Page 244 - Acquisition and Processing of Marine Seismic Data

4.10 SAMPLING THEORY 235

FIG. 4.21 (A) A real shot gather, and (B) its τ-p transform. S, seabed reflection; M, multiple reflection; D, direct wave; R,
refracted wave.

trace interpolation by the τ-p transform. This The maximum available frequency after digiti-
allows us to reduce the trace interval in a CDP zation at regular Δt intervals is known as the
or shot gather, and spatial sampling can be Nyquist frequency (f N ) and is determined only
increased. This is particularly useful in preven- by the sampling interval. The Nyquist frequency
tion of spatial aliasing during f-k filtering. is expressed as
1
f N ¼ (4.35)
4.10 SAMPLING THEORY 2Δt
2f N 1
Δf ¼ ¼ (4.36)
Digitizing of a continuously observed analog N NΔt
signal in regular time intervals for further digital
processing is termed sampling. If the continuous where Δf is the frequency sampling interval. The
signal observed between 0 t T is digitized higher the sampling interval Δt chosen, the
at Δt time intervals, discrete data will consist smoother the digitized signal that is obtained,
of N ¼ (T/Δt) + 1 discrete amplitude samples. which results in a complete loss of high