Parameter Estimation and Inverse Problems

Parameter Estimation and Inverse Problems

1st Edition - December 28, 2004

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  • Authors: Richard C. Aster, Brian Borchers, Clifford H. Thurber
  • eBook ISBN: 9780080470559

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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.

Key Features

  • 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.

Table of Contents

  • 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

Product details

  • No. of pages: 320
  • Language: English
  • Copyright: © Academic Press 2004
  • Published: December 28, 2004
  • Imprint: Academic Press
  • eBook ISBN: 9780080470559

About the Authors

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, USA

Brian Borchers

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, USA

Clifford H. Thurber

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, USA

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