Download or read book An Analysis of Variational Equations for the Direct Evaluation of the Earth s Gravity Field written by Ohio State University. Department of Geodetic Science and published by . This book was released on 1971 with total page 456 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book An Analysis of Variational Equations for the Direct Evaluation of the Earth s Gravity Field written by Willard D. Haverland and published by . This book was released on 1971 with total page 188 pages. Available in PDF, EPUB and Kindle. Book excerpt: The variational equations, proposed by Obenson and proposed by Rapp, which are used to generate observation equation coefficients in the direct combination of satellite and gravimetric data are critically reviewed. Each procedure is tested with respect to accuracy as a function of step size, integration procedure, and orbit time. The two procedures are combined into a single program that combines the best features of the original proposals. The study concludes that if an orbit arc of less than 15 hours is being considered, Rapp's method with a fixed fourth-order predictor and a fifth order corrector gives the best results. If orbit arcs greater than 15 hours are being used, the combine solution composed of a fixed fourth order predictor and fifth order corrector for anomaly integration and Obenson's method for element integration gives the best results. (Author).
Download or read book The Gravity Field of the Earth from Classical and Modern Methods written by Michele Caputo and published by . This book was released on 1967 with total page 224 pages. Available in PDF, EPUB and Kindle. Book excerpt:
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 Analysis of the Gravity Field written by Fernando Sansò and published by Springer Nature. This book was released on 2022-06-09 with total page 542 pages. Available in PDF, EPUB and Kindle. Book excerpt: This textbook presents a comprehensive treatment of the theory and implementation of inverse methods in the analysis and interpretation of Earth’s gravity field. By restricting their consideration to a local rather than global level, the authors focus on the use of observations and data that are more sensitive to local mass anomalies. All necessary theoretical aspects are reformulated in terms of a Euclidean framework so that less complex tools from mathematical analysis can be utilized. Divided into three parts, the text begins with a review of basic mathematical properties of gravitation, computing gravity from mass distributions, and relevant methods from Fourier analysis. In the second part of the text, the Earth’s gravity field and its properties are introduced, and the preprocessing and processing of gravity data are explored. Finally, elementary inverse theory is discussed, after which the general inversion problem is considered via application of both the Tikhonov deterministic approach and a stochastic MCMC model. Throughout, examples and exercises are provided to both clarify material and to illustrate real-word applications for readers. Analysis of the Gravity Field: Direct and Inverse Problems is carefully written to be accessible to both mathematicians and geophysicists without sacrificing mathematical rigor. Readers should have a familiarity with the basics of mathematical analysis, as well as some knowledge of statistics and probability theory. Detailed proofs of more advanced results are relegated to appendices so that readers can concentrate on solution algorithms.
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 Mathematical Formulation of the Variational Equations for the Determination of the Earth s Gravity Field written by James C. Perry and published by . This book was released on 1974 with total page 28 pages. Available in PDF, EPUB and Kindle. Book excerpt: Expressions for the coefficients and forcing term are derived for the variational equations to be used in a new computer program being developed to determine the earth's gravity field (Program TERRA). Also a brief idea of the role of variational equations is sketched. (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 A Student s Guide to Geophysical Equations written by William Lowrie and published by Cambridge University Press. This book was released on 2011-05-26 with total page 297 pages. Available in PDF, EPUB and Kindle. Book excerpt: The advent of accessible student computing packages has meant that geophysics students can now easily manipulate datasets and gain first-hand modeling experience - essential in developing an intuitive understanding of the physics of the Earth. Yet to gain a more in-depth understanding of physical theory, and to develop new models and solutions, it is necessary to be able to derive the relevant equations from first principles. This compact, handy book fills a gap left by most modern geophysics textbooks, which generally do not have space to derive all of the important formulae, showing the intermediate steps. This guide presents full derivations for the classical equations of gravitation, gravity, tides, earth rotation, heat, geomagnetism and foundational seismology, illustrated with simple schematic diagrams. It supports students through the successive steps and explains the logical sequence of a derivation - facilitating self-study and helping students to tackle homework exercises and prepare for exams.
Download or read book The Analysis of the Earth s Gravity Field written by and published by . This book was released on 1971 with total page 172 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book The Analysis of the Earth s Gravity Field written by Ronald S. Mather and published by . This book was released on 1971 with total page 176 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book The Earth s Shape and Gravity written by G. D. Garland and published by Elsevier. This book was released on 2016-01-26 with total page 192 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Earth's Shape and Gravity focuses on the progress of the use of geophysical methods in investigating the interior of the earth and its shape. The publication first offers information on gravity, geophysics, geodesy, and geology and gravity measurements. Discussions focus on gravity measurements and reductions, potential and equipotential surfaces, absolute and relative measurements, and gravity networks. The text then elaborates on the shape of the sea-level surface and reduction of gravity observations. The text takes a look at gravity anomalies and structures in the earth's crust; interpretation of gravity anomalies; and gravity anomalies and the interior of the earth. Topics include general principle; direct and indirect methods; low order harmonics in the gravitational field; rock densities; ocean trenches; and sedimentary basins. The book then examines the place of gravity measurements in geophysical prospecting and tidal variations of gravity. The manuscript is a dependable source of information for readers interested in the shape and gravity of the earth.
Download or read book Direct Evaluation of the Earth s Gravity Anomaly Field from Orbital Analysis of Artifical Earth Satellites written by Gabriel F. T. Obenson and published by . This book was released on 1970 with total page 135 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Direct Evaluation of the Earth s Gravity Anomaly Field from Orbital Analysis of Artificial Earth Satellites written by Gabriel F. T. Obenson and published by . This book was released on 1969 with total page 552 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Direct Evaluation of the Earth s Gravity Anomaly Fielde from Orbital Analysis of Artificial Earth Satellites written by G.F.T. Obenson and published by . This book was released on 1970 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book The Earth s gravitiy field from GOCE written by Weiyong Yi and published by . This book was released on 2012 with total page 144 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Methods for Study of the External Gravitational Field and Figure of the Earth written by M. S. Molodenskiĭ and published by . This book was released on 1962 with total page 264 pages. Available in PDF, EPUB and Kindle. Book excerpt:
