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I just showed that the inclusion of
the velocity-depth trend increased significantly the match between the original
and the inverted sonic log. The question now is: Why didn't we get an even better
match in the sonic logs? An obvious explanation is that the sonic log in this case
was sub-sampled to 10 feet which is still a very thin interval when it comes to
the depth resolution that we can achieve with typical seismic data. In order
to get a better match we would need higher frequencies, so
there is always a limit in the quality of the match that we can reasonably expect
to obtain in the inversion of the sonic log. To illustrate this point,
Figure shows the same comparison as in
the bottom panles of Figure except that the peak
frequency of the
Ricker wavelet was halved. Clearly, the lack of high frequencies have a very
detrimental effect in the quality of the match of the sonic logs. See in
particular the depth intervals between about 300-400 ft, 450-550 ft and
700-800 ft.
L2_inv_trend_low_freq
Figure 5 Comparison of reference and
matched trace (left panel) and of original and inverted log using the
L2 norm when the velocity-depth trend was taken into account and the
peak frequency of the Ricker wavelet was halved.
It should also be noted that the example here is not very realistic because I used
the exact same approach to compute the seismic data to be matched and
to compute the trial solutions. In a real situation the reference trace will
be obtained from a real seismic survey whereas the trial solutions will still
be computed with a procedure similar to the one used here (perhaps improved by
allowing random noise or multiples or attenuation). Therefore, there will be
reasons other than the velocity-depth trend or the frequency content of the data
that will play a role. The estimation of the seismic wavelet, for example, is
well-recognized as a very important issue when inverting for real data.
Next: Conclusions and Future Work
Up: Inversion with the Velocity-depth
Previous: Inversion with the Velocity-depth
Stanford Exploration Project
11/11/2002