Download or read book Accurate Multiresolution Modeling of the Earth s Gravitational Field written by and published by . This book was released on 2001 with total page 25 pages. Available in PDF, EPUB and Kindle. Book excerpt: The thrust of this project has been two-fold, namely, (1) to improve the performance of existing models of Earth's gravitational field, mainly with respect to speed of evaluation; and (2) to develop new multi resolution estimation techniques to produce new gravitational models. We have constructed two local models of the gravitational field, both of which map the surface of a sphere to the surface of a cube. These models differ in the choice of basis functions. The first uses multi-wavelets to represent the gravitational field at a fixed distance from Earth, and the second model uses B-splines. Both models use polynomial interpolation to compute the variation in height of the gravity field. Significant progress has been made towards implementing a procedure for estimating gravity models directly from physical measurements. We have developed a new estimation algorithm, a multi-resolution rank-revealing QR decomposition. This algorithm produces the 'minimum detail' solution instead of the usual minimum norm solution of the ill-conditioned least squares problem. A basis for bandlimited functions has been constructed using a new method for computing the generalized Gaussian quadratures for exponentials. These bases are closely related to the prolate spheroidal wave functions, and we plan to create the next generation of models for evaluation and estimation of the gravity field using such bases. These bases are nearly optimal in terms of the number of coefficients necessary to represent a bandlimited function.

Download or read book Methods and Technologies for Measuring the Earth s Gravity Field Parameters written by V. G. Peshekhonov and published by Springer Nature. This book was released on 2022-11-30 with total page 396 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book offers extensive information on the operation of gravimeters, including airborne, marine and terrestrial ones, and on the associated data processing methods such as optimal and adaptive filtering, smoothing, structural and parametric identification. Further, it describes specific features relating to the study of the gravitational field in remote areas of the Earth, with the necessary modifications of equipment and software for all-latitude applications. Findings from gravity studies in such remote areas are also presented. Advanced methods for studying the gravitational field, including those for simultaneous determination of gravity anomalies and deflection of the vertical are described and analyzed in detail. Gravity gradiometers and cold atom gravimeters are also covered. Last but not least, the book deals with the development of Earth’s gravity field models and their various applications, including map-aided navigation, with a special attention to model accuracy estimation. Gathering research findings and best practice recommendations relating to Earth’s gravity field measurements, collected by a team of researchers and professionals, the book offers a unique guide for engineers, scientists and graduate students dealing with terrestrial, marine and airborne gravimetry. It will also help other specialists involved in developing and using navigation systems in practice, including designers of gravimetric equipment and navigators.

Download or read book Gravity Field and Dynamics of the Earth written by Milan Bursa and published by Springer Science & Business Media. This book was released on 2013-12-01 with total page 339 pages. Available in PDF, EPUB and Kindle. Book excerpt: Since the Czech edition was published four years ago, the authors have revised the original text tobring it up to date. During these four years, thanks to satellite altimetry the accuracy of the global descrip tion of the gravity field (model GEM-T2), of the fundamental astro geodetic constants, of the principal moments of inertia of the Earth and, in particular, of their differences, of the precession constant, and of a number of other dynamical parameters of the Earth have been improved. The authors have included most of these improvements in the revised English edition. They have, of course, also made factual, formal and other corrections and have modified some of the figures. Additions to the index and references have also been made. Praha, Czech Republic M. BuRSA and K. PF:c August 1993 Contents Preface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . V Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Fundamentals of Determining the Parameters 1 Defining the Earth's Gravitational Field by Satellite Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 1. 1 Satellite Equations of Motion . . . . . . . . . . . . . . . . . 6 1. 2 Perturbing Function and Perturbing Potential . . . . 23 1. 3 General Definitions . . . . . . . . . . . . . . . . . . . . . . . . . 23 1. 3. 1 Perturbing Gravitational Potential of the Earth in 1. 3. 2 Outer Space . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24 Perturbations due to the Moon and the Sun . . . . . . 27 1. 3. 3 Solution of the Perturbed Motion . . . . . . . . . . . . . . 28 1. 4 1. 5 Transformation of the Perturbing Gravitational Potential into the Function of the Satellite's Orbital Elements . . . . . . . . . . . . . . . . . . . . . . . . . . . 32 1. 5. 1 Transformation of Potential Rs$ . . . . . . . . . . . . . . . 32 1. 5. 2 Transformation of Potentials L1 Vs»' L1 Vso . . . . . . . .

Download or read book An Ensemble Solution for the Earth s Time varying Gravitational Field from the NASA DLR GRACE Mission written by Carly Frances Sakumura and published by . This book was released on 2013 with total page 234 pages. Available in PDF, EPUB and Kindle. Book excerpt: Several groups produce estimates of the Earth's time-varying gravitational field with data provided by the NASA/DLR Gravity Recovery and Climate Experiment (GRACE) mission. These unprecedented highly accurate global data sets track the time-variable transport of mass across and underneath the surface of the Earth and give insight into secular, seasonal, and sub seasonal variations in the global water supply. Knowledge gained from these products can inform and be incorporated into ocean and hydrological models and advise environmental policy planning. Therefore, a complete understanding of the accuracy and variations between these different fields is necessary, and the most accurate possible solutions desired. While the various gravity fields are similar, differences in processing strategies and tuning parameters result in solutions with regionally specific variations and error patterns. This study analyzed the spatial, temporal, and spectral variations between four different gravity field products. The knowledge gained in this analysis was used to develop an ensemble solution that harnesses the best characteristics of each individual field to create an optimal model. Multiple methods were used to combine and analyze the individual and ensemble solutions. First a simple mean model was created; then the different solutions were weighted based on the formal error estimates as well as the monthly deviation from the arithmetic mean ensemble. These ensemble models as well as the four individual data center solutions were analyzed for bias, long term trend, and regional variations between the solutions, evaluated statistically to assess the noise and scatter within the solutions, and compared to independent hydrological models. Therefore, the form and cause of the deviations between the models, as well as the impact of these variations, is characterized. The three ensemble solutions constructed in this analysis were all effective at reducing noise in the models and better correlate to hydrological processes than any individual solution. However, the scale of these improvements is constrained by the relative variation between the individual solutions as the deviation of these individual data products from the hydrological model output is much larger than the variations between the individual and ensemble solutions.

Download or read book Satellite Gravity and the Geosphere written by National Research Council and published by National Academies Press. This book was released on 1997-09-02 with total page 126 pages. Available in PDF, EPUB and Kindle. Book excerpt: For the past three decades, it has been possible to measure the earth's static gravity from satellites. Such measurements have been used to address many important scientific problems, including the earth's internal structure, and geologically slow processes like mantle convection. In principle, it is possible to resolve the time-varying component of the gravity field by improving the accuracy of satellite gravity measurements. These temporal variations are caused by dynamic processes that change the mass distribution in the earth, oceans, and atmosphere. Acquisition of improved time-varying gravity data would open a new class of important scientific problems to analysis, including crustal motions associated with earthquakes and changes in groundwater levels, ice dynamics, sea-level changes, and atmospheric and oceanic circulation patterns. This book evaluates the potential for using satellite technologies to measure the time-varying component of the gravity field and assess the utility of these data for addressing problems of interest to the earth sciences, natural hazards, and resource communities.

Download or read book Development of finite element models for the earth s gravity field written by John L. Junkins and published by . This book was released on 1977 with total page 214 pages. Available in PDF, EPUB and Kindle. Book excerpt: As alternatives to lengthy globally valid series representations of the geopotential, piecewise modeling for the gravity field is investigated. A degree 23 spherical harmonic representation is replaced by 1500 local gravity functions within the spherical shell from 1 to 1.2 earth radii. Worst case acceleration errors enter in the 7th significant digit, computational speed is improved by an order of magnitude. (Author).

Download or read book An Improved Model of the Earth s Gravitational Field written by J. G. Marsh and published by . This book was released on 1987 with total page 372 pages. Available in PDF, EPUB and Kindle. Book excerpt: GEM-T1 (Goddard Earth Model) a model which has been developed from an analysis of direct satellite tracking observations, is the first in this series of models produced. GEM-T1 is complete to degree and order 36.

Download or read book System Earth via Geodetic Geophysical Space Techniques written by Frank M. Flechtner and published by Springer Science & Business Media. This book was released on 2010-07-10 with total page 587 pages. Available in PDF, EPUB and Kindle. Book excerpt: Our planet is currently experiencing substantial changes due to natural phen- ena and direct or indirect human interactions. Observations from space are the only means to monitor and quantify these changes on a global and long-term p- spective. Continuous time series of a large set of Earth system parameters are needed in order to better understand the processes causing these changes, as well as their interactions. This knowledge is needed to build comprehensive Earth s- tem models used for analysis and prediction of the changing Earth. Geodesy and geophysics contribute to the understanding of system Earth through the observation of global parameter sets in space and time, such as tectonic motion, Earth surface deformation, sea level changes and gravity, magnetic and atmospheric elds. In the framework of the German geoscience research and development p- gramme GEOTECHNOLOGIEN, research projects related to the theme “Observing the Earth System from Space” have been funded within two consecutive phases since 2002, both covering 3 years. The projects address data analysis and model development using the satellite missions CHAMP, GRACE, GOCE and comp- mentary ground or airborne observations. The results of the rst phase projects have been published in the Springer book, titled “Observation of the Earth System from Space”, edited by Flury, Rummel, Reigber, Rothacher, Boedecker and Schreiber in 2006. The present book, titled “System Earth via Geodetic-Geophysical Space Techniques” summarizes in 40 scienti c papers the results of eight coordinated research projects funded in the second phase of this programme (2005–2008).

Download or read book Gravity Field Estimation for Next Generation Satellite Missions written by Christopher Michael McCullough and published by . This book was released on 2017 with total page 504 pages. Available in PDF, EPUB and Kindle. Book excerpt: For the past, nearly 15 years, the Gravity Recovery and Climate Experiment (GRACE) has provided an invaluable view of mass variability in the Earth system. During its time on orbit it has enabled unprecedented contributions to hydrology, oceanography, and the cryosphere; however, GRACE is currently approaching the end of its lifetime. As this approaches and future dedicated satellite gravity missions are poised to continue its legacy, it's important to highlight limitations in our current knowledge and explore areas of improvement for future analysis. This work returns to the first principles of gravity field estimation and explores some of the basic assumptions and idiosyncrasies inherent in the estimation of Earth's gravitational field. Current gravity field estimation from GRACE attempts to optimally combine GPS observables, which provide absolute positioning, with high accuracy, relative inter-satellite measurements (KBR). While an optimal data fusion procedure is utilized, empirical analysis has indicated that artificial down-weighting of the GPS observable provides significant improvements to estimates of the gravitational field. The necessity of this ad-hoc treatment signals a misunderstanding in the contribution of each observable to gravity field estimates and deficiencies in the modeling of each observable. The analysis of this misunderstanding begins with an examination of the GPS observable's ability to independently recover estimates of the spherical harmonic coefficients. This not only provides insight into the effect of GPS on the gravitational field, but examines the efficacy of using a single satellite to fill a possible gap between GRACE and its follow-on mission. While these single satellite derived gravitational fields have limited accuracy, their combination with satellite laser ranging (SLR) allows for the determination of large spatial scale, long term trends from low degree harmonics (7x7). Additionally, thorough examination of the combined gravity field solutions indicates that the GPS observable is vital to stabilization of estimated parameters which perturb at low frequencies, a significant weakness for the relative inter-satellite ranging observable. These low frequency parameters -- which include the satellite initial conditions, accelerometer dynamicals, low degree harmonics, sectorial harmonics, and harmonics of resonant order -- are also the most susceptible to contamination by dynamical modeling error. Therefore, it is necessary to stochastically model the observation error with high fidelity, most notably the frequency dependence caused by errors in the background dynamical models. Accurate stochastic modeling of the observables is achieved by reexamining the GRACE estimation problem from the Bayesian perspective. This viewpoint highlights typical assumptions made in nominal GRACE processing, most importantly that observation errors are independently Gaussian distributed. Analysis of this assumption indicates its inaccuracy, necessitating the utilization of algorithms which enable modeling of the frequency dependence of the observable errors, through the observation covariance. The most important of these error sources is the manifestation of dynamical modeling error, which perturbs predominantly at low frequency and the orbital period, similarly to the main contributions of the GPS observable. Accounting for the frequency dependence of the observation errors shows the ability to improve optimal data fusion, reduce error in estimates of the gravitational field by mitigating stripes and, most importantly, drastically improves the formal characterization of error in the estimated gravitational fields; facilitating scientific interpretation and prognostication of Earth's climate variability, optimal combination with independent datasets and a priori constraints, and optimal assimilation of GRACE data products with Earth system models.

Download or read book Observation of the Earth System from Space written by Jakob Flury and published by Springer Science & Business Media. This book was released on 2006-02-28 with total page 484 pages. Available in PDF, EPUB and Kindle. Book excerpt: In the recent years, space-based observation methods have led to a subst- tially improved understanding of Earth system. Geodesy and geophysics are contributing to this development by measuring the temporal and spatial va- ations of the Earth’s shape, gravity ?eld, and magnetic ?eld, as well as at- sphere density. In the frame of the GermanR&D programmeGEOTECHNO- LOGIEN,researchprojectshavebeen launchedin2002relatedto the satellite missions CHAMP, GRACE and ESA’s planned mission GOCE, to comp- mentary terrestrial and airborne sensor systems and to consistent and stable high-precision global reference systems for satellite and other techniques. In the initial 3-year phase of the research programme (2002-2004), new gravity ?eld models have been computed from CHAMP and GRACE data which outperform previous models in accuracy by up to two orders of m- nitude for the long and medium wavelengths. A special highlight is the - termination of seasonal gravity variations caused by changes in continental water masses. For GOCE, to be launched in 2006, new gravity ?eld analysis methods are under development and integrated into the ESA processing s- tem. 200,000 GPS radio occultation pro?les, observed by CHAMP, have been processed on an operational basis. They represent new and excellent inf- mation on atmospheric refractivity, temperature and water vapor. These new developments require geodetic space techniques (such as VLBI, SLR, LLR, GPS) to be combined and synchronized as if being one global instrument.

Download or read book From Mars to Greenland Charting Gravity With Space and Airborne Instruments written by Oscar L. Colombo and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 353 pages. Available in PDF, EPUB and Kindle. Book excerpt: Precise and continuous tracking with multi-satellite systems of aircraft andlow flying satellites, accurate airborne measurement of gravity and gravity gradients, and satellite gradiometry have fundamentally changed our view on the de- termination of the Earth's gravity field. The papers in this volume describe these techniques in detail. The ideas are presentedas complementary, and are used to develop new theoretical concepts of gravity field analysis. Computatio- nal models using these techniques are also discussed and are tested in simulations. The papers presented in this volume are the result of an IAG symposium held during the XX General Assembly of the Inter- national Union of Geodesy and Geophysics in Vienna, Austria, August 11-24, 1991.

Download or read book An Improved Model of the Earth s Gravitational Field written by NASA. and published by . This book was released on 1987 with total page 354 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Proceedings of Symposium on the Earth s Gravitational Field and Secular Variations in Position written by Ronald S. Mather and published by School of Surveying University of New South Wales. This book was released on 1974 with total page 770 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Handbook of Geomathematics written by Willi Freeden and published by Springer Science & Business Media. This book was released on 2010-08-13 with total page 1371 pages. Available in PDF, EPUB and Kindle. Book excerpt: During the last three decades geosciences and geo-engineering were influenced by two essential scenarios: First, the technological progress has changed completely the observational and measurement techniques. Modern high speed computers and satellite based techniques are entering more and more all geodisciplines. Second, there is a growing public concern about the future of our planet, its climate, its environment, and about an expected shortage of natural resources. Obviously, both aspects, viz. efficient strategies of protection against threats of a changing Earth and the exceptional situation of getting terrestrial, airborne as well as spaceborne data of better and better quality explain the strong need of new mathematical structures, tools, and methods. Mathematics concerned with geoscientific problems, i.e., Geomathematics, is becoming increasingly important. The ‘Handbook Geomathematics’ as a central reference work in this area comprises the following scientific fields: (I) observational and measurement key technologies (II) modelling of the system Earth (geosphere, cryosphere, hydrosphere, atmosphere, biosphere) (III) analytic, algebraic, and operator-theoretic methods (IV) statistical and stochastic methods (V) computational and numerical analysis methods (VI) historical background and future perspectives.

Download or read book On Concepts for Modeling the Earth s Gravity Field written by Dieter Lelgemann and published by . This book was released on 2001 with total page 51 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book The Gravity Field of the Earth written by D. G. King Hele and published by . This book was released on 1978 with total page 27 pages. Available in PDF, EPUB and Kindle. Book excerpt: In recent years the Earth's gravitational field has been determined with continually improving accuracy, using hundreds of thousands of observations of Earth satellites, chiefly optical, laser and Doppler, together with surface gravimetry and, most recently, altimeter measurements from the Geos 3 satellite. The geopotential is usually expressed as a double series of tesseral harmonics, and several hundred of the harmonic coefficients are evaluated. Progress in this work during the 1970s is briefly outlined, and some attempt is made to assess the accuracy of current geoid maps and sets of harmonic coefficients, as exemplified in the latest models derived at the Goddard Space Flight Center. The harmonic coefficients of order 14, 15 and 30 in the Goddard Earth Model 10B are compared with values obtained independently by analysis of resonant orbits: the results suggest that the values in GEM 10B are realistic for these orders, and presumably others. It appears that the accuracy of the geoid maps is now approaching 1 m.

Download or read book Gravitational Fields of Earth Models and the Structure of the Earth s Interior written by Deane Oberste-Lehn and published by . This book was released on 1963 with total page 28 pages. Available in PDF, EPUB and Kindle. Book excerpt: