Mixed domain method

Instead of taking the minimum of the two surveys, as in equation (3), I took the lower value if it was below some threshold, B₁, and the higher value if it was greater than another threshold, B₂. For values in between I took a scaled linear combination:

$$A(\omega) = \left( \frac{S_{lower}(\omega) - B_2}{B_1 - B_2}... ...1 - S_{lower}(\omega)}{B_1 - B_2} \right) \; S_{higher}(\omega)$$ (7)

For the example shown in Figure 6, I used $B_1 = 10\%$ and $B_2 = 80\%$ of $max\{S(\omega)\}$. The bandwidth equalization was done in the frequency domain and the phase matching in the time domain. Figure 7 shows the spectra of the difference sections for this approach and the standard mixed domain approach. The bandwidth has been increased by a small amount, while the noise level has remained constant, so this approach has worked to a small extent.

 

optimal
Figure 6 Cross-equalization while maximizing bandwidth of difference signal. Left is filtered base survey, center is filtered monitor survey and right is the difference. S/N = 9.24

 

opt.spec Figure 7 Spectra of difference plots. Solid line is standard mixed domain approach, and dashed line is `optimal' mixed domain approach.