the upper boundary, the FVM solution is fixed to the disturbing potential generated from the GO_CONS_GCF_2_DIR_R5 model while exploiting information from the GRACE and GOCE satellite missions.</p>

Joint inversion of the lithospheric density struture in the North China Craton based on GOCE satellite gravity gradient data and surface gravity data

<p>The North China Craton (NCC) is one of the oldest cratons in the world. Currently, the destruction mechanism and geodynamics of the NCC still remain controversial. All of the proposed views regarding the issues involve studying the internal density structure of the NCC lithosphere. Gravity field data are one of the most important data in regard to investigating the lithospheric density structure, the gravity gradient data and the gravity data possess their own advantages. Given the inconsistency of the on orbit GOCE satellite gravity gradient and surface gravity observation plane height, also effects of the initial density model upon of the inversion results, the joint inversion of gravity gradient and gravity are divided into two integrated processes. By using the preconditioned conjugate gradient (PCG) inversion algorithm, the density data are calculated using the preprocessed remaining gravity anomaly data. The newly obtained high resolution density data are then used as the initial density model, which can be served as the constraints for the subsequent gravity gradient inversion. Downward continuation, terrain correction, interface undulation correction and long wavelength correction are performed for the four gravity gradient tensor data(<strong>T</strong><sub>xx</sub>，<strong>T</strong><sub>xz</sub>，<strong>T</strong><sub>yy</sub>，<strong>T</strong><sub>zz</sub>)of the Gravity field and steady-state Ocean Circulation Explorer (GOCE) satellite,  after which the remaining gravity gradient anomaly data(<strong>T</strong>'<sub>xx</sub>，<strong>T</strong>'<sub>xz</sub>，<strong>T</strong>'<sub>yy</sub>，<strong>T</strong>'<sub>zz</sub>) are used as the new observation quantity. Finally, the ultimate lithospheric density distribution within the depth range of 0–180 km in the NCC is obtained using the same PCG algorithm.</p>

Efficiency of the piecewise constant acceleration modeling - GOCE case study

<p>One of the valuable products of the Gravity Field and Steady-State Ocean Circulation Explorer (GOCE) mission is a centimeter-accuracy orbit of the GOCE satellite called the precise science orbit (PSO). This orbit, delivered by the European Space Agency (ESA), was the reference for the GOCE orbit modeling using the piecewise constant acceleration approach. Besides initial conditions, the piecewise constant accelerations (i.e. empirical accelerations) were estimated in the radial, along-track and cross-track direction, employing the dedicated package called Torun Orbit Processor (TOP). The TOP software is based on the classical least squares adjustment including the Cowell 8-th order numerical integration for an orbit prediction and the orbit improvement module, taking into account the gravity field model and the background models (BM) describing gravitational and non-gravitational perturbing forces. The positions of GOCE satellite on the reduced-dynamic PSO orbit were treated as observations in the orbit improvement process. A measure of the fit of estimated arcs and their accuracy was the RMS of the residuals between the estimated orbits and the corresponding reference ones. Different variants of the orbit estimation were obtained for the shorter  arcs (22.5, 45, 90 and 180 minutes)  and for the longer 1-day arcs. The solution variants were determined for different numbers of the estimated piecewise constant accelerations. Moreover, these numbers were different for the radial, along-track and cross-track direction. The obtained solutions depend on a kind of computational mode – with and without the BM models in the GOCE orbit modeling using the estimated piecewise constant accelerations. Additionally, for selected solutions, the distributions of the residuals in the aforementioned directions along the estimated arcs are presented. </p>

Joint inversion of the lithospheric density struture in the North China Craton based on GOCE satellite gravity gradient data and surface gravity data

The North China Craton (NCC) is one of the oldest cratons in the world. Currently, the destruction mechanism and geodynamics of the NCC still remain controversial. All of the proposed views regarding the issues involve studying the internal density structure of the NCC lithosphere. Gravity field data are one of the most important data in regard to investigating the lithospheric density structure, the gravity gradient data and the gravity data possess their own advantages. Given the inconsistency of the on orbit GOCE satellite gravity gradient and surface gravity observation plane height, also effects of the initial density model upon of the inversion results, the joint inversion of gravity gradient and gravity are divided into two integrated processes. By using the preconditioned conjugate gradient (PCG) inversion algorithm, the density data are calculated using the preprocessed remaining gravity anomaly data. The newly obtained high resolution density data are then used as the initial density model, which can be served as the constraints for the subsequent gravity gradient inversion. Several essential corrections are performed for the four gravity gradient tensor (Txx，Txz，Tyy，Tzz) of the GOCE satellite, after which the remaining gravity gradient anomaly (T'xx，