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Table of contents
- Contentsxiii
- Prefacevii
- Introductionix
- Chapter 1. Introduction to amplitude inversion1
- 1.1 Introduction1
- 1.2 Velocity-depth ambiguity in traveltime inversion3
- 1.3 Resolving ambiguity by using amplitude information4
- 1.4 Overview of amplitude inversion7
- 1.5 Analytical expression for the geometrical spreading function for layered structures11
- Chapter 2. Traveltime and ray-amplitude in heterogeneous media15
- 2.1 Introduction15
- 2.2 Bending ray tracing method17
- 2.3 Traveltime and its perturbations20
- 2.4 Propagator of paraxial rays and geometrical spreading23
- 2.5 Ray perturbations due to model perturbations27
- 2.6 Ray amplitude32
- Chapter 3. Amplitude coefficients and approximations35
- 3.1 Introduction35
- 3.2 The Zöppritz equations36
- 3.3 The pseudo-p 2 expressions38
- 3.4 Quadratic expressions in terms of elastic contrasts39
- 3.5 Accuracy of the quadratic approximations41
- 3.6 Amplitude coefficients represented as a function of three elastic parameters44
- 3.7 Three elastic parameters from amplitude inversion45
- 3.8 Implication for fluid substitution modelling48
- Chapter 4. Amplitude inversion for interface geometry51
- 4.1 Introduction51
- 4.2 Parameterization and forward modelling52
- 4.3 Subspace gradient inversion method54
- 4.4 A simple example of reflection amplitude inversion57
- 4.5 Inversion for an interface represented as a sum of harmonic functions64
- 4.6 Stability of the amplitude inversion70
- 4.7 Strategy for the choice of Ak and M72
- 4.8 Discussion76
- Chapter 5. Amplitude inversion for velocity variation79
- 5.1 Introduction79
- 5.2 Amplitude dependence on slowness perturbation80
- 5.3 Inversion algorithm83
- 5.4 Inversion example of 1-D slowness distribution87
- 5.5 Constraining higher wavenumber components89
- 5.6 Robustness of the inversion in the presence of model error or data noise93
- 5.7 Inversion of arbitrary smooth velocity anomalies95
- 5.8 Discussion101
- Chapter 6. Sensitivities of traveltimes and amplitudes in joint inversion103
- 6.1 Introduction103
- 6.2 The Hessian and the norm in model space105
- 6.3 Sensitivities to interface geometry111
- 6.4 Sensitivities to 2-D slowness variation125
- 6.5 Inversion formula131
- 6.6 Joint inversion for an interface135
- 6.7 Joint inversion for slowness136
- 6.8 Discussion140
- Chapter 7. Amplitude inversion of a multi-layered structure143
- 7.1 Introduction143
- 7.2 Forward calculation and inverse method144
- 7.3 Preliminary inversion test148
- 7.4 Damped subspace method152
- 7.5 Multi-scale scheme155
- 7.6 Multi-stage damped subspace method157
- Chapter 8. Practical approach to application163
- 8.1 Introduction163
- 8.2 Amplitudes estimated from migrated gathers165
- 8.3 Demigration of reflection amplitudes169
- 8.4 Winnowing amplitudes by LOESS172
- 8.5 Inversion procedure174
- 8.6 Inversion results177
- Chapter 9. Simultaneous inversion for model geometry and elastic parameters183
- 9.1 Introduction183
- 9.2 Ray-amplitude and its approximation184
- 9.3 Inversion method185
- 9.4 Inversion example190
- 9.5 Measurements for lithological interpretation195
- 9.6 Structural effects on amplitude variation198
- Chapter 10. Decomposition of structural effect and AVO attributes201
- 10.1 Introduction201
- 10.2 Decomposition of ray-amplitude202
- 10.3 The inverse problem204
- 10.4 Sample dataset of gas-water contact206
- 10.5 Inversion results209
- 10.6 The Chebyshev spectra of the AVO attributes212
- Chapter 11. Amplitude tomography in practice217
- 11.1 Introduction217
- 11.2 Estimate of amplitudes, traveltimes and data uncertainties219
- 11.3 Tomographic inversion incorporating more information and using an improved forward calculation221
- 11.4 Consideration of factors influencing amplitudes222
- 11.5 Turning-ray tomography for near-surface velocity structure and attenuation226
- 11.6 Prestack seismic trace inversion for ray elastic impedance227
- Appendices235
- A.1 Derivation of the geometrical spreading function235
- A.2 Derivation of reflection amplitude demigration239
- References243
- Author Index251
- Topic Index253
- Vendor Elsevier S & T
- SKU 9780080442433
- ISBN-13 9780080540870
Do you have questions about this book?
The emphasis of seismic exploration is on imaging techniques, so that seismic section can be interpreted directly as a geological section. In contrast it is perhaps ironic that, in decades of industrial seismology, one major aspect of waveform data that potentially is easier to measure and analyse has generally been ignored. That is, the information content of seismic amplitudes. Perhaps the potential complexity has deterred most researchers from a more thorough investigation of the practical use of seismic amplitude data. The author of this volume presents an authoritative and detailed study of amplitude data, as used in conjunction with traveltime data, to provide better constraints on the variation of seismic wave speed in the subsurface.
One of the fundamental problems in conventional reflection seismic tomography using only traveltime data is the possible ambiguity between the velocity variation and the reflector depth. The inclusion of amplitude data in the inversion may help to resolve this problem because the amplitudes and traveltimes are sensitive to different features of the subsurface model, and thereby provide more accurate information about the subsurface structure and the velocity distribution. An essential goal of this monograph is to make the amplitude inversion method work with real reflection seismic data.
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