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Analysis of the gravity field : direct and inverse problems / Fernando Sansò, Daniele Sampietro.

Sansò, F. (Fernando), 1945- author.; Sampietro, Daniele, author.
2022
QC178
Available Online
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Title
Analysis of the gravity field : direct and inverse problems / Fernando Sansò, Daniele Sampietro.
Author
Sansò, F. (Fernando), 1945- author.
ISBN
9783030743536 (electronic bk.)
3030743535 (electronic bk.)
9783030743529 (print)
DOI
https://doi.org/10.1007/978-3-030-74353-6
Published
Cham, Switzerland : Birkhäuser, 2022.
Language
English
Description
1 online resource (xiv, 541 pages) : illustrations (some color).
Item Number
10.1007/978-3-030-74353-6 doi
Call Number
QC178
Dewey Decimal Classification
531/.14
Summary
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.
Bibliography, etc. Note
Includes bibliographical references and index.
Access Note
Access limited to authorized users.
Source of Description
Online resource; title from PDF title page (SpringerLink, viewed June 14, 2022).
Added Author
Sampietro, Daniele, author.
Series
Lecture notes in geosystems mathematics and computing.
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Introduction
Part I: Forward Modelling of the Gravity Field
The Vertical Gravitational Signal of Homogeneous Bodies, Bounded in the Horizon Plane
Fourier Methods
Part II: The Preprocessing and Processing of Gravity Data: From Observations to a Gravity Map on a Local Horizontal Plane
The Gravity Field of Earth
Gravity Surveying and Preprocessing
Gravity Processing
Part III: Inverse Theory and Applications
Elementary Inverse Theory
On the Mathematical Characterization of the Inverse Gravity Problem
General Inversion Approaches
Some Conclusions
Part IV: Appendices
Mathematical Auxillia
The Theory of Random Fields and the Wiener-Kolmogorov Prediction Method
The Tikhonov Regularization and Morozov's Discrepancy Principle.

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