This book gives a comprehensive picture of the present stage of development of spectral analysis and filter theory in geophysics. The principles and theories behind classical and modern methods are described and the effectiveness of these methods is assessed; selected examples of their practical application in geophysics are discussed. The modern methods include, for example, spectral analysis by fitting random models to the data, the maximum-entropy and maximum-likelihood spectral analysis procedures, the Wiener and Kalman filters, homomorphic deconvolution, and adaptive procedures for…mehr
This book gives a comprehensive picture of the present stage of development of spectral analysis and filter theory in geophysics. The principles and theories behind classical and modern methods are described and the effectiveness of these methods is assessed; selected examples of their practical application in geophysics are discussed. The modern methods include, for example, spectral analysis by fitting random models to the data, the maximum-entropy and maximum-likelihood spectral analysis procedures, the Wiener and Kalman filters, homomorphic deconvolution, and adaptive procedures for non-stationary processes. This book represents a valuable aid in education and research and for solving practical problems in geophysics and related disciplines.
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.
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.
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