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Analysis of the Gravity Field

Analysis of the Gravity Field
Author: Fernando Sansò
Publisher: Springer Nature
Total Pages: 542
Release: 2022-06-09
Genre: Mathematics
ISBN: 3030743535

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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.


Global Gravity Field Modeling from Satellite-to-Satellite Tracking Data

Global Gravity Field Modeling from Satellite-to-Satellite Tracking Data
Author: Majid Naeimi
Publisher: Springer
Total Pages: 181
Release: 2017-02-10
Genre: Science
ISBN: 3319499416

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This book provides a sound theoretical basis for the the different gravity field recovery methods and the numerics of satellite-to-satellite tracking data. It represents lectures given at the ‘Wilhelm and Else Heraeus Autumn School’ in Bad Honnef, Germany, October 4-9, 2015. The emphasis of the school was on providing a sound theoretical basis for the different gravity field recovery methods and the numerics of data analysis. The approaches covered here are the variational equations (classical approach), the acceleration approach and the energy balance approach, all of which are used for global gravity field recovery on the basis of satellite observations. The theory of parameter estimation in satellite gravimetry and concepts for orbit determination are also included. The book guides readers through a broad range of topics in satellite gravimetry, supplemented by the necessary theoretical background and numerical examples. While it provides a comprehensive overview for those readers who are already familiar with satellite gravity data processing, it also offers an essential reference guide for graduate and undergraduate students interested in this field.


Earth Gravity Field from Space - from Sensors to Earth Sciences

Earth Gravity Field from Space - from Sensors to Earth Sciences
Author: G. Beutler
Publisher: Springer Science & Business Media
Total Pages: 442
Release: 2003-10-31
Genre: Science
ISBN: 9781402014086

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Volume resulting from an ISSI Workshop, 11-15 March 2002, Bern, Switzerland


Gravity Interpretation

Gravity Interpretation
Author: Wolfgang Jacoby
Publisher: Springer Science & Business Media
Total Pages: 413
Release: 2009-02-01
Genre: Science
ISBN: 3540853294

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Gravity interpretation involves inversion of data into models, but it is more. Gravity interpretation is used in a “holistic” sense going beyond “inversion”. Inversion is like optimization within certain a priori assumptions, i.e., all anticipated models lie in a limited domain of the a priori errors. No source should exist outside the anticipated model volume, but that is never literally true. Interpretation goes beyond by taking “outside” possibilities into account in the widest sense. Any neglected possibility carries the danger of seriously affecting the interpretation. Gravity interpretation pertains to wider questions such as the shape of the Earth, the nature of the continental and oceanic crust, isostasy, forces and stresses, geol- ical structure, nding useful resources, climate change, etc. Interpretation is often used synonymously with modelling and inversion of observations toward models. Interpretation places the inversion results into the wider geological or economic context and into the framework of science and humanity. Models play a central role in science. They are images of phenomena of the physical world, for example, scale images or metaphors, enabling the human mind to describe observations and re- tionships by abstract mathematical means. Models served orientation and survival in a complex, partly invisible physical and social environment.


Acquisition and Analysis of Terrestrial Gravity Data

Acquisition and Analysis of Terrestrial Gravity Data
Author: Leland Timothy Long
Publisher: Cambridge University Press
Total Pages: 183
Release: 2013-01-17
Genre: Science
ISBN: 1107024137

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A one-stop manual for graduate students and professionals, combining introductory gravity survey procedures with full explanations of analysis techniques.


Geoid Determination

Geoid Determination
Author: Fernando Sansò
Publisher: Springer Science & Business Media
Total Pages: 748
Release: 2013-02-13
Genre: Science
ISBN: 3540747001

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This book will be based on the material of the lecture noties in several International Schools for the Determination and Use of the Geoid, organized by the International Geoid Serivice of the International Association of Geodesy. It consolidates, unifies, and streamlines this material in a unique way not covereed by the few other books that exist on this subjext. More specifically, the book presents (for the first time in a single volume) the theory and methodology of the most common technique used for precise determination of the geoid, including the computation of the marine geoid from satellite altimetry data. These are illustrated by specific examples and actual computations of local geoids. In addition, the book provides the fundamentals of estimating orthometric heights without spirit levelling, by properly combining a geoid with heights from GPS. Besides the geodectic and geophysical uses, this last application has made geoid computation methods very popular in recent years because the entire GPS and GIS user communities are interested in estimating geoid undulations in order to convert GPS heights to physically meaningful orthometric heights (elevations above mean sea level). The overall purpose of the book is, therefore, to provide the user community (academics, graduate students, geophysicists, engineers, oceanographers, GIS and GPS users, researchers) with a self-contained textbook, which will supply them with the complete roadmap of estimating geoid undulations, from the theoretical definitions and formulas to the available numerical methods and their implementation and the test in practice.