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The results of the previous section illustrate the need to consider the
velocitydepth trend as a constraint to the inversion. I used a
SavitzkyGolay smoothing filter Press et al. (1992) to compute the
trend from the sonic log. This filter is particularly wellsuited for this purpose
because it is easy to control the number of samples of the input log that
are used to compute a sample of the smoothed log and the degree of the smoothing
polynomial.
Figure 3 shows the original subsampled log (top) and
the computed velocitydepth trend (bottom) after applying a SavitzkyGolay filter
with 33 points (16 to each side) with a sixthorder smoothing polynomial.
Extrapolation was used in the original log to 16 points off each of the ends of
the log to avoid endeffect problems with the filter. The velocitydepth trend is
well recovered, in particular for the deeper samples. This trend will be used as a
constraint to the inversion.
velocity_depth_trend
Figure 3 Subsampled original sonic log
and velocitydepth trend computed with 33point sixth order SavitzkyGolay
filter.

 
Next: Inversion with the Velocitydepth
Up: Alvarez: Velocity inversion
Previous: Results
Stanford Exploration Project
11/11/2002