# Parameter Estimation and Inverse Problems, 1. cilt

Academic Press, 11 Oca 2005 - 301 sayfa

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

### İçindekiler

 1 INTRODUCTION 1 2 LINEAR REGRESSION 15 3 DISCRETIZING CONTINUOUS INVERSE PROBLEMS 41 4 RANK DEFICIENCY AND ILLCONDITIONING 55 5 TIKHONOV REGULARIZATION 89 6 ITERATIVE METHODS 119 7 ADDITIONAL REGULARIZATION TECHNIQUES 139 8 FOURIER TECHNIQUES 153
 11 BAYESIAN METHODS 201 Appendix A REVIEW OF LINEAR ALGEBRA 219 Appendix B REVIEW OF PROBABILITY AND STATISTICS 251 Appendix C REVIEW OF VECTOR CALCULUS 273 Appendix D GLOSSARY OF NOTATION 281 BIBLIOGRAPHY 283 INDEX 291 International Geophysics Series 297

 9 NONLINEAR REGRESSION 171 10 NONLINEAR INVERSE PROBLEMS 191
 About the CDROM 303 Telif Hakkı

### Popüler pasajlar

Sayfa 288 - In G. Nolet, editor, Seismic Tomography with Applications in Global Seismology and Exploration Geophysics, chapter 3, pages 49-83.
Sayfa 288 - CF Van Loan. Generalizing the singular value decomposition. SIAM Journal on Numerical Analysis, 13:76-83, 1976.
Sayfa 288 - Leveque, J.-J., 1990. Simultaneous iterative reconstruction technique: physical interpretation based on the generalized least squares solution. J. Geophys. Res. 95, 12553-12559.

### Yazar hakkında (2005)

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. 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. 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.