Page 330 - Acquisition and Processing of Marine Seismic Data

6.2 ASSUMPTIONS FOR DECONVOLUTION 321

Amplitude spectra
Time
t=0 Amplitude
(A) Minimum phase

Time
t=0
(B) Maximum phase (E) 0 Frequency

Phase spectra
p
Time Maximum phase
t=0
(C) Mixed phase Mixed phase
Zero phase
Phase 0 Frequency
Minimum phase
Time
t =0
(D) Zero phase (F) −p
FIG. 6.8 Schematic illustration of (A) minimum, (B) maximum, (C) mixed, and (D) zero phase wavelets. (E) All of these
wavelets have the same amplitude spectrum, and (F) the only difference in frequency domain is their phase spectra.

and maximum phase. Fig. 6.8 shows their sche- source wavelet in the seismic trace is not mini-
matic displays with corresponding amplitude mum phase, the deconvolution produces unsta-
and phase spectra. The wavelet energy is ble results. In such cases, it is necessary to
front-loaded, middle-loaded, and back-loaded convert the source wavelet into its minimum
for minimum phase, mixed phase, and maxi- phase equivalent. Although Vibroseis data in
mum phase wavelets, respectively. A zero phase land surveys is zero phase, and water gun data
wavelet is symmetrical with a maximum at time is maximum or mixed phase, fortunately the
zero. Zero phase wavelets have energy before remaining land and marine impulsive sources
time zero, which makes them noncausal, and generally produce minimum phase source
therefore they are not physically realizable. signals.
A zero phase wavelet has a shorter duration
than its minimum phase equivalent, which 6.2.6 Assumption 6: Random Reflectivity
makes it a wavelet with higher resolving power.
All of the wavelets in Fig. 6.8 are of the same This assumption suggests that the reflectivity
amplitude spectrum; the only difference is their series is random. Although it is commonly not
phase spectra. easy to understand the yields of this simple
The phase characteristics of the source wave- assumption, it is one of the most important pre-
let embedded in the seismic traces have great requisites that enable us to perform deconvolu-
importance in the deconvolution process. tion. The importance of this assumption arises
According to Assumption 5, the seismic wavelet for the calculation of the deconvolution opera-
is always minimum phase, which is a causal sig- tor. As will be explained in Section 6.3.3, auto-
nal and its energy is zero before time zero. If the correlation of the source wavelet, not the