Page 326 - Acquisition and Processing of Marine Seismic Data

6.1 CONVOLUTIONAL MODEL 317

TABLE 6.1 Different Deconvolution Techniques and response.Fig.6.5Bschematicallyshowsthereflec-
Their Application Areas tivity series obtained from the earth model given
in Fig. 6.5A. In reality, the reflectivity series of the
earth’sinteriorismuchmorecomplicatedandcan
Deconvolution Application
be obtained from sonic and density logs from
Method
Spiking deconvolution Converts the source wavelet in nearby wells for computations of 1D synthetic
the seismic data into a spike and
sections.
improves the temporal resolution
The convolutional model suggests that the
Predictive Predicts and removes multiple recorded seismogram is obtained by convolving
deconvolution reflections from the seismic data
the reflection coefficients of the interfaces with
Waveform Transforms one waveform into the source wavelet. Fig. 6.6A shows a minimum
deconvolution another (generally converts a phase source wavelet which is convolved by
mixed phase wavelet into the reflection coefficients or the earth’s reflectivity
minimum phase)
series (Fig. 6.6B) to obtain the synthetic seismic
Adaptive Deconvolution parameters are trace (Fig. 6.6C) where each interface is repre-
deconvolution automatically updated during the sented by an individual source wavelet after
application
convolution. If there is sufficient distance
Homomorphic Transforms the data into between the interfaces (e.g., if they are thick
deconvolution cepstrum domain where the enough) – in other words, if there is enough time
wavelet and reflectivity series can
be decomposed span between the successive reflection coeffi-
cients in the reflectivity series – then it is possible
Maximum entropy Uses entropy approach to obtain to discriminate each individual reflection from
(Burg) deconvolution random and predictable
components in the data every interface on the trace. However, as in
the seismogram shown in Fig. 6.6C, the events
Minimum entropy Tries to reduce the disorder of the from closely spaced interfaces overlap, since
deconvolution signal in order to improve the
vertical resolution the source wavelet has a time length determined
by its dominant frequency, and this phenome-
Surface consistent Decomposes the signal into non is known as interference. Attaining the
deconvolution source, receiver, offset, and
reflectivity coefficients, generally reflectivity series from seismic data by decom-
used for amplitude vs. offset posing the interfered events is actually the
(AVO) studies inverse of the convolution process and is termed
deconvolution.
Frequency domain Deconvolution filter operator is
deconvolution determined in frequency domain The convolutional model implies that the
recorded seismogram involves the source wave-
let reappearing at every individual reflection
event. As a simple approach, if we can remove
separates.Fig.6.5Ashowsasimpleearthmodelof the effect of the source wavelet from the seismic
four horizontal layers to calculate the reflection traces, then what we have is the earth’s reflectiv-
coefficients using layer velocities. The series con- ity series, which is the ultimate goal to acousti-
sisting of the earth’s reflection coefficients from cally define the subsurface. Deconvolution
several successive interfaces is termed the tries to derive the reflectivity series (or impulse
impulse response or reflectivity series. Theoreti- response) of the subsurface by eliminating the
cally, this is the series obtained as the earth’s seis- source wavelet from the recorded seismogram,
mic response if an impulse could be used as the in ideal conditions converting it into a spike.
source signal, which is why we call it the impulse By means of the convolutional model, the