Parameter estimation and inverse problems

Parameter Estimation and Inverse Problems, 2e provides 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. --Publisher description.

Preface -- 1. Introduction -- 2. Linear regression -- 3. Rank deficiency and ill conditioning -- 4. Tikhonov regularization -- 5. Discretizing inverse problems using basis functions -- 6. Iterative Methods -- 7. Additional Regularization Techniques -- 8. Fourier Techniques -- 9. Nonlinear regression -- 10. Nonlinear inverse problems -- 11. Bayesian methods -- 12. Epilogue -- Appendix A : Review of linear algebra -- Appendix B : Review of probability and statistics -- C. Review of vector calculus -- Appendix D : Glossary of notation.