Time Series Analysis and Inverse Theory for Geophysicists
Time Series Analysis and Inverse Theory for Geophysicists
This unique textbook provides the foundation for understanding and applying techniques commonly used in geophysics to process and interpret modern digital data. The geophysicist's toolkit contains a range of techniques which may be divided into two main groups: processing, which concerns time series analysis and is used to separate the signal of interest from background noise; and inversion, which involves generating some map or physical model from the data. These two groups of techniques are normally taught separately, but are here presented together as parts I and II of the book. Part III describes some real applications and includes case studies in seismology, geomagnetism, and gravity. This textbook gives students and practitioners the theoretical background and practical experience, through case studies, computer examples and exercises, to understand and apply new processing methods to modern geophysical datasets. Solutions to the exercises are available on a website at http://publishing.cambridge.org/resources/0521819652
- Was the first textbook on this topic aimed at undergraduate and graduate students
- Features summary boxes for specific results and techniques
- Includes numerous paper and computer exercises for which the necessary software and solutions are available on the Internet
- Contains appendices explaining key mathematical derivations and results
Reviews & endorsements
'… 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 . … 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
''Any body with an interest in geophysical time series and inverse problems is truly well served with this beautifully written volume.' The Leading Edge
Product details
March 2004Hardback
9780521819657
272 pages
255 × 179 × 15 mm
0.7kg
49 b/w illus. 7 tables 71 exercises
Available
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.
