Parameter Estimation and Inverse Problems

1. Introduction2. Linear Regression3. Rank Deficiency and Ill Conditioning 4. Tikhonov Regularization5. Discretizing Inverse Problems Using Basis Functions6. Iterative Methods7. Additional Regularization Techniques8. Fourier Techniques9. Nonlinear Regression10. Nonlinear Inverse Problems11. Bayesian Methods12. EpilogueA. Review of Linear AlgebraB. Review of Probability and StatisticsC. Review of Vector CalculusD. Glossary of Notation

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. 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. 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.

"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

"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