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Seismic Inverse Q Filtering

248 pages
Seismic inverse Q filtering is a data processing technology for enhancing the resolution of seismic images. It employs a wave propagation reversal procedure that compensates for energy absorption and corrects wavelet distortion due to velocity dispersion. By compensating for amplitude attenuation, seismic data can provide true relative-amplitude information for amplitude inversion and subsequent reservoir characterization. By correcting the phase distortion, seismic data with enhanced vertical resolution can yield correct timings for lithological identification.

This monograph presents the theory of inverse Q filtering and a series of algorithms, collected with the following selection criteria in mind: robustness, effectiveness and practicality.

The book is written for processing geophysicists who are attempting to improve the quality of seismic data in terms of resolution and signal-to-noise ratio, as well as for reservoir geophysicists who are concerned about seismic fidelity in terms of true amplitudes, true timings and true frequencies. It will also be particularly valuable as a guide for seasoned geophysicists who are attempting to develop seismic software for various research settings. Finally, it can be used as a reference work or textbook for postgraduate students in seismic and reservoir geophysics.

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Contents Preface viii 1 Introduction to inverseQfiltering 1 1.1 The earthQ2effect on seismic waves 1.2 InverseQ filters 5 1.3 The effectiveness of inverseQfiltering 8 Part I MathematicalQmodels 15 2 Kolsky’s model for seismic attenuation and dispersion 17 2.1 Kolsky’s attenuationdispersion model 18 2.2 Modification to the Kolsky model 19 2.3 Accurate velocity dispersion correction 22 2.4 Comparison with differentQmodels 25 3 Mathematical definition of the earthQmodels 39 3.1 Mathematical definition ofQ 40 3.2 Kolsky’sQmodel and the complex wavenumber 44 3.3 The StrickAzimiQ model 46 3.4 Kjartansson’s constantQmodel 46 3.5 Azimi’s second and thirdQmodels 47 3.6 Müller’sQ model 48 3.7 The Zener or standard linear solid model 50 3.8 The ColeColeQ model 52 3.9 A general linear model 54
Part II InverseQfilters 57 4 Stabilized inverseQ59filtering algorithm 4.1 Basics of inverseQfiltering 60 4.2 Numerical instability of inverseQfiltering 62 4.3 Stabilized inverseQfilter 66 4.4 Comparison with gainlimited inverseQfilter 68 4.5 Comparison with a conventional inverseQfilter 74 4.6 Synthetic and real data examples 79 5 InverseQ85filtering for phase and amplitude separately 5.1 Phaseonly inverseQ86 filtering 5.2 Amplitudeonly inverseQ87 filtering 5.3 ForwardQ90 filtering 5.4 Summary of inverse and forwardQfilters by downward continuation 93 5.5 Different stabilization schemes 95 6 Layered implementation of inverseQfilters 99 6.1 The layered approach to inverseQfiltering 100 6.2 InverseQfiltering within a constantQlayer 103 6.3 Phase or amplitudeonly inverseQfiltering 107 6.4 ForwardQfiltering 110 6.5 Application of layered inverseQfiltering 113 7 InverseQfiltering in the Gabor transformdomain119 7.1 Stabilized inverseQfilter 120 7.2 The Gabor transform 122 7.3 InverseQ125filtering by Gabor transform 7.4 ForwardQ126filtering by Gabor transform 7.5 An empirical formula for the stabilization factor 128 8 The effectiveness of stabilized inverseQfiltering1338.1 InverseQfiltering of a land seismic section 134 8.2 Flattening the amplitude spectrum and strengthening the relative amplitude 136 8.3 Increasing the spectral bandwidth 139 8.4 Improving the signaltonoise ratio 140 8.5 Enhancing seismic resolution 141
8.6 Sensitivity of the resolution enhancement toQvalues 143
9 Migration with inverseQfiltering 147 9.1 InverseQfiltered migration in the wavenumber frequency domain 148 9.2 Stabilized migration with lateral variation in velocity andQ models 156 9.3 The implicit finitedifference extrapolator in the space frequency domain 159 9.4 Migration examples 162 Part IIIQestimation 167
10Qestimation from vertical seismic profiling data 169 10.1 The attenuation effect on VSP waveform 170 10.2 Spectral ratio method forQ174 estimation 10.3 The multitaper technique for spectral estimation 176 10.4 RobustQestimation from real VSP data 181 11Q187analysis from reflection seismic data 11.1Q analysis 188based on amplitude attenuation 11.2Qanalysis based on amplitude compensation 195 11.3 Correction of spherical divergence prior toQanalysis 199 11.4Qanalyses on thePPandPSVwave sections 201 12 Crosshole seismic tomography for theQmodel 209 12.1 Inverse theory for waveform tomography 211 12.2 Issues in real data application 215 12.3 Waveform inversion for the velocity model 218 12.4 Waveform tomography for the attenuation model 222 References 227 Author index 235 Subject index 237