Parameter Estimation and Inverse Problems / Edition 2

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Overview

Parameter Estimation and Inverse Problems, 2eprovides 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, 2e 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. A companion website features computational examples (including all examples contained in the textbook) and useful subroutines using MATLAB.

  • Includes appendices for review of needed concepts in linear, statistics, and vector calculus.
  • Companion website contains comprehensive MATLAB code for all examples, which readers can reproduce, experiment with, and modify.
  • Online instructor’s guide helps professors teach, customize exercises, and select homework problems
  • Accessible to students and professionals without a highly specialized mathematical background.

Parameter Estimation and Inverse Problems primarily serves as a textbook for advanced undergraduate and introductory graduate courses. Class notes have been developed and reside on the World Wide Web for faciliting use and feedback by teaching colleagues.

The authors' treatment promotes an understanding of fundamental and practical issus associated with parameter fitting and inverse problems including basic theory of inverse problems, statistical issues, computational issues, and an understanding of how to analyze the success and limitations of solutions to these probles. The text is also a practical resource for general students and professional researchers, where techniques and concepts can be readily picked up on a chapter-by-chapter basis.

Parameter Estimation and Inverse Problems is structured around a course at New Mexico Tech and is designed to be accessible to typical graduate students in the physical sciences who may not have an extensive mathematical background. It is accompanied by a Web site that contains Matlab code corresponding to all examples. Designed to be accessible to graduate students and professionals in physical sciences without an extensive mathematical background

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Editorial Reviews

From the Publisher
"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, page 860
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Product Details

  • ISBN-13: 9780123850485
  • Publisher: Elsevier Science
  • Publication date: 2/4/2012
  • Edition description: New Edition
  • Edition number: 2
  • Pages: 376
  • Sales rank: 1,222,270
  • Product dimensions: 7.50 (w) x 9.30 (h) x 0.90 (d)

Table of Contents

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

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