Time domain

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:

$${\bf A s_1} - {\bf s_2} \approx {\bf 0}$$ (6)

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, ${\bf A s_1} - {\bf s_2} = {\bf s_2}$.

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.

 

time
Figure 4 Results of time domain match-filtering. Left is filtered base survey, center is filtered monitor survey and right is the difference. S/N = 9.54

Another advantage of this approach is that the random noise is naturally attenuated in the filtered monitor survey.