Earth's Time-variable Gravity Research Articles

Effect of Earth-Moon’s gravity on TianQin’s range acceleration noise. III. An analytical model

TianQin is a proposed space-based gravitational-wave detector designed to operate in circular high Earth orbits. As a sequel to [Zhang et al. Phys. Rev. D 103, 062001 (2021)], this work provides an analytical model to account for the perturbing effect of the Earth's gravity field on the range acceleration noise between two TianQin satellites. For such an ``orbital noise,'' the Earth's contribution dominates above $5\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}5}\text{ }\text{ }\mathrm{Hz}$ in the frequency spectrum, and the noise calibration and mitigation, if needed, can benefit from in-depth noise modeling. Our model derivation is based on Kaula's theory of satellite gravimetry with Fourier-style decomposition and uses circular reference orbits as an approximation. To validate the model, we compare the analytical and numerical results in two main scenarios. First, in the case of the Earth's static gravity field, both noise spectra are shown to agree well with each other at various orbital inclinations and radii, confirming our previous numerical work while providing more insight. Second, the model is extended to incorporate the Earth's time-variable gravity. Particularly relevant to TianQin, we augment the formulas to capture the disturbance from the Earth's free oscillations triggered by earthquakes, of which the mode frequencies enter TianQin's measurement band above 0.1 mHz. The analytical model may find applications in gravity environment monitoring and noise-reduction pipelines for TianQin.

Gravitational inversion for arbitrary surface mass distribution—application to earth's time-variable gravity with topography

SUMMARY The aim of this paper is gravitational inversion, that is, the determination of the mass density distribution of a central body when given the observed external gravitational field that is produced by the mass itself. This inversion for a 3-D mass distribution is known to be grossly non-unique; whereas that for a 2-D mass distribution on a spherical surface is known to be unique. The latter justifies the surface ‘mascon’, or equivalent-water-thickness, solutions when not considering any interior mass transports for the Earth's time-variable gravity as observed by the GRACE satellite. In this paper, using the gravitational multipole formalism cast in the framework of linear Hilbert space with the notion of inner product, we do two things further: (i) we prove mathematically that the 2-D gravitational inversion on an arbitrary surface is unique; and (ii) we derive the algorithm that leads to the unique exact 2-D mass distribution solution, up to a truncated finite spherical harmonic degree. This pertains directly to reaching refined GRACE mascon solutions that account for the actual Earth surface shape including the ellipsoidal figure and the topography. In the process, we also (re)formulate the exact equations, for spherical or arbitrary shape, unifying the formulae that have appeared in the GRACE-relevant literature.

Deep mass redistribution prior to the 2010 Mw 8.8 Maule (Chile) Earthquake revealed by GRACE satellite gravity

Subduction zones megathrust faults constitute a considerable hazard as they produce most of the world's largest earthquakes. However, the role in megathrust earthquake generation exerted by deeper subduction processes remains poorly understood. Here, we analyze the 2003 – 2014 space-time variations of the Earth's gravity gradients derived from three datasets of GRACE geoid models over a large region surrounding the rupture zone of the Mw 8.8 Maule earthquake. In all these datasets, our analysis reveals a large-amplitude gravity gradient signal, progressively increasing in the three months before the earthquake, North of the epicentral area. We show that such signals are equivalent to a 60km3 water storage decrease over 2 months and cannot be explained by hydrological sources nor artefacts, but rather find origin from mass redistributions within the solid Earth on the continental side of the subduction zone. These gravity gradient variations could be explained by an extensional deformation of the slab around 150-km depth along the Nazca Plate subduction direction, associated with large-scale fluid release. Furthermore, the lateral migration of the gravity signal towards the surface from a low coupling segment around −32.5∘ North to the high coupling one in the South suggests that the Mw 8.8 earthquake may have originated from the propagation up to the trench of this deeper slab deformation. Our results highlight the importance of observations of the Earth's time-varying gravity field from satellites in order to probe slow mass redistributions in-depth major plate boundaries and provide new information on dynamic processes in the subduction system, essential to better understand the seismic cycle as a whole.

Time-variable gravity fields and ocean mass change from 37 months of kinematic Swarm orbits

Abstract. Measuring the spatiotemporal variation of ocean mass allows for partitioning of volumetric sea level change, sampled by radar altimeters, into mass-driven and steric parts. The latter is related to ocean heat change and the current Earth's energy imbalance. Since 2002, the Gravity Recovery and Climate Experiment (GRACE) mission has provided monthly snapshots of the Earth's time-variable gravity field, from which one can derive ocean mass variability. However, GRACE has reached the end of its lifetime with data degradation and several gaps occurred during the last years, and there will be a prolonged gap until the launch of the follow-on mission GRACE-FO. Therefore, efforts focus on generating a long and consistent ocean mass time series by analyzing kinematic orbits from other low-flying satellites, i.e. extending the GRACE time series. Here we utilize data from the European Space Agency's (ESA) Swarm Earth Explorer satellites to derive and investigate ocean mass variations. For this aim, we use the integral equation approach with short arcs (Mayer-Gürr, 2006) to compute more than 500 time-variable gravity fields with different parameterizations from kinematic orbits. We investigate the potential to bridge the gap between the GRACE and the GRACE-FO mission and to substitute missing monthly solutions with Swarm results of significantly lower resolution. Our monthly Swarm solutions have a root mean square error (RMSE) of 4.0 mm with respect to GRACE, whereas directly estimating constant, trend, annual, and semiannual (CTAS) signal terms leads to an RMSE of only 1.7 mm. Concerning monthly gaps, our CTAS Swarm solution appears better than interpolating existing GRACE data in 13.5 % of all cases, when artificially removing one solution. In the case of an 18-month artificial gap, 80.0 % of all CTAS Swarm solutions were found closer to the observed GRACE data compared to interpolated GRACE data. Furthermore, we show that precise modeling of non-gravitational forces acting on the Swarm satellites is the key for reaching these accuracies. Our results have implications for sea level budget studies, but they may also guide further research in gravity field analysis schemes, including satellites not dedicated to gravity field studies.

Orbit-related sea level errors for TOPEX altimetry at seasonal to decadal timescales

Abstract. Interannual to decadal sea level trends are indicators of climate variability and change. A major source of global and regional sea level data is satellite radar altimetry, which relies on precise knowledge of the satellite's orbit. Here, we assess the error budget of the radial orbit component for the TOPEX/Poseidon mission for the period 1993 to 2004 from a set of different orbit solutions. The errors for seasonal, interannual (5-year), and decadal periods are estimated on global and regional scales based on radial orbit differences from three state-of-the-art orbit solutions provided by different research teams: the German Research Centre for Geosciences (GFZ), the Groupe de Recherche de Géodésie Spatiale (GRGS), and the Goddard Space Flight Center (GSFC). The global mean sea level error related to orbit uncertainties is of the order of 1 mm (8 % of the global mean sea level variability) with negligible contributions on the annual and decadal timescales. In contrast, the orbit-related error of the interannual trend is 0.1 mm yr−1 (27 % of the corresponding sea level variability) and might hamper the estimation of an acceleration of the global mean sea level rise. For regional scales, the gridded orbit-related error is up to 11 mm, and for about half the ocean the orbit error accounts for at least 10 % of the observed sea level variability. The seasonal orbit error amounts to 10 % of the observed seasonal sea level signal in the Southern Ocean. At interannual and decadal timescales, the orbit-related trend uncertainties reach regionally more than 1 mm yr−1. The interannual trend errors account for 10 % of the observed sea level signal in the tropical Atlantic and the south-eastern Pacific. For decadal scales, the orbit-related trend errors are prominent in a several regions including the South Atlantic, western North Atlantic, central Pacific, South Australian Basin, and the Mediterranean Sea. Based on a set of test orbits calculated at GFZ, the sources of the observed orbit-related errors are further investigated. The main contributors on all timescales are uncertainties in Earth's time-variable gravity field models and on annual to interannual timescales discrepancies of the tracking station subnetworks, i.e. satellite laser ranging (SLR) and Doppler Orbitography and Radiopositioning Integrated by Satellite (DORIS).

Global and regional seasonal variations of the geoid detected by GRACE

Since 2002, the US-German GRACE (Gravity Recovery and Climate Experiment) mission has been providing a precise survey of the Earth's time-variable gravity field, with unprecedented temporal and spatial sampling. GRACE time-variable gravity fields provide a means of measuring the temporal and spatial variations of mass redistribution within the Earth system. The GRACE mission has started a new era in studying a series of geophysical problems ranging from deep Earth structure to tracking mass redistribution on and near the surface of the Earth. Time variability of the gravity field presented here is based on the transformation of “monthly gravity field models” to the geoid. We show the changes caused by the global water cycle and land hydrology.

Feasibility of estimating groundwater storage changes in western Kansas using Gravity Recovery and Climate Experiment (GRACE) data

Groundwater storage is a spatial and temporal variable that represents an essential part of the global hydrological cycle. Traditionally, many wells (i.e., a large number), spatially distributed across a basin, are measured annually to monitor changes in the groundwater (GW) level. It has been shown that invasive measuring of water levels in agricultural wells during winter months is most representative because the wells are normally not in use and have had sufficient time to rebound from seasonal use. However, traditional invasive measurements are inefficient, labor-intensive, and expensive with significant regional obstacles that can inhibit good spatial representation. Thus, satellite observations of the Earth's time-variable gravity field from the Gravity Recovery and Climate Experiment (GRACE) mission provide a unique opportunity to monitor changes in groundwater storage from space (Rodell and Famiglietti, 2002; Tapley et al., 2004).

Simulation study of a follow-on gravity mission to GRACE

The gravity recovery and climate experiment (GRACE) has been providing monthly estimates of the Earth's time-variable gravity field since its launch in March 2002. The GRACE gravity estimates are used to study temporal mass variations on global and regional scales, which are largely caused by a redistribution of water mass in the Earth system. The accuracy of the GRACE gravity fields are primarily limited by the satellite-to-satellite range-rate measurement noise, accelerometer errors, attitude errors, orbit errors, and temporal aliasing caused by unmodeled high-frequency variations in the gravity signal. Recent work by Ball Aerospace and Technologies Corp., Boulder, CO has resulted in the successful development of an interferometric laser ranging system to specifically address the limitations of the K-band microwave ranging system that provides the satellite-to-satellite measurements for the GRACE mission. Full numerical simulations are performed for several possible configurations of a GRACE Follow-On (GFO) mission to determine if a future satellite gravity recovery mission equipped with a laser ranging system will provide better estimates of time-variable gravity, thus benefiting many areas of Earth systems research. The laser ranging system improves the range-rate measurement precision to approximately 0.6 nm/s as compared to approx. 0.2 micro-seconds for the GRACE K-band microwave ranging instrument. Four different mission scenarios are simulated to investigate the effect of the better instrument at two different altitudes. The first pair of simulated missions is flown at GRACE altitude (approx. 480 km) assuming on-board accelerometers with the same noise characteristics as those currently used for GRACE. The second pair of missions is flown at an altitude of approx. 250 km which requires a drag-free system to prevent satellite re-entry. In addition to allowing a lower satellite altitude, the drag-free system also reduces the errors associated with the accelerometer. All simulated mission scenarios assume a two satellite co-orbiting pair similar to GRACE in a near-polar, near-circular orbit. A method for local time variable gravity recovery through mass concentration blocks (mascons) is used to form simulated gravity estimates for Greenland and the Amazon region for three GFO configurations and GRACE. Simulation results show that the increased precision of the laser does not improve gravity estimation when flown with on-board accelerometers at the same altitude and spacecraft separation as GRACE, even when time-varying background models are not included. This study also shows that only modest improvement is realized for the best-case scenario (laser, low-altitude, drag-free) as compared to GRACE due to temporal aliasing errors. These errors are caused by high-frequency variations in the hydrology signal and imperfections in the atmospheric, oceanographic, and tidal models which are used to remove unwanted signal. This work concludes that applying the updated technologies alone will not immediately advance the accuracy of the gravity estimates. If the scientific objectives of a GFO mission require more accurate gravity estimates, then future work should focus on improvements in the geophysical models, and ways in which the mission design or data processing could reduce the effects of temporal aliasing.

Using Satellite Constellations for ImprovedDetermination of Earth's Time-Variable Gravity

Covers advancements in spacecraft and tactical and strategic missile systems, including subsystem design and application, mission design and analysis, materials and structures, developments in space sciences, space processing and manufacturing, space operations, and applications of space technologies to other fields.

Time-variable gravity from space and present-day mass redistribution in theEarth system

Since 2002, the US–German GRACE (Gravity Recovery and Climate Experiment) mission has been providing a precise survey of Earth's time-variable gravity field, with unprecedented temporal and spatial sampling. GRACE time-variable gravity fields provide a means of measuring temporal and spatial variations of mass redistribution within the Earth system. The GRACE mission has launched a new era in studying a series of geophysical problems ranging from deep Earth structure to tracking mass redistribution on and near the surface of the Earth. GRACE has greatly improved understanding of mass redistribution in various compartments of the climate system (atmosphere, oceans, terrestrial water, and cryosphere). In this review, we use examples to show how GRACE has fundamentally enriched a number of fields, including (but not limited to) the global water cycle and land hydrology, mass balance of polar ice sheets and mountain glaciers, ocean mass and global sea level change, and solid Earth geophysics.