
Analysis of the Gravity Field
Direct and Inverse Problems
Birkhäuser (Publisher)
1st Edition
Published on 10. June 2022
Book
Paperback/Softback
XIV, 541 pages
978-3-030-74355-0 (ISBN)
Description
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.
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.
Reviews / Votes
"The book contains extensive material on the theory of gravitational fields, both necessary for an initial acquaintance with the subject and useful for specialists dealing with problems of gravity exploration." (Ilia V. Boikov, zbMATH 1506.86015, 2023)More details
Product info
Paperback
Series
Edition
1st ed. 2022
Language
English
Place of publication
Cham
Switzerland
Publishing group
Springer International Publishing
Target group
Professional and scholarly
Illustrations
52
45 farbige Abbildungen, 52 s/w Abbildungen
XIV, 541 p. 97 illus., 45 illus. in color.
Dimensions
Height: 235 mm
Width: 155 mm
Thickness: 30 mm
Weight
832 gr
ISBN-13
978-3-030-74355-0 (9783030743550)
DOI
10.1007/978-3-030-74353-6
Schweitzer Classification
Other editions
Additional editions

E-Book
06/2022
Birkhäuser
€80.24
Available for download
Book
09/2021
Birkhauser
€106.99
The article will not be published
Persons
Fernando Sansò
is Professor Emeritus at the Polytechnic University of Milan, an Honorary President of the International Association of Geoscience, and a full member of the Accademia dei Lincei. His fields of research encompass gravity field modeling and inversion, boundary value problems, statistics, generalized random fields, and GNSS theory.
Daniele Sampietro is a senior researcher at Geomatics Research & Development srl. His main research activity concerns the processing and interpretation of the Earth's gravity field at regional and local scales for resource exploration activities.
Daniele Sampietro is a senior researcher at Geomatics Research & Development srl. His main research activity concerns the processing and interpretation of the Earth's gravity field at regional and local scales for resource exploration activities.
Content
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.