Page 235 - Acquisition and Processing of Marine Seismic Data

226 4. FUNDAMENTALS OF DATA PROCESSING

FIG. 4.13 Zero offset synthetic sections consisting of linear events with increasing dips formed by monochromatic
sinusoids of 60 Hz and their corresponding f-k spectra (lower panels).

crisscross events in the time section. The ampli- spectra. The amplitudes of all frequency compo-
tudes of the events with 12 and 15 ms/trace dip nents with 0° dip appear at their corresponding
are located at negative panels in the f-k spectra, frequency value along the k ¼ 0 axis in the f-k
indicating that 60-Hz monochromatic events panel, indicating that there is no spatial aliasing.
with 12 and 15 ms/trace dip are spatially Each dipping event seems to be aligned on the
aliased. This is also evident at the synthetic sec- dashed blue line passing through the origin of
tions where the dip of the events is incorrect in the f-k panel. As the dip of linear events in the
the negative direction. Furthermore, the events time domain increases, the inclination of this line
with 20 ms/trace dip appear at the positive also increases, approaching the horizontal wave-
panel, indicating that they are aliased twice, number axis, which ultimately results in spatial
and therefore their dips on the time sections aliasing in the f-k domain. Aliasing occurs at
are again in a positive direction. higher frequency components first. For instance,
Let’s assume that we have seismograms com- althoughtheamplitudesofeventswith20,60and
posed of linear summation of several sinusoids 80 Hz appears exactly at their expected wave-
with different frequencies but the same dip. number value on the f-k panel for the seismo-
Fig. 4.14 shows zero offset synthetic seismo- grams with 5 ms/trace dip, the amplitude of
grams consisting of linear events with increasing the 140-Hz event is located at the negative f-k
dips formed by superposition of 20-, 60-, 80- and panel, that is, only the amplitudes of 140-Hz
140-Hz sinusoids, and their corresponding f-k events are spatially aliased for 5 ms/trace dip.