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Time-frequency Analysis of Seismic Signals [Kõva köide]

  • Formaat: Hardback, 240 pages, kõrgus x laius x paksus: 247x176x15 mm, kaal: 680 g
  • Ilmumisaeg: 27-Oct-2022
  • Kirjastus: John Wiley & Sons Inc
  • ISBN-10: 1119892341
  • ISBN-13: 9781119892342
Teised raamatud teemal:
  • Formaat: Hardback, 240 pages, kõrgus x laius x paksus: 247x176x15 mm, kaal: 680 g
  • Ilmumisaeg: 27-Oct-2022
  • Kirjastus: John Wiley & Sons Inc
  • ISBN-10: 1119892341
  • ISBN-13: 9781119892342
Teised raamatud teemal:

A practical and insightful discussion of time-frequency analysis methods and technologies

Time–frequency analysis of seismic signals aims to reveal the local properties of nonstationary signals. The local properties, such as time-period, frequency, and spectral content, vary with time, and the time of a seismic signal is a proxy of geologic depth. Therefore, the time–frequency spectrum is composed of the frequency spectra that are generated by using the classic Fourier transform at different time positions.

Different time–frequency analysis methods are distinguished in the construction of the local kernel prior to using the Fourier transform. Based on the difference in constructing the Fourier transform kernel, this book categorises time–frequency analysis methods into two groups: Gabor transform-type methods and energy density distribution methods.

This book systematically presents time–frequency analysis methods, including technologies which have not been previously discussed in print or in which the author has been instrumental in developing. In the presentation of each method, the fundamental theory and mathematical concepts are summarised, with an emphasis on the engineering aspects.

This book also provides a practical guide to geophysicists who attempt to generate geophysically meaningful time–frequency spectra, who attempt to process seismic data with time-dependent operations for the fidelity of nonstationary signals, and who attempt to exploit the time–frequency space seismic attributes for quantitative characterisation of hydrocarbon reservoirs.

Preface ix
1 Nonstationary Signals and Spectral Properties
1(18)
1.1 Stationary Signals
1(4)
1.2 Nonstationary Signals
5(2)
1.3 The Fourier Transform and the Average Properties
7(3)
1.4 The Analytic Signal and the Instantaneous Properties
10(3)
1.5 Computation of the Instantaneous Frequency
13(3)
1.6 Two Groups of Time-Frequency Analysis Methods
16(3)
2 The Gabor Transform
19(28)
2.1 Short-time Fourier Transform
19(4)
2.2 The Gabor Transform
23(3)
2.3 The Cosine Function Windows
26(5)
2.4 Spectral Leakage of Window Functions
31(2)
2.5 The Gabor Limit of Time-Frequency Resolution
33(3)
2.6 Implementation of the Gabor Transform
36(4)
2.7 The Inverse Gabor Transform
40(2)
2.8 Application in Inverse Q Filtering
42(5)
3 The Continuous Wavelet Transform
47(26)
3.1 Basics of the Continuous Wavelet Transform
47(4)
3.2 The Complex Morlet Wavelet
51(3)
3.3 The Complex Morse Wavelet
54(4)
3.4 The Generalised Seismic Wavelet
58(4)
3.5 The Pseudo-frequency Representation
62(3)
3.6 The Inverse Wavelet Transform
65(2)
3.7 Implementation of the Continuous Wavelet Transform
67(2)
3.8 Hydrocarbon Reservoir Characterisation
69(4)
4 The S Transform
73(22)
4.1 Basics of the S Transform
74(3)
4.2 The Generalised S Transform
77(2)
4.3 The Fractional Fourier Transform
79(4)
4.4 The Fractional S Transform
83(3)
4.5 Implementation of the S Transforms
86(2)
4.6 The Inverse S Transforms
88(5)
4.7 Application to Clastic and Carbonate Reservoirs
93(2)
5 The W Transform
95(22)
5.1 Basics of the W Transform
95(4)
5.2 The Generalised W Transform
99(7)
5.3 Implementation of Nonstationary Convolution
106(2)
5.4 The Inverse W Transform
108(1)
5.5 Application to Detecting Hydrocarbon Reservoirs
109(3)
5.6 Application to Detecting Karst Voids
112(5)
6 The Wigner--Ville Distribution
117(34)
6.1 Basics of the Wigner--Ville Distribution (WVD)
117(3)
6.2 Defining the WVD with an Analytic Signal
120(3)
6.3 Properties of the WVD
123(3)
6.4 The Smoothed WVD
126(6)
6.5 The Generalised Class of Time-Frequency Representations
132(2)
6.6 The Ambiguity Function and the Generalised WVD
134(6)
6.7 Implementation of the Standard and Smoothed WVDs
140(7)
6.8 Implementation of the Ambiguity Function and the Generalised WVD
147(4)
7 Matching Pursuit
151(24)
7.1 Basics of Matching Pursuit
151(2)
7.2 Three-stage Matching Pursuit
153(4)
7.3 Matching Pursuit with the Morlet Wavelet
157(2)
7.4 The Sigma Filter
159(4)
7.5 Multichannel Matching Pursuit
163(5)
7.6 Structure-adaptive Matching Pursuit
168(2)
7.7 Three Applications
170(5)
8 Local Power Spectra with Multiple Windows
175(22)
8.1 Multiple Orthogonal Windows
176(2)
8.2 Multiple Windows Defined by the Prolate Spheroidal Wavefunctions
178(2)
8.3 Multiple Windows Constructed by Solving a Discretised Eigenvalue Problem
180(4)
8.4 Multiple Windows Constructed by Gaussian Functions
184(3)
8.5 The Gabor Transform with Multiple Windows
187(4)
8.6 The WVD with Multiple Windows
191(4)
8.7 Prospective of Time-Frequency Analysis without Windowing
195(2)
Appendices
197(22)
A The Gaussian Integrals, the Gamma Function, and the Gaussian Error Functions
197(3)
B Fourier Transforms of the Tapered Boxcar Window, the Truncated Gaussian Window, and the Weighted Cosine Window
200(3)
C The Generalised Seismic Wavelet in the Time Domain
203(2)
D Implementation of the Fractional Fourier Transform
205(1)
E Marginal Properties and the Analytic Signal in the WVD Definition
206(5)
F The Prolate Spheroidal Wavefunctions, the Associated and the Ordinary Legendre Polynomials
211(8)
References 219(8)
Author Index 227(2)
Subject Index 229
Yanghua Wang is a Professor of Geophysics at Imperial College London and the Director of the Resource Geophysics Academy. He is a Fellow of the Royal Academy of Engineering (FREng). He has received the Conrad Schlumberger Award (2021) from the European Association of Geo-scientists & Engineers for his scientific contribution to geophysics.