Temporal Gravity Research Articles

Geodynamics implication of GPS and satellite altimeter and gravity observations to the Eastern Mediterranean

The Eastern Mediterranean region is one of the interested regions from both tectonic and seismic point of views. It shows an active geologic structure attributed to the tectonic movement of the African and Eurasian plates from one side and the Arabian plate from other side. This tectonic setting is attributed with continuous seismological activity, which affects almost all the countries of the Eastern Mediterranean including Egypt.Crustal deformation as deduced from both European and Egyptian permanent GPS networks provides significant horizontal deformation velocities along this region. GPS crustal deformation parameters were able to reveal the complication of the deformation of the studied region.Spatial gravity map of the selected region indicates important mass discontinuities zones correlated well with the seismological and deformation activities.Temporal gravity variation as computed from the Gravity Recovery and Climate Experiment (GRACE) of the considered region were able to determine important mass redistribution zones and shed more light on its geodynamics pattern.Results show important zones of mass discontinuity in this region correlated with the seismological activities and temporal gravity variations agree with the crustal deformation obtained from GPS observations. The current study indicates that satellite gravity data is a valuable source of data in understanding the geodynamical behavior of the studied region and that satellite gravity data is an important contemporary source of data in the geodynamical studies.

Accuracy of scaled GRACE terrestrial water storage estimates

We assess the accuracy of global‐gridded terrestrial water storage (TWS) estimates derived from temporal gravity field variations observed by the Gravity Recovery and Climate Experiment (GRACE) satellites. The TWS data set has been corrected for signal modification due to filtering and truncation. Simulations of terrestrial water storage variations from land‐hydrology models are used to infer relationships between regional time series representing different spatial scales. These relationships, which are independent of the actual GRACE data, are used to extrapolate the GRACE TWS estimates from their effective spatial resolution (length scales of a few hundred kilometers) to finer spatial scales (∼100 km). Gridded, scaled data like these enable users who lack expertise in processing and filtering the standard GRACE spherical harmonic geopotential coefficients to estimate the time series of TWS over arbitrarily shaped regions. In addition, we provide gridded fields of leakage and GRACE measurement errors that allow users to rigorously estimate the associated regional TWS uncertainties. These fields are available for download from the GRACE project website (available at http://grace.jpl.nasa.gov). Three scaling relationships are examined: a single gain factor based on regionally averaged time series, spatially distributed (i.e., gridded) gain factors based on time series at each grid point, and gridded‐gain factors estimated as a function of temporal frequency. While regional gain factors have typically been used in previously published studies, we find that comparable accuracies can be obtained from scaled time series based on gridded gain factors. In regions where different temporal modes of TWS variability have significantly different spatial scales, gain factors based on the first two methods may reduce the accuracy of the scaled time series. In these cases, gain factors estimated separately as a function of frequency may be necessary to achieve accurate results.

Gravity Recovery and Interior Laboratory Simulations of Static and Temporal Gravity Field

Gravity Recovery and Interior Laboratory Simulations of Static and Temporal Gravity Field

Gravity Recovery and Interior Laboratory Simulations of Static and Temporal Gravity Field

Gravity Recovery and Interior Laboratory Simulations of Static and Temporal Gravity Field

Improved daily GRACE gravity field solutions using a Kalman smoother

Different GRACE data analysis centers provide temporal variations of the Earth's gravity field as monthly, 10-daily or weekly solutions. These temporal mean fields cannot model the variations occurring during the respective time span. The aim of our approach is to extract as much temporal information as possible out of the given GRACE data. Therefore the temporal resolution shall be increased with the goal to derive daily snapshots. Yet, such an increase in temporal resolution is accompanied by a loss of redundancy and therefore in a reduced accuracy if the daily solutions are calculated individually. The approach presented here therefore introduces spatial and temporal correlations of the expected gravity field signal derived from geophysical models in addition to the daily observations, thus effectively constraining the spatial and temporal evolution of the GRACE solution. The GRACE data processing is then performed within the framework of a Kalman filter and smoother estimation procedure.The approach is at first investigated in a closed-loop simulation scenario and then applied to the original GRACE observations (level-1B data) to calculate daily solutions as part of the gravity field model ITG-Grace2010. Finally, the daily models are compared to vertical GPS station displacements and ocean bottom pressure observations.From these comparisons it can be concluded that particular in higher latitudes the daily solutions contain high-frequent temporal gravity field information and represent an improvement to existing geophysical models.

Temporal gravity changes before the 2008 Yutian Ms7.3 earthquake

Based on the data of the repeated gravity observation network in Chinese mainland since 1998, we analyzed the temporal changes of regional gravity field before the 2008 Yutian M s7. 3 earthquake. The result shows some mid-to-long term (two to ten years) changes during the earthquake’s preparation. Notable features are a gravity increase lasting several years and a relatively large-scaled gradient zone of gravity change, the former indicating a continuous energy accumulation and the latter a possible location of seismic rupture. These gravity changes showed a trend of increase-accelerated increase-decelerated increase, similar to that of the Tangshan M s7. 8 earthquake in 1976. The maximum accumulated gravity change related to the earthquake reached 200 × 10 − 8 ms − 2 .

Expected improvements in determining continental hydrology, ice mass variations, ocean bottom pressure signals, and earthquakes using two pairs of dedicated satellites for temporal gravity recovery

[1] The Gravity Recovery and Climate Experiment mission has demonstrated the ability to quantify global mass variations at large spatial scales with monthly to sub-monthly temporal resolution. Future missions of this type taking advantage of improved measurement technologies will be limited by temporal aliasing errors. We suggest the addition of a second pair of satellites to reduce these errors. Using an optimized mission architecture consisting of a polar pair of satellites coupled with a lower inclined pair of satellites (72°), both in 13-day repeating orbits, we quantify the expected scientific improvements that having two pairs of satellites will provide over one pair. Numerical simulations to spherical harmonic degree 100 are run over one full year. Analysis using empirical orthogonal functions reveals that two satellite pairs determine annual mass variations in small basins which are undetected using one pair of satellites. Averaging kernels are used to show that two satellite pairs offer an 80% reduction in the level of error in determining mass variations in 53 hydrological basins and 12 Greenland basins over the year. After standard GRACE post-processing techniques have been applied to the one-pair solutions, it is seen that two satellite pairs (with no post-processing) still offer a 25%–75% improvement in determining the mass variations. Spatiospectral localization analysis is used to show increased spatial resolution and higher signal-to-noise ratios in recovering hydrology in the Amazon River basin, ocean bottom pressure signals in the Southeast Pacific basin, and a simulated earthquake signal representative of the 2010 Maule, Chile earthquake.

Simulation of the time-variable gravity field by means of coupled geophysical models

Abstract. Time variable gravity fields, reflecting variations of mass distribution in the system Earth is one of the key parameters to understand the changing Earth. Mass variations are caused either by redistribution of mass in, on or above the Earth's surface or by geophysical processes in the Earth's interior. The first set of observations of monthly variations of the Earth gravity field was provided by the US/German GRACE satellite mission beginning in 2002. This mission is still providing valuable information to the science community. However, as GRACE has outlived its expected lifetime, the geoscience community is currently seeking successor missions in order to maintain the long time series of climate change that was begun by GRACE. Several studies on science requirements and technical feasibility have been conducted in the recent years. These studies required a realistic model of the time variable gravity field in order to perform simulation studies on sensitivity of satellites and their instrumentation. This was the primary reason for the European Space Agency (ESA) to initiate a study on ''Monitoring and Modelling individual Sources of Mass Distribution and Transport in the Earth System by Means of Satellites''. The goal of this interdisciplinary study was to create as realistic as possible simulated time variable gravity fields based on coupled geophysical models, which could be used in the simulation processes in a controlled environment. For this purpose global atmosphere, ocean, continental hydrology and ice models were used. The coupling was performed by using consistent forcing throughout the models and by including water flow between the different domains of the Earth system. In addition gravity field changes due to solid Earth processes like continuous glacial isostatic adjustment (GIA) and a sudden earthquake with co-seismic and post-seismic signals were modelled. All individual model results were combined and converted to gravity field spherical harmonic series, which is the quantity commonly used to describe the Earth's global gravity field. The result of this study is a twelve-year time-series of 6-hourly time variable gravity field spherical harmonics up to degree and order 180 corresponding to a global spatial resolution of 1 degree in latitude and longitude. In this paper, we outline the input data sets and the process of combining these data sets into a coherent model of temporal gravity field changes. The resulting time series was used in some follow-on studies and is available to anybody interested.

Trend of mass change in the Antarctic ice sheet recovered from the GRACE temporal gravity field

It is important to quantify mass variations in the Antarctic ice sheet to study the global sea-level rise and climate change. A hybrid filtering scheme employing a combination of the decorrelated filter P3M6 and 300 km Fan filter was used, and the surface mass variations over the Antarctic are recovered from GRACE CSR RL04 monthly gravity field models from August 2002 to June 2010. After deduction of leakage errors using the GLDAS hydrological model and postglacial rebound effects using the glacial isostatic adjustment model IJ05, the variations in the ice sheet mass are obtained. The results reveal that the rate of melting of the Antarctic ice sheet is 80.0 Gt/a and increasing and contributes 0.22 mm/a to the global sea-level rise; the mass loss rate is 78.3 Gt/a in the West Antarctic and 1.6 Gt/a in the East Antarctic. The average mass loss rate increases from 39.3 Gt/a for the period 2002–2005 to 104.2 Gt/a for the period 2006–2010, and its corresponding contribution to the global sea-level rise increases from 0.11 to 0.29 mm/a, which indicates accelerated ice mass loss over the Antarctic since 2006. Moreover, the mass accumulation rates for Enderby Land and Wilkes Land along the coast of East Antarctica decrease for the period 2006–2008 but increase evidently after 2009.

The expanding Earth at present: evidence from temporal gravity field and space-geodetic data

The Earth expansion problem has attracted great interest, and the present study demonstrates that the Earth has been expanding, at least over the recent several decades. Space-geodetic data recorded at stations distributed globally were used (including global positioning system data, very-long-baseline interferometry, satellite laser ranging stations, and stations for Doppler orbitography and radiopositioning integrated by satellite), which covered a period of more than 10 years in the International Terrestrial Reference Frame 2008. A triangular network covering the surface of the Earth was thus constructed based on the spherical Delaunay approach, and average-weighted vertical variations in the Earth surface were estimated. Calculations show that the Earth is expanding at present at a rate of 0.24 ± 0.04 mm/yr. Furthermore, based on the Earth Gravitational Model 2008 and the secular variation rates of the second-degree coefficients estimated by satellite laser ranging and Earth mean-pole data, the principal inertia moments of the Earth (A, B, C) and in particular their temporal variations, were determined: the simple mean value of the three principal inertia moments (i.e., [A+B+C]/3) is gradually increasing. This clearly demonstrates that the Earth has been expanding, at least over the recent decades, and the data show that the Earth is expanding at a rate ranging from 0.17 ± 0.02 mm/yr to 0.21 ± 0.02 mm/yr, which coincides with the space geodetic evidence. Hence, based on both space geodetic observations and gravimetric data, we conclude that the Earth has been expanding at a rate of about 0.2 mm/yr over recent decades.

How Wartime Violence Affects Social Cohesion: The Spatial–Temporal Gravity Model

Local communities such as villages are commonly assumed to be vital partners in counterinsurgency and post-conflict reconstruction. However, the success of all policies based on this assumption depends on the level of social cohesion at the community level: communities with internal cleavages and fissures will be less effective in making external efforts a success. In this article, we study how exposure to violence during civil war affects the internal cohesion of a community. On the one hand, we could assume that exposure to a common threat strengthens social ties. On the other hand, shifting power structures in conflict regions could introduce new loyalties and cleavages at the village level, thus eroding a community's social glue. We use data from a survey conducted in northern Afghanistan and combine it with the data on violent events from military records. Our results provide evidence for the second mechanism: exposure to violence causes villagers to diverge in their support for conflicting parties. We estimate a spatial–temporal gravity model, where spatially and temporally proximate events have the highest impact on this divergence at the village level.

Recent changes in the Earth's oblateness driven by Greenland and Antarctic ice mass loss

[1] We use temporal gravity variations from GRACE to investigate changes in a 34-year time series of Earth's oblateness (J2) observed by satellite laser ranging (SLR). We use 2002–2010 GRACE data to compute the effects of Greenland and Antarctic ice mass variations on J2 (2.0 and 1.7 × 10−11/year respectively). Their combined effect on the J2 trend during the GRACE mission is 3.7 × 10−11/year, which agrees well with the GIA-corrected SLR J2 trend over the same time period. The results suggest that at least since 2002, ice loss from Greenland and Antarctica has been the dominant contributor to the current GIA-corrected J2 trend, which apparently began sometime in the 1990s.

GOCE, Satellite Gravimetry and Antarctic Mass Transports

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

Recent gravity changes in China Mainland

Abstract: Based on results of the mobile gravity measurements of the Crustal Movement Observation Network of China and Digital Earthquake Observation Network of China, this paper shows the pattern of temporal gravity changes in China mainland on a time scale of 2 – 3 years since 1998, and gives an analysis of the patterns. The result shows that the temporal gravity changes basically reflect the current mass movement and occurrence of strong earthquakes.

Relation between GRACE-derived surface mass variations and precipitation over Australia

Surface mass changes (SMCs) obtained from time-variable gravity observations of the Gravity Recovery and Climate Experiment (GRACE) satellite mission and precipitation data from the Australian Bureau of Metrology and the Tropical Rainfall Measurement Mission are analysed over the Australian continent to determine whether there is a statistically significant correlation between them. The multiple linear regression analysis and the principal-component analysis techniques are applied in order to reveal the spatial and temporal variability of each data set separately as well as their mutual relationships. The study provides results and their statistical significance for the whole of Australia including the Murray Darling Basin in the southeast. The results suggest a significant decrease in water storage in the southeast of Australia and a dominant annual cycle over the majority of the continent for the four year period considered (January 2003 to December 2006), both in the surface mass and rainfall time series. The study revealed a direct relation between the data sets over most parts of Australia as confirmed by visual comparison and correlation analysis. When compared with precipitation data GRACE-derived SMCs exhibit smoother spatial and temporal variations. The latter is better suited to detect long-term trends in the presence of strong annual signals, which can adversely affect long-term trend estimates. Results regarding the magnitude of the annual signal suggest that only about a fourth of the precipitation's water masses remain sufficiently long in an area to be detected as a gravity change. The respective phases of the annual signals show an average time lag of about 40 days between precipitation and SMCs, suggesting that it takes about one to two months until a temporal gravity observation can detect a precipitation event.

Reducing local hydrology from high-precision gravity measurements: a lysimeter-based approach

Temporal gravimeter observations, used in geodesy and geophysics to study the Earth's gravity field variations, are influenced by local water storage changes (WSC). At the Geodetic Observatory Wettzell (Germany), WSC in the snow pack, top soil, unsaturated saprolite and fractured aquifer are all important terms of the local water budget. In this study, lysimeter measurements are used for the first time to estimate the hydrological influence on temporal gravimeter observations. Lysimeter data are used to estimate WSC at the field scale in combination with complementary observations and a hydrological 1-D model. From these estimated WSC, we calculate the hydrological gravity response. The results are compared to other methods used in the past to correct temporal gravity observations for the local hydrological influence. Lysimeter measurements significantly improve the independent estimation of WSC and thus provide a better way of reducing the local hydrological effect from gravimeter measurements. We find that the gravity residuals are caused to a larger extent by local WSC than previously stated. At sites where temporal gravity observations are used to study geophysical processes beyond local hydrology, the installation of a lysimeter is recommended.

Measuring the effect of local water storage changes on in situ gravity observations: Case study of the Geodetic Observatory Wettzell, Germany

Local water storage changes (WSC) are a key component of many hydrological issues, but their quantification is associated with a high level of uncertainty. High precision in situ gravity measurements are influenced by these WSC. This study evaluates the influence of local WSC (estimated using hydrological techniques) on gravity observations at the Geodetic Observatory Wettzell, Germany. WSC are comprehensively measured in all relevant storage components, namely groundwater, saprolite, soil, topsoil, and snow storage, and their gravity response is calculated. Total local WSC are derived, and uncertainties are assessed. With the exception of snow, all storage components have gravity responses of the same order of magnitude and are therefore relevant for gravity observations. The comparison of the total gravity response of local WSC to the gravity residuals obtained from a superconducting gravimeter shows similarities in both short‐term and seasonal dynamics. A large proportion of the gravity residuals can be explained by local WSC. The results demonstrate the limitations of measuring total local WSC using hydrological methods and the potential use of in situ temporal gravity measurements for this purpose. Nevertheless, due to their integrative nature, gravity data must be interpreted with great care in hydrological studies.

Evaluating local hydrological modelling by temporal gravity observations and a gravimetric three-dimensional model

SUMMARY An approach for the evaluation of local hydrological modelling is presented: the deployment of temporal terrestrial gravity measurements and gravimetric 3-D modelling in addition to hydrological point observations. Of particular interest is to what extent such information can be used to improve the understanding of hydrological process dynamics and to evaluate hydrological models. Because temporal gravity data contain integral information about hydrological mass changes they can be considered as a valuable augmentation to traditional hydrological observations. On the other hand, hydrological effects need to be eliminated from high-quality gravity time-series because they interfere with small geodynamic signals. In areas with hilly topography and/or inhomogeneous subsoil, a simple reduction based on hydrological point measurements is usually not sufficient. For such situations, the underlying hydrological processes in the soil and the disaggregated bedrock need to be considered in their spatial and temporal dynamics to allow the development of a more sophisticated reduction. Regarding these issues interdisciplinary research has been carried out in the surroundings of the Geodynamic Observatory Moxa, Germany. At Moxa, hydrologically induced gravity variations of several 10 nm s−2 are observed by the stationarily operating superconducting gravimeter and by spatially distributed and repeated high-precision measurements with transportable relative instruments. In addition, hydrological parameters are monitored which serve as input for a local hydrological catchment model for the area of about 2 km2 around the observatory. From this model, spatial hydrological variations are gained in hourly time steps and included as density changes of the subsoil in a well-constrained gravimetric 3-D model to derive temporal modelled gravity variations. The gravity variations obtained from this combined modelling correspond very well to the observed hydrological gravity changes for both, short period and seasonal signals. From the modelling the amplitude of the impact on gravity of hydrological changes occurring in different distances to the gravimeter location can be inferred. Possible modifications on the local hydrological model are discussed to further improve the quality of the model. Furthermore, a successful reduction of local hydrological effects in the superconducting gravimeter data is developed. After this reduction global seasonal fluctuations are unmasked which are in correspondence to GRACE observations and to global hydrological models.

Space-borne gravimetric satellite constellations and ocean tides: aliasing effects

Ocean tides redistribute mass at high temporal frequencies. Satellite missions that aim to observe medium to low frequency mass variations need to take into account this rapidly varying mass signal. Correcting for the effects of ocean tides by means of imperfect models might hamper the observation of other temporal gravity field signals of interest. This paper explores different methods for mitigating aliasing errors for the specific example of observing mass variations due to land hydrology, including temporal filtering of time-series of gravity solutions, spatial smoothing and the use of satellite constellations. For this purpose, an Earth System Model (ESM) was constructed, which included state-of-the-art time varying components for ocean, atmosphere, solid Earth, hydrology, ice-sheets and ocean tides. Using the ESM, we simulated the retrieval of the hydrologically driven gravity field changes using a number of different satellite constellations. We find that (1) the ocean tide aliasing strongly depends on the satellite constellation, the choice of orbital parameters and the length of the data span; (2) the aliasing effect manifests itself differently for different geographical regions; (3) the aliasing causes a peculiar striping pattern along the ground track of the satellite orbits; (4) optimizing the choice of orbital parameters of a single GRACE-type tandem can be more effective at reducing the aliasing of ocean tide model errors than flying more tandems. Finally, we corroborate the experiences with GRACE data analysis that appropriate post-processing techniques can significantly improve the quality of the retrieved gravity changes.

Satellite gravity gradiometry: Secular gravity field change over polar regions

Abstract The ESA Gravity and steady state Ocean and Circulation Explorer, GOCE, mission will utilise the principle of satellite gravity gradiometry to measure the long to medium wavelengths in the static gravity field. Previous studies have demonstrated the low sensitivity of GOCE to ocean tides and to temporal gravity field variations at the seasonal scale. In this study we investigate the sensitivity of satellite gradiometry missions such as GOCE to secular signals due to ice-mass change observed in Greenland and Antarctica. We show that unaccounted ice-mass change signal is likely to increase GOCE-related noise but that the expected present-day polar ice-mass change is below the GOCE sensitivity for an 18-month mission. Furthermore, 2–3 orders of magnitude improvement in the gradiometry in future gradiometer missions is necessary to detect ice-mass change with sufficient accuracy at the spatial resolution of interest.