Parameter Estimation and Inverse Problems by Aster, Richard C.; Borchers, Brian; Thurber, Clifford H.;

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Kiadás sorszáma 2
Kiadó Academic Press
Megjelenés dátuma 2016. augusztus 19.

ISBN 9780128100929
Kötéstípus Puhakötés
Terjedelem376 oldal
Méret 240x197 mm
Súly 680 g
Nyelv angol

Kategóriák

A matematika általános kérdései Analízis Irodai szoftverek, táblázatkezelők Geofizika Földtudományok általában Geológia

Hosszú leírás:

Parameter Estimation and Inverse Problems, Second Edition provides geoscience students and professionals with answers to common questions like how one can derive a physical model from a finite set of observations containing errors, and how one may determine the quality of such a model. This book takes on these fundamental and challenging problems, introducing students and professionals to the broad range of approaches that lie in the realm of inverse theory. The authors present both the underlying theory and practical algorithms for solving inverse problems. The authors' treatment is appropriate for geoscience graduate students and advanced undergraduates with a basic working knowledge of calculus, linear algebra, and statistics.

Parameter Estimation and Inverse Problems, Second Edition introduces readers to both Classical and Bayesian approaches to linear and nonlinear problems with particular attention paid to computational, mathematical, and statistical issues related to their application to geophysical problems. The textbook includes Appendices covering essential linear algebra, statistics, and notation in the context of the subject.

Includes appendices for review of needed concepts in linear, statistics, and vector calculus.
Accessible to students and professionals without a highly specialized mathematical background.

"A few years ago, it was my pleasure to review for the TLE this book's first edition, published in 2005.The present revised version is some 60 pages longer and contains several significant modifications. As is true of the original, the book continues to be one of the clearest as well as the most comprehensive elementary expositions of discrete geophysical inverse theory. It is ideally suited for beginners as well as a fine resource for those searching for a particular inverse problem. Each algorithm is presented in the form of pseudo-code, then backed up by a collection of MATLAB codes downloadable from an Elsevier Web site.All examples in the book are beautifully illustrated with simple, easy to follow "cartoon" problems, and all painstakingly designed to illuminate the details of a particular numerical method." --The Leading Edge, July 2012

Több

Tartalomjegyzék:

1. Introduction
2. Linear Regression
3. Rank Deficiency and Ill Conditioning
4. Tikhonov Regularization
5. Discretizing Inverse Problems Using Basis Functions
6. Iterative Methods
7. Additional Regularization Techniques
8. Fourier Techniques
9. Nonlinear Regression
10. Nonlinear Inverse Problems
11. Bayesian Methods
12. Epilogue
A. Review of Linear Algebra
B. Review of Probability and Statistics
C. Review of Vector Calculus
D. Glossary of Notation