Parameter Estimation and Inverse Problems
- 1st Edition - December 28, 2004
- Authors: Richard C. Aster, Brian Borchers, Clifford H. Thurber
- Language: English
Parameter Estimation and Inverse Problems primarily serves as a textbook for advanced undergraduate and introductory graduate courses. It promotes a fundamental understan… Read more
Parameter Estimation and Inverse Problems primarily serves as a textbook for advanced undergraduate and introductory graduate courses. It promotes a fundamental understanding of parameter estimation and inverse problem philosophy and methodology.
It introduces readers to Classical and Bayesian approaches to linear and nonlinear problems, with particular attention to computational, mathematical, and statistical issues related to their application to geophysical problems. Four appendices review foundational concepts in linear algebra, statistics, vector calculus, and notation. Pedagogy includes hundreds of highlighted equations, examples, and definitions; introductory chapter synopses; end-of-chapter exercises, both programming and theoretical; and suggestions for further reading.
The text is designed to be accessible to graduate students and professionals in physical sciences without an extensive mathematical background.
- Designed to be accessible to graduate students and professionals in physical sciences without an extensive mathematical background
- Includes three appendices for review of linear algebra and crucial concepts in statistics
- Battle-tested in courses at several universities
- MATLAB exercises facilitate exploration of material
Students and professionals in Astrophysics, Applied Mathematics, Atmospheric Science, Geologiocal Engineering, Geophysics, Hydrology, Oceanography and related fields.
Preface
1. Introduction
2. Linear Regression
3. Discretizing Continuous Inverse Problems
4. Rank Deficiency and Ill-Conditioning
5. Tikhonov Regularization
6. Iterative Methods
7. Other Regularization Techniques
8. Fourier Techniques
9. Nonlinear Regression
10. Nonlinear Inverse Problems
11. Bayesian Methods
Appendix A: Review of Linear Algebra
Appendix B: Review of Probability and Statistics
Appendix C: Glossary of Notation
Bibliography
Index
1. Introduction
2. Linear Regression
3. Discretizing Continuous Inverse Problems
4. Rank Deficiency and Ill-Conditioning
5. Tikhonov Regularization
6. Iterative Methods
7. Other Regularization Techniques
8. Fourier Techniques
9. Nonlinear Regression
10. Nonlinear Inverse Problems
11. Bayesian Methods
Appendix A: Review of Linear Algebra
Appendix B: Review of Probability and Statistics
Appendix C: Glossary of Notation
Bibliography
Index
"...a very useful textbook at undergraduate and graduate-level courses teaching the numerical techniques used in parameter estimation...it will certainly be a very useful reference also for practitioners who need a guide in selecting the proper mathematical approach when solving real problems, not only in geophysics, but also other branches of science and engineering."—Wojciech Debski, Institute of Geophysics, Polish Academy of Sciences
"The great strength of this book is that it is a 'one-shop-stop' for solving inverse problems; it contains many different methods for solving your particular problems and, in general, all of the background mathematics to help you understand the method itself."—John Brittan, in THE LEADING EDGE, SEPT 2005
"The writing is uniformly clear; one unfamiliar with even the most basic ideas of inverse theory will find it ideal for self-study. ...I found the authors’ treatment of such concepts as existence, uniqueness, instability, resolution, and ill-posedness to be particularly succinct. They do a fine job in distinguishing the continuous from the discrete case, and they point out some of the pitfalls that can arise when going from one to the other, yet without becoming bogged down in sterile mathematical detail. ...This is an exceptionally well written introductory text which, for a change, is reasonably priced, placing it at least within reach of a college student."—Sven Treitel, The Leading Edge, March 2006
“This is a well designed textbook with a very clean approach [and] a fine introduction for inverse problems in applied fields. …The tone of the writing is conversational in a way that allows the ideas to come across clearly, while the content is mathematically rigorous, presenting details relevent to the topic and providing references for the rest.” —Paul Phillips, University of Dallas for MAA, February 2006
"A well-presented textbook [and] a one-stop-shop for solving inverse problems...a well recommended addition to the technical library of anybody who has to deal with inverse problems on a regular basis."—John Brittan, Walton-on-Thames, UK for "The Leading Edge", September 2005
"The great strength of this book is that it is a 'one-shop-stop' for solving inverse problems; it contains many different methods for solving your particular problems and, in general, all of the background mathematics to help you understand the method itself."—John Brittan, in THE LEADING EDGE, SEPT 2005
"The writing is uniformly clear; one unfamiliar with even the most basic ideas of inverse theory will find it ideal for self-study. ...I found the authors’ treatment of such concepts as existence, uniqueness, instability, resolution, and ill-posedness to be particularly succinct. They do a fine job in distinguishing the continuous from the discrete case, and they point out some of the pitfalls that can arise when going from one to the other, yet without becoming bogged down in sterile mathematical detail. ...This is an exceptionally well written introductory text which, for a change, is reasonably priced, placing it at least within reach of a college student."—Sven Treitel, The Leading Edge, March 2006
“This is a well designed textbook with a very clean approach [and] a fine introduction for inverse problems in applied fields. …The tone of the writing is conversational in a way that allows the ideas to come across clearly, while the content is mathematically rigorous, presenting details relevent to the topic and providing references for the rest.” —Paul Phillips, University of Dallas for MAA, February 2006
"A well-presented textbook [and] a one-stop-shop for solving inverse problems...a well recommended addition to the technical library of anybody who has to deal with inverse problems on a regular basis."—John Brittan, Walton-on-Thames, UK for "The Leading Edge", September 2005
- Edition: 1
- Published: December 28, 2004
- Language: English
RA
Richard C. Aster
Professor Aster is an Earth scientist with broad interests in geophysics, seismological imaging and source studies, and Earth processes. His work has included significant field research in western North America, Italy, and Antarctica. Professor Aster also has strong teaching and research interests in geophysical inverse and signal processing methods and is the lead author on the previous two editions. Aster was on the Seismological Society of America Board of Directors, 2008-2014 and won the IRIS Leadership Award, 2014.
Affiliations and expertise
New Mexico Institute of Mining and Technology, Socorro, USABB
Brian Borchers
Dr. Borchers’ primary research and teaching interests are in optimization and inverse problems. He teaches a number of undergraduate and graduate courses at NMT in linear programming, nonlinear programming, time series analysis, and geophysical inverse problems. Dr. Borchers’ research has focused on interior point methods for linear and semidefinite programming and applications of these techniques to combinatorial optimization problems. He has also done work on inverse problems in geophysics and hydrology using linear and nonlinear least squares and Tikhonov regularization.
Affiliations and expertise
New Mexico Institute of Mining and Technology, Socorro, USACT
Clifford H. Thurber
Professor Thurber is an international leader in research on three-dimensional seismic imaging ("seismic tomography") using earthquakes. His primary research interests are in the application of seismic tomography to fault zones, volcanoes, and subduction zones, with a long-term focus on the San Andreas fault in central California and volcanoes in Hawaii and Alaska. Other areas of expertise include earthquake location (the topic of a book he edited) and geophysical inverse theory.
Affiliations and expertise
University of Wisconsin-Madison, USARead Parameter Estimation and Inverse Problems on ScienceDirect