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.
- Time-variant deconvolution
- Time-variant spectral whitening
- Inverse Q filtering
- Deconvolution strategies
- The problem of nonstationarity