Time-Frequency Analysis of Seismic Signals

ISBN-13: 9781119892342 / Angielski / Twarda / 2022 / 256 str.

Y Wang

Spis treści

Preface viii1 Nonstationary signals and spectral properties 11.1 Stationary signals 11.2 Nonstationary signals 51.3 The Fourier transform and the average properties 71.4 The analytic signal and the instantaneous properties 101.5 Computation of the instantaneous frequency 131.6 Two groups of time-frequency analysis methods 172 The Gabor transform 192.1 Short-time Fourier transform 192.2 The Gabor transform 232.3 The cosine function windows 262.4 Spectral leakage 312.5 The Gabor limit of time-frequency resolution 332.6 Implementation of the Gabor transform 362.7 The inverse Gabor transform 402.8 Application in inverse Q Filtering 423 The continuous wavelet transform 473.1 Basics of the continuous wavelet transform 473.2 The complex Morlet wavelet 513.3 The Morse wavelet 543.4 The generalised seismic wavelet 583.5 The frequency representation 623.6 The inverse wavelet transform 643.7 Implementation of the continuous wavelet transform 663.8 Hydrocarbon reservoir characterisation 684 The S transform 734.1 Basics of the S transform 744.2 The generalised S transform 77Time-Frequency vi Analysis of Seismic Signals4.3 The fractional Fourier transform 794.4 The fractional S transform 834.5 Implementation of the S transform 864.6 The inverse S transform 884.7 Application to clastic and carbonate reservoirs 935 The W transform 955.1 Basics of the W transform 955.2 The generalised W transform 995.3 Implementation of nonstationary convolution 1065.4 The inverse W transform 1085.5 Application to detect hydrocarbon reservoirs 1095.6 Application to detect karst voids 1126 The Wigner-Ville distribution 1176.1 Basics of the Wigner-Ville distribution (WVD) 1176.2 Defining the WVD with the analytic signal 1206.3 Properties of the WVD 1236.4 The smoothed WVD 1266.5 The generalised class of time-frequency representations 1326.6 The ambiguity function and the generalised WVD 1346.7 Implementation of the standard and smoothed WVDs 1406.8 Implementation of the ambiguity function and thegeneralised WVD 1477 Matching pursuit 1517.1 Basics of matching pursuit 1517.2 Three-stage matching pursuit 1537.3 Matching pursuit with the Morlet wavelet 1577.4 The sigma filter 1597.5 Multichannel matching pursuit 1637.6 Structure-adaptive matching pursuit 1687.7 Three applications 1708 Local power spectra with multiple windows 1758.1 Multiple orthogonal windows 1768.2 Multiple windows defined by the prolate spheroidalwave functions 1788.3 Multiple windows constructed by solving a discretisedeigenvalue problem 1808.4 Multiple windows constructed by Gaussian functions 1848.5 The Gabor transform with multiple windows 1878.6 The WVD with multiple windows 190Contents viiAppendices 195A The Gaussian integrals, the Gamma function, and theGauss error functions 195B The Fourier transform of the tapered boxcar window,the truncated Gaussian window, and the Blackmanwindow 198C The generalised seismic wavelet 201D The fractional Fourier transform 203E Marginal conditions and the analytic signal in the WVDdefinition 204F Prolate spheroidal wave functions and the associatedLegendre polynomials 209References 215Author index 223Subject index 225

O autorze

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.