The objective of the Next Generation Gravity Mission (NGGM) is long-term monitoring of the temporal variations of Earth’s gravity field at high resolution in time (temporal resolution with sub-cycles down to 3 days) and space (spatial resolution comparable to GOCE, on the order of 100 km). Such variations carry information about mass transport in the Earth’s system produced by the water cycle and the related mass exchange among atmosphere, oceans, cryosphere and land, and will complete our picture of Global Change with otherwise unavailable data.
The information is derived from the variation of the distance between two satellites measured by a laser interferometer; as a necessary complement, accelerometers on each satellite measure the non-gravitational accelerations which must be separated from the gravity signal in the data processing. The optimal satellite system comprises two pairs of satellites on low (around 340 km) circular orbits, at 100 km mutual distance, one pair near-polar and the other around 65° inclination. Depending on users' needs, further optimization of the orbits and the constellation is possible.
The satellite-to-satellite tracking technique for detecting the temporal variations of gravity is well established since the launch more than 15 years ago of the US-German GRACE (Gravity Recovery and Climate Experiment) project, which has reached 300-400 km spatial resolution at monthly intervals, using tracking in the microwave band. Laser interferometry can improve the resolution by a factor of 50, opening up a host of new applications in observing and quantifying the water cycle. For example, by increasing the spatial resolution to 150 km, mass change would become observable in 80% of all hydrologically significant river basins, up from 10% achieved with GRACE. Higher temporal resolution would reveal large-scale daily mass variations, with applications in water management and operational prediction of floods and draughts.
The paper describes the latest developments achieved in the ESA-sponsored NGGM studies, concerning both the platform (featuring drag-free control, high-stability temperature control, drawing on the heritage of GOCE) and the laser interferometer instrument, which can be conceived in two different designs, the “Transponder” scheme and the “Retro-Reflector” scheme. A hybrid breadboard of the “off-axis” Retro-Reflector concept is being built and will be tested in the TAS-I labs.

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Climate change is one of the biggest societal challenges today, and understanding the underlying processes, which are most frequently related to mass transport in the Earth system, are a key element of Earth observation. Observing the gravity field of the Earth from space is the only available tool to observe and monitor mass distribution and mass transport in the system Earth consistently and globally. Such observations enable the quantification of the global water cycle and closure of the global water budget, melting of ice sheets and glaciers, determination of ocean circulation, mass contributions to sea level change, and constraining the geophysical and earthquake modelling. The value of such observations was proven by the GRACE and GOCE and is now continued by the successfully launched GRACE Follow-On mission. Consolidated science and user needs have be derived in an international initiative under the umbrella of IUGG (Pail et al. 2015), and the need for sustained observation of mass transport from space is also expressed by a corresponding IUGG resolution (IUGG 2015).

In recent years various future mission concepts for observing mass transport in the Earth system, which can fulfil the ambitious requirements of Earth science disciplines asking for mass transport observations with higher temporal and spatial resolutions as it can be achieved nowadays, have been performed. In the ESA-project “Additional Constellation and Scientific Analysis Studies of the Next Generation Gravity Mission (ADDCON)”, by means of extensive numerical closed-loop mission simulations the achievable performance of so-called Bender constellations of two satellite pairs flying in different inclined orbits are analysed, and innovative methods of data exploitation are being developed. Currently we are investigating, in cooperation with a Chinese study team, the benefit of adding a third and fourth pair to the constellation. The impact of different obit configurations and noise characteristics of the key instruments on the achievable space-time resolution and resulting mission performance are investigated by numerical simulations which are performed jointly by the contributing study teams.

An alternative concept of high-precision ranging between high- and low-flying satellites is currently investigated in the frame of a national German project (Hauk et al. 2017). Since such a constellation observes mainly the radial component of gravity-induced orbit perturbations, the error structure is close to isotropic and significantly reduces artefacts of along-track ranging low-low formations (GRACE, GRACE-Follow-On) such as the typical striping patterns. This high-low concept was proposed as MOBILE mission (Mass variation OBservIng system by high-Low inter-satellitE links) by a group of European scientists with the support of technological and industrial partners as Earth Explorer 10 mission to ESA (Pail et al. 2018).

In conjunction with the mission concept, an important aspect of scientific processing is the optimum parameterization of the spatial-temporal signal content provided by these mission constellations, and simultaneously the reduction and/or mitigation of temporal aliasing. By means of co-parameterization of daily long-wavelength gravity fields based on an idea by Wiese et al. (2011), which was further adapted by Daras and Pail (2017), a significant amount of non-tidal temporal aliasing can be prevented, and it could be shown that such a strategy might help to avoid the use of external atmosphere and ocean models for a-priori dealiasing. Additionally, explicit parameterization strategies of ocean tide signal were investigated (Hauk and Pail 2018).

In this contribution, based on full-fledged numerical closed-loop simulations with realistic error assumptions different mission constellations (Bender double-pair, multi-pairs, precise high-low tracking) are assessed and compared, especially regarding their overall performance, their dealiasing potential, and recovery performance of short-periodic gravity signals. The performance of the constellations and associated processing strategies is also analysed in view of their capabilities to retrieve gravity field information with short latencies (Purkhauser et al. 2018) to be used for societally relevant service applications, such as water management, groundwater monitoring, and forecasting of droughts and floods.

References:

Daras I., Pail R. (2017). Treatment of temporal aliasing effects in the context of next generation satellite gravimetry missions. Journal of Geophysical Research: Solid Earth, 122(9):7343-7362, doi: 10.1002/2017JB014250.

Hauk M., Schlicht A., Pail R., Murböck M. (2017). Gravity field recovery in the framework of a Geodesy and Time Reference in Space (GETRIS). Advances in Space Research 59(8): 2032-2047, DOI 10.1016/j.asr.2017.01.028

Hauk M., Pail R. (2018). Treatment of Ocean Tide Aliasing in the context of a Next Generation Gravity Field Mission. Geophysical Journal International, 214(1): 345–365, doi: https://doi.org/10.1093/gji/ggy145.

IUGG, International Union of Geodesy and Geophysics (2015). Resolutions adopted by the council at the XXVI General Assembly Prague, Czech Republic 22. June to 2. July 2015.

Pail and European gravity science team (2018): Mass variation observing system by high low inter-satellite links (MOBILE) – a new 1 concept for sustained observation of mass transport from space. Submitted to Journal of Geodetic Science, in review.

Pail R., Bingham R., Braitenberg C., Dobslaw H., Eicker A., Güntner A., Horwath M., Ivins E., Longuevergne L., Panet I., Wouters B., IUGG Expert Panel (2015). Science and user needs for observing global mass transport to understand global change and benefit society. Surveys in Geophysics, 36(6), 743-772, doi: 10.1007/s10712-015-9348-9.

Purkhauser A., Pail R. (2018): Next generation gravity missions: near-real time gravity field retrieval strategy. Geophsical Journal International, in review.

Wiese D.N., Visser P.N.A.M., Nerem R.S. (2011). Estimating low resolution gravity fields at short time intervals to reduce temporal aliasing errors. Adv. Space Res. 48:1094–1107, doi: 10.1016/j.asr.2011.05.027.

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The main purpose of this study is to investigate the impact of the Baltic Sea non-tidal loading on GNSS observations in the territory of Latvia, by way of using Latvian GNSS permanent station daily coordinate time series and Latvian tide gauge observation data.
The detailed models and algorithms for eliminating the influence of ocean and atmospheric tidal loading effects on GNSS station positions are given in the IERS Conventions, and mostly ensured through the scientific post-processing software packages. Correction for non-tidal ocean loading still needs further investigation, especially in the case of the Baltic region, which is unique with the postglacial land uplift of Fennoscandia and the Baltic Sea itself. The Baltic Sea exhibits a number of remarkable phenomena. One of them is the sea level variations due to winds, complicated by the shape of gulfs and islands. In the case of tidal variations of the Baltic Sea the range is in the order of centimetres only, but under mentioned influence, the range of sea level variations can reach 3 m on the coasts of gulfs. Such loading effect, occurred due to changing redistribution of the water masses, cannot be neglected in coastal regions.
Latvian GNSS station one-year velocities greatly exceed cumulative velocities. As well as their orientation is mostly different from year to year. Moreover, there is well observable similar tendency of orientation in the case of horizontal velocities during one year in the western part of Latvia, which coast is washed by the open sea.
Latvian GNSS station coordinate time series and tide gauge records for the observation period from 2012 up to 2018 are used in this analysis. Preliminary results of a study on the correlation have shown that the Baltic Sea loading is well detectable in GNSS time series, and it is most prominent in the East and Up components. The correlation coefficient reaches 0.6 in the East component and 0.5 in the Up component. The moderate and strong correlations are typical to GNSS stations, which are located in the western part of Latvia and at the east coast of the Gulf of Riga.
The results of this research have own contribution in understanding of the geodynamic processes occurring in the territory of Latvia. The effect of post-glacial rebound in study area is relatively small: according to the deformation model NKG2016LU_abs for absolute land uplift the range of velocities is about 2 mm/yr with positive values; however, in the case of land uplift relative to the mean sea level, another scenario can be observed – velocities mostly have negative values. This is the reason for obtaining a reliable velocity field and forecasting future scenarios of Latvian shoreline changes.

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On the determination of vertical displacements using GRACE and GNSS data – A case study of Poland

Walyeldeen Godah, Malgorzata Szelachowska, Jagat Dwipendra Ray, Jan Krynski

Institute of Geodesy and Cartography, Centre of Geodesy and Geodynamics, 27 Jacka Kaczmarskiego St., 02-679 Warsaw, Poland
Tel.: +48 22 3291903, Fax: +48 22 3291950, e-mail: walyeldeen.godah@igik.edu.pl

Abstract

Over decades, the Global Navigation Satellite System (GNSS) has been reliably used for geodynamic processes. On the other hand, last decade brought numerous valuable information concerning the determination of temporal mass variations within the Earth system using space geodetic data such as GRACE (Gravity Recovery And Climate Experiment) mission data. In May 2018, the GRACE Follow-On (GRACE-FO) satellite mission has been launched for a long-term sustainable information on temporal mass variations within the Earth system. The main aim of this study is to determine vertical displacements of the Earth’s surface over the area of Poland induced from temporal mass variations within the Earth system.
GNSS data from permanent GNSS stations located in Poland as well as the latest release of GRACE/GRACE-FO-based Global Geopotential Models (GGMs) and GRACE/GRACE-FO-based Mascons (Mass concentration) were used. The IGiK‒TVGMF and the GAMIT/GLOBK packages were utilized to process GRACE-based GGMs and GNSS data, respectively. The equivalent water thickness obtained from GRACE-based Mascons solutions was inverted into vertical displacements using the Green function and the Terzaghi’s Principle methods. The main findings were presented and analyzed. The comparative results of vertical displacements of the Earth’s surface over the investigated area obtained from GRACE/GRACE-FO and from GNSS data were discussed.

Keywords: GNSS, GRACE/GRACE-FO, temporal mass variations, vertical displacements

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Over earthquake cycles, major fault segments are locked most of the time, accumulating strain imposed by the continuous motion of plate tectonics, and release the corresponding elastic stress during large earthquakes. On other fault segments, slip can be dominantly aseismic (i.e. creeping fault), with significant implications on the slip budget of the fault. The seismic behaviour of active faults is controlled by various factors, including the spatial distribution of rheological properties and the spatio-temporal evolution of stress in crust. In addition, the aseismic behavior of a fault has a significant influence on the nucleation, the propagation and the arrest of seismic ruptures.

The central segment of the North Anatolian Fault (NAF) is known to be creeping at least since the last M7.3 earthquake in 1944. Both InSAR and GPS data collected within the past 20 years and dynamic models suggest that this 80 km-long-section of the fault, located near the city of Ismetpasa, slips aseismically at a velocity of 7-8 mm/yr between the surface and a depth of 4 km. Recent slip measurements from a local creepmeter and InSAR time series derived from data acquired by the Cosmo-SkyMed constellation highlighted that slip is not constant in time within the last 20 years but occurs within days-to-month long slip episodes, hence calling for a new assessment of the physics of fault slip along this segment.

Up to now, most satellites measurements were too sparse in time and space to capture small-scale slow slips events. The recent European Space Agency (ESA) Synthetic Aperture Radar (SAR) satellites Sentinel-1 A and B, respectively launched in 2014 and 2016, now provide measurements of surface deformation every 6 days over wide area with a tens-of-meter resolution. Such dataset allows to derive temporally and spatially dense time series of surface displacements and systematically search for millimeter scale slow slip events, opening a new window to the fine scale of slow slip along continental faults.

Detecting millimeter-scale, short-living displacements with InSAR requires some improvements to data processing. First, the radar electromagnetic wave is affected by changes in refractivity index in the troposphere and in the electronic content of the ionosphere, biasing significantly measurements of deformation. Second, measuring surface displacements from interferograms generated from two SAR acquisitions requires the unwrapping of interferometric phase. Such unwrapping strongly depends on phase coherence and may be biased in noisy regions, resulting in artificial phase offsets. Here we show how we correct for these sources of noise and derive time series of displacements along the creeping section of the North Anatolian Fault. We then derive the spatial extension of aseismic slip at depth and along-strike using a Bayesian approach.

We process 1420 SAR images acquired along four tracks of Sentinel-1 satellites to generate 2500 interferograms over the 2014-2018 period using the InSAR Scientific Computing Environment (ISCE, JPL/NASA). We also process 65 PALSAR acquisitions along 4 tracks of the late ALOS satellite to generate 159 interferograms over the 2006-2011 period. We correct interferograms from stratified tropospheric delays using the three latest global reanalysis models from ECMWF, ERA-Interim, ERA-5 and High RESolution 10-day forecast (HRES), and compare their efficiency. We correct ALOS interferograms for ionospheric perturbations using the split-spectrum method and highlight the efficiency of such approach. Then, we describe an original algorithm for correction of unwrapping errors, based on systematic and automatic identification of phase misclosures. We describe the performances of our algorithm and assess its efficiency for time series analysis. Finally, we use the Generic InSAR Analysis Toolbox (GIAnT) to perform time series analysis on these 8 tracks. We generate 8 Line-Of-Sight maps of ground velocity and search for transient events within the observation periods. Finally, we use a Bayesian approach to derive the spatial extension of aseismic slip at depth and along-strike. We discuss our results in the light of previous geodetic studies along the creeping section of the NAF.

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On 21 September 1999, the Mw 7.6 Chi-Chi earthquake, one of the largest inland earthquakes in Taiwan happened. It struck the Taipei Basin, in the Central western part of the island, killing more than 2400 people and damaging 100 000 structures. The rupture was complex with several dislocations along the 100-km long Chelungpu thrust fault. Revisiting this earthquake with a range of earth observations will allow better understanding of regional fault properties.
ERS images from the descending track 232 and covering the period from 21 January 1999 to 28 October 1999 were interferometrically processed using the ESA open-software SNAP to investigate the co-seismic deformation. With InSAR, only the footwall can be analyzed because the hanging-wall, which likely experienced the main deformation in this event, is densely vegetated resulting in low coherence in the interferograms. Co-seismic interferograms show about 10-11 fringes in the footwall which is equivalent to a surface displacement of up to approximately 30 cm. In order to obtain observations of the hanging-wall, Cosi-Corr software was used to correlate pre and post SPOT optical images. In addition to these two datasets, GNSS and leveling data were also used.
PSOKINV (Particle Swarm Optimization and Okada Inversion package), a geodetic inversion package, was used to determine the fault geometry and the slip distribution. First, the non-linear problem is solved by using the Particle Swarm Optimization (PSO) for geodetic modelling with the assumption of a uniform slip on a rectangular fault. Second, a joint inversion of InSAR and geodetic data (SPOT, GNSS and leveling) is realized. These datasets enable us to get information about the hanging-wall of the fault and to improve the modelling. The slip distribution is determined as a linear problem, optimally-smoothed parameters are obtained.

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Solid Earth mass rearrangement and ocean water redistribution caused by great earthquakes are made visible by their time-dependent gravity signature, nowadays detectable by the Gravity Recovery And Climate Experiment (GRACE) space mission. The co-seismic gravity jump is caused by earthquake-induced elastic deformation and only depends on the fault slip distribution. The following post-seismic gravity anomaly, instead, is caused by earthquake-induced stress relaxation by viscous flow and, so, still depends on the fault slip distribution, but also on the rheological stratification. In light of this, we have developed a fully Bayesian inverse method which jointly estimates the slip distribution and the rheological stratification on the basis of spherical symmetric self-gravitating compressible Maxwell Earth models from the GRACE data time series, after spatial localization in a spherical cup centred at the epicentre of the centroid-moment-tensor solution. Additional hydrological, residual ocean circulation and solid Earth signals are also jointly estimated and simply modelled in terms of static mean values, linear trends and periodic annual, semi-annual and 161 days (due to the bias of the S2 tidal model) functions. Different from other previous approaches, our method does not rely on any preliminary step for discriminating the co-seismic and post-seismic gravity signatures only on the basis of their characteristic temporal evolutions and avoids any simplification in the description of the seismic source (like point-like seismic source or homogeneous slip model). Furthermore, taking into account the GRACE error structure, our method does not require any additional spatial filtering, but for the spatial localization of the data in the surrounding of the earthquake.

The estimated slip distribution resembles those obtained with seismological or GPS data. Consistently with the GRACE spatial resolution and the strong dependence of the viscoelastic response on the seismic source depth, the slip distribution is poorly constrained along strike and is sensitive to the size of the spherical cup used for the spatial localization, while it is better constrained along dip. Also, the estimated rheological stratification is consistent with our general understanding of the shallow portion of the Earth and constrained in terms of the asthenospheric and upper mantle viscosities and lithospheric thickness. These results show the effectiveness of directly fitting the physical model to space gravity data in order to take advantage of the physical relation between the spatial pattern and the evolution in time of the gravity anomalies and constitute the necessary step towards the integration of these geodetic data with seismological, tsunami and GPS data.

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The main objective of this paper is to investigate the possibility of improving the accuracy of the last geoid model GEOIDALG09 using the tailored Global Gravitational Model EIGEN-6C4 based in GOCE data, two-dimensional topographic mass density model and satellite altimetry-derived marine gravity anomalies. For this purpose, a new gravimetric geoid model for Algeria has been computed using the land gravity data supplied by BGI, EIGEN-6C4 as the reference field, Digital Elevation Model based on SRTM and lateral density model for topographic correction, and DTU13 altimetry-derived gravity anomalies offshore. The residual geoid heights were computed using the 1-D fast Fourier transform technique. This solution, the last published Algerian geoid model GEOIDALG09 and the African geoid model were fitted to 48 GPS/levelling points located in northern part of Algeria using the least-squares Collocation approach in iterative process. According to our numerical results, the new geoid shows an improvement in precision and reliability, fitting the geoidal heights of these GPS/levelling points better than the previous and tested geoids models. Its standard deviation fits with GPS/levelling data are 12.7cm and 1.8cm before and after fitting using the seven-parameter similarity transformation model as corrector surface. Moreover, the analysis of the results shows that the signals in GPS/levelling benchmarks are dominated by errors in the geoid due to the inaccurate and sparse land gravity, while the noise level indicates the presence of errors in national vertical datum. This new geoid model will be used for practical surveying in Algeria and to support Levelling by GPS at least for the low order levelling network densification.
Keywords: DTU13 altimetry-derived gravity anomalies, EIGEN-6C4, two-dimensional topographic mass density model, Collocation approach

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The European Space Agency (ESA) Earth Explorer Swarm satellites quantify Earth mass transport processes at spatial scales longer than roughly 1500 km on a monthly basis. This is made possible by the data collected by the on-board high-precision, dual-frequency Global Positioning System (GPS) receivers. To mitigate possible systematic processing biases, we combine individual solutions produced from four different gravity field inversion strategies, namely the Celestial Mechanics Approach (Beutler et al. 2010), the Decorrelated Acceleration Approach (Bezdek et al. 2014), the Short-Arcs Approach (Mayer-Gürr 2006) and the Improved Energy Balance Approach (Shang et al. 2015). The individual solutions are combined at the level of Normal Equations so that the sensitivity of the different approaches to Earth gravity field variations can be optimally exploited and the highest quality of gravity field solutions can be obtained.

We demonstrate that the Swarm mission serves as an interesting source of global gravimetric data to fill gaps and periods not covered by the GRACE and GRACE-FO missions, be it with reduced spatial resolution. We illustrate that major geophysical signals that take place during such periods can be observed by Swarm at regional scales. For the first 3 years of the Swarm mission, we also compare Swarm-based estimates of time variable gravity with corresponding GRACE-based estimates and demonstrate a high level of consistency at large spatial scales.

References:

- Beutler, G., Jäggi, A., Mervart, L., & Meyer, U. (2010). The celestial mechanics approach: theoretical foundations. Journal of Geodesy, 84(10), 605–624. https://doi.org/10.1007/s00190-010-0401-7

- Bezděk, A., Sebera, J., Teixeira da Encarnação, J., & Klokočník, J. (2016). Time-variable gravity fields derived from GPS tracking of Swarm. Geophysical Journal International, 205(3), 1665–1669. https://doi.org/10.1093/gji/ggw094

- Mayer-Gürr, T. (2006). Gravitationsfeldbestimmung aus der Analyse kurzer Bahnbögen am Beispiel der Satellitenmissionen CHAMP und GRACE. Rheinischen Friedrich-Wilhelms Universität Bonn. Retrieved from http://hss.ulb.uni-bonn.de
/2006/0904/0904.pdf
- Shang, K., Guo, J., Shum, C. K., Dai, C., & Luo, J. (2015). GRACE time-variable gravity field recovery using an improved energy balance approach. Geophysical Journal International, 203(3), 1773–1786. https://doi.org/10.1093/gji/ggv392

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Time-series of monthly gravity fields derived from GRACE observations (2002-2017) and continued by GRACE-FO (science phase starting in January 2019) are a major source for studies on large scale mass transport in the system Earth and for quantification of the effects of climate change. But up to date there is not one correct, agreed upon way of processing the satellite gravimetric observables, but a number of approaches that result in an equal number of time-series. We present a comparison, validation and combination of the latest of these time-series, based on the recent RL03 of the GRACE-L1B observation data. A focus will be laid on the effect of different background modeling strategies on the resulting gravity field models. The validation and combination are performed in the frame of the Combination Service for Time-variable Gravity models (COST-G), a new product center of the International Association of Geodesy (IAG).

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The Gravity field and steady-state Ocean Circulation Explorer (GOCE, Drinkwater et al. 2003) was the first mission which carried a novel instrument, gradiometer, which allowed to measure the second-order directional derivatives of the gravitational potential or gravitational gradients with a uniform quality and a near-global coverage. More than three years of the outstanding measurements resulted in two levels of data products (Level 1b and Level 2), five releases of global gravitational models (GGMs), and several grids of gravitational gradients (see, e.g., ESA-funded GOCE+ GeoExplore project or Space-wise GOCE products). The grids of gravitational gradients represent a step between gravitational gradients measured directly along the GOCE orbit and data directly from GGMs. One could use grids of gravitational gradients for geodetic as well as for geophysical applications.
In this contribution we are going to validate grids of gravitational gradients by terrestrial gravity anomalies over the area of Czech republic and Slovakia. This area is located between parallels 12° and 23° and meridians 47° and 51° in the central part of Europe. It was collected more than 500 000 point-wise values of gravity between years 1956-1992 with estimated accuracy about 0.1 mGal. A mathematical model based on a spectral combination method will be developed and the corresponding spectral weights will be derived for validation gravitational gradients grids. This model allows as continued the gravitational gradients grids downward Earth’s surface (not to a mean sphere) and transform them to gravity anomalies in one step. Before we compare results obtained by spectral downward continuation we have to remove high-frequency part of the gravitational signal from terrestrial data because gravitational gradients measured at GOCE satellite altitude do not contain it. To do so we will employ EGM2008 (Pavlis et al., 2012) up to d/o 2190 and the residual terrain model effect (e.g., Forsberg 1984) will be calculated above d/o 2190.

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In this study, we updated the loose integration approach of high- rate GPS and SM data by adding GPS coloured noise to the KF. In this approach, the grid search method was first applied to estimate the GPS noise parameters based on GPS pre-event noise; then, two parallel KF were used: the first KF added GPS coloured noise to the state vector, and the other added SM baseline shifts to the state vector. Validation analysis was conducted at collocated stations in Italy and southern California. The results show that the combined displacement considering GPS coloured noise can avoid the inter- ference caused by GPS low-frequency noise and is more stable and reliable than the displacement associated with traditional loose inte- gration. Further use of the moving average method can smooth the high-frequency sawtooth of combined displacements in real time.

Currently, the use of high-rate GPS data for the deformation mon- itoring of earthquakes is under constant development. Compared with traditional instruments such as seismometers and SM sensors, the main advantage of this technique is the ability to provide dy- namic displacements without saturation or drift in real time. From the perspective of data sources, it is important to develop real-time GPS filtering methods. However, the effect of seismic deformation on GPS noise characteristics still cannot be extracted quantitatively. In our study, we used the noise characteristics of pre-event GPS data to describe the GPS noise during an earthquake. This noise mod- elling method can be applied in real time but may not completely explain the coseismic noise in some cases. For example, at 25–35 s in the vertical direction in Fig. 3, the CNKF displacement diverges from both the GPS and corrected SM data, which is caused by the defective coloured noise model. Therefore, it is necessary to further quantify the relationship between pre-seismic and coseismic GPS noise in the future.

In our study, the effect of our combination approach on col- located stations with low SNR is more visible. This is expected because the impact of noise on GPS stations with strong seismic signals is small, and the filtering effect is limited. Additionally, the displacement waveforms of these stations are sufficiently accurate for most studies in seismology, such as the inversion of source parameters and the assessment of coseismic slip distribution. How- ever, for GPS stations with low SNR, filtering is urgently needed to extract available signals. This can lead to the topic of filtering value. Although GPS stations with low SNR contribute little to seismic inversion, the separation of noise and signals in these stations can still play a role in other aspects, such as the refinement of statisti- cal models in earthquake early warning systems and the fine-scale modelling of GPS noise. For example, high-rate GPS data can pro- vide earthquake magnitude without saturation for use in earthquake early warning systems (Melgar et al. 2015). When establishing a statistical model of magnitude, it is necessary to accumulate data from multiseismic cases and multiple stations. Thus, the statistical regression model can be refined by extracting signals from more sta- tions by filtering. Moreover, the magnitude can be estimated rapidly by P-wave peak displacement ( Pd ) after integrating high-rate GPS and SM data (Crowell et al. 2013). Because Pd itself represents a
weak deformation signal, we can theoretically obtain a more accu- rate Pd by updating the combination method with a more precise noise model. This inference could be partly verified using our com- bination approach and the statistical relationship between Pd and earthquake magnitude. However, further validation of this method depends on the use of more earthquake cases and more collocated stations, and it is currently difficult to implement because of the limited number of collocated stations.

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Three-dimensional (3D) measurements of earth surface deformation can provide much information about the dynamics of ice sheets, landslides, eruptions of earthquakes, and volcano activities, which plays a significant role in understanding the processes of the geophysical movement and global climate change. However, due to their polar-orbits and zero-Doppler acquisition geometries, current spaceborne SAR systems have limited measuring capability of the North-South (N-S) deformation component (since it is roughly perpendicular to their line of sight directions).
The multistatic STEREOID system, which is chosen as one of the three ESA Earth Explorer 10 candidate missions, can realize high-accuracy 3D deformation monitoring by exploiting the geometry diversity provided by its flexible configuration [1]. Under the designed Stereo configuration of the system, two passive SAR satellites (STEREOID-A and STEREOID-B) fly at roughly 250 km distance before and after the active Sentinel-1 SAR. Two passive sensors will cooperate with Sentinel-1 SAR to form the multistatic geometry. Benefited from the large separation between the differently located STEREOID satellites, the novel system has an order of magnitude higher sensitivity to the N-S deformation. In particular, STEREOID can conveniently obtain the high-accuracy two-dimensional (2D) deformation by multiple aperture interferometric processing of the forward STEREOID-1 and backward STEREOID-2 looking interferograms [2]. Combining the ascending and descending data, 3D deformation can be finally estimated by least-square method [3]. The basic 3D deformation measuring formation of STEREOID system is shown in Figure 1.
Considering the STEREOID’s complex multistatic configuration, our research focuses on several special issues. First and foremost, we provide the optimal design for STEREOID’s along-track separation, which is based on the evaluations of the N-S deformation measuring accuracy, the observation period for the targets, and the safe distance between the satellites. In addition, some possible key factors and their impacts for 3D deformation retrieval accuracy, such as the atmospheric artifacts, residual synchronization errors, and the baseline knowledge error, are also considered. Especially, since the STEREOID system operates in C band, both the tropospheric and the ionospheric effects can threaten the designed deformation accuracy of the STEREOID mission (cm-level). Finally, STEREOID’s 3-D deformation performance analysis is conducted under different conditions, which considers the configurations of the satellites (e.g., formation, look angle, etc), atmospheric states, and the geographical locations of the observed scene.

Reference:
[1] P. Lopez-Dekker. Stereo Thermo-Optically Enhanced Radar for Eearth, Ocean, Ice, and land Dynamices_(STEREOID). ESA Ref: CEE10/012.
[2] Noa B.D. Bechor and H.A. Zebker, “Measuring two-dimensional movements using a single InSAR pair,” Geophys. Res. Lett., vol. 33, no. 16, pp. L16311, Aug 2006.
[3] P. Prats-Iraola, P. Lopez-Dekker, F. De Zan, N. Yagüe-Martínez, M. Zonno, M. Rodriguez-Cassola, “Performance of 3-D Surface Deformation Estimation for Simultaneous Squinted SAR Acquisitions,” IEEE Trans. Geosci. Remote Sens., vol. 56, no. 4, pp. 2147-2158, Apr. 2018.

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After the end of the GOCE mission in November 2013, the High-level Processing Facility (HPF) computed and delivered to the scientific community the final GOCE Level-2 products based on the whole mission period, including the fifth release (R5) of the gravity field solutions. Among them, the space-wise approach was employed to compute high-resolution spherical grids of gravity gradients at GOCE satellite altitude in the Terrestrial Reference Frame (TRF). In fact, for science applications these grid values can be more easily exploited than the original observations thanks to their regular spatial distribution, their orbit-independent orientation and (as a consequence of the filtering) their smaller errors. The grid data can be also used to solve the boundary value problem and derive potential spherical harmonic coefficients.
The main input data for the space-wise grid computation are the satellite orbits, used to estimate the long wavelengths of the gravity field, and the observed gravity gradients from which the medium-short wavelengths are determined. The former are Level-2 products computed within HPF, the latter are Level-1B products derived from the measurements of the on-board accelerometers after proper calibration. A reprocessing of these input data was recently performed, leading to a mitigation of the systematical orbit errors along the geomagnetic equator and to a general improvement of the Level-1B gravity gradients, especially for the diagonal component in the out-of-plane direction, i.e. the so-called YY-component. These reasons motivated the computation of a new release (R6) of the space-wise approach solution, alongside the computation of the direct and time-wise approach solutions as well.
The key idea of the space-wise approach is to filter the original data in both the time and the space domain, taking into account the time correlation of the gradiometer noise and spatial correlation of the gravity field. Therefore, the procedure consists in different filtering-gridding steps dedicated to different parts of the harmonic spectrum. The output of each step is used to reduce the input data of the next one. Initially, the energy integral method is applied to the satellite kinematic orbits to estimate the low degrees of the gravity field. Then, a Wiener filter followed by a local collocation gridding are applied to the gradiometric data to catch the medium degrees. Finally, a White filter followed by a local collocation gridding on much smaller patches of gradiometric data are further applied to refine the estimation of the high degrees.
The main difference between the space-wise approach and the other two official methods is that the GOCE data acquired (and filtered) along the orbit are moved onto global grids by applying collocation on local data patches, each of them with its own locally adapted signal covariance. In this way the filtering level is locally controlled, while in the other solutions a global regularization on spherical harmonic coefficients is applied.
The output grids at 0.2° x 0.2° spatial resolution are provided with their error standard deviations, computed through Monte Carlo simulations. Furthermore, from the grids a set of spherical harmonic coefficients is straightforwardly derived by numerical integration and global regularization, together with the corresponding full error covariance matrix.
In this work the sixth release of the space-wise GOCE-only solution is presented, showing the different stages of the data processing and assessing the quality of the obtained products by comparing them with the fifth release and with other global grids and spherical harmonic models.

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In gravity field studies satellite and terrestrial data complement each other. Potential theory forms the respective basis, but the problem considered is overdetermined by nature. Therefore, methods for solving boundary-value problems are combined with optimization concepts. In the first stage an implementation of Green’s function method is discussed. The approach is iterative. A transformation of spatial coordinates is used that opens a possibility for an alternative between the boundary complexity and the complexity of the coefficients of Laplace’s equation governing the solution. The solution domain is carried onto a spherical layer (domain bounded by two concentric spheres). Obviously, the structure of the Laplacian is more complex after the transformation. Nevertheless, the construction of the respective Green’s function is simpler for the solution domain transformed. The integral representation of the solution gives a better insight into the role, which the input data have in the global and the local modelling of the gravity field. Subsequently, the continuation of the solution is discussed with a particular view to its harmonic nature, analytic extension and regularity at infinity. The reasoning leads to compatibility examinations of the two data sources and to energy preserving optimization concepts considered in the paper.

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In recent years, sensors from geodetic missions such as CHAMP, GRACE, GOCE, Swarm and others have provided an enormous wealth of science data with high quality, very low noise and excellent coverage, leading to important contributions to the Global Geodetic Observing System, to global reference frames and Essential Climate Variables, and to an improved, high-precision understanding of orbital dynamics. Due to the high measurement precision, the sensor data are characterized by complex systematic effects related to sensor properties, due to the orbital and satellite platform environment, and due to sampling limitations. We report on recent analysis and re-processing efforts to investigate, separate and model such effects in GRACE, GOCE, Microscope and Swarm data, in order to achieve better modeling of observations, better science signals, and an improved understanding of the orbital environment. In particular, the combination of the data from the different satellite missions provides a rich material for joint analysis. We examine and discuss methods and findings can be transferred to the analysis of data from other missions. The need to investigate and precisely model such systematic effects is likely to further increase for future geodetic sensor systems including quantum sensor systems.

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We present modelling of the static gravity field in spatial domain purely from the filtered GOCE gravity gradients. For such purposes we apply meshless boundary collocation techniques like the method of fundamental solutions (MFS) and singular boundary method (SBM). These numerical methods use the fundamental solution of the Laplace equation as basis functions. Hence, the system matrix is created by the second radial derivatives of the fundamental solution that depend solely on geometrical parameters, i.e. on 3D positions of the GOCE observations and source points located on the Earth’s surface. Such a configuration is free of singularities and MFS can be applied to derive unknown coefficients in the source points. From these coefficients the disturbing potential and gravity disturbances can be evaluated in any point above the Earth’s surface. To obtain their values directly on the Earth’s surface, e.g. at the source points, SBM can be applied. The key idea of SBM is to isolate singularities of the fundamental solution and its derivatives using some appropriate regularization techniques.
To obtain “cm-level” precision of the final static gravity field model, the source points are regularly distributed over the Earth’s surface with the high-resolution of 0.05 deg (12,960,002 points). The GOCE gravity gradients as input data are firstly filtered using the nonlinear diffusion filtering. This step includes pre-processing of the original GOCE observation, detection of outliers and ‘jumps’ in time series, modelling and removing of systematic tendencies in low-frequencies and filtering the noise by an appropriate nonlinear filter. Afterwards large-scale parallel computations of MFS are performed on the cluster with 1.2 TB of the distributed memory. Enormous memory requirements are reduced by an iterative approach developed for an elimination of far zones’ interactions. Finally, the obtained coefficients in the source points, which represent source densities of the Earth’s gravity field, are used to evaluate the disturbing potential or gravity disturbances above the Earth’s surface. Their values are compared with ones generated from the SH-based satellite-only geopotential models like GO_CONS_GCF_2_DIR_R5 or GO_CONS_GCF_2_TIM_R5.

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The complex dynamics of the Earth is driven by geophysical processes which induce mass redistribution and affect the gravity field and the position of the geocenter.
Geodetic techniques allow to monitor the main mass variations of our planet reflected by variations of the Earth’s figure axis and oblateness, which are described by the second-degree geopotential coefficients, and by variations of the positions of the center of mass of the entire Earth system, equivalent to degree one gravity harmonics.
Due to the long record of accurate and continuous observations, Satellite Laser Ranging (SLR) is known as the only current space technique capable to monitor variations of the Earth’s gravity field over decades. On the other hand, SLR provides the best estimation of the translations of the Earth’ center of mass relative to the International Terrestrial Reference Frame (ITRF), generally referred to as “geocenter motion”.
This work presents our analysis of SLR data (spanning more than 30 years) from several geodetic satellites to recover time series of low degree geopotential coefficients. Models and results, together with accuracies and spectral content, will be shown and discussed.

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The contribution deals with filtering of the GOCE gravity gradients (GGs) by the nonlinear diffusion filters and curvature driven filters in the spatial domain, which is constructed at a mean altitude of the GOCE satellite orbits. In order to see better noise in the signal, we evaluate residuals between the GOCE GGs in GRF (EGG_NOM_2 product) and GGs generated from the SH-based model GO_CONS_GCF_2_TIM_R5 model up to d/o 280. Such a residuals represent our new processing time series. From all these time series we can see large biases of different components as well as some trend in data, especially for the Vyy component. Moreover, there are several large "jumps" in the time series which need to be detected and removed. For data preprocessing we create automatic "jump" detection based on the nonlinear along track diffusion of series. Such a method is based on finding trends in processing time series and detection of the large variation in this trends. For the surface filtering, we define a surface finite volume method to approximate numerically the nonlinear parabolic partial differential equation. The surface is approximated by a polyhedral surface created by planar triangles and we use a piece-wise linear approximation of a solution in space and the backward discretization in time. A numerical experiment presents filtering of residuals on the closed computational domain, separately for data from ascending and descending satellite tracks and the comparison with along track nonlinear diffusion filtering. Surprisingly, the residuals include some “systematic tendencies” which look different for ascending and descending tracks. They have different behaviour for every GGs component but in all cases, they have a long-wavelength character with amplitudes reaching several mE. To overcome this problem, we have decided to model the ’systematic tendencies’ using curvature driven filters and remove them from the GOCE GGs. After this correction, we are able to use nonlinear filtering to reduce the noise while preserving important structures as much as possible.

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We outline the new DTU18MSS mean sea surface, which is the latest release of the global high resolution mean sea surface from DTU Space. The major new advance leading up to the release of this DTU18MSS is an improved 7 years Cryosat-2 LRM record which has been corrected for dynamic ocean topography. A new processing chain with updated editing and data correction (i.e., using FES2014 as Ocean tide model) has been implemented. In the ice-covered parts of the Polar Regions a new Cryosat-2 dataset based on empirical Gaussian retracking was preferred. After calculating retracking bias with other alitimetric datasets the data were ingested into the DTU18MSS. In general the differences with DTU15 is small (up to 5 cm). However in the Polar regions the corrections are substantially larger. A general lowering of the MSS within ice-covered Polar regions between 13 and 15 cm was found both for Antarctic and Arctic. Furthermore consolidating the newer geodetic mission data from Cryosat-2 and SARAL and Jason-2 onto a past 20 year mean sea surface derived was investigated as well. The 20 year period between 1993-2012 is still the fundamental period for mean sea surface determination for the DTU18MSS.
DTU18MSS is equipped with a functionality to determine time specific MSS estimates in which annual offsets to the mean sea surface is used to correct the period onto the time specific period (i.e. 2003-2007) which is useful when comparison with i.e. episodically observations are made. The first evaluation into this is also performed using the S3-A and presented in this talk.
In this presentation we will also present an evaluation against the Sentinel-3A two year mean profiles and the first 0.5 years Sentinel 3B mean profiles. Furthermore an investigation into areas of possible short wavelength residual signals will be performed to investigate the importance of SAR altimetry for mapping short wavelength.

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The latest lobal high resolution global marine free air gravity field called DTU17 is presented in this presentation. Data from the latest generation of high-class geodetic missions creates the basis for this new global marine gravity field. A total of 9 years from three geodetic missions including (8 years of Cryosat-2 (369 days repeat mission) as well as one year of Jason-1 and 1.5 years of Jason-2 end-of-life mission and three year of SARA/AltiKa geodetic mission). Older geodetic missions (ERS-1 and GEOSAT) are now nearly retired in DTU17 and do not even provide marginal information due to their inferior signal to noise ratio..

In the Arctic Ocean we will present results from several new developments in high resolution gravity field modelling. One is a a new dual-pass retracking of SARAL/AltiKa together with an new combined empirical/physical retracking system for Cryosat-2 that uses physical retracking of the LRM data in combination with empirical retracking of the SAR and SAR-In data. We also try to evaluate Cryosat-2 data in the Arctic retracked using the SAMOSA retracker via the ESA GPOD service.

A new medium wavelength correction based on altimetry and GOCE have been introduced to deal with problems in the older remove restore technology based on EGM2008. This is particularly important for Cryosat-2 due to its ability of provide new accurate sea surface height information for gravity field determination all the way up to 88N where no altimeters have measured before.

We perform a detailed comparision for the medium wavelength with gravity derived from the GOCE satellites to spherical harmonic degree and order 200 to evaluate these wavelength in the gravity field and find that the altimetric gravity fields are now superior in quality to compilations of marine gravity field observations in large parts of the Arctic Ocean. We also perform evaluation around Antarctica with data from Mission IceBridge flown during recent years.

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The main scope of the GEOMED2 project is the determination of a high-accuracy and high-resolution geoid and DOT models for the Mediterranean Sea.
The processing methodology is based on the well-known remove-compute-restore procedure and both stochastic and integral/spectral methods for the determination of the geoid and the rigorous combination of heterogeneous data. All the available gravity observations for the wider Mediterranean basin were collected, validated, homogenized and unified in terms of their horizontal coordinates and gravity systems, so as to derive a reliable gravity data base to be used for the determination of the geoid. Particularly, marine gravity were track by track debiased in order to remove existing inconsistencies among the different gravity campaigns.
Base on the collected data, the geoid has been computed in the wider Mediterranean area, i.e. in the area bounded between 30° < φ < 48° -10° < λ < 40°. The available gravity data have been gridded on a regular 2’ x 2’ grid in the computation area employing ordinary kriging, servicing both as input to the geoid estimation methodologies and as a project deliverable to be disseminated as a new approximation of the gravity field over the Mediterranean. Fast-collocation, 1dFFT and 2dFFT employing the original Wong-Gore modified Stokes kernel and the KTH methods have been applied in order to get the geoid estimate. The different geoid estimates have been then compared with altimeter data to obtain different estimates of the Dynamic Ocean Topography (DOT), which will allow the definition of the currents pattern in the Mediterranean Sea.

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Global sea level change differs regionally, as its contributors, such as self-attraction and loading, freshwater flux due to melting of glaciers, Greenland- and Antarctic-ice-sheets or variability in land water storage effects vary globally. In addition, if sea level rise is observed with tide gauges, then one should also correct the estimates for Vertical Land Motion (VLM) at the tide gauges by for example Glacial Isostatic Adjustment (GIA). Near plate boundaries, tectonic plate motion creates earthquakes and post-seismic deformation that affect VLM. In this research, we study sea level rise in the Pacific using tide gauge data, eliminating the non-linear VLM derived from the Global Positioning System (GPS) observations. We provided the case study of the Tohoku-Oki earthquake (Mw9.1, National Earthquake Information Center, NEIC) which occurred on 11th March 2011, epicenter at 38.322°N, 142.369°E. However, having knowledge of about more than 3 500 earthquakes of magnitude greater than 6 which occurred from 1995 in the vicinity of tide gauges, this kind of correction is of great importance to connect relative sea level to absolute sea level in a proper way.
The GPS-derived VLM is analyzed in two ways: using standard Constant Velocity Model (CVM) and using the optimal model, which includes a change between pre- and post-seismic velocities along with the post-relaxation logarithmic and exponential functions (here denoted as Extended Trajectory Model). Within the latter, two velocities are separated by the vertical offset which occurred at the time of the earthquake. Both models are then applied to correct the tide-gauge records from 38 Pacific stations collected by Permanent Service for Mean Sea Level (PSMSL). Finally, the absolute sea level rise from corrected gauge data is compared to the Essential Climate Variable (ECV) altimetric dataset of the ESA Climate Change Initiative (CCI) project. The time span of analysis is selected to January 1993 - December 2015. We show that applying the non-linear vertical land model, the mean tide gauges-derived absolute sea level rise is 3.84±0.29 mm/year, which is in close agreement with satellite altimetry estimates at the tide gauge location of 3.96±0.20 mm/year. Otherwise, the rise is 3.44±0.32 mm/year. We also prove, that adding the offset in the time of the earthquake is extremely important, otherwise, an error of up to 2 mm/year in absolute sea level rise would be committed.

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Compared to the past GeoSat and ERS-1 geodetic missions, which was launched in 1980s and 1990s respectively. Today, with CryoSat-2, Jason-1, and SARAL in their drifting (or geodetic) phases, we have observations of new generation of radar altimeters that allows us to improve drastically the shortest wavelengths of the finest geophysical structures of the gravity field and those of the Mean Sea Surface.
However, the determination of these two reference fields are still affected by imperfections that remains a major challenge, and which can be exposed in 2 points.
The first point concerns the removing of the seasonal and interannual ocean variability which is theoretically accessible only from repetitive missions (T/P, ERS-2, Jason-1/2/3, EnviSat, and Sentinel-3A). Specific analysis using results of objective analysis of sea level anomalies (SLA) were also carried out in order to apply a better correction. Nevertheless, it has been shown that these non-repetitive data are still affected by a residual effect of the oceanic variability for scales less than 200 km and at a level of few centimeters, particularly in oceanic regions of strong currents. It is always necessary to improve this correction of the residual effect of the ocean variability and especially for missions in the geodetic phase.
The second point consists in the use of the new generation of data as those of J1GM, CryoSat-2, Sentinel-3A and SARAL. In order to access to the shortest wavelengths of the MSS, for example these lower than 30 km, we can no longer use the data sampled at 1 Hz (7 km along track). The use of these new altimeters data that are sampled at 40 Hz for AltiKa and at 20 Hz for the others J1GM, CryoSat-2, Sentinel-3A altimeters respectively appears fully sufficient.
However, analysis have shown that at these frequencies the noise level is too high and can affect the determination of the shortest wavelengths of the MSS. It is therefore a quest for finding an optimal compromise between the reduction of the noise and the filtering of the signal.
We purpose here a synthesis of these various analyses and their impact on the determination of the MSS.

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Many studies have compared the global positioning system (GPS) measurements of vertical crustal displacements due to surface loading and the predicted displacements converted from the time-varying gravity field measured by Gravity Recovery and Climate Experiment (GRACE). Measurements from the Greenland Global Positioning System network (GNET) have shown that all the GPS sites mounted on bedrock around coastal Greenland have been undergoing steady uplift in the past decade, in response to the present-day ice mass loss from the Greenland Ice Sheet. However, the GPS uplift trends are larger, by factors of 1 to 3, than the GRACE-predicted trends due to truncation and filtering of GRACE. In this study, we first synthesize the GPS measurements from more than 40 GNET sites and the most recent release (RL06) of the GRACE GSM products (Level-2) from the Center for Space Research, University of Texas Austin. We show the gain factors tend to vary linearly with the magnitude of the GPS uplift trends. Using the theory of the Earth’s elastic response to a surface disk load, we further reveal a linear correspondence between the gain factors and the uplift divided by a unit loading mass. Such a simple linear relationship can well explain the GPS and GRACE observations over Greenland. Based on both the empirical results and theoretical modeling, we propose two independent methods for scaling the GRACE-predicted vertical loading displacements. After scaling, the GRACE-predicted displacements can be directly compared with GPS observations to infer the present-day ice mass changes over Greenland. Furthermore, combining the scaled-GRACE and GPS measurements can improve isolation of elastic and glacial isostatic adjustment uplifts caused by present-day and historical ice mass changes, respectively. Similar methods can be applied to other regions and can improve the effectiveness of combining GPS and GRACE measurements for studying surface fluid changes of the Earth systems.

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The GOCE User Toolbox GUT is a compilation of tools for the utilisation and analysis of GOCE Level 2 products.GUT support applications in Geodesy, Oceanography and Solid Earth Physics. The GUT Tutorial provides informationand guidance in how to use the toolbox for a variety of applications. GUT consists of a series of advancedcomputer routines that carry out the required computations. It may be used on Windows PCs, UNIX/Linux Workstations,and Mac. The toolbox is supported by The GUT Algorithm Description and User Guide and The GUTInstall Guide. A set of a-priori data and models are made available as well. Without any doubt the developmentof the GOCE user toolbox have played a major role in paving the way to successful use of the GOCE data foroceanography. The GUT version 2.2 was released in April 2014 and beside some bug-fixes it adds the capability for the computation of Simple Bouguer Anomaly (Solid-Earth).
A new GUT version 3 has been released. GUTv3 was further developed through a collaborative effort where the scientific communities participate aimingon an implementation of remaining functionalities facilitating a wider span of research in the fields of Geodesy,Oceanography and Solid earth studies.Accordingly, the GUT version 3 has:
- An attractive and easy to use Graphic User Interface (GUI) for the toolbox,
- Enhance the toolbox with some further software functionalities such as to facilitate the use of gradients,anisotropic diffusive filtering and computation of Bouguer and isostatic gravity anomalies.
- An associated GUT VCM tool for analysing the GOCE variance covariance matrices.

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