In the time domain, the bandwidth and phase problems are not as easily separable, since it is difficult to constrain the phase of a time domain filter. However, the two steps can be tackled together by designing a filter on the training window that maps the monitor survey, s2, onto the base survey, s1, minimizing the regression:
This approach effectively looks for components of s1 that are present in s2. If there are none, then A will equal 0, and the difference, .
The results of match-filtering in the time-domain are shown in Figure 4. The approach was at least as successful as the frequency domain approach, although there were only 12 free coefficients in the filter compared to several hundred in the frequency domain approach.
Another advantage of this approach is that the random noise is naturally attenuated in the filtered monitor survey.