Steady-state Ocean Circulation Explorer Research Articles

Stationary depletions in thermospheric atomic oxygen concentration and mass density observed with WINDII, GUVI, GOCE and simulated by NRLMSISE-00

Observations of thermospheric atomic oxygen concentrations [O] by the Wind Imaging Interferometer (WINDII) and the Global Ultra Violet Imager (GUVI) derived from daytime airglow observations clearly show a persistent depletion in [O], for WINDII by about 63% below background, in the southern mid-latitudes, near 40° S latitude and 100° longitude. It appears less strongly in the northern hemisphere at about 250° longitude and is not evident in local winter for either hemisphere. The same feature appears strongly in the NRLMSISE-00 empirical model. Mass density observations by the Gravity field and steady-state Ocean Circulation Explorer (GOCE) available at dawn and dusk local times at times show similar depletions with a smaller reduction of about 20% but do not consistently agree with those of [O]. It has been shown elsewhere that Total Electron Content (TEC) observations are strongly related to the column ratio ΣO/N2. These observations clearly show the Weddell Sea Anomaly (WSA) enhancement as well as the [O] depletion at a similar latitude; these are oppositely phased and 180° apart in longitude, suggesting a common source.

Autonomous orbit determination using epoch-differenced gravity gradients and starlight refraction

Autonomous orbit determination via integration of epoch-differenced gravity gradients and starlight refraction is proposed in this paper for low-Earth-orbiting satellites operating in GPS-denied environments. Starlight refraction compensates for the significant along-track position error that occurs from only using gravity gradients and benefits from integration in terms of improved accuracy in radial and cross-track position estimates. The between-epoch differencing of gravity gradients is employed to eliminate slowly varying measurement biases and noise near the orbit revolution frequency. The refraction angle measurements are directly used and its Jacobian matrix derived from an implicit observation equation. An information fusion filter based on a sequential extended Kalman filter is developed for the orbit determination. Truth-model simulations are used to test the performance of the algorithm, and the effects of differencing intervals and orbital heights are analyzed. A semi-simulation study using actual gravity gradient data from the Gravity field and steady-state Ocean Circulation Explorer (GOCE) combined with simulated starlight refraction measurements is further conducted, and a three-dimensional position accuracy of better than 100m is achieved.

From GOCE to NGGM: Automatic Control Breakthroughs for European future Gravity Missions

After the successful European gravity mission GOCE (Gravity field and steady-state Ocean Circulation Explorer), which provided an unprecedented high resolution static global map of the Earth’s gravity field, the European Space Agency has proposed several preparatory studies for a Next Generation Gravity Mission (NGGM). The NGGM mission objective aims at measuring the temporal variations of the Earth gravity field over a long time span with an unprecedented level of accuracy, both in spatial and temporal resolution. The GOCE technological heritage is leveraged as starting point while defining the NGGM future mission concept. Nonetheless, to accomplish its challenging scientific objective, the NGGM mission concept envisages a wide range of innovations, with respect to the past or flying missions, both on technological and automatic control side. Thus, this paper focuses on the guidance, navigation and control design evolution for the European gravity missions, from GOCE to NGGM. After recalling the GOCE GNC main design concepts, the paper will describe the most important innovation required by NGGM. Indeed, such a future concept will consist of a two-satellite long-distance loose formation, where each satellite is controlled independently to be drag-free, GOCE-like. The satellite-to-satellite distance variations, encoding gravity anomalies, will be then measured by laser heterodyne interferometry for inter-satellite ranging at 20 nm resolution, or better. Hence, an orbit and formation control is now required to counteract bias and drift of the residual drag-free accelerations, in order to reach a bounded orbit/formation long-term stability. Finally, GOCE control flight results as well as NGGM simulated results, via a high-fidelity simulator, will be provided. These results highlight the GOCE GNC in-flight achievements as well as the NGGM concept validity, showing that the expected control performances are in agreement with the consolidated mission requirements, all over the 10-year mission.

EGY-HGM2016: an improved hybrid local geoid model for Egypt based on the combination of GOCE-based geopotential model with gravimetric and GNSS/levelling measurements

An improved hybrid gravimetric geoid model for Egypt, EGY-HGM2016, has been recently computed implementing the least-squares collocation (LSC) method through the remove-compute-restore (RCR) procedure. The computation of EGY-HGM2016 involves different datasets in terms of gravity anomalies determined from the GOCE (gravity field and steady-state ocean circulation explorer)-based global geopotential model (SPW-R4) up to d/o 200 and EGM2008 from d/o 201 to 720 combined with terrestrial gravity datasets in terms of 2140 gravity field anomalies and about 121,480 marine surface gravity anomalies. In addition, orthometric heights from 17 GPS/levelling measurements have been considered during the modelling process to improve the determination of the hybrid gravimetric geoid over the Egyptian region. The EGY-HGM2016 model estimated over Egypt provides geoid heights that are ranging from 7.677 to 21.095 m with a standard deviation (st. dev.) of about 2.534 m in the northwest of the country excluding the involvement of the orthometric heights from GPS/levelling measurements. When the later dataset is considered during the implementation of LSC process, hybrid residual height anomalies ranging from −1.5 to +0.9 m, with a mean of 0.22 m and a st. dev. of 0.17 m, are obtained. Comparison of the predicted hybrid gravimetric geoid with the corresponding ones obtained from EGM2008, GOCE-based SPW R4 model, and GPS/levelling reveals considerable improvements of our EGY-HGM2016 model over Egypt.

Comparison of spectral and spatial methods for a Moho recovery from gravity and vertical gravity-gradient data

In global studies investigating the Earth’s lithospheric structure, the spectral expressions for the gravimetric forward and inverse modeling of the global gravitational and crustal structure models are preferably used, because of their numerical efficiency. In regional studies, the applied numerical schemes typically utilize the expressions in spatial form. Since the gravity-gradient observations have a more localized support than the gravity measurements, the gravity-gradient data (such as products from the Gravity field and steady-state Ocean Circulation Explorer - GOCE - gravity-gradiometry satellite mission) could preferably be used in regional studies, because of reducing significantly the spatial data-coverage required for a regional inversion or interpretation. In this study, we investigate this aspect in context of a regional Moho recovery. In particular, we compare the numerical performance of solving the Vening Meinesz-Moritz’s (VMM) inverse problem of isostasy in spectral and spatial domains from the gravity and (vertical) gravity-gradient data. We demonstrate that the VMM spectral solutions from the gravity and gravity-gradient data are (almost) the same, while the VMM spatial solutions differ from the corresponding spectral solutions, especially when using the gravity-gradient data. The validation of the VMM solutions, however, reveals that the VMM spatial solution from the gravity-gradient data has a slightly better agreement with seismic models. A more detailed numerical analysis shows that the VMM spatial solution formulated for the gravity gradient is very sensitive to horizontal spatial variations of the vertical gravity gradient, especially in vicinity of the computation point. Consequently, this solution provides better results in regions with a relatively well-known crustal structure, while suppressing errors caused by crustal model uncertainties from distant zones. Based on these findings we argue that the gravity-gradient data are more suitable than the gravity data for a regional Moho recovery.

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.

Earth\u2019s gravity field modelling based on satellite accelerations derived from onboard GPS phase measurements

GPS data collected by satellite gravity missions can be used for extracting the long-wavelength part of the Earth’s gravity field. We propose a new data processing method which makes use of the ‘average acceleration’ approach to gravity field modelling. In this method, satellite accelerations are directly derived from GPS carrier phase measurements with an epoch-differenced scheme. As a result, no ambiguity solutions are needed and the systematic errors that do not change much from epoch to epoch are largely eliminated. The GPS data collected by the Gravity Field and Steady-State Ocean Circulation Explorer (GOCE) satellite mission are used to demonstrate the added value of the proposed method. An analysis of the residual accelerations shows that accelerations derived in this way are more precise, with noise being reduced by about 20 and 5% at the cross-track component and the other two components, respectively, as compared to those based on kinematic orbits. The accelerations obtained in this way allow the recovery of the gravity field to a slightly higher maximum degree compared to the solution based on kinematic orbits. Furthermore, the gravity field solution has an overall better performance. Errors in spherical harmonic coefficients are smaller, especially at low degrees. The cumulative geoid height error is reduced by about 15 and 5% up to degree 50 and 150, respectively. An analysis in the spatial domain shows that large errors along the geomagnetic equator, which are caused by a high electron density coupled with large short-term variations, are substantially reduced. Finally, the new method allows for a better observation of mass transport signals. In particular, sufficiently realistic signatures of regional mass anomalies in North America and south-west Africa are obtained.

Local recovery of lithospheric stress tensor from GOCE gravitational tensor

The sublithospheric stress due to mantle convection can be computed from gravity data and propagated through the lithosphere by solving the boundary-value problem of elasticity for the Earth's lithosphere. In this case, a full tensor of stress can be computed at any point inside this elastic layer. Here, we present mathematical foundations for recovering such a tensor from gravitational tensor measured at satellite altitudes. The mathematical relations will be much simpler in this way than the case of using gravity data as no derivative of spherical harmonics (SHs) or Legendre polynomials is involved in the expressions. Here, new relations between the SH coefficients of the stress and gravitational tensor elements are presented. Thereafter, integral equations are established from them to recover the elements of stress tensor from those of the gravitational tensor. The integrals have no closed-form kernels, but they are easy to invert and their spatial truncation errors are reducible. The integral equations are used to invert the real data of the gravity field and steady-state ocean circulation explorer mission (GOCE), in 2009 November, over the South American plate and its surroundings to recover the stress tensor at a depth of 35 km. The recovered stress fields are in good agreement with the tectonic and geological features of the area.

Semi-empirical thermosphere model evaluation at low altitude with GOCE densities

Aims : The quality of the Committee on Space Research (COSPAR) International Reference Atmosphere models NRLMSISE-00, JB2008, and DTM2013 in the 150–300 km altitude range has never been thoroughly evaluated due to a lack of good density data. This study aims at providing the model accuracies thanks to the recent high-resolution high-accuracy Gravity field and steady-state Ocean Circulation Explorer (GOCE) density dataset. The evaluation was performed on yearly, monthly, and daily time scales, which are important for different applications such as mission design, mission operation, or re-entry predictions. Methods : The accuracy of the models was evaluated by comparing to the GOCE density observations of the Science Mission (1 November 2009–20 October 2013) and new density data at the lowest altitudes derived for the last weeks before the re-entry (22 October–8 November 2013) according to a metric, which consists of computing mean, standard deviation and root mean square (RMS) of the observed-to-model ratios, and correlation. Mean statistics are then calculated over the three time scales. Results : The range of model biases, standard deviations, and correlations becomes larger when the time interval decreases, and this study provides COSPAR International Reference Atmosphere (CIRA) model statistics in the altitude range of 275–170 km. DTM2013 is the least biased and most accurate model on all time scales, essentially thanks to the database, notably containing two years of GOCE densities, to which it was fitted. NRLMSISE-00 performs worst, with considerable bias of about 20% in 2009 and 2013, and systematically higher standard deviations (lower correlations) than JB2008 and DTM2013. The performance of JB2008 is presently only slightly behind DTM2013, thanks to the new release 4_2g solar activity proxies. However, it still presents some weakness under the lowest solar activity conditions in 2009 and 2010. Comparison to Challenging Mini-Satellite Payload (CHAMP) density data showed that the results based on GOCE densities, despite limited local solar time coverage of 6–8 am & pm, are representative of model performance.

On High-Frequency Topography-Implied Gravity Signals for a Height System Unification Using GOCE-Based Global Geopotential Models

National height reference systems have conventionally been linked to the local mean sea level, observed at individual tide gauges. Due to variations in the sea surface topography, the reference levels of these systems are inconsistent, causing height datum offsets of up to ±1–2 m. For the unification of height systems, a satellite-based method is presented that utilizes global geopotential models (GGMs) derived from ESA’s satellite mission Gravity field and steady-state Ocean Circulation Explorer (GOCE). In this context, height datum offsets are estimated within a least squares adjustment by comparing the GGM information with measured GNSS/leveling data. While the GNSS/leveling data comprises the full spectral information, GOCE GGMs are restricted to long wavelengths according to the maximum degree of their spherical harmonic representation. To provide accurate height datum offsets, it is indispensable to account for the remaining signal above this maximum degree, known as the omission error of the GGM. Therefore, a combination of the GOCE information with the high-resolution Earth Gravitational Model 2008 (EGM2008) is performed. The main contribution of this paper is to analyze the benefit, when high-frequency topography-implied gravity signals are additionally used to reduce the remaining omission error of EGM2008. In terms of a spectral extension, a new method is proposed that does not rely on an assumed spectral consistency of topographic heights and implied gravity as is the case for the residual terrain modeling (RTM) technique. In the first step of this new approach, gravity forward modeling based on tesseroid mass bodies is performed according to the Rock–Water–Ice (RWI) approach. In a second step, the resulting full spectral RWI-based topographic potential values are reduced by the effect of the topographic gravity field model RWI_TOPO_2015, thus, removing the long to medium wavelengths. By using the latest GOCE GGMs, the impact of topography-implied gravity signals on the estimation of height datum offsets is analyzed in detail for representative GNSS/leveling data sets in Germany, Austria, and Brazil. Besides considerable changes in the estimated offset of up to 3 cm, the conducted analyses show that significant improvements of 30–40% can be achieved in terms of a reduced standard deviation and range of the least squares adjusted residuals.

Surface velocity estimates of the North Indian Ocean from satellite gravity and altimeter missions

ABSTRACTThe circulation in the North Indian Ocean (NIO) is one of the most complex systems compared with other regions of global oceans, mostly due to its interactions with the monsoon winds. In recent years, our ability to measure the ocean’s mean dynamic topography (MDT) from space has improved immensely with the availability of satellite gravity measurements from Gravity Recovery and Climate Experiment (GRACE) and Gravity Field and Steady-State Ocean Circulation Explorer (GOCE) missions. The present study uses data from GOCE and GRACE satellite gravity missions together with altimeter data in retrieving the geoid, satellite-only MDT, and surface velocities in the NIO. The study estimates geoid heights of the NIO from all five releases of the direct approach and the time-wise GOCE gravity data. The formal error associated with geoid heights at different resolutions is found to be the lowest for the latest release of direct approach GOCE data. In addition, a new satellite-only MDT is estimated from the direct approach GOCE geoid and the CNES_CLS11 mean sea surface. This MDT corrected to a 20-year time reference is used together with the newly reprocessed sea level anomaly data to estimate absolute dynamic topography and surface geostrophic velocities in the NIO. The total surface velocities computed from the Ekman and geostrophic velocity fields reproduce all major surface currents in the NIO, along with their seasonality. Furthermore, total surface velocity estimates computed here are validated using surface drifters and are found to be highly comparable (difference within ± 10 cm s–1) with more than 170,000 individual surface drifter observations. Finally, the total velocities estimated here are used to examine the variability of the East India Coastal Current.

Comparison of Selected Geopotential Models in Terms of the GOCE Orbit Determination Using Simulated GPS Observations

This work contains a comparative study of the performance of six geopotential models in an orbit estimation process of the satellite of the Gravity Field and Steady-State Ocean Circulation Explorer (GOCE) mission. For testing, such models as ULUX_CHAMP2013S, ITG-GRACE 2010S, EIGEN-51C, EIGEN5S, EGM2008, EGM96, were adopted. Different sets of pseudo-range simulations along reference GOCE satellite orbital arcs were obtained using real orbits of the Global Positioning System satellites. These sets were the basic observation data used in the adjustment. The centimeter-accuracy Precise Science Orbit (PSO) for the GOCE satellite provided by the European Space Agency (ESA) was adopted as the GOCE reference orbit. Comparing various variants of the orbital solutions, the relative accuracy of geopotential models in an orbital aspect is determined. Full geopotential models were used in the adjustment process. The solutions were also determined taking into account truncated geopotential models. In such case, an accuracy of the solutions was slightly enhanced. Different arc lengths were taken for the computation.

On the Contribution of GOCE Satellite-Based GGMs to Improve GNSS/Leveling Geoid Heights Determination in Saudi Arabia

The global geopotential models (GGMs) derived from the gravity field and steady-state ocean circulation explorer (GOCE) mission provide important information about Earth gravity functionals (e.g., geoid heights, gravity anomalies, and disturbances). Among gravity functionals, we utilize geoid heights which have been determined from several recent GOCE-based GGMs and validate them against 5187 collocated Global Navigation Satellite System (GNSS)/leveling observations over a network of dedicated benchmarks in Saudi Arabia. Our aim is to consider the spectral consistency between GOCE-based GGMs and ground-based data. Accordingly, we incorporate high/very high frequencies of gravity functionals, i.e., the gravity signal beyond the maximum d/o of GOCE-based GGMs, using EGM2008 and a high-resolution digital terrain model based on the Shuttle Radar Topography Mission (SRTM). This investigation indicates that completing the missing high-frequency component of geoid heights in GOCE-based GGMs, using EGM2008 and SRTM data, results in an improvement of about 16% in the reduction in the standard deviation (SD) of the differences. This is provided by DIR_R5 at SH d/o 230, which shows improvement from 37.5 cm, without applying the spectral enhancement method (SEM), compared to 31.4 cm when applying the SEM. Finally, three types of transformation models, namely four-, five-, and seven-parameter transformations, are examined to deal with the data biases and to provide a better fitting of geoid heights obtained from the studied GOCE-based GGMs to those from GNSS/leveling data. These models reveal that the SD of vertical datum over the region of Saudi Arabia is at the level of about 22 cm.

On inversion of the second- and third-order gravitational tensors by Stokes’ integral formula for a regional gravity recovery

A regional recovery of the Earth’s gravity field from satellite observables has become particularly important in various geoscience studies in order to better localize stochastic properties of observed data, while allowing the inversion of a large amount of data, collected with a high spatial resolution only over the area of interest. One way of doing this is to use observables, which have a more localized support. As acquired in recent studies related to a regional inversion of the Gravity field and steady-state Ocean Circulation Explorer (GOCE) data, the satellite gravity-gradient observables have a more localized support than the gravity observations. Following this principle, we compare here the performance of the second- and third-order derivatives of the gravitational potential in context of a regional gravity modeling, namely estimating the gravity anomalies. A functional relation between these two types of observables and the gravity anomalies is formulated by means of the extended Stokes’ integral formula (or more explicitly its second- and third-order derivatives) while the inverse solution is carried out by applying a least-squares technique and the ill-posed inverse problem is stabilized by applying Tikhonov’s regularization. Our results reveal that the third-order radial derivatives of the gravitational potential are the most suitable among investigated input data types for a regional gravity recovery, because these observables preserve more information on a higher-frequency part of the gravitational spectrum compared to the vertical gravitational gradients. We also demonstrate that the higher-order horizontal derivatives of the gravitational potential do not necessary improve the results. We explain this by the fact that most of the gravity signal is comprised in its radial component, while the horizontal components are considerably less sensitive to spatial variations of the gravity field.

GRAVITY ANOMALY ASSESSMENT USING GGMS AND AIRBORNE GRAVITY DATA TOWARDS BATHYMETRY ESTIMATION

Abstract. The Earth’s potential information is important for exploration of the Earth’s gravity field. The techniques of measuring the Earth’s gravity using the terrestrial and ship borne technique are time consuming and have limitation on the vast area. With the space-based measuring technique, these limitations can be overcome. The satellite gravity missions such as Challenging Mini-satellite Payload (CHAMP), Gravity Recovery and Climate Experiment (GRACE), and Gravity-Field and Steady-State Ocean Circulation Explorer Mission (GOCE) has introduced a better way in providing the information on the Earth’s gravity field. From these satellite gravity missions, the Global Geopotential Models (GGMs) has been produced from the spherical harmonics coefficient data type. The information of the gravity anomaly can be used to predict the bathymetry because the gravity anomaly and bathymetry have relationships between each other. There are many GGMs that have been published and each of the models gives a different value of the Earth’s gravity field information. Therefore, this study is conducted to assess the most reliable GGM for the Malaysian Seas. This study covered the area of the marine area on the South China Sea at Sabah extent. Seven GGMs have been selected from the three satellite gravity missions. The gravity anomalies derived from the GGMs are compared with the airborne gravity anomaly, in order to figure out the correlation (R2) and the root mean square error (RMSE) of the data. From these assessments, the most suitable GGMs for the study area is GOCE model, GO_CONS_GCF_2_TIMR4 with the R2 and RMSE value of 0.7899 and 9.886 mGal, respectively. This selected model will be used in the estimating the bathymetry for Malaysian Seas in future.

Towards sub-lithospheric stress determination from seismic Moho, topographic heights and GOCE data

Sub-lithospheric stresses can be estimated by analysis of gravity field measurements. Depending on the measured gravimetric quantity, different methods can be employed to estimate those sub-lithospheric stresses. Here, we further develop the Runcorn’s theory for estimation of mantle stresses (1967) such that a Moho model and full topographic information are used to recover the function from which the stress can be computed by taking derivatives northwards and eastwards. We develop new integral equations for such a purpose and recover this function by solving those integral equations locally over the Indo-Pak (India-Pakistan) region from (1) a gravimetric Moho model computed from the SRTM (Shuttle Radar Topography Mission) and the Earth gravity model EGM2008, (2) SRTM and the seismic Moho model of CRUST1.0 and (3) data and measurements of the GOCE (Gravity field and steady-state Ocean Circulation Explorer) mission. Finally, we perform a joint inversion of seismic and GOCE data for the same purpose. The numerical results show that the use of a seismic Moho model recovers information about the stress field which is not seen in the results derived from a gravimetric Moho model. A combination of the seismic Moho model, SRTM and GOCE yields a better stress field than that of either the seismic and/or gravimetric data alone. The magnitudes of the sub-lithospheric stress are computed from the shear stress components over the area and good agreement is seen between the recovered combined stress field, the regional tectonic boundaries and the seismicity of the World Stress Map 2008 database.

RTM-based omission error corrections for global geopotential models: Case study in Central Europe

The aim of this paper is to evaluate the effects of residual terrain model (RTM) on potential and on gravity and to point out how significant can the omission error of global geopotential models (GGMs) be and how it can influence their testing. The RTM for Central Europe is computed in the spherical approximation. The topography is modelled by spherical tesseroids and the gravitational effect of the topography is obtained as a sum of their partial gravitational effects. A detailed picture of RTM in Slovakia is shown. The testing of GOCE (Gravity Field and Steady-State Ocean Circulation Explorer) global geopotential models in Central Europe published earlier is re-evaluated with the more rigorous omission error estimation. Experimental results show significantly better agreement between the gravity anomalies computed from global geopotential models with the omission-error estimation and gravity anomalies obtained from the direct measurements. On the other hand, for height anomalies such an improvement is not observed. The results are discussed in context of the other previously published studies.

Orbit determination and estimation of non-gravitational accelerations for the GOCE reentry phase

During its reentry phase from 21 October to 10 November 2013, the European Space Agency (ESA) Gravity field and steady-state Ocean Circulation Explorer (GOCE) continued to provide high-quality, dual-frequency observations by its Global Positioning System (GPS) receiver, star tracker and accelerometers. This resulted in a unique data set for testing high-precision orbit determination at altitudes down to as low as 137km. In addition, the accelerometers kept working down to this altitude as well, be it with growing periods during which they were saturated. This made it possible to test the capability of estimating non-gravitational accelerations in high drag environments by GPS.A reduced-dynamic orbit determination based on an extended Kalman filter approach was adopted to cope with the estimation of the orbit parameters, including the exponentially growing non-gravitational accelerations. The orbits were found to be consistent with Satellite Laser Ranging (SLR) observations at a level of just a few centimeters for a few passes collected up to 2 November 2013. Also orbit overlap comparisons and comparisons with external orbit solutions indicate a 3-dimensional orbit quality at the dm level or better. In addition, high correlations were found between the estimated non-gravitational accelerations and those from the accelerometers during all periods when they were not saturated: typically close to 0.99 for the X axis of the gradiometer reference frame (close to the flight direction), for which the non-gravitational acceleration signal is by far the largest. High correlations were found as well for the Y axis (0.68–0.96) and Z axis (0.61–0.93), predominantly aligned with respectively the cross-track and height direction. The highest correlations were found for the last days, as long as the accelerometers were not saturated.

An approach to Moho discontinuity recovery from on-orbit GOCE data with application over Indo-Pak region

In this research, a modified form of Vening Meinesz-Moritz (VMM) theory of isostasy for the second-order radial derivative of gravitational potential, measured from the Gravity field and steady-state Ocean Circulation Explorer (GOCE), is developed for local Moho depth recovery. An integral equation is organised for inverting the GOCE data to compute a Moho model in combination with topographic/bathymetric heights of SRTM30, sediment and consolidated crystalline basement and the laterally-varying density contrast model of CRUST1.0. A Moho model from EGM2008 to degree and order 180 is also computed based on the same principle for the purpose of comparison. In addition, we compare both of them with the 3 available seismic Moho models; two global and one regional over the Indo-Pak region. Numerical results show that our GOCE-based Moho model is closer to the all seismic models than that of EGM2008. The model is closest to the regional one with a standard deviation of 5.5km and a root mean squares error of 7.8km, which is 2.3km smaller than the corresponding one based on EGM2008.

A regional background model for the Arabian Peninsula from modeling satellite gravity gradients and their invariants

Gravity gradients of the GOCE (Gravity field and steady state Ocean Circulation Explorer) mission are available and provide free available data with global homogeneous coverage. The spatial resolution is about 80km which makes it possible to construct regional models of large or remote areas. We study the benefit of using this data for compiling a 3D regional density model of the lithosphere with emphasis on the crustal structure for the Arabian Peninsula. We keep the data at satellite level to avoid noise amplification. The initial density model was set up with only a few seismic constraints and modified by forward modeling. Forward models benefits from the use of the full gravity gradient tensor and the invariants. The misfits between the measured and calculated field are more easily recognized in the gravity gradient tensor than in the gravity field alone. Different shape and location of anomalies are visible in the different components. Hence, modeling is better controlled as geometries which fit one component do not necessarily fit all other components. Regional models are important for a general understanding of any area and as a background for local interpretations. Here, we explain how to construct density models from satellite gravity gradients and show the advantage of such an approach by comparison to earlier studies based on either seismic or gravity data.