Appendix O: Exercises

Digital Imaging and Deconvolution: The ABCs of Seismic Exploration and Processing

Series	Geophysical References Series
Title	Digital Imaging and Deconvolution: The ABCs of Seismic Exploration and Processing
Author	Enders A. Robinson and Sven Treitel
Chapter	14
DOI	http://dx.doi.org/10.1190/1.9781560801610
ISBN	9781560801481
Store	SEG Online Store

1. Discuss what is meant by making temporally and spatially variant Q compensation to seismic data.
2. Discuss why, when absorption is present, the more precise convolutional model of the seismic trace with a time-varying wavelet is useful.
3. Dispersion is the variation of velocity with frequency. Dispersion distorts the waveform shape, so it appears that peaks and troughs advance toward (or recede from) the bulk of the waveform as it travels. The dispersion of seismic body waves is quite small under most circumstances, but surface waves can show appreciable dispersion in the presence of near-surface velocity layering. In a more precise version of the absorption model, high frequencies travel faster than low frequencies do, and thus the propagating wavelet is distorted. Why, in seismic processing, is it usually assumed that each frequency travels at the same velocity?
4. What is multigate deconvolution? A problem with this technique is that the filters must be derived from smaller windows than otherwise are used. As a result, some of the shorter windows might not meet the requirements necessary for the statistical assumptions made. Such short-windowed zones often exhibit phase distortions at the point of overlap.
5. How does the inverse Q filter correct for the effects of attenuation? After inverse Q filtering, will the conditions of single-gate deconvolution be filled more closely?
6. Devise a technique that uses an iterative convolution of short operators to do time-variant inverse Q filtering.
7. Why is the interval velocity divided by 100 a good approximation for instantaneous Q?
8. In words, describe the three pulses for Q = 50 and their respective inverses for depths 1, 2, and 3 km, as shown in Figure O-1.
9. In words, describe each of the items shown in Figure O-2.
10. Why do Q values generally increase with increasing time?
11. For a section with an effective Q of 100, show that the difference in input for 100 Hz and 30 Hz is about 24.5 dB — that is, an increase in amplitude of 16.8.

Figure O-1.  Constant Q pulses and their inverses for depths 1, 2, and 3 km.

Figure O-2.  A constant Q pulse and its inverse, the log-amplitude spectrum of each, and the phase spectrum of each.

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Also in this chapter

• Attenuation
• Useful attenuation mechanisms
• Practical considerations

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