It is important to mention that the final solution depends not so much on the initial form of the wavelet, but on its initial phase. For the examples in Figures 8 and 9 the same final solution was reached when a delayed spike was used as the initial wavelet, as long as the delay was equal to the lag of the absolute maximum of the used wavelet.

The iterative algorithm described by equation (17) was
applied to the same synthetic trace of the previous sections.
Figure 8 compares the results of three different
deconvolution approachs: predictive decon *(c)*; ICP decon using
the minimum-phase wavelet corresponding to a smoothed version
of the trace spectrum *(e)*; and convolution with the inverse filter of
the same minimum-phase wavelet *(d)*.
As we should expect, *(c)* and *(d)*
are very similar because both methods are linear, and while one uses
a minimum-phase wavelet, the other implicitly assumes the wavelet
to be minimum-phase. Here again the ICP decon provides the sharper version
of the reflectivity sequence since it keeps the same frequency
distribution as the original series.

Figure 8

Figure 9 compares the true wavelet with the initial and final wavelets corresponding to the application of the ICP decon to the trace of Figure 8. The final estimated wavelet resembles the true wavelet, except by a constant time-shift, and some small oscillations on the tail.

Figure 9

Finally, I applied the ICP decon to a CMP gather recorded for British
Petroleum in a deep-water environment of Alaska off-shore.
Figure 10 shows *(a)* the unprocessed CMP gather,
*(b)* the same data
after predictive deconvolution, and *(c)* after the ICP deconvolution.
The two deconvolution results are very similar, except by a slightly
improved sharpness
of the ICP deconvolution, as can be observed in the two reflections
between 1.2 and 1.3 seconds; in *(a)* it is not possible to resolve the
polarity of the reflections, while in *(b)* they were reduced to two
main white events with small black side-lobs, and in *(c)* the black
side-lobs have almost disappeared.
We can also notice that in *(c)* the ocean floor reflection was
also reduced to a single white event, without the black successor
that appear in *(a)* and *(b)*.

I plan next, to extend the method to works in a multi-channel basis. Possible advantages of this extension are an improvement in the stability of the process, and an a more consistent estimation of the wavelet.

Figure 10

1/13/1998