Examples
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Series | Geophysical References Series |
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Title | Digital Imaging and Deconvolution: The ABCs of Seismic Exploration and Processing |
Author | Enders A. Robinson and Sven Treitel |
Chapter | 8 |
DOI | http://dx.doi.org/10.1190/1.9781560801610 |
ISBN | 9781560801481 |
Store | SEG Online Store |
Let us now discuss a model consisting of a surface interface overlying two buried interfaces, with the three interfaces separated by arbitrary two-way layer traveltimes. Let the reflection coefficients be given by a, b, c. Let the two-way traveltime between the surface and the first buried interface be S, and let the two-way traveltime between the first buried interface and the second buried interface be T. In other words, the surface reflection coefficient is , the reflection coefficient for the first buried interface is , and the reflection coefficient for the second buried interface is . The Z-transform of the reflectivity is
( )
The right-hand side of the autocorrelation of the reflectivity is
( )
If we replace by 1, we obtain the feedback loop
( )
There are three reverberations. The reverberation between the surface and the first buried interface contributes , the reverberation between the second and third buried interfaces contributes , and the reverberation between the surface and third buried interface contributes . The synthetic trace now is given by the feedforward-feedback filter (Figure 11):
( )
Suppose that . Then the synthetic trace is given by
( )
which is
( )
The shot occurs at time 0, the first primary b occurs at time 2, the first-surface- first-interface multiple occurs at time 4, the second-surface–first-interface multiple occurs at time 6, the second primary occurs at time 7, the third-surface–first-interface multiple occurs at time 8, the peg-leg multiple occurs at time 9, and so on. Figure 11a shows the reflectivity for the case . The leading portion of the corresponding impulsive synthetic trace is shown in Figure 11b.
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Synthetic seismogram with multiples | Small and white reflection coefficients |
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Wavelets | Wavelet Processing |
Also in this chapter
- Introduction
- Polarity
- Reflection coefficients and transmission coefficients
- Ghost reflection
- Layer-cake model
- Synthetic seismogram without multiples
- Water reverberations
- Synthetic seismogram with multiples
- Small and white reflection coefficients
- Appendix H: Exercises