288 pages, b/w illustrations, tables
Covering spectral analysis as well as inversion of geophysical data, David Gubbins introduces the necessary theory and techniques and then demonstrates how they may be practically applied to interpret various types of geophysical signals, including seismic, magnetic and gravity data. Featuring summary boxes, extensive mathematical and computing exercises (solutions and software available on the Internet), and a set of mathematical appendices, Time Series Analysis and Inverse Theory for Geophysicists will prove invaluable to geophysics students and instructors.
"The book Time Series Analysis and Inverse Theory for Geophysicists by D. Gubbins is according to the author, aimed at "providing the students of geophysics with an introduction to these [digital] techniques and an understanding of the underlying philosophy and mathematical theory." My impression is that the author has achieved this goal quite well. I would recommend the book as an introductory textbook at undergraduate- and graduate-level courses intended as a general introduction to the numerical techniques used in the processing of geophysical data. The advanced topics of the inverse theory briefly covered in the book can also be interesting for practitioners who need a guide in selecting the proper mathematical approach when solving real problems."
- Pageoph, Wojciech Dębski, Institute of Geophysics, Polish Academy of Sciences
"Professor Gubbins is very well qualified by training, aptitude and experience to write a book of this nature. This fine book reveals years of wisdom and experience in teaching extensive and hard topics. The treatment is elegant, clear, logical, warm and surprisingly full for a book that is not large, and contains many interesting snippets of information and relevant illustrations."
- Clive Randall and Andrzej Kijko, Birkhauser Verlag, Basel
"[...] this excellent textbook fills a much neglected gap [...] the group that will benefit most from its guidance will be future generations of geophysics students[...]"
- Journal of Geological Magazine
"For the student, this is an excellent text well suited for its intended level of instruction with many exercises following each chapter, some requiring computer programs obtainable from various web sites. [...] I suggest that any instructor planning to teach time series and inverse theory examine this book as a potential text . [...] Any body with an interest in geophysical time series and inverse problems is truly well served with this beautifully written volume [...] In summary, this book has more than adequately filled the role for which it was written, namely as a text for introductory courses in time series analysis and inverse theory."
- The Leading Edge
Part I. Processing:
2. Mathematical preliminaries
3. Practical estimation of spectra
5. Processing two-dimensional data
Part II. Inversion:
6. Linear parameter estimation
7. The underdetermined problem
8. Nonlinear inverse problems
9. Continuous inverse theory
Part III. Applications:
10. Fourier analysis as an inverse problem
11. Seismic travel times and tomography
Appendix 1. Fourier series
Appendix 2. The Fourier integral transform
Appendix 3. Shannon's sampling theorem
Appendix 4. Linear algebra
Appendix 5. Vector spaces and the function space
Appendix 6. Lagrange multipliers and penalty parameters
Appendix 7. Files for the computer exercises
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