Search

An amendment to this paper has been published and can be accessed via a link at the top of the paper.

Curvature components derived from satellite gravity gradients provide new global views of Earth’s structure. The satellite gravity gradients are based on the GOCE satellite mission and we illustrate by curvature images how the Earth is seen differently compared to seismic imaging. Tectonic domains with similar seismic characteristic can exhibit distinct differences in satellite gravity gradients maps, which points to differences in the lithospheric build-up. This is particularly apparent for the cratonic regions of the Earth. The comparisons demonstrate that the combination of seismological, and satellite gravity gradient imaging has significant potential to enhance our knowledge of Earth’s structure. In remote frontiers like the Antarctic continent, where even basic knowledge of lithospheric scale features remains incomplete, the curvature images help unveil the heterogeneity in lithospheric structure, e.g. between the composite East Antarctic Craton and the West Antarctic Rift System.

The long wavelength part of the Earth’s gravity field can be determined, with varying accuracy, from satellite laser ranging (SLR). In this study, we investigate the combination of up to ten geodetic SLR satellites using iterative variance component estimation. SLR observations to different satellites are combined in order to identify the impact of each satellite on the estimated Stokes coefficients. The combination of satellite-specific weekly or monthly arcs allows to reduce parameter correlations of the single-satellite solutions and leads to alternative estimates of the second-degree Stokes coefficients. This alternative time series might be helpful for assessing the uncertainty in the impact of the low-degree Stokes coefficients on geophysical investigations. In order to validate the obtained time series of second-degree Stokes coefficients, a comparison with the SLR RL05 time series of the Center of Space Research (CSR) is done. This investigation shows that all time series are comparable to the CSR time series. The precision of the weekly/monthly $$C_{21}$$ and $$S_{21}$$ coefficients is analyzed by comparing mass-related equatorial excitation functions $$\chi ^{\text {mass}}_{1,2}$$ with geophysical model results and reduced geodetic excitation functions. In case of $$\chi ^{\text {mass}}_{1}$$ , the annual amplitude and phase of the DGFI solution agrees better with three of four geophysical model combinations than other time series. In case of $$\chi ^{\text {mass}}_{2}$$ , all time series agree very well to each other. The impact of $$C_{20}$$ on the ice mass trend estimates for Antarctica are compared based on CSR GRACE RL05 solutions, in which different monthly $$C_{20}$$ time series are used for replacing. We found differences in the long-term Antarctic ice loss of $$12.3$$ Gt/year between the GRACE solutions induced by the different $$C_{20}$$ SLR time series of CSR and DGFI, which is about 13 % of the total ice loss of Antarctica. This result shows that Antarctic ice mass loss quantifications must be carefully interpreted.

The orbit and instrumental measurement of the Gravity Field and Steady State Ocean Circulation Explorer (GOCE) satellite mission offer the highest ever resolution capabilities for mapping Earth's gravity field from space. However, past analysis predicted that GOCE would not detect changes in ice sheet mass. Here we demonstrate that GOCE gravity gradiometry observations can be combined with Gravity Recovery and Climate Experiment (GRACE) gravity data to estimate mass changes in the Amundsen Sea Sector. This refined resolution allows land ice changes within the Pine Island Glacier (PIG), Thwaites Glacier, and Getz Ice Shelf drainage systems to be measured at respectively ?67?±?7, ?63?±?12, and ?55?±?9 Gt/yr over the GOCE observing period of November 2009 to June 2012. This is the most accurate pure satellite gravimetry measurement to date of current mass loss from PIG, known as the “weak underbelly” of West Antarctica because of its retrograde bed slope and high potential for raising future sea level.

An assessment has been made of the possibility to estimate time-variable gravity from GPS-derived orbit perturbations and common-mode accelerometer observations of ESA’s GOCE Earth Explorer. A number of 20-day time series of Earth’s global long-wavelength gravity field have been derived for the period November 2009 to November 2012 using different parameter setups and estimation techniques. These techniques include a conventional approach where for each period, one set of gravity coefficients is estimated, either excluding or including empirical accelerations, and the so-called Wiese approach where higher frequency coefficients are estimated for the very long wavelengths. A principal component analysis of especially the time series of gravity field coefficients obtained by the Wiese approach and the conventional approach with empirical accelerations reveals an annual signal. When fitting this annual signal directly through the time series, the sine component (maximum in spring) displays features that are similar to well-known continental hydrological mass changes for the low latitude areas, such as mass variations in the Amazon basin, Africa and Australia for spatial scales down to 1,500 km. The cosine component (maximum in winter), however, displays large signals that can not be attributed to actual mass variations in the Earth system. The estimated gravity field changes from GOCE orbit perturbations are likely affected by missing GPS observations in case of high ionospheric perturbations during periods of increased solar activity, which is minimal in Summer and maximal towards the end of autumn.

The Japan Tohoku-Oki earthquake (9.0 Mw) of 11 March 2011 has left signatures in the Earth's gravity field that are detectable by data of the Gravity field Recovery and Climate Experiment (GRACE) mission. Because the European Space Agency's (ESA) satellite gravity mission Gravity field and steady-state Ocean Circulation Explorer (GOCE)—launched in 2009—aims at high spatial resolution, its measurements could complement the GRACE information on coseismic gravity changes, although time-variable gravity was not foreseen as goal of the GOCE mission. We modeled the coseismic earthquake geoid signal and converted this signal to vertical gravity gradients at GOCE satellite altitude. We combined the single gradient observations in a novel way reducing the noise level, required to detect the coseismic gravity change, subtracted a global gravity model, and applied tailored outlier detection to the resulting gradient residuals. Furthermore, the measured gradients were along-track filtered using different gradient bandwidths where in the space domain Gaussian smoothing has been applied. One-year periods before and after earthquake occurrence have been compared with the modeled gradients. The comparison reveals that the earthquake signal is well above the accuracy of the vertical gravity gradients at orbital height. Moreover, the obtained signal from GOCE shows a 1.3 times higher amplitude compared with the modeled signal. Besides the statistical significance of the obtained signal, it has a high spatial correlation of ~0.7 with the forward modeled signal. We conclude therefore that the coseismic gravity change of the Japan Tohoku-Oki earthquake left a statistically significant signal in the GOCE measured gravity gradients.

[1] 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.

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.

International audience; Joint analysis of the seismic velocities and geoid, gravity and gravity gradients are used to constrain the viscosity profile within the mantle as well as the lateral density variations. Recent ESA's Gravity field and steady-state Ocean Circulation Explorer measurements of the second-order derivatives of the Earth's gravity potential give new possibilities to determine these mantle properties. Using a simple mantle model and seismic tomography results, we investigate how the gravitational potential, the three components of the gravity vector and the gravity gradients can bring information on the radial viscosity profile and on the mantle mass anomalies. We start with lateral density variations in the Earth's mantle based either on slab history or deduced from seismic tomography. The main uncertainties are: for the latter case, the relationship between seismic velocity and density-the so-called density/velocity scaling factor-and for the former case, the variation with depth of the density contrast between the cold slabs and the surrounding mantle. We perform a Monte Carlo search for the viscosity and the density/velocity scaling factor profiles within the mantle, which allows to fit the observed geoid, gravity and gradients of gravity. We compute the posterior probability distribution of the unknown parameters, and find that the gravity gradients improve the estimate of the scaling factor within the upper mantle, because of their sensitivity to the masses within the upper mantle, whereas the geoid and the gravity better constrain the scaling factor in the lower mantle. In the upper mantle, it is less than 0.02 in the upper part and about 0.08-0.14 in the lower part, and it is significantly larger for depths greater than 1200 km (about 0.32-0.34). In any case, the density/velocity scaling factor between 670 and 1150 km depth is not well constrained. We show that the viscosity of the upper part of the mantle is strongly correlated with the viscosity of the lower part of the mantle and that the viscosity profile is characterized by a decrease in the lower part of the upper mantle (about 10 20-2 × 10 20 Pa s) and by an increase (about 10 23-2 × 10 23 Pa s) at the top of the lower mantle (between 670 and 1150 km).

SUMMARY 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.

Gravity data observed on or reduced to the ellipsoid are preferably represented using ellipsoidal harmonics instead of spherical harmonics. Ellipsoidal harmonics, however, are difficult to use in practice because the computation of the associated Legendre functions of the second kind that occur in the ellipsoidal harmonic expansions is not straightforward. Jekeli’s renormalization simplifies the computation of the associated Legendre functions. We extended the direct computation of these functions—as well as that of their ratio—up to the second derivatives and minimized the number of required recurrences by a suitable hypergeometric transformation. Compared with the original Jekeli’s renormalization the associated Legendre differential equation is fulfilled up to much higher degrees and orders for our optimized recurrences. The derived functions were tested by comparing functionals of the gravitational potential computed with both ellipsoidal and spherical harmonic syntheses. As an input, the high resolution global gravity field model EGM2008 was used. The relative agreement we found between the results of ellipsoidal and spherical syntheses is 10−14, 10−12 and 10−8 for the potential and its first and second derivatives, respectively. Using the original renormalization, this agreement is 10−12, 10−8 and 10−5, respectively. In addition, our optimized recurrences require less computation time as the number of required terms for the hypergeometric functions is less.

The GOCE satellite gravity emission was launched in 2009 to measure the gravity gradient with high accuracy and spatial resolution. GOCE gravity data may improve the understanding and modeling of the Earth's interior and its dynamic processes, contributing to new insights into the geodynamics associated with the lithosphere, mantle composition and rheology, uplift and subduction processes. However, to achieve this challenging target, GOCE should be used in combination with additional data sources, such as in-situ gravimetric, magnetic, and seismic data sets

The vertical gradients of gravity anomaly and gravity disturbance can be related to horizontal first derivatives of deflection of the vertical or second derivatives of geoidal undulations. These are simplified relations of which different variations have found application in satellite altimetry with the implicit assumption that the neglected terms—using remove-restore—are sufficiently small. In this paper, the different simplified relations are rigorously connected and the neglected terms are made explicit. The main neglected terms are a curvilinear term that accounts for the difference between second derivatives in a Cartesian system and on a spherical surface, and a small circle term that stems from the difference between second derivatives on a great and small circle. The neglected terms were compared with the dynamic ocean topography (DOT) and the requirements on the GOCE gravity gradients. In addition, the signal root-mean-square (RMS) of the neglected terms and vertical gravity gradient were compared, and the effect of a remove-restore procedure was studied. These analyses show that both neglected terms have the same order of magnitude as the DOT gradient signal and may be above the GOCE requirements, and should be accounted for when combining altimetry derived and GOCE measured gradients. The signal RMS of both neglected terms is in general small when compared with the signal RMS of the vertical gravity gradient, but they may introduce gradient errors above the spherical approximation error. Remove-restore with gravity field models reduces the errors in the vertical gravity gradient, but it appears that errors above the spherical approximation error cannot be avoided at individual locations. When computing the vertical gradient of gravity anomaly from satellite altimeter data using deflections of the vertical, the small circle term is readily available and can be included. The direct computation of the vertical gradient of gravity disturbance from satellite altimeter data is more difficult than the computation of the vertical gradient of gravity anomaly because in the former case the curvilinear term is needed, which is not readily available.

SUMMARY ESA's GOCE mission aims at improved global and regional gravity field information with high spatial resolution by measuring gravity gradients. A local analysis of the GOCE gravity gradient tensor may benefit from a rotation from the gradiometer reference frame to local reference frames such as the local north oriented reference frame. As the GOCE gravity gradients include accurate and less accurate measured gradients, the point-wise tensor rotation of the GOCE-only measurements may suffer from the projection of the errors of the less accurate gravity gradients onto the accurate gravity gradients. In addition, the GOCE gravity gradients have high accuracy in the measurement bandwidth but low accuracy below, and tensor rotation may cause leakage of the large error below the measurement bandwidth to the measurement bandwidth. Degradation of the rotated gravity gradients is circumvented by replacing the less accurate tensor components, as well as the signal below the measurement bandwidth of the accurate gravity gradients, with model signal. The combination of GOCE and model gravity gradients is performed by determining the effective measurement bandwidth (EMB), that is, the bandwidth in which the integrated signal-to-noise ratio of the GOCE gravity gradients is maximized. We find that the determination of the EMB is relatively independent of the reference gravity field model that is used. The lower bound of the EMB is well below the pre-mission specifications for the four accurate gravity gradients. In addition, we assess how much GOCE contributes to the gravity gradient signal in local frames and how much the model. For the radial gravity gradient the relative GOCE contribution is 98 per cent on average, whereas this is 65–97 per cent for the other gravity gradients. These numbers strongly depend on the local frame under consideration and on the geographical position.

With satellite radar altimetry, the oceanic geoid can be determined with high precision and resolution. Double differentiation of these data along satellite altimeter ground tracks yields along-track gravity gradients that can be used to compute vertical gravity gradients at ground track crossovers. One way to counteract the noise amplification due to the differentiation is to smooth the data using smoothing splines. Although the effect of satellite altimeter data noise has been investigated to some extent, the associated systematic errors have not been assessed so far. Here we show that some of the systematic errors cannot be neglected. In particular, we found that the negligence of the dynamic ocean topography (DOT) may introduce errors that are greater than the measurement noise induced errors. If the gravity gradients are to be used for GOCE validation, then also in this case the DOT may not be neglected as the signal at GOCE altitude of 260 km may be above the GOCE requirements. In addition, we show ...

A reliable and accurate gradiometer calibration is essential for the scientific return of the gravity field and steady-state ocean circulation explorer (GOCE) mission. This paper describes a new method for external calibration of the GOCE gradiometer accelerations. A global gravity field model in combination with star sensor quaternions is used to compute reference differential accelerations, which may be used to estimate various combinations of gradiometer scale factors, internal gradiometer misalignments and misalignments between star sensor and gradiometer. In many aspects, the new method is complementary to the GOCE in-flight calibration. In contrast to the in-flight calibration, which requires a satellite-shaking phase, the new method uses data from the nominal measurement phases. The results of a simulation study show that gradiometer scale factors can be estimated on a weekly basis with accuracies better than 2 × 10−3 for the ultrasensitive and 10−2 for the less sensitive axes, which is compatible with the requirements of the gravity gradient error. Based on a 58-day data set, scale factors are found that can reduce the errors of the in-flight-calibrated measurements. The elements of the complete inverse calibration matrix, representing both the internal gradiometer misalignments and scale factors, can be estimated with accuracies in general better than 10−3.

The Gravity field and steady-state Ocean Circulation Explorer (GOCE) satellite aimed at determining the Earth’s mean gravity field. GOCE delivered gravity gradients containing directional information, which are complicated to use because of their error characteristics and because they are given in a rotating instrument frame indirectly related to the Earth. We compute gravity gradients in grids at 225 km and 255 km altitude above the reference ellipsoid corresponding to the GOCE nominal and lower orbit phases respectively, and find that the grids may contain additional high-frequency content compared with GOCE-based global models. We discuss the gradient sensitivity for crustal depth slices using a 3D lithospheric model of the North-East Atlantic region, which shows that the depth sensitivity differs from gradient to gradient. In addition, the relative signal power for the individual gradient component changes comparing the 225 km and 255 km grids, implying that using all components at different heights reduces parameter uncertainties in geophysical modelling. Furthermore, since gravity gradients contain complementary information to gravity, we foresee the use of the grids in a wide range of applications from lithospheric modelling to studies on dynamic topography, and glacial isostatic adjustment, to bedrock geometry determination under ice sheets.

It is beyond doubt that calibration and validation are essential tools in the process of reaching the goals of gravity missions like GRACE and GOCE and to obtain results of the highest possible quality. Both tools, although general and obvious instruments for any mission, have specific features for gravity missions. Therefore, it is necessary to define exactly what is expected (and what cannot be expected) from calibration and what from validation and how these tools should work in our case. The general calibration and validation schemes for GRACE and GOCE arc outlined. Calibration will be linked directly to the instrument and the measurements whereas validation will he linked to data derived from the original measurements. Calibration includes on-ground, internal. and external calibration as well as error assessment. The calibration phase results in corrected measurements along with an a posteriori error model. Validation of e.g. calibrated measurements or geoid heights means checking against independent data to assess whether there are no systematic errors left and/or whether the error model describes the true error reasonably well. Geodetic methods for calibration typically refer lo external calibration and error assessment, and will be illustrated With an example.

The satellite gravity mission GOCE measured the second-order derivatives of the Earth’s gravitational potential with high accuracy. The GOCE data enrich our gravity field knowledge especially at spatial resolutions from 750 km down to 80 km. In this paper we carry out regional gravity field analysis using radial localising basis functions that permit the combination of different data types tailored to their accuracy and spectral signal content. We formulate observation equations for each individual GOCE gravity gradient as they are distinctive reflections of the gravity field and contain directional information. To optimally use the original GOCE measurements, we derive the mathematical expressions in the gradiometer reference frame. The expressions and their implementation are validated for a test area in Scandinavia by comparison with the global gravity field model GOCO03s, which yields small differences of less than ± 1 mE. The relative weighting of the observations is determined by variance component estimation. Moreover manually fixing the weights leads to smaller residuals with respect to GOCO03s, which is probably caused by systematic errors in the gradients. We demonstrate the capabilities of our method through a combination of the gradient data with terrestrial free-air anomalies. At spatial resolutions down to 40 km the terrestrial data get much larger relative weights than the GOCE data, which indicates the proper performance of the combination method.

Since 2002, the satellite mission GRACE observes the Earth’s static gravity field and its natural changes. The estimation of degree 1 and 2 coefficients is difficult, especially the accuracy of the flattening coefficient C2, 0 is weak. In temporal GRACE gravity field models, C2, 0 is therefore often replaced by a value based on Satellite Laser Ranging measurements. In this study, we combine both techniques to get a consistent normal equation matrix, which allows us to study correlations between spherical harmonic coefficients. Unlike common practice, we use 8 SLR satellites and set-up normal equations up to degree 20. The combination is done using different weighting factors to investigate the influence of both techniques on the combined normal equation matrix. Our results show that especially the coefficient C2, 0 benefits from SLR data, but also (near-) sectorial coefficients and coefficients which correspond to resonance frequencies of SLR satellites. Moreover, we find that high correlations in the SLR normal equation between zonal coefficients are reduced by the combination.

Till the present day the recovery of the lunar gravity field from satellite tracking data depends in a crucial way on the level and method of regularisation. With Earth-based tracking only, the spatial data coverage is limited to only slightly more than 50% and the inverse problem remains severely ill-posed. The development of global gravity models suitable for precise orbit modeling as well as geophysical studies therefore requires a significant level of regularisation, limiting the solution power over the far-side where no gravity information is available. Unconstrained solutions, within the framework of global harmonic base functions, are only possible for very low degrees (

We discuss the gravity gradient signal measured at the height of the GOCE satellite and compare it with the gravity gradients related to the density contrast between crust and mantle. The gravity gradients are reduced for the topographic masses to emphasize the lithospheric signal. Comparison with the Moho-related signal shows that with a density contrast of 400 kg/m3, the amplitude of the calculated gradients is almost twice that of the observed field. The differences can only partly be explained by the uncertainty of the crustal thickness, but is clearly related to the applied density contrast. Calculation of the gravity gradients requires a reduced density contrast, which is an important consideration for establishing global models, which might otherwise overestimate crustal thickness.

To meet increased demands in mapping, surveying, geodesy, and large infrastructure projects, an accurate national geoid model for Saudi Arabia is required to transform ellipsoid heights to orthometric heights. The lack of data and the nature of the topography make the computation of a geoid model in Saudi Arabia a difficult task. Two regional geoids were developed for the Kingdom of Saudi Arabia (KSA): (1) the KSA geoid developed by the General Directorate of Survey (GDS); and (2) a geoid developed by the Ministry of Municipality and Rural Affairs (MOMRA). The KSA model was developed using a remove and restore technique and over 5,000 observations of Global Positioning System (GPS) ellipsoidal heights on leveling benchmarks (GPS/BM). The MOMRA geoid was estimated from 861GPS/Levelling with a kriging approach. A GPS/Levelling test campaign (T campaign) was carried out in 2010 by re-observing about 391 BM stations common to the two geoid models. The two geoid models are first compared against each other and EGM2008 at the 391 BM stations from the T campaign. The absolute differences between models may reach several meters, whereas the standard deviation of the differences ranges between 0.5 and 1.5 m. Analysis revealed that KSA and MOMRA geoids seem not to coincide. Both are biased (means of 0.46 m) and highly scattered (standard deviation is ±0.72 m). Next, geoid models developed using GOCE satellite data are used to validate the T campaign data.

Abstract A 3D basin modeling study was carried out to reconstruct the regional heat flow and source rock maturity in the Rub'al-Khali basin. Gravity gradient data from the GOCE satellite were used to model deep structures, such as the Moho interface. Tectonic heat flow was modeled using the GOCE-based Moho interface to reflect heat flow variations in the basin though time and space. The thermal maturity of Silurian and Jurassic source rocks in the Rub'al-Khali was calculated using the GOCE-constrained basal heat flow model. GOCE-based Moho depth map was calibrated to data from known seismic stations in the region. This map provided input to constrain the heat flow in eth basin. Modeled heat flow values are consistent with known values of heat flow in the region. The model indicates that the Silurian and Jurassic source rocks are generally in the hydrocarbon generation window and the modeled maturity trends are in agreement with the observations in the area.

A 3D basin modeling study was carried out to reconstruct the regional heat flow and source rock maturity in the Rub'al-Khali basin. Gravity gradient data from the GOCE satellite were used to model deep structures, such as the Moho interface. Tectonic heat flow was modeled using the GOCE-based Moho interface to reflect heat flow variations in the basin though time and space. The thermal maturity of Silurian and Jurassic source rocks in the Rub'al-Khali was calculated using the GOCE-constrained basal heat flow model. GOCE-based Moho depth map was calibrated to data from known seismic stations in the region. This map provided input to constrain the heat flow in eth basin. Modeled heat flow values are consistent with known values of heat flow in the region. The model indicates that the Silurian and Jurassic source rocks are generally in the hydrocarbon generation window and the modeled maturity trends are in agreement with the observations in the area. Copyright 2014, International Petroleum Technology Conference. ConocoPhillips; et al.; ExxonMobil; Maersk Oil; Qatar Petroleum; Shell

GOCE gravity gradients are a new satellite observable, which are given in the instrument frame that is only indirectly connected to the Earth. A rotation to other frames requires to take the different accuracies of the gradients into account. We show that replacing the less accurate gradients with model information allows to rotate the tensor, but for the diagonal gradients \(V_{XX}\) and \(V_{YY}\) the model information can reach up to 50 % in the Local-North Oriented Frame, whereas it is only a few percent for \(V_{ZZ}\). We also show that in the direct comparison of GOCE gravity gradients and satellite altimetry derived gradients one has to account for the difference between the along-track altimeter derivatives and the GOCE gradients in a Cartesian frame, as well as the dynamic ocean topography signal. A validation of GOCE using ERS-1 data shows that both data sets are consistent at levels where GOCE is sensitive. For high spatial resolutions below 40 km wavelength GOCE does not contribute, as expected.

In recent years, global gravity models, both based only on satellite data and from combination with terrestrial data, are increasingly available and particularly useful to construct regional models before more local interpretations on the exploration scale are carried out. Often it is challenging to distinguish clearly between near-surface and regional or even subcrustal signals in the gravity field. Applying simple techniques like wavelength-filtering might lead to an incorrect estimate of the regional and residual field, which may significantly alter estimates of the thickness of sedimentary basins or the size of mineral deposits. An alternative is to use satellite gravity gradients to establish the regional components before studying local geology. Sampietro (2011) presented a global Mohorovicic discontinuity (Moho) depth map, which sparked a discussion about the validity of such results. Especially the question remains about whether crustal thickness estimates based on Gravity field and steady-state Ocean Circulation Explorer (GOCE) satellite data have a higher accuracy than models based on global gravity models or terrestrial data. For example, the density contrast between crust and mantle remains a main factor of uncertainty. Here we join this discussion by describing how satellite gravity gradients can be used in addition to terrestrial data sets or global models like EGM2008, and how the combined use of data sets at multiple levels above the Earth’s surface can help confine the uncertainty in both regional and local modeling studies

[1] Global dynamic processes cause variations in the Earth's rotation, which are monitored by various geometric observation techniques such as Global Navigation Satellite Systems (GNSS), Satellite Laser Ranging (SLR), and Very Long Baseline Interferometry (VLBI) with millimeter accuracy. The integral effect on Earth rotation of mass displacements and motion is therefore precisely known, but the separation of contributions from particular geodynamic processes remains a challenge. Here we show that the oceanic mass effect on Earth rotation can be derived from both time variable gravity field solutions from the Gravity Recovery And Climate Experiment (GRACE) and sea level anomalies (SLA) observed from satellite altimeter missions. The GRACE solutions require filtering and the application of an ocean mask, whereas the SLA need to be corrected for the steric effect as polar motion is only affected by mass redistributions. We assess the accuracy of our oceanic polar motion excitations by using GRACE and SLA solutions from different processing centers. In addition, we compare polar motion excitations from GRACE, satellite altimeter data and their combinations with excitations estimated from ocean models. We show that the combination of gravimetric and altimetric solutions reduces systematic errors of the individual solutions. The combined solutions are about 2 times more accurate than ocean model results and about 3 times more accurate than the so-called reduced geodetic excitation functions. We anticipate our analysis to be valuable input for improved modeling of oceanic mass redistributions.

We present a case study for the North-East Atlantic margin, where we analyze the use of satellite gravity gradients by comparison with a well-constrained 3D model. The model is based on a wealth of seismic profiles, commercial and scientific borehole data from the shelf and mainland Norway, petrophysical sampling and a dense coverage of gravity and aeromagnetic data. The 3D model provides a detailed picture from the upper mantle to the top basement (base of sediments). We analyze how gravity gradients can increase confidence in the modeled structures. Initial results indicate for example that a lateral variable surface density, which reflects geology, has a small influence on the gravity gradients at satellite height. However, the gravity gradients are sensitive to the crustal geometry and upper mantle density structure, which make them an ideal addition to forward and inverse modeling of the lithosphere. The next step will be to calculate a sensitivity matrix for the entire 3D model. This sensitivity matrix describes the relation between calculated gravity gradient data and geological structures with respect to their depth, extent and relative density contrast, and will be used for joint inversion of gravity and gravity gradients.

GOCE is ESA’s gravity field mission and the first satellite ever that measures gravitational gradients in space, that is, the second spatial derivatives of the Earth’s gravitational potential. The goal is to determine the Earth’s mean gravitational field with unprecedented accuracy at spatial resolutions down to 100 km. GOCE carries a gravity gradiometer that allows deriving the gravitational gradients with very high precision to achieve this goal. There are two types of GOCE Level 2 gravitational gradients (GGs) along the orbit: the gravitational gradients in the gradiometer reference frame (GRF) and the gravitational gradients in the local north oriented frame (LNOF) derived from the GGs in the GRF by point-wise rotation. Because the V XX , V YY , V ZZ and V XZ are much more accurate than V XY and V YZ , and because the error of the accurate GGs increases for low frequencies, the rotation requires that part of the measured GG signal is replaced by model signal. However, the actual quality of the gradients in GRF and LNOF needs to be assessed. We analysed the outliers in the GGs, validated the GGs in the GRF using independent gravity field information and compared their assessed error with the requirements. In addition, we compared the GGs in the LNOF with state-of-the-art global gravity field models and determined the model contribution to the rotated GGs. We found that the percentage of detected outliers is below 0.1% for all GGs, and external gravity data confirm that the GG scale factors do not differ from one down to the 10?3 level. Furthermore, we found that the error of V XX and V YY is approximately at the level of the requirement on the gravitational gradient trace, whereas the V ZZ error is a factor of 2–3 above the requirement for higher frequencies. We show that the model contribution in the rotated GGs is 2–35% dependent on the gravitational gradient. Finally, we found that GOCE gravitational gradients and gradients derived from EIGEN-5C and EGM2008 are consistent over the oceans, but that over the continents the consistency may be less, especially in areas with poor terrestrial gravity data. All in all, our analyses show that the quality of the GOCE gravitational gradients is good and that with this type of data valuable new gravity field information is obtained.

The GOCE satellite gravity mission was launched in 2009 to measure the gravity gradient with high accuracy and spatial resolution. GOCE gravity data may improve the understanding and modeling of the Earth’s interior and its dynamic processes, contributing to new insights into the geodynamics associated with the lithosphere, mantle composition and rheology, uplift and subduction processes. However, to achieve this challenging target, GOCE should be used in combination with additional data sources, such as in-situ gravimetric, magnetic, and seismic data sets.

“What's up?” is a question that is answered by the gravity field. Gravity not only determines what is up and down but also reflects the Earth's mass distribution and its changes with time.

The expected high resolution and precision of a global gravity field model derived from satellite gradiometric observations is unprecedented compared to nowadays satellite-only models. However, a dedicated gravity field mission will most certainly fly in a non-polar (sun-synchronous) orbit, such that small polar regions will not be covered with observations. The resulting inhomogeneous global data coverage, together with the downward continuation problem, leads to unstable global solutions and regularization is necessary. Regularization gives rise to a bias in the solution, mainly in the polar areas although in other regions as well.

One of the products derived from the gravity field and steady-state ocean circulation explorer (GOCE) observations are the gravity gradients. These gravity gradients are provided in the gradiometer reference frame (GRF) and are calibrated in-flight using satellite shaking and star sensor data. To use these gravity gradients for application in Earth scienes and gravity field analysis, additional preprocessing needs to be done, including corrections for temporal gravity field signals to isolate the static gravity field part, screening for outliers, calibration by comparison with existing external gravity field information and error assessment. The temporal gravity gradient corrections consist of tidal and nontidal corrections. These are all generally below the gravity gradient error level, which is predicted to show a 1/f behaviour for low frequencies. In the outlier detection, the 1/f error is compensated for by subtracting a local median from the data, while the data error is assessed using the median absolute deviation. The local median acts as a high-pass filter and it is robust as is the median absolute deviation. Three different methods have been implemented for the calibration of the gravity gradients. All three methods use a high-pass filter to compensate for the 1/f gravity gradient error. The baseline method uses state-of-the-art global gravity field models and the most accurate results are obtained if star sensor misalignments are estimated along with the calibration parameters. A second calibration method uses GOCE GPS data to estimate a low-degree gravity field model as well as gravity gradient scale factors. Both methods allow to estimate gravity gradient scale factors down to the 10?3 level. The third calibration method uses high accurate terrestrial gravity data in selected regions to validate the gravity gradient scale factors, focussing on the measurement band. Gravity gradient scale factors may be estimated down to the 10?2 level with this method.