Gravity field recovery using two low satellites in different orbital planes

This study is concerned with gravity field recovery from low-low satellite to satellite range rate data. An improvement over a coplanar mission is predicted in the errors associated with certain parts of the geopotential by the separation of the orbital planes of the two satellites. Using Hill's equations an analytical scheme to model the range rate residuals is developed. It is flexible enough to model equally well the residuals between pairs of satellites in the same orbital plane or whose planes are separated in right ascension. The possible benefits of such an orientation to gravity field recovery from range rate data can therefore be analysed, and this is done by means of an extensive error analysis. The results of this analysis show that for an optimal planar mission improvements can be made by separating the satellites in right ascension. Gravity field recoveries are performed in order to verify and gauge the limitations of the analytical model, and to support the results of the error analysis. Finally the possible problem of the differential decay rates of two satellites due to the diurnal bulge are evaluated.

Modeling the impact of large-scale solid mass transfers on the gravity field

The focus of this thesis is to explore and quantify the response of large-scale solid mass transfer events on satellite-based gravity observations. The gravity signature of large-scale solid mass transfers has not been deeply explored yet; mainly due to the lack of significant events during dedicated satellite gravity missions‘ lifespans. In light of the next generation of gravity missions, the feasibility of employing satellite gravity observations to detect submarine and surface mass transfers is of importance for geoscience (improves the understanding of geodynamic processes) and for geodesy (improves the understanding of the dynamic gravity field). The aim of this thesis is twofold and focuses on assessing the feasibility of using satellite gravity observations for detecting large-scale solid mass transfers and on modeling the impact on the gravity field caused by these events. A methodology that employs 3D forward modeling simulations and 2D wavelet multiresolution analysis is suggested to estimate the impact of solid mass transfers on satellite gravity observations. The gravity signature of various submarine and subaerial events that occurred in the past was estimated. Case studies were conducted to assess the sensitivity and resolvability required in order to observe gravity differences caused by solid mass transfers. Simulation studies were also employed in order to assess the expected contribution of the Next Generation of Gravity Missions for this application.

Strong gravity and the Yukawa field

A study of strong gravity field coupled to the Yukawa field is carried out for a conformally flat space-time. A quantitative relation between the strong interaction coupling constantg 2/hstrokc and the strong gravity constants (Lambda f~1028 cm–2,G f ~6.6×1030 C.G.S. units) is obtained givingg 2/hstroksim17, which is of the right order of magnitude. This justifies the contention that strong gravity is relevant for elementary particles (e.g., hadrons).

Unsteady Free-Convection Flow on a Rotating flat-Plate Under Nonuniform Gravity

The free convection problem with nonuniform gravity finds applications in several fields. For example, centrifugal gravity fieldsarisein many rotating machinery applications. A gravity field is also created artificially in an orbital space station by rotation. The effect of nonuniform gravity due to the rotation of isothermal or nonisothermal plates has been studied by several authors [l-5] using various mathematical techniques.

Time-variable gravity signal in Greenland revealed by high-low satellite-to-satellite tracking

[1] In the event of a termination of the Gravity Recovery and Climate Experiment (GRACE) mission before the launch of GRACE Follow-On (due for launch in 2017), high-low satellite-to-satellite tracking (hl-SST) will be the only dedicated observing system with global coverage available to measure the time-variable gravity field (TVG) on a monthly or even shorter time scale. Until recently, hl-SST TVG observations were of poor quality and hardly improved the performance of Satellite Laser Ranging observations. To date, they have been of only very limited usefulness to geophysical or environmental investigations. In this paper, we apply a thorough reprocessing strategy and a dedicated Kalman filter to Challenging Minisatellite Payload (CHAMP) data to demonstrate that it is possible to derive the very long-wavelength TVG features down to spatial scales of approximately 2000 km at the annual frequency and for multi-year trends. The results are validated against GRACE data and surface height changes from long-term GPS ground stations in Greenland. We find that the quality of the CHAMP solutions is sufficient to derive long-term trends and annual amplitudes of mass change over Greenland. We conclude that hl-SST is a viable source of information for TVG and can serve to some extent to bridge a possible gap between the end-of-life of GRACE and the availability of GRACE Follow-On.

Comparison of GOCE-GPS gravity fields derived by different approaches

Several techniques have been proposed to exploit GNSS-derived kinematic orbit information for the determination of long-wavelength gravity field features. These methods include the (i) celestial mechanics approach, (ii) short-arc approach, (iii) point-wise acceleration approach, (iv) averaged acceleration approach, and (v) energy balance approach. Although there is a general consensus that—except for energy balance—these methods theoretically provide equivalent results, real data gravity field solutions from kinematic orbit analysis have never been evaluated against each other within a consistent data processing environment. This contribution strives to close this gap. Target consistency criteria for our study are the input data sets, period of investigation, spherical harmonic resolution, a priori gravity field information, etc. We compare GOCE gravity field estimates based on the aforementioned approaches as computed at the Graz University of Technology, the University of Bern, the University of Stuttgart/Austrian Academy of Sciences, and by RHEA Systems for the European Space Agency. The involved research groups complied with most of the consistency criterions. Deviations only occur where technical unfeasibility exists. Performance measures include formal errors, differences with respect to a state-of-the-art GRACE gravity field, (cumulative) geoid height differences, and SLR residuals from precise orbit determination of geodetic satellites. We found that for the approaches (i) to (iv), the cumulative geoid height differences at spherical harmonic degree 100 differ by only ≈10 % ; in the absence of the polar data gap, SLR residuals agree by ≈96 % . From our investigations, we conclude that real data analysis results are in agreement with the theoretical considerations concerning the (relative) performance of the different approaches.

Time Variable Gravity: Contributions of GOCE Satellite Data to Monthly and Bi-monthly GRACE Gravity Estimates

A feasibility study by Pail et al. (Can GOCE help to improve temporal gravity field estimates? In: Ouwehand L (ed) Proceedings of the 4th International GOCE User Workshop, ESA Publication SP-696, 2011b) shows that GOCE (‘Gravity field and steady-state Ocean Circulation Explorer’) satellite gravity gradiometer (SGG) data in combination with GPS derived orbit data (satellite-to-satellite tracking: SST-hl) can be used to stabilize and reduce the striping pattern of a bi-monthly GRACE (‘Gravity Recovery and Climate Experiment’) gravity field estimate. In this study several monthly (and bi-monthly) combinations of GRACE with GOCE SGG and GOCE SST-hl data on the basis of normal equations are investigated. Our aim is to assess the role of the gradients (solely) in the combination and whether already one month of GOCE observations provides sufficient data for having an impact in the combination. The estimation of clean and stable monthly GOCE SGG normal equations at high resolution ( >  d/o 150) is found to be difficult, and the SGG component, solely, does not show significant added value to monthly and bi-monthly GRACE gravity fields. Comparisons of GRACE-only and combined monthly and bi-monthly solutions show that the striping pattern can only be reduced when using both GOCE observation types (SGG, SST-hl), and mainly between d/o 45 and 60.

Gravity potential spherical harmonic series

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.

Gravity mapping in the southern Weddell Sea region, Antarctica (Scale 1:2 000 000)

New maps of free-air and the Bouguer gravity anomalies on the Weddell Sea sector (70-81° S, 6-75° W) of Antarctica are presented. These maps are based on the first computer compilation of available gravity data collected by ''Sevmorgeologia'' in 1976-89 in the southern Weddell Sea and adjacent coasts of western Dronning Maud Land (WDML) and Coats Land. The accomplished gravity studies comprise airborne observations with a line spacing of about 20 km and conventional measurements at over-the-ice points, which were spaced at 10-30 km and supplemented by seismic soundings. Hence, anomalies on the maps represent mainly large-scale and deep crustal features. The dominant feature in free-air gravity map is a large dipolar gravity anomaly stretching along the continental margin. Following the major grain of seabed morphology this shelf-edge/slope anomaly (SESA) is clearly divided into three segments characterized by diverse anomaly amplitudes, wavelengths and trends. They are associated with continental margins of different geotectonic provinces of Antarctica surrounding the Weddell Sea. Apparent distinctions in the SESA signatures are interpreted as the gravity expression of tectonic, deep crustal structure segmentation of the continental margin. The prominent gravity highs (100-140 mGal) of the shelf edge anomaly mapped along WDML are assumed to represent high-density mantle injections intruded into the middle/lower crust during initial rifting of continental breakup. Enlarged wavelengths and diminished amplitudes of the gravity anomaly westwards, along the Weddell Sea embayment (WSE) margin, reflect a widening of the continental slope and a significant increase in thickness of underlying sediment strata. Low amplitude, negative free-air anomalies in the Filchner-Ronne Ice Shelves (FRIS) contrast sharply with the dominating positive anomalies offshore. This indicates a greater sedimentary thickness of the basin in this area. Crustal response to the enlarged sediment load is impressed in mostly positive features of the Bouguer gravity field observed here. Two pronounced positive Bouguer anomalies of 50-70 mGal and an average widths of 200 km dominate the Weddell Sea embayment margins towards the Antarctic Peninsula and the East Antarctic craton. They correlate well with very deep seabed troughs (> 1000 m below sea level). The gravity highs are most likely caused by a shallow upper mantle underneath graben-rift structures evolved at the margins of the WSE basin. A regional zone (> 100 km in width) of the prominent Bouguer and free-air negative anomalies (-40 to -60 mGal) adjacent Coats Land to the north of the ice shelf edge may indicate the presence of the thick old cratonic crust far offshore beneath the Weddell Sea Embayment.

Grönlannin mannerjäätikön tulevaisuus: merenpinnan nousu maailmanlaajuisesti ja Itämerellä

Sea level rise is among the most worrying consequences of climate change, and the biggest uncertainty of sea level predictions lies in the future behaviour of the ice sheets of Greenland and Antarctica. In this work, a literature review is made concerning the future of the Greenland ice sheet and the effect of its melting on Baltic Sea level. The relation between sea level and ice sheets is also considered more generally from a theoretical and historical point of view. Lately, surprisingly rapid changes in the amount of ice discharging into the sea have been observed along the coastal areas of the ice sheets, and the mass deficit of Greenland and West Antarctic ice sheets which are considered vulnerable to warming has been increasing from the 1990s. The changes are probably related to atmospheric or oceanic temperature variations which affect the flow speed of ice either via meltwater penetrating to the bottom of the ice sheet or via changes in the flow resistance generated by the floating parts of an ice stream. These phenomena are assumed to increase the mass deficit of the ice sheets in the warming climate; however, there is no comprehensive theory to explain and model them. Thus, it is not yet possible to make reliable predictions of the ice sheet contribution to sea level rise. On the grounds of the historical evidence it appears that sea level can rise rather rapidly, 1 2 metres per century, even during warm climate periods. Sea level rise projections of similar magnitude have been made with so-called semiempirical methods that are based on modelling the link between sea level and global mean temperature. Such a rapid rise would require considerable acceleration of the ice sheet flow. Stronger rise appears rather unlikely, among other things because the mountainous coastline restricts ice discharge from Greenland. The upper limit of sea level rise from Greenland alone has been estimated at half a metre by the end of this century. Due to changes in the Earth s gravity field, the sea level rise caused by melting ice is not spatially uniform. Near the melting ice sheet the sea level rise is considerably smaller than the global average, whereas farther away it is slightly greater than the average. Because of this phenomenon, the effect of the Greenland ice sheet on Baltic Sea level will probably be rather small during this century, 15 cm at most. Melting of the Antarctic ice sheet is clearly more dangerous for the Baltic Sea, but also very uncertain. It is likely that the sea level predictions will become more accurate in the near future as the ice sheet models develop.

Numerical simulation of g-jitter effects on half floating zone convection under microgravity environment

The g-jitter effects on the thermocapillary convection in liquid bridge of floating half zone were studied by numerical simulation for unsteady and axi-symmetric model in the cylindrical coordinate system. The g-jitter field was given by a steady microgravity field in addition to an oscillatory low-gravity field, and the effects on the flow field, temperature distribution and free surface deformation were analyzed numerically.

A study on stratification of concentration in crystal-growth of alpha-liio3 by holographic-interferometry

A new thermoplastic-photoconductor laser holographic recording system has been used for real-time and in situ observation of alpha-LiIO3 crystal growth. The influence of crystallization-driven convection on the concentration stratification in solution has been studied under gravity field. It is found that the stratification is closely related to the seed orientation of alpha-LiIO3 crystal. When the optical axis of crystal seed C is parallel to the gravity vector g, the velocity of the concentration stratification is two times larger than that in the case of C perpendicular-to g. It needs 40 h for the crystalline system of alpha-LiIO3 to reach stable concentration distribution (expressed as tau) at 47.6-degrees-C. The time tau is not sensitive to the seed orientation. Our results provide valuable data for designing the crystal growth experiments ia space.

活动构造区区域地壳稳定性研究——以金沙江水电梯级工程规划区为例

The study of regional crustal stability of active tectonic region basically includes analysis of recent activity of Earth's crust, single factor assessment, study of complexity, and comprehensive assessment of crust stability. In this thesis, some work are made as follows: · Based on abundant data from gravity field, aeromagnetic survey, magnetism, magnetotelluric deep sounding, remote sensing and geotectonic as well as earthquakes observed in recent years around this region and adjacent zones, we can get a through understanding about the structural features and activity of the earth's crust in Chuan-Dian region. The results from explosion earthquake and telluric electromagnetic sounding are consistent with the structural features of the crust manifested by the geophysical field. The data of deep geologic structures are important for us to work out a vivid three-dimensional model of the earth's crustal structure of the Jinsha River region. According to a synthesis, the author of this thesis proposes some indicators for dividing the faulted blocks. It can also be inferred that the movement of the Chuan-Dian faulted block, which is the relatively active part of southwestern China, is controlled by the boundary faults, and the intensive activity and deformation are concentrated along the boundaries of the block. · Mainly discussing respectively the mechanism and laws of active faults, earthquakes, and geological hazards activity, and their influences on the stability and security of engineering, also trying to probe into the way to assess the risk of single factor in this section. Especially with the method of fractal geometry, the thesis has discussed how to study the complexity of each factor. These geologic hazards which are distributed at the uppermost part of the crust in this region form a typical mountainous set of the active tectonic areas. The results of survey show that some slopes are liable- to -sliding with a weak layer of low shear strength. Occurrences of landslides are to a great extent related to local geological structures, in particular active faults. This is why numerous landslides have occurred simultaneously around the epicenter of a strong earthquake or the center of a strong rainfall, which are related to active faults. · The analysis of the crustal stability is based on a regional grid division, and a fuzzy comprehensive analysis method is used to determine the grade of the quality in each grid. The evaluation factors and their weights are taken from the results of the hierarchical analysis. The evaluation indexes consist of qualitative and quantitative ones. The qualitative ones can be quantified through the experts weighing system, while the quantitative ones can be obtained from statistical analysis. For quality grades, four levels are used: stable, essentially stable, sub-stable, and unstable. The results of the evaluation on Jinshajiang region demonstrate that the crustal stability become distinctly worse in the areas controlled by active deep faults. Therefore, detailed investigations on the active faulting and geologic hazards, include earthquake activity are especially necessary for those areas adjacent to the deep fault belts. On the bases of the data available and the survey results, we have made a preliminary assessment for the construction conditions and adaptability of every planned site in the middle or lower reaches of Jinsha River. Finally, the thesis prospected the vista of the study of crustal stability.

Análise de terrenos na porção setentrional da Província Borborema, NE do Brasil: integração de dados geológicos e gravimétricos

It is presently assumed that the Borborema Province resulted from a complex collisional process associated with the convergent movement of plates, possibly involving amalgamation and accretion of microplates. This process was consolidated at the end of the Brasiliano event. It is investigated the possible limits for the tectonostratigraphic terranes in the northern portion of the province based on an integrated study of geological and gravity data. The study area comprises the portion of the Borborema Province located north of the Patos Lineament, limited by longitudes 33º00 W and 43º29 44"W and latitudes 1º36 S and 8º00 S. A revision of the regional geology allowed to identify areas presenting contrasting geological attributes, possibly representing different terranes whose limits are always shear zones of Brasiliano-age. The Sobral-Pedro II shear zone is the only one undoubtedly presenting geological attributes of sutures zones. The other shear zones are very likely associated with a geodinymic context of accretion, involving oblique collisions (docking), transcurrent and/or transforming sutures, and deep intracrustal shear zones. The gravity data contributed as a tool to identify strong lateral contrasts of density inside the upper crust possibly associated with crustal blocks tectonically juxtaposed. The dominant long wavelength anomaly in the Bouguer anomaly map is an expressive gradient, grossly parallel to the continental margin, caused by density variation across the crust-mantle interface in the transition from the continental crust to the oceanic crust originated by the separation between South America and Africa. Medium to small wavelength anomalies are due to intracrustal heterogeneities such as different Precambrian crustal blocks, Brasiliano-age granites and Mesozoic sedimentary basins. A regional-residual separation of the Bouguer anomaly map was performed in order to enhance in the residual map the effect due to intracrustal heterogeneities. The methodology used for this separation was a robust polinomial fitting. The inversion of residual gravity field resulted in a density contrast map (Δρ), in an equivalent layer that provided more accurated anomalies contours and consolidated the model which the sources of residual anomalies are located in the upper part of the present crust. Based on the coincidence of gravity lineaments in the residual map and Brasiliano shear zones, and using additional geological information, the following shear zones are proposed as limits between terranes: Patos shear zone, Sobral-Pedro II shear zone, Picuí-João Câmara shear zone, Remígio-Pocinhos shear zone, Senador Pompeu shear zone, Tauá shear zone, and Portalegre shear zone. Based on the geological/geophysical information it is attributed a higher level of confidence to the first three proposed limits(Patos, Sobral Pedro II, and Picuí-João Câmara shear zones). From west to east, these shear zones individualize the following terranes: Northwest of Ceará terrane, Central Ceará terrane, Tauá terrane, Orós-Jaguaribe terrane, Seridó terrane, and São José de Campestre terrane. In our study, the Rio Piranhas and Patos terranes are questioned because their previously proposed limits do not present good geological and gravimetric evidences. On the other hand, the previously proposed Cearense terrane is now subdivided into Central Ceará and Tauá terranes. Two residual gravity profiles located in the Seridó belt were interpreted using 2 ½ D direct gravity modeling. The main result of the modeling process is that all anomalies, with the exception of one, can be explained by outcroppring bodies, therefore restricted to the upper part of the present crust

Simple orbit determination using GPS based on a least-squares algorithm employing sequential givens rotations

A low-cost computer procedure to determine the orbit of an artificial satellite by using short arc data from an onboard GPS receiver is proposed. Pseudoranges are used as measurements to estimate the orbit via recursive least squares method. The algorithm applies orthogonal Givens rotations for solving recursive and sequential orbit determination problems. To assess the procedure, it was applied to the TOPEX/POSEIDON satellite for data batches of one orbital period (approximately two hours), and force modelling, due to the full JGM-2 gravity field model, was considered. When compared with the reference Precision Orbit Ephemeris (POE) of JPL/NASA, the results have indicated that precision better than 9 m is easily obtained, even when short batches of data are used. Copyright (c) 2007.