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# Seismic Amplitude Inversion in Reflection Tomography

- 1st Edition, Volume 33 - February 25, 2003
- Author: Yanghua Wang
- Language: English
- Paperback ISBN:9 7 8 - 0 - 4 4 4 - 5 4 2 6 0 - 1
- eBook ISBN:9 7 8 - 0 - 0 8 - 0 5 4 0 8 7 - 0

This is the first book of its kind on seismic amplitude inversion in the context of reflection tomography. The aim of the monograph is to advocate the use of ray-amplitude data,… Read more

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Request a sales quoteThe 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.

**1. Introduction to amplitude inversion.**Introduction. Velocity-depth ambiguity in traveltime inversion. Resolving ambiguity by using amplitude information. Overview of amplitude inversion. Analytical expression for the geometrical spreading function for layered structures.

**2. Traveltime and ray-amplitude in heterogeneous media.**Introduction. Bending ray tracing method. Traveltime and its perturbations. Propagator of paraxial rays and geometrical spreading. Ray perturbations due to model perturbations. Ray amplitude.

**3. Amplitude coefficients and approximations.**Introduction. The Zoeppritz equations. The pseudo-p

^{2}expressions. Quadratic expressions in terms of elastic contrasts. Accuracy of the quadratic approximations. Amplitude coefficients represented as a function of three elastic parameters. Three elastic parameters from amplitude inversion. Implication for fluid substitution modelling.

**4. Amplitude inversion for interface geometry.**Introduction. Parameterization and forward modelling. Subspace gradient inversion method. A simple example of reflection amplitude inversion. Inversion for an interface represented as a sum of harmonic functions. Stability of the amplitude inversion. Strategy for the choice of &Dgr;k and M. Discussion.

**5. Amplitude inversion for velocity variation.**Introduction. Amplitude dependence on slowness perturbation. Inversion algorithm. Inversion example of 1-D slowness distribution. Constraining higher wavenumber components. Robustness of the inversion in the presence of model error or data noise. Inversion of arbitrary smooth velocity anomalies. Discussion.

**6. Sensitivities of traveltimes and amplitudes in joint inversion.**Introduction. The Hessian and the norm in model space. Sensitivities to interface geometry. Sensitivities to 2-D slowness variation. Inversion formula. Joint inversion for an interface. Joint inversion for slowness. Discussion.

**7. Amplitude inversion of a multi-layered structure.**Introduction. Forward calculation and inverse method. Preliminary inversion test. Damped subspace method. Multi-scale scheme. Multi-stage damped subspace method.

**8. Practical approach to application.**Introduction. Amplitudes estimated from migrated gathers. Demigration of reflection amplitudes. Winnowing amplitudes by LOESS. Inversion procedure. Inversion results.

**9. Simultaneous inversion for model geometry and elastic parameters.**Introduction. Ray-amplitude and its approximation. Inversion method. Inversion example. Measurements for lithological interpretation. Structural effects on amplitude variation.

**10. Decomposition of structural effect and AVO attributes.**Introduction. Decomposition of ray-amplitude. The inverse problem. Sample dataset of gas-water contact. Inversion results. The Chebyshev spectra of the AVO attributes.

**11. Amplitude tomography in practice.**Introduction. Estimate of amplitudes, traveltimes and data uncertainties. Tomographic inversion incorporating more information and using an improved forward calculation. Consideration of factors influencing amplitudes. Turning-ray tomography for near-surface velocity structure and attenuation. Prestack seismic trace inversion for ray elastic impedance.

**Appendices.**Derivation of the geometrical spreading function. Derivation of reflection amplitude demigration. References. Author Index. Topic Index.

- No. of pages: 270
- Language: English
- Edition: 1
- Volume: 33
- Published: February 25, 2003
- Imprint: Pergamon
- Paperback ISBN: 9780444542601
- eBook ISBN: 9780080540870

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