Spectral Analysis and Filter Theory in Applied Geophysics

I Spectral Analysis of Deterministic Processes.- 1 Fourier Series Representation of Periodic Functions.- 2 Spectral Representation of Nonperiodic Processes.- 3 The Dirac Delta Function and its Fourier Transform.- 4 Spectral Analysis of Time-Limited Observations of Infinitely Long Processes.- 5 Spectral Analysis of Discrete Functions.- 6 z-Transform Representation of Time Series.- 7 Examples of the Use of the Fourier Transform in Applied Seismics.- II Spectral Analysis of Random Processes.- 8 Characterization of Random Processes in the Time and Frequency Domains.- 9 Estimation of the Power Spectral Density Function.- 10 Evaluation of Magnetotelluric Survey Data.- III Spectral Analysis of Random Processes by Model Fitting.- 11 Spectral Estimation by Model Fitting.- 12 Estimating Power Spectra using Criteria from Information Theory.- IV Fundamentals of Filter Theory.- 13 Filtering from the Viewpoint of System Theory.- 14 Filtering in the Frequency Domain.- V Digital Filtering.- 15 Basics of Digital Filtering.- 16 Filtering using Simple Mathematical Operations.- 17 Designing Nonrecursive Digital Filters of Finite Length.- 18 Synthesis of Recursive Digital Filters.- VI Fundamentals of Optimum Filtering.- 19 Designing Analog and Digital Optimum Filters.- 20 Application of Optimum Filters to Reflection Seismic Data.- 21 Kalman Filters.- VII Fundamentals of Deconvolution and their Application to Reflection Seismic Data.- 22 Mathematical Basis of Deconvolution.- 23 Deconvolution: Problems and Approaches in Reflection Seismics.- VIII Multidimensional and Multichannel Filters.- 24 Multidimensional Filters.- 25 Two-Dimensional Filters for Gravity and Magnetic Data.- 26 Multichannel Filtering of Seismic Data.- Author Index.