Spectral Analysis and Filter Theory in Applied Geophysics

✍ Scribed by Dr. Burkhard Buttkus (auth.)

• Publisher: Springer-Verlag Berlin Heidelberg
• Year: 2000
• Tongue: English
• Leaves: 664
• Edition: 1
• Category: Library

✦ Synopsis

This book is intended to be an introduction to the fundamentals and methods of spectral analysis and filter theory and their appli­ cations in geophysics. The principles and theoretical basis of the various methods are described, their efficiency and effectiveness eval­ uated, and instructions provided for their practical application. Be­ sides the conventional methods, newer methods arediscussed, such as the spectral analysis ofrandom processes by fitting models to the ob­ served data, maximum-entropy spectral analysis and maximum-like­ lihood spectral analysis, the Wiener and Kalman filtering methods, homomorphic deconvolution, and adaptive methods for nonstation­ ary processes. Multidimensional spectral analysis and filtering, as well as multichannel filters, are given extensive treatment. The book provides a survey of the state-of-the-art of spectral analysis and fil­ ter theory. The importance and possibilities ofspectral analysis and filter theory in geophysics for data acquisition, processing and eval­ uation are illustrated with practical examples from various fields of applied geophysics. Although this book was planned primarily as a textbook for a course on the analysis of geophysical time· series, it may also be of interest to scientists and engineers who process other digital data. It provides a comprehensive discussion of the theoretical fundamen­ tals and a compilation of the extensive literature on the subject. I hope that I have succeeded in presenting the various principles and methods of time-series analysis comprehensively and without error. Comments on errors or suggestions for improvements are welcome.

✦ Table of Contents

Front Matter....Pages I-XV
Introduction....Pages 1-5
Front Matter....Pages 7-7
Fourier Series Representation of Periodic Functions....Pages 9-12
Spectral Representation of Nonperiodic Processes....Pages 13-40
The Dirac Delta Function and its Fourier Transform....Pages 41-47
Spectral Analysis of Time-Limited Observations of Infinitely Long Processes....Pages 49-57
Spectral Analysis of Discrete Functions....Pages 59-84
z-Transform Representation of Time Series....Pages 85-100
Examples of the Use of the Fourier Transform in Applied Seismics....Pages 101-142
Back Matter....Pages 143-148
Front Matter....Pages 149-149
Characterization of Random Processes in the Time and Frequency Domains....Pages 151-178
Estimation of the Power Spectral Density Function....Pages 179-213
Evaluation of Magnetotelluric Survey Data....Pages 215-233
Back Matter....Pages 234-236
Front Matter....Pages 237-237
Spectral Estimation by Model Fitting....Pages 239-278
Estimating Power Spectra using Criteria from Information Theory....Pages 279-294
Back Matter....Pages 295-298
Front Matter....Pages 299-299
Filtering from the Viewpoint of System Theory....Pages 301-324
Filtering in the Frequency Domain....Pages 325-343
Back Matter....Pages 344-345
Front Matter....Pages 347-347
Basics of Digital Filtering....Pages 349-360
Filtering using Simple Mathematical Operations....Pages 361-365
Designing Nonrecursive Digital Filters of Finite Length....Pages 367-378
Synthesis of Recursive Digital Filters....Pages 379-403
Back Matter....Pages 404-405
Front Matter....Pages 407-407
Designing Analog and Digital Optimum Filters....Pages 409-438
Back Matter....Pages 490-492
Front Matter....Pages 407-407
Application of Optimum Filters to Reflection Seismic Data....Pages 439-454
Kalman Filters....Pages 455-489
Back Matter....Pages 490-492
Front Matter....Pages 493-493
Mathematical Basis of Deconvolution....Pages 495-514
Deconvolution: Problems and Approaches in Reflection Seismics....Pages 515-543
Back Matter....Pages 544-546
Front Matter....Pages 547-547
Multidimensional Filters....Pages 549-580
Two-Dimensional Filters for Gravity and Magnetic Data....Pages 581-607
Multichannel Filtering of Seismic Data....Pages 609-639
Back Matter....Pages 640-643
Back Matter....Pages 645-667

✦ Subjects

Geophysics and Environmental Physics; Geology; Functional Analysis; Geophysics/Geodesy; Astronomy, Observations and Techniques; Astrophysics and Astroparticles