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Spectral Analysis and Filter Theory in Applied Geophysics

  • Book
  • © 2000

Overview

Authors:
  1. Burkhard Buttkus

    1. Federal Institute for Geosciences and Natural Resources, Hannover, Germany

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  • Broad spectrum of applications

  • Treatment of classical and modern methods

  • Both theoretical and practical aspects

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Table of contents (27 chapters)

  1. Front Matter

    Pages I-XV
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  2. Introduction

    1. Introduction

      • Burkhard Buttkus
      Pages 1-5

  3. Spectral Analysis of Deterministic Processes

    1. Front Matter

      Pages 7-7
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    2. Fourier Series Representation of Periodic Functions

      • Burkhard Buttkus
      Pages 9-12

    3. Spectral Representation of Nonperiodic Processes

      • Burkhard Buttkus
      Pages 13-40

    4. The Dirac Delta Function and its Fourier Transform

      • Burkhard Buttkus
      Pages 41-47

    5. Spectral Analysis of Time-Limited Observations of Infinitely Long Processes

      • Burkhard Buttkus
      Pages 49-57

    6. Spectral Analysis of Discrete Functions

      • Burkhard Buttkus
      Pages 59-84

    7. z-Transform Representation of Time Series

      • Burkhard Buttkus
      Pages 85-100

    8. Examples of the Use of the Fourier Transform in Applied Seismics

      • Burkhard Buttkus
      Pages 101-142

  4. Back Matter

    Pages 143-148
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  5. Spectral Analysis of Random Processes

    1. Front Matter

      Pages 149-149
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    2. Characterization of Random Processes in the Time and Frequency Domains

      • Burkhard Buttkus
      Pages 151-178

    3. Estimation of the Power Spectral Density Function

      • Burkhard Buttkus
      Pages 179-213

    4. Evaluation of Magnetotelluric Survey Data

      • Burkhard Buttkus
      Pages 215-233

  6. Back Matter

    Pages 234-236
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  7. Spectral Analysis of Random Processes by Model Fitting

    1. Front Matter

      Pages 237-237
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    2. Spectral Estimation by Model Fitting

      • Burkhard Buttkus
      Pages 239-278

    3. Estimating Power Spectra using Criteria from Information Theory

      • Burkhard Buttkus
      Pages 279-294

  8. Back Matter

    Pages 295-298
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Keywords

About this book

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.

Authors and Affiliations

  • Federal Institute for Geosciences and Natural Resources, Hannover, Germany

    Burkhard Buttkus

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