Deconvolution and Vertical Seismic Profiles
, by Ronald F. Ullmann
Two methods of deconvolution were tested on vertical seismic profile (VSP)
data for the purpose of finding out which method resolves the events on a
VSP better. The first method of deconvolution was calculated in the time
domain through inverse filters derived through Backus-Gilbert inverse theory.
The second method of deconvolution was calculated in the frequency domain by
dividing the Fourier transform of the trace by the smoothed Fourier transform of
the source waveform. Source waveorms were taken from uphole geophone recordings
and from the first break on the traces recorded by the well geophone. Various
deconvolutions were done with these two different source waveforms to determine
which gave sharper results for the events on the VSP. The following processing
steps were foud to produce the best deconvolved VSP:
1. Before any gain has been applied to the data, window traces from the well
geophone to separate the first break event from the rest of the data.
2. Find the autocorrelation of the source waveforms obtained in step 1.
3. Average the autocorrelation of each trace with the autocorrelations from
neighboring waveforms.
4. Find the Fourier transform of the averaged autocorrelation and smooth it with
a short window function in the frequency domain.
5. Find the Fourier transform of the entire trace and divide it by the smoothed
function found in step 4.
6. Take the inverse Fourier transform of the results of step 5.
STANFORD