Gravity Field And Steady-state Ocean Circulation Explorer Gravity Gradients Research Articles

The earth\u2019s gravity field recovery using the third invariant of the gravity gradient tensor from GOCE

Due to the independence of the gradiometer instrument’s orientation in space, the second invariant I_2 of gravity gradients in combination with individual gravity gradients are demonstrated to be valid for gravity field determination. In this contribution, we develop a novel gravity field model named I3GG, which is built mainly based on three novel elements: (1) proposing to utilize the third invariant I_3 of the gravity field and steady-state ocean circulation explorer (GOCE) gravity gradient tensor, instead of using the I_2, similar to the previous studies; (2) applying an alternative two-dimensional fast fourier transform (2D FFT) method; (3) showing the advantages of I_3 over I_2 in the effect of measurement noise from the theoretical and practical computations. For the purpose of implementing the linearization of the third invariant, this study employs the theory of boundary value problems with sphere approximation at an accuracy level of O(J_2^2cdot T_{ij}). In order to efficiently solve the boundary value problems, we proposed an alternative method of 2D FFT, which uses the coherent sampling theory to obtain the relationship between the 2D FFT and the third invariant measurements and uses the pseudo-inverse via QR factorization to transform the 2D Fourier coefficients to spherical harmonic ones. Based on the GOCE gravity gradient data of the nominal mission phase, a novel global gravity field model (I3GG) is derived up to maximum degree/order 240, corresponding to a spatial resolution of 83 km at the equator. Moreover, in order to investigate the differences of gravity field determination between I_3 with I_2, we applied the same processing strategy on the second invariant measurements of the GOCE mission and we obtained another gravity field model (I2GG) with a maximum degree of 220, which is 20 degrees lower than that of I3GG. The root-mean-square (RMS) values of geoid differences indicates that the effects of measurement noise of I3GG is about 20% lower than that on I2GG when compared to the gravity field model EGM2008 (Earth Gravitational Model 2008) or EIGEN-5C (EIGEN: European Improved Gravity model of the Earth by New techniques). Then the accuracy of I3GG is evaluated independently by comparison the RMS differences between Global Navigation Satellite System (GNSS)/leveling data and the model-derived geoid heights. Meanwhile, the re-calibrated GOCE data released in 2018 is also dealt with and the corresponding result also shows the similar characteristics.

Moho depth model for the Central Asian Orogenic Belt from satellite gravity gradients

AbstractThe main purpose of this study is to construct a new 3‐D model of the Central Asian Orogenic Belt (CAOB) crust, which can be used as a starting point for future lithospheric studies. The CAOB is a Paleozoic accretionary orogen surrounded by the Siberian Craton to the north and the North China and Tarim Cratons to the south. This area is of great interest due to its enigmatic and still not completely understood geodynamic evolution. First, we estimate an initial crustal thickness by inversion of the vertical gravity component of the Gravity Field and Steady‐State Ocean Circulation Explorer (GOCE) and DTU10 models. Second, 3‐D forward modeling of the GOCE gravity gradients is performed, which determines the topography of the Moho, the geometry, and the density distribution of the deeper parts of the CAOB and its surroundings, taking into account the lateral and vertical density variations of the crust. The model is constrained by seismic refraction, reflection, and receiver function studies and geological studies. In addition, we discuss the isostatic implications of the differences between the seismic Moho and the resulting 3‐D gravity Moho, complemented by the analysis of the lithostatic load distribution at the upper mantle level. Finally, the correlation between the contrasting tectonic domains and the thickness of the crust reveals the inheritance of Paleozoic and Mesozoic geodynamics, particularly the magmatic provinces and the orocline which preserve their crustal features.

Regional gravity field recovery using the GOCE gravity gradient tensor and heterogeneous gravimetry and altimetry data

AbstractA regional approach using Poisson wavelets is applied for gravity field recovery using the GOCE (Gravity Field and Steady‐State Ocean Circulation Explorer) gravity gradient tensor, heterogeneous gravimetry data, and altimetry measurements. The added value to the regional model introduced by GOCE data is validated and quantified. The performances of the solutions modeled with different diagonal components of GOCE data and their combinations are investigated. Numerical experiments in a region in Europe show that the effects introduced by GOCE data demonstrate long‐wavelength patterns on the centimeter scale in terms of quasi‐geoid heights, which may allow reducing the remaining long‐wavelength errors in ground‐based data, and improve the regional model. The accuracy of the gravimetric quasi‐geoid computed with a combination of three diagonal components is improved by 0.6 cm (0.5 cm) in the Netherlands (Belgium) compared to that derived from gravimetry and altimetry data alone, when GOCO05s is used as the reference model. Moreover, the added value from GOCE data reduces the mean values of the misfit between the gravimetric solution and GPS/leveling data. Performances of different components and their combinations are not identical, and the solution with vertical gradients is best when a single component is used. The incorporation of multiple components shows further improvements, and the combination of three components best fits the local GPS/leveling data. Further comparison shows that our solution is the highest quality and may be substituted for existing models for engineering purposes and geophysical investigations over the target area.

Adaptive filtering of GOCE-derived gravity gradients of the disturbing potential in the context of the space-wise approach

Filtering and signal processing techniques have been widely used in the processing of satellite gravity observations to reduce measurement noise and correlation errors. The parameters and types of filters used depend on the statistical and spectral properties of the signal under investigation. Filtering is usually applied in a non-real-time environment. The present work focuses on the implementation of an adaptive filtering technique to process satellite gravity gradiometry data for gravity field modeling. Adaptive filtering algorithms are commonly used in communication systems, noise and echo cancellation, and biomedical applications. Two independent studies have been performed to introduce adaptive signal processing techniques and test the performance of the least mean-squared (LMS) adaptive algorithm for filtering satellite measurements obtained by the gravity field and steady-state ocean circulation explorer (GOCE) mission. In the first study, a Monte Carlo simulation is performed in order to gain insights about the implementation of the LMS algorithm on data with spectral behavior close to that of real GOCE data. In the second study, the LMS algorithm is implemented on real GOCE data. Experiments are also performed to determine suitable filtering parameters. Only the four accurate components of the full GOCE gravity gradient tensor of the disturbing potential are used. The characteristics of the filtered gravity gradients are examined in the time and spectral domain. The obtained filtered GOCE gravity gradients show an agreement of 63–84 mEotvos (depending on the gravity gradient component), in terms of RMS error, when compared to the gravity gradients derived from the EGM2008 geopotential model. Spectral-domain analysis of the filtered gradients shows that the adaptive filters slightly suppress frequencies in the bandwidth of approximately 10–30 mHz. The limitations of the adaptive LMS algorithm are also discussed. The tested filtering algorithm can be connected to and employed in the first computational steps of the space-wise approach, where a time-wise Wiener filter is applied at the first stage of GOCE gravity gradient filtering. The results of this work can be extended to using other adaptive filtering algorithms, such as the recursive least-squares and recursive least-squares lattice filters.

Moho Density Contrast in Central Eurasia from GOCE Gravity Gradients

Seismic data are primarily used in studies of the Earth’s inner structure. Since large parts of the world are not yet sufficiently covered by seismic surveys, products from the Earth’s satellite observation systems have more often been used for this purpose in recent years. In this study we use the gravity-gradient data derived from the Gravity field and steady-state Ocean Circulation Explorer (GOCE), the elevation data from the Shuttle Radar Topography Mission (SRTM) and other global datasets to determine the Moho density contrast at the study area which comprises most of the Eurasian plate (including parts of surrounding continental and oceanic tectonic plates). A regional Moho recovery is realized by solving the Vening Meinesz-Moritz’s (VMM) inverse problem of isostasy and a seismic crustal model is applied to constrain the gravimetric solution. Our results reveal that the Moho density contrast reaches minima along the mid-oceanic rift zones and maxima under the continental crust. This spatial pattern closely agrees with that seen in the CRUST1.0 seismic crustal model as well as in the KTH1.0 gravimetric-seismic Moho model. However, these results differ considerably from some previously published gravimetric studies. In particular, we demonstrate that there is no significant spatial correlation between the Moho density contrast and Moho deepening under major orogens of Himalaya and Tibet. In fact, the Moho density contrast under most of the continental crustal structure is typically much more uniform.

Application of Gravity Gradients in the Process of GOCE Orbit Determination

The possibility of improving the Gravity Field and Steady-State Ocean Circulation Explorer (GOCE) mission satellite orbit using gravity gradient observations was investigated. The orbit improvement is performed by a dedicated software package, called the Orbital Computation System (OCS), which is based on the classical least squares method. The corrections to the initial satellite state vector components are estimated in an iterative process, using dynamic models describing gravitational perturbations. An important component implemented in the OCS package is the 8th order Cowell numerical integration procedure, which directly generates the satellite orbit. Taking into account the real and simulated GOCE gravity gradients, different variants of the solution of the orbit improvement process were obtained. The improved orbits were compared to the GOCE reference orbits (Precise Science Orbits for the GOCE satellite provided by the European Space Agency) using the root mean squares (RMS) of the differences between the satellite positions in these orbits. The comparison between the improved orbits and the reference orbits was performed with respect to the inertial reference frame (IRF) at J2000.0 epoch. The RMS values for the solutions based on the real gravity gradient measurements are at a level of hundreds of kilometers and more. This means that orbit improvement using the real gravity gradients is ineffective. However, all solutions using simulated gravity gradients have RMS values below the threshold determined by the RMS values for the computed orbits (without the improvement). The most promising results were achieved when short orbital arcs with lengths up to tens of minutes were improved. For these short arcs, the RMS values reach the level of centimeters, which is close to the accuracy of the Precise Science Orbit for the GOCE satellite. Additional research has provided requirements for efficient orbit improvement in terms of the accuracy and spectral content of the measured gravity gradients.

Distributed fault slip model for the 2011 Tohoku‐Oki earthquake from GNSS and GRACE/GOCE satellite gravimetry

AbstractThe Gravity Recovery and Climate Experiment (GRACE) mission (launched 2002) and the Gravity Field and Steady‐State Ocean Circulation Explorer (GOCE) mission (March 2009 to November 2013) collected spaceborne gravity data for the preseismic and postseismic periods of the 2011 Tohoku‐Oki earthquake. In addition, the dense Japan GeoNet Global Navigation Satellite Systems (GNSS) network measured with approximately 1050 stations the coseismic and postseismic surface displacements. We use a novel combination of GNSS, GRACE, and GOCE observations for a distributed fault slip model addressing the issues with gravimetric and geometric change over consistent time windows. Our model integrates the coseismic and postseismic effects as we include GOCE observations averaged over a 2 year interval, but their inclusion reveals the gravity change with unprecedented spatial accuracy. The gravity gradient grid, evaluated at GOCE orbit height of 265 km, has an estimated formal error of 0.20 mE which provides sensitivity to the mainly coseismic and integrated postseismic‐induced gravity gradient signal of −1.03 mE. We show that an increased resolution of the gravity change provides valuable information, with GOCE gravity gradient observations sensitive to a more focused slip distribution in contrast to the filtered GRACE equivalent. The 2 year averaging window of the observations makes it important to incorporate estimates of the variance/covariance of unmodeled processes in the inversion. The GNSS and GRACE/GOCE combined model shows a slip pattern with 20 m peak slip at the trench. The total gravity change (≈200 μGal) and the spatial mapping accuracy would have been considerably lower by omitting the GOCE‐derived fine‐scale gravity field information.

A Wavelet-Based Assessment of Topographic-Isostatic Reductions for GOCE Gravity Gradients

Gravity gradient measurements from ESA’s satellite mission Gravity field and steady-state Ocean Circulation Explorer (GOCE) contain significant high- and mid-frequency signal components, which are primarily caused by the attraction of the Earth’s topographic and isostatic masses. In order to mitigate the resulting numerical instability of a harmonic downward continuation, the observed gradients can be smoothed with respect to topographic-isostatic effects using a remove–compute–restore technique. For this reason, topographic-isostatic reductions are calculated by forward modeling that employs the advanced Rock–Water–Ice methodology. The basis of this approach is a three-layer decomposition of the topography with variable density values and a modified Airy–Heiskanen isostatic concept incorporating a depth model of the Mohorovicic discontinuity. Moreover, tesseroid bodies are utilized for mass discretization and arranged on an ellipsoidal reference surface. To evaluate the degree of smoothing via topographic-isostatic reduction of GOCE gravity gradients, a wavelet-based assessment is presented in this paper and compared with statistical inferences in the space domain. Using the Morlet wavelet, continuous wavelet transforms are applied to measured GOCE gravity gradients before and after reducing topographic-isostatic signals. By analyzing a representative data set in the Himalayan region, an employment of the reductions leads to significantly smoothed gradients. In addition, smoothing effects that are invisible in the space domain can be detected in wavelet scalograms, making a wavelet-based spectral analysis a powerful tool.

Perturbing effects of sub-lithospheric mass anomalies in GOCE gravity gradient and other gravity data modelling: Application to the Atlantic-Mediterranean transition zone

The GOCE (Gravity field and steady-state Ocean Circulation Explorer) mission, launched on March 2009, included a new type of satellite instrument, an on-board three-axis gradiometer able to measure the Earth's gravity gradients at the satellite height (255km). The potential of this new type of measurement and its derived products (i.e., global gravity field models), together with other land-based geophysical observables (Bouguer and geoid anomalies), to image sub-lithospheric thermal and compositional anomalies is evaluated in this study. We focus on the Atlantic-Mediterranean Transition Region (AMTR), the diffuse, transpressive contact between the Iberian Peninsula and North Africa. The present-day lithospheric structure in the area is characterized by a wide band of active deformation, large lateral variations in the lithosphere and the presence of a positive seismic-velocity anomaly in the uppermost mantle beneath the Betics and the westernmost Alboran Basin-Gibraltar Arc. Here, the perturbing effects of deep, sub-lithospheric density anomalies in GOCE gravity gradients and other land-based geophysical data are assessed, and its impact in lithospheric-scale geophysical-petrological modeling within a thermodynamically consistent framework analyzed. Some of the gravity gradients computed at the satellite altitude are rather sensitive to the presence of even a relatively small sub-lithospheric cold slab, like the one observed in the AMTR, showing the potential of the new GOCE data to map upper mantle anomalies. Lithospheric models ignoring the AMTR sub-lithospheric heterogeneities could be significantly biased. In particular, extreme changes of 4–6km and 60–70km in the crustal and lithospheric thickness, respectively, are required to include sub-lithospheric mantle contributions to land-based and satellite gravity data.

GOCE gravity gradient data for lithospheric modeling

The Gravity field and steady-state Ocean Circulation Explorer (GOCE) is the European Space Agency's (ESA) satellite gravity mission to determine the Earth's mean gravity field. GOCE delivers gravity gradients, a new type of satellite data. We study how these data can improve modeling of the Earth's lithosphere. We discuss the use of the original GOCE gravity gradients versus the use of gravity gradients in grids at satellite altitude or close the Earth's surface and conclude that grids are easier to handle than the original data because one does not have to deal with very different error characteristics of the different gradients, given in a rotating frame at varying heights. The downward continuation to the surface enhances signal and better reflects the near-surface geology. But this does not outweigh the amplification of noise and omission errors, which is why we recommend using the field at mean satellite altitude for lithospheric modeling. The North-East Atlantic region is ideal to analyze the additional value of GOCE gravity gradients because it is a well-studied region in terms of regional geophysics. We calculated the gradient sensitivity for crustal depth slices using a 3D lithospheric model. This reveals that especially interfaces with large density contrasts have a distinct signal in the gravity gradients, but that they are quite insensitive to intra-crustal density sources, which can have quite a large effect on surface gravity data. We also show that the satellite gradients have a depth sensitivity well suited to study the upper mantle density structure, making them complementary to gravity and seismic tomography. In the underexplored Rub’al-Khali area the GOCE vertical gradient was used to invert for crustal thickness. The updated Moho model gives a good fit to four of the six gradients and independent depths from seismic stations. The Moho model was used to update the heat flow model and source rock maturity maps, which are generally consistent with known source rock maturity trends in the surrounding regions. GOCE gradients are therefore useful to map crustal thickness and deep regional structures for frontier areas. In combination with other data, heat flow can be modeled which is essential for basin maturity evaluation.

GOCE, Satellite Gravimetry and Antarctic Mass Transports

In 2009 the European Space Agency satellite mission GOCE (Gravity Field and Steady-State Ocean Circulation Explorer) was launched. Its objectives are the precise and detailed determination of the Earth’s gravity field and geoid. Its core instrument, a three axis gravitational gradiometer, measures the gravity gradient components V xx , V yy , V zz and V xz (second-order derivatives of the gravity potential V) with high precision and V xy , V yz with low precision, all in the instrument reference frame. The long wavelength gravity field is recovered from the orbit, measured by GPS (Global Positioning System). Characteristic elements of the mission are precise star tracking, a Sun-synchronous and very low (260 km) orbit, angular control by magnetic torquing and an extremely stiff and thermally stable instrument environment. GOCE is complementary to GRACE (Gravity Recovery and Climate Experiment), another satellite gravity mission, launched in 2002. While GRACE is designed to measure temporal gravity variations, albeit with limited spatial resolution, GOCE is aiming at maximum spatial resolution, at the expense of accuracy at large spatial scales. Thus, GOCE will not provide temporal variations but is tailored to the recovery of the fine scales of the stationary field. GRACE is very successful in delivering time series of large-scale mass changes of the Antarctic ice sheet, among other things. Currently, emphasis of respective GRACE analyses is on regional refinement and on changes of temporal trends. One of the challenges is the separation of ice mass changes from glacial isostatic adjustment. Already from a few months of GOCE data, detailed gravity gradients can be recovered. They are presented here for the area of Antarctica. As one application, GOCE gravity gradients are an important addition to the sparse gravity data of Antarctica. They will help studies of the crustal and lithospheric field. A second area of application is ocean circulation. The geoid surface from the gravity field model GOCO01S allows us now to generate rather detailed maps of the mean dynamic ocean topography and of geostrophic flow velocities in the region of the Antarctic Circumpolar Current.

Numerical study on the mixed model in the GOCE polar gap problem

Gravity gradients acquired by the Gravity field and steady-state Ocean Circulation Explorer (GOCE) do not cover the entire earth because of its sun-synchronous orbit leaving data gaps with a radius of about 6.5° in the polar regions. Previous studies showed that the loss of data in the polar regions deteriorates the accuracy of the low order (or near zonal) coefficients of the earth gravity model, which is the so-called polar gap problem in geodesy. In order to find a stable solution for the earth gravity model from the GOCE gravity gradients, three models, i.e. the Gauss-Markov model, light constraint model and the mixed model, are compared and evaluated numerically with the gravity gradient simulated with the EGM2008. The comparison shows that the Best Linear Uniformly Unbiased Estimation (BLUUE) estimator of the mixed model can solve the polar gap problem as effectively as the light constraint model; furthermore, the mixed model is more rigorous in dealing with the supplementary information and leads to a better accuracy in determining the global geoid.

Efficient gravity field recovery from GOCE gravity gradient observations

An efficient algorithm is proposed for gravity field recovery from Gravity Field and Steady-State Ocean Circulation Explorer (GOCE) satellite gravity gradient observations. The mathematical model is formulated in the time domain, which allows the inclusion of realistic observational noise models. The algorithm combines the iterative solution of the normal equations, using a Richardson-type iteration scheme, with the fast computation of the right-hand side of the normal equations in each iteration step by a suitable approximation of the design matrix. The convergence of the iteration is investigated, error estimates are provided, and the unbiasedness of the method is proved. It is also shown that the method does not converge to the solution of the normal equations. The performance of the approach for white noise and coloured noise is demonstrated along a simulated GOCE orbit up to spherical harmonic degree and order 180. The results also indicate that the approximation error may be neglected.