دانلود کتاب Time-frequency Analysis of Seismic Signals

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Cover
Title Page
Copyright
Contents
Preface
1 Nonstationary Signals and Spectral Properties
1.1 Stationary Signals
1.2 Nonstationary Signals
1.3 The Fourier Transform and the Average Properties
1.4 The Analytic Signal and the Instantaneous Properties
1.5 Computation of the Instantaneous Frequency
1.6 Two Groups of Time–Frequency Analysis Methods
2 The Gabor Transform
2.1 Short-time Fourier Transform
2.2 The Gabor Transform
2.3 The Cosine Function Windows
2.4 Spectral Leakage of Window Functions
2.5 The Gabor Limit of Time–Frequency Resolution
2.6 Implementation of the Gabor Transform
2.7 The Inverse Gabor Transform
2.8 Application in Inverse Q Filtering
3 The Continuous Wavelet Transform
3.1 Basics of the Continuous Wavelet Transform
3.2 The Complex Morlet Wavelet
3.3 The Complex Morse Wavelet
3.4 The Generalised Seismic Wavelet
3.5 The Pseudo-frequency Representation
3.6 The Inverse Wavelet Transform
3.7 Implementation of the Continuous Wavelet Transform
3.8 Hydrocarbon Reservoir Characterisation
4 The S Transform
4.1 Basics of the S Transform
4.2 The Generalised S Transform
4.3 The Fractional Fourier Transform
4.4 The Fractional S Transform
4.5 Implementation of the S Transforms
4.6 The Inverse S Transforms
4.7 Application to Clastic and Carbonate Reservoirs
5 The W Transform
5.1 Basics of the W Transform
5.2 The Generalised W Transform
5.3 Implementation of Nonstationary Convolution
5.4 The Inverse W Transform
5.5 Application to Detecting Hydrocarbon Reservoirs
5.6 Application to Detecting Karst Voids
6 The Wigner–Ville Distribution
6.1 Basics of the Wigner–Ville Distribution (WVD)
6.2 Defining the WVD with an Analytic Signal
6.3 Properties of the WVD
6.4 The Smoothed WVD
6.5 The Generalised Class of Time–Frequency Representations
6.6 The Ambiguity Function and the Generalised WVD
6.7 Implementation of the Standard and Smoothed WVDs
6.8 Implementation of the Ambiguity Function and the Generalised WVD
7 Matching Pursuit
7.1 Basics of Matching Pursuit
7.2 Three-stage Matching Pursuit
7.3 Matching Pursuit with the Morlet Wavelet
7.4 The Sigma Filter
7.5 Multichannel Matching Pursuit
7.6 Structure-adaptive Matching Pursuit
7.7 Three Applications
8 Local Power Spectra with Multiple Windows
8.1 Multiple Orthogonal Windows
8.2 Multiple Windows Defined by the Prolate Spheroidal Wavefunctions
8.3 Multiple Windows Constructed by Solving a Discretised Eigenvalue Problem
8.4 Multiple Windows Constructed by Gaussian Functions
8.5 The Gabor Transform with Multiple Windows
8.6 The WVD with Multiple Windows
8.7 Prospective of Time–Frequency Analysis without Windowing
Appendices
A The Gaussian Integrals, the Gamma Function, and the Gaussian Error Functions
B Fourier Transforms of the Tapered Boxcar Window, the Truncated Gaussian Window, and the Weighted Cosine Window
B.1 The Fourier Transform of the Tapered Boxcar Window
B.2 The Fourier Transform of the Truncated Gaussian Window Function
B.3 The Fourier Transform of the Weighted Cosine Window Function
C The Generalised Seismic Wavelet in the Time Domain
D Implementation of the Fractional Fourier Transform
E Marginal Properties and the Analytic Signal in the WVD Definition
E.1 Marginal Properties of the WVD Definition
E.2 The WVD Definition Using an Analytic Signal or a Real Signal
F The Prolate Spheroidal Wavefunctions, the Associated and the Ordinary Legendre Polynomials
F.1 Prolate Spheroidal Wavefunctions
F.2 The Associated Legendre Polynomials
F.3 The Ordinary Legendre Polynomials
References
Author Index
Subject Index
EULA