Synopses & Reviews
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, this textbook will prove invaluable to geophysics students and instructors.
Review
"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 D^D,ebski, 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
Synopsis
The first textbook covering spectral analysis and geophysical data inversion for undergraduate and graduate students.
Table of Contents
1. Introduction; Part I. Processing: 2. Mathematical preliminaries; 3. Practical estimation of spectra; 4. Filtering; 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; 12. Geomagnetism; 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; References; Index.