Frequency-domain deconvolution

**Seismic Data Analysis**
Series	Investigations in Geophysics
Author	Öz Yilmaz
DOI	http://dx.doi.org/10.1190/1.9781560801580
ISBN	ISBN 978-1-56080-094-1
Store	SEG Online Store

Spectral flattening can be achieved by an alternate approach in the frequency domain. As discussed in Appendix B.4, minimum-phase spiking deconvolution can be formulated in the frequency domain. Alternatively, we can flatten the amplitude spectrum without modifying the phase. This is called zero-phase frequency-domain deconvolution. When performed over multiple time gates down the trace, it is essentially equivalent to time-variant spectral flattening. If we only want to flatten the spectrum, then the approach shown in Figure 2.6-15 can be taken.

Although the domains of operations may differ, both minimum-phase frequency-domain and Wiener-Levinson deconvolution techniques should yield equivalent results. Differences between the results shown in Figures 2.6-11 and 2.6-16 mainly are due to their computational aspects.

The zero-phase frequency-domain deconvolution aimed at achieving time-variant spectral whitening requires partitioning the input seismogram into small time gates, as well as designing and applying the process described in Figure 2.6-15 to each gate, individually. Figure 2.6-17 shows the field records after zero-phase frequency-domain deconvolution. The output is comparable to the time-variant spectral flattening output shown in Figure 2.6-12.

Figure 2.6-11 Spiking deconvolution applied to the CMP gathers in Figure 2.6-10.
Figure 2.6-12 Time-variant spectral whitening (TVSW) applied to the CMP gathers in Figure 2.6-10. Compare this with Figures 2.6-11, 2.6-16, and 2.6-17.
Figure 2.6-15 A flowchart for a frequency-domain deconvolution.
Figure 2.6-16 Minimum-phase frequency-domain deconvolution applied to the CMP gathers in Figure 2.6-10. Compare this with Figures 2.6-11, 2.6-12, and 2.6-17.
Figure 2.6-17 Zero-phase frequency-domain deconvolution applied to the CMP gathers in Figure 2.6-10. Compare this with Figures 2.6-11, 2.6-12, and 2.6-16.