Page 386 - Acquisition and Processing of Marine Seismic Data

7.2 PREDICTIVE DECONVOLUTION 377

primary reflection (P) at 200 ms and its two suc- deconvolution can be applied one more time
cessive multiples (M 1 and M 2 ) at 400 and 600 ms. to remove the second-order multiple using a
Outputs of the predictive deconvolution with prediction lag of α ¼ 350 ms. In Fig. 7.12C, a
corresponding amplitude spectra and autocor- spiking deconvolution using n ¼ 100 ms and
relation traces are computed for a range of pre- α ¼ 2 ms is applied to the seismogram following
diction lag values for a constant operator length the predictive deconvolution to improve
of n ¼ 100 ms. The periodic events such as mul- the temporal resolution. Specifically, the first
tiples in the input time series result in notches in zero crossing time of the autocorrelogram
the amplitude spectrum of the seismogram. (α ¼ 6 ms) can also be used to improve the reso-
Small prediction lags, such as α ¼ 20 ms, shorten lution, which makes the data more band-limited
the seismic wavelet and hence improve the res- (Fig. 7.12D). The application order of predictive
olution, yet do not contribute to the suppression and spiking deconvolutions is changeable and
of multiple amplitudes (Fig. 7.11). However, either predictive or spiking deconvolution can
deconvolution outputs for α ¼ 120 ms and be applied first.
α ¼ 350 ms indicate interesting results. For Fig. 7.13 shows the effects of different opera-
α ¼ 120 ms, the first-order multiple M 1 is tor lengths and prediction lags on a precondi-
completely removed by deconvolution, and tioned real marine shot gather. Predictive
there are almost no amplitudes for M 1 in the deconvolution suppresses the amplitudes in
autocorrelogram. For α ¼ 350 ms, on the other the autocorrelograms in a specific gate between
hand, second-order multiple M 2 is completely (α) and (α + nΔt), where Δt is the sampling inter-
suppressed. That is because the periods of the val, and n is the operator length in time samples.
first- and second-order multiples are 120 and The time length of these gates is nΔt, indicated
350 ms, respectively, indicated by T 1 and T 2 in by double arrows in Fig. 7.13. For instance, in
the autocorrelogram of the input seismogram. the autocorrelograms of the predictive deconvo-
If there are more than one order of multiples lution output for n ¼ 40 ms and α ¼ 100 ms in
in the data, periods of each individual multiples Fig. 7.13, the amplitudes between 100 and
in the autocorrelogram are used as prediction 140 ms are significantly suppressed. If the
lag values and more than one predictive decon- amplitudes corresponding to the multiple
volution can be applied successively to the data, reflections coincide with this gate, then almost
each of which can suppress one individual all of the multiple reflections are removed from
multiple. the shots. For the example shot in Fig. 7.13,
In order to remove a source wavelet from the n ¼ 80 ms and α ¼ 60 ms produce the best
seismic trace, a spiking deconvolution can also deconvolution result, since most of the multiple
be applied following the predictive deconvolu- energy (except that at the far offsets) are within
tion. Fig. 7.12A shows the same synthetic the gate.
seismogram as in Fig. 7.11A. Fig. 7.12B illus- In summary, prediction lag (α) must be longer
trates its predictive deconvolution output for than the time length of the first isolated energy
n ¼ 100 ms and α ¼ 120 ms. Only primary and in the input trace’s autocorrelogram. If not, some
second-order multiple amplitudes exist in the of the amplitudes in the autocorrelation corre-
seismogram since the first-order multiple is sponding to the seismic wavelet will be zeroed
completely removed after predictive deconvolu- out by deconvolution. In practice, the optimal
tion. Amplitudes associated with the first-order output is obtained when prediction lag equals
multiple in the autocorrelogram are diminished, the multiple period. Predictive deconvolution
and the periodic notches in the amplitude suppresses the amplitudes between (α) and
spectrum disappear. If desired, predictive (α + nΔt), and therefore it is preferred to set