One-dimensional well-ties

Figure 1 shows a seismic section from which I drew two hypothetical sonic logs. The task was then to match them to each other. The fault that cuts through the section and the poor data quality in the lower part cause problems from matching algorithms.

 

data Figure 1 Seismic section from which two hypothetical sonic logs were drawn. ${\bf d}_1$ was drawn at X=31 km and ${\bf d}_2$ was drawn at X=32 km.

Figures 2 and 3 compare the results of the two warping algorithms. The shaping filters themselves change more smoothly as a function of time than the local cross-correlelograms. The warped difference (trace 3 in both figures) also contains less energy in Figure 3 than Figure 2 indicating the shaping filters have found a better match. Clip levels for the wiggle displays are the same for both Figures 2 and 3.

 

xcorr1
Figure 2 Cross-correlation results. The top panel shows cross-correlelograms and picked maxima. The bottom panel shows ${\bf d}_1$ (0), ${\bf d}_2$ (1), ${\rm warped} \; {\bf d}_1$ (2), ${\bf d}_2 - {\rm warped} \; {\bf d}_1$ (3), and ${\bf d}_2 - {\bf d}_1$ (4).

 

xcorr2
Figure 3 Non-stationary shaping filter results. The top panel shows cross-correlelograms and picked maxima. The bottom panel shows ${\bf d}_1$ (0), ${\bf d}_2$ (1), ${\rm warped} \; {\bf d}_1$ (2), ${\bf d}_2 - {\rm warped} \; {\bf d}_1$ (3), and ${\bf d}_2 - {\bf d}_1$ (4).