Page 358 - Acquisition and Processing of Marine Seismic Data

6.7 MAXIMUM ENTROPY (BURG) DECONVOLUTION 349

prediction lag is α ¼ 8 ms, which both widens aiming to improve the spectral content of the
the amplitude spectrum and suppresses the seismic data based on the maximum entropy
amplitudes in the autocorrelograms. concept. The basic principle is to select a spec-
trum corresponding to the most unpredictable
6.6 POSTSTACK series that has an autocorrelogram conforming
DECONVOLUTION the known series. It was first applied to seismic
data by Burg (1967) to improve resolution
using the power spectrum estimation algorithm,
Although it is a general convention to apply
which was indeed a different approach to the
the deconvolution to prestack data, due to a
power spectrum calculation.
number of practical reasons, deconvolution
If the Fourier transform of a given f(t) series is
can also be applied to stack sections, which is
known as deconvolution after stack (DAS). F(ω), an H(ω) transfer function whitening the f(t)
These reasons include series is defined as (Ulrych, 1972)
• After prestack deconvolution, a minor F ωðÞH ωðÞ ¼ k (6.22)
wavelet effect remains in the seismic data where k is given by
because almost none of the deconvolution
2 2 2
j
assumptions are entirely satisfied, and this j F ωðÞj ¼ k = H ωðÞj (6.23)
residual wavelet effect can be removed by a where the absolute value sign means amplitude
poststack deconvolution. spectrum. The righthand side of Eq. (6.23) is an
• Because the stack section is an approximation estimation of the power of the f(t) function.
to a zero-offset section, predictive Accordingly, this approach can also be used to
deconvolution can be successful in widen the amplitude spectrum of the seismic data
suppressing the multiples on the stack data. based on a prediction-error filter. Burg (1967) cal-
culated the autocorrelation function in normal
Fig. 6.35 shows an example application of
equations given by Eq. (6.18),minimizing
poststack deconvolution. After deconvolution,
the power of a prediction filter applied to the data
the amplitude spectrum widens to include both
both in forward and backward directions. This
high- and low-frequency amplitudes, indicating
method is today known as the Burg algorithm,
a significant temporal resolution improvement.
based on the maximum entropy theory, and it
Since migration may change the period of the
is a powerful spectral balancing technique
multiples, DAS is generally applied before
(Ulrych, 1972).
migration. DAS parameters are determined as
The only parameter to be determined for Burg
in the parameter determination for prestack
deconvolution is the operator length. Fig. 6.36
deconvolution: A new autocorrelation gate and
a deconvolution design gate are picked, and showsananalysisofBurgdeconvolutiononamin-
the operator length and prediction lag parame- imum phase synthetic seismogram for different
ters can be determined from autocorrelograms operator lengths. Shorter operator lengths leave
of the stack section. some residual noise, the amplitudes of which
decrease as the operator length increases. For this
synthetic trace, n ¼ 100 ms is suitable. Fig. 6.37
6.7 MAXIMUM ENTROPY (BURG) shows a similar analysis on a marine shot gather
DECONVOLUTION for different operator lengths. As the operator
length increases, the amplitudes in the autocorre-
The term entropy determines the amount of lation series are diminished, and the amplitude
disorder in a given system. Maximum entropy spectrum becomes broader after deconvolution,
is an alternative spectral estimation approach indicating a significant improvement in the