Analysis of the Gravity Field: Direct and Inverse Problems: Lecture Notes in Geosystems Mathematics and Computing
Autor Fernando Sansò, Daniele Sampietroen Limba Engleză Paperback – 10 iun 2022
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.
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Specificații
ISBN-13: 9783030743550
ISBN-10: 3030743551
Pagini: 541
Ilustrații: XIV, 541 p. 97 illus., 45 illus. in color.
Dimensiuni: 155 x 235 mm
Greutate: 0.84 kg
Ediția:1st ed. 2022
Editura: Springer International Publishing
Colecția Birkhäuser
Seria Lecture Notes in Geosystems Mathematics and Computing
Locul publicării:Cham, Switzerland
ISBN-10: 3030743551
Pagini: 541
Ilustrații: XIV, 541 p. 97 illus., 45 illus. in color.
Dimensiuni: 155 x 235 mm
Greutate: 0.84 kg
Ediția:1st ed. 2022
Editura: Springer International Publishing
Colecția Birkhäuser
Seria Lecture Notes in Geosystems Mathematics and Computing
Locul publicării:Cham, Switzerland
Cuprins
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.
Recenzii
“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)
Notă biografică
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.
Textul de pe ultima copertă
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.
Caracteristici
Highlights the use of inverse methods in exploration geophysics by concentrating on the analysis and interpretation of Earth's gravity field at a local level Carefully written to be accessible to both mathematicians and geophysicists without sacrificing mathematical rigor Provides practical, real-world examples that gradually build in complexity through the text