Results

The top left panel of Figure 2 shows a comparison between the synthetic trace obtained from the real sonic log, and the one obtained with the genetic algorithm using the L₁ norm. The top right panel shows a similar comparison between the original and the inverted log. Although the match of the seismic traces is not perfect, the main features in the original trace were remarkably well recovered. The result for the sonic logs, however, is not so auspicious and the lack of the general velocity-depth trend makes it very difficult to evaluate the ``goodness'' of the match. If we forget about the trend and examine the details in the logs, we can see that most features of the log were indeed recovered, but the overall result is not satisfactory. The bottom panels show the same comparisons using the L₂ norm. The results are similar: good match of the seismic traces and poor match of the sonic logs because of our inability to recover the velocity-depth trend.

 

L1L2_inv_no_trend
Figure 2 Comparison of the synthetic trace and the inverted trace (top left panel) and the original log and the inverted log (top right panel) using the L₁ norm. The bottom panels show similar comparisons using the L₂ norm.