Page 346 - Acquisition and Processing of Marine Seismic Data

6.5 DETERMINATION OF DECONVOLUTION PARAMETERS 337

The term on the righthand side of Eq. (6.20) is α ¼ unity (the sampling rate), the process is
the α units advanced version of the autocorrela- equivalent to a spiking deconvolution.
tion function. The actual predictive deconvolu- In general, predictive deconvolution has two
applications:
tion output calculated by convolving the h i
coefficients with the f i input series is given in i. Application for a spiking deconvolution
Table 6.14. The output is a prediction of the input using a unit (or close to unit) prediction
f i series for α ¼ 3 units. Here, the (h 0 , h 1 , h 2 , h 3 , h 4 , lag: used for temporal resolution
h 5 ) series is termed a prediction filter, which
improvement.
yields the predictable components in the seismic
ii. Prediction of the input trace in a future time
trace corresponding to multiple reflections,
period defined by the prediction lag: used to
whereas the (1, 0, 0, h 0 , h 1 , h 2 , h 3 , h 4 )
predict and suppress multiples.
series is known as a prediction error filter, which
yields the error in the prediction process corre- The effects of the spiking and predictive decon-
sponding to primary reflections. volution approaches on the whitening of the
In a generalized form, the normal equations amplitudespectrum,andhenceimprovingtheres-
for prediction lag of α and prediction filter olutionoftheseismicdata,aredifferent.InFig.6.23,
length of n can be rewritten as (Peacock and a stack section without deconvolution iscompared
Treitel, 1969) to its versions with spiking and predictive decon-
volutionapplications,alongwiththeircorrespond-
2 3 2 3 2 3
a 0 a 1 a 2 … a n 1 h 0 a α ing amplitude spectra and autocorrelograms. In
general, spiking deconvolution strengthens the
6 7 6 7 6 7
6 a 1 a 0 a 1 … a n 2 7 6 h 1 7 6 a α +1 7
6 7 6 7 6 7 high-frequency components in the seismic data
6 7 6 7 6 7
6 a 2 a 1 a 0 … a n 3 7 6 h 2 7 6 a α +2 7 and provides a higher resolution output.
6 7 6 7 6 7
6 7 6 7 6 7
: : : : : :
6 … 7 6 7 ¼ 6 7
6 7 6 7 6 7
6 7 6 7 6 7
6 : : : … : 7 6 : 7 6 : 7 6.5 DETERMINATION OF
6 7 6 7 6 7
DECONVOLUTION PARAMETERS
6 7 6 7 6 7
: : : : : :
6 … 7 6 7 6 7
4 5 4 5 4 5
a 0 h n 1 a α + n 1 Before digital seismic recording, the aim of
a n 1 a n 2 a n 3 …
(6.21) prestack deconvolution applied to marine seis-
mic data was to remove the multiple reflections
The design of a prediction filter needs only the rather than enhance the resolution. In practice,
autocorrelation of the input. According to deconvolution is applied to prestack marine
Assumption 6, the reflectivity series is random, seismic data on a trace-by-trace basis on the shot
and therefore everything in the seismic data or CDP gathers. Since deconvolution is very sen-
(such as primary reflections) except the multi- sitive to the noise, data must be properly precon-
ples cannot be predicted. In fact, a predictive ditioned to remove the random and coherent
deconvolution is a general technique that also noise during preprocessing.
involves the spiking deconvolution. Before the application, the parameters that
In summary, a prediction error filter shortens should be properly designated are the deconvo-
the input wavelet with a length of (n + α) into an lution operator length and prediction lag. In fact,
output wavelet with a length of α. Therefore, pre- there is no exact mathematical rule that restricts
dictive deconvolution is a general approach that the prediction lag and/or operator length,
can control how shortened the wavelet is, and and these are commonly determined by several
thus it also controls the improvement in the tem- tests based on user experience with the autocor-
poral resolution (Peacock and Treitel, 1969). For relograms of seismic traces. In addition, the