Seismic Inverse Q Filtering

1. Introduction to inverse Q filtering.

1.1 The earth Q effect on seismic waves.

1.2 Inverse Q filters.

1.3 The effectiveness of inverse Q filtering.

Part I: Mathematical Q models.

2. Kolsky’s model for seismic attenuation and dispersion.

2.1 Kolsky’s attenuation-dispersion model.

2.2 Modification to the Kolsky model.

2.3 Accurate velocity dispersion correction.

2.4 Comparison with different Q models.

3. Mathematical definition of the earth Q models.

3.1 Mathematical definition of Q.

3.2 Kolsky’s Q model and the complex wavenumber.

3.3 The Strick–Azimi Q model.

3.4 Kjartansson’s constant-Q model.

3.5 Azimi’s second and third Q models.

3.6 Müller’s Q model.

3.7 The Zener or standard linear solid model.

3.8 The Cole–Cole Q model.

3.9 A general linear model.

Part II: Inverse Q filters.

4. Stabilized inverse Q filtering algorithm.

4.1 Basics of inverse Q filtering.

4.2 Numerical instability of inverse Q filtering.

4.3 Stabilized inverse Q filter.

4.4 Comparison with gain-limited inverse Q filter.

4.5 Comparison with a conventional inverse Q filter.

4.6 Synthetic and real data examples.

5. Inverse Q filtering for phase and amplitude separately.

5.1 Phase-only inverse Q filtering.

5.2 Amplitude-only inverse Q filtering.

5.3 Forward Q filtering.

5.4 Summary of inverse and forward Q filters by downward.

continuation.

5.5 Different stabilization schemes.

6. Layered implementation of inverse Q filters.

6.1 The layered approach to inverse Q filtering.

6.2 Inverse Q filtering within a constant-Q layer.

6.3 Phase- or amplitude-only inverse Q filtering.

6.4 Forward Q filtering.

6.5 Application of layered inverse Q filtering.

7. Inverse Q filtering in the Gabor transform domain.

7.1 Stabilized inverse Q filter.

7.2 The Gabor transform.

7.3 Inverse Q filtering by Gabor transform.

7.4 Forward Q filtering by Gabor transform.

7.5 An empirical formula for the stabilization factor.

8. The effectiveness of stabilized inverse Q filtering.

8.1 Inverse Q filtering of a land seismic section.

8.2 Flattening the amplitude spectrum and strengthening.

the relative amplitude.

8.3 Increasing the spectral bandwidth.

8.4 Improving the signal-to-noise ratio.

8.5 Enhancing seismic resolution.

8.6 Sensitivity of the resolution enhancement to Q values.

9. Migration with inverse Q filtering.

9.1 Inverse Q filtered migration in the wavenumberfrequency.

domain.

9.2 Stabilized migration with lateral variation in velocity.

and Q models.

9.3 The implicit finite-difference extrapolator in the spacefrequency.

domain.

9.4 Migration examples.

Part III: Q estimation.

10. Q estimation from vertical seismic profiling data.

10.1 The attenuation effect on VSP waveform.

10.2 Spectral ratio method for Q estimation.

10.3 The multitaper technique for spectral estimation.

10.4 Robust Q estimation from real VSP data.

11. Q analysis from reflection seismic data.

11.1 Q analysis based on amplitude attenuation.

11.2 Q analysis based on amplitude compensation.

11.3 Interval-Q calculation by linear inversion.

11.4 Q analyses on the P-P and P-SV wave sections.

12. Crosshole seismic tomography for the Q model.

12.1 Inverse theory for waveform tomography.

12.2 Issues in real data application.

12.3 Waveform inversion for the velocity model.

12.4 Waveform tomography for the attenuation model.

References.

Author index.

Subject index