Page 248 - Acquisition and Processing of Marine Seismic Data

4.10 SAMPLING THEORY 239

Δt is determined to be equal to or smaller than rate that is sufficiently small to prevent aliasing,
half of the smallest period present in the becausewedo not know thehighest frequency
observed signal f(t), aliasing does not occur in we record before shooting. Therefore, electroni-
the digitized signal. cally designed low-pass and wide-band filter cir-
Degradation of the spectrum due to low- cuits, termed anti-aliasing filters, are designed
frequencysamplingusingasparsesamplinginter- (Section 2.5.2.3).Theseare specific bandpassfilters
valpresents practical issues. When f(t) is band lim- of wide passband and their higher frequency cut-
ited, thatis, when its maximum frequencyis finite, off is generally 80% of the Nyquist frequency.
the analog f(t) signal can be reconstructed from a A sufficiently small sampling rate is decided on
digitized discrete signal f r (t) without any informa- during the acquisition, and the frequency compo-
tion loss. In practice, however, such band-limited nents higher than the Nyquist frequency of the
signals are rarely observed. In addition, the sam- determined sampling rate are filtered out by
pling rate must be determined before recording anti-aliasing filters so that the data becomes band
during seismic acquisition. Yet, it is not practically limited.Thus,nodatawithfrequencycomponents
possible to determine the appropriate sampling beyond the Nyquist frequency is digitized.