Aster R.C., Borchers B., Thurber C. Parameter Estimation and Inverse Problems

Elsevier-Academic Press, New York, London, 2005. — 315 p. — (International Geophysics Series, Volume 90).This textbook evolved from a course in geophysical inverse methods taught during the past decade at New Mexico Tech, first by Rick Aster and, for the past 5 years, jointly between Rick Aster and Brian Borchers. The audience for the course has included a broad range of first- or second-year graduate students (and occasionally advanced undergraduates) from geophysics, hydrology, mathematics, astronomy, and other disciplines. Cliff Thurber joined this collaboration during the past 3 years and has taught a similar course at the University of Wisconsin-Madison. Our principal goal for this text is to promote fundamental understanding of parameter estimation and inverse problem philosophy and methodology, specifically regarding such key issues as uncertainty, ill–posedness, regularization, bias, and resolution. We emphasize theoretical points with illustrative examples, and MatLAB codes that implement these examples are provided on a companion CD. Throughout the examples and exercises, a CD icon indicates that there is additional material on the CD. Exercises include a mix of programming and theoretical problems. Please refer to the very last page of the book for more information on the contents of the CD as well as a link to a companion Web site.Linear regression.
Discretizing continuous inverse problems.
Rank deficiencyand ill-conditioning.
Tikhonov regularization.
Iterative methods.
Additionalregularizationtechniques.
Fourier techniques.
Nonlinear regression.
Nonlinear inverse problems.
Bayesian methods.
Appendices.