Page 513 - Acquisition and Processing of Marine Seismic Data

504 11. SEISMIC MIGRATION

require relatively narrow apertures, whereas which is sufficiently large for an effective migra-
much wider aperture widths are necessary for tion but small enough to prevent unnecessarily
deeper parts. Since wider aperture, or higher long computational time, must be used. It must
velocity, denotes more migration, deeper be approximately twice the migration halo dis-
events are migrated more than shallower tance. To determine the optimum aperture value,
events, providing a constant dip. This situation average widths of the diffraction hyperbolas on
results in the Kirchhoff migration being effec- the stack sections can be computed to use as an
tive in a conical area termed the migration cone initial aperture width for tests on a small portion
(Fig. 11.12). In some cases, degradations may of the input dataset. For a specific reflection event
arise in areas close to the edges of the migrated with a dip of θ and a depth of h, the aperture
section outside of the migration cone. Since the width d can be computed from
effective area gets narrow towards the deeper d ¼ h=tanθ (11.1)
parts of the seismic sections, relatively short
lines are avoided to apply Kirchhoff migration, Migration aperture is also important in collaps-
since its effective area in deeper parts will be ing the diffraction hyperbolas. Fig. 11.13 shows
extremely narrow. applications of Kirchhoff migration with differ-
The effectiveness of Kirchhoff migration is ent aperture widths to collapse of a theoretical
directly proportional to the aperture width: diffraction hyperbola in a constant velocity
wider apertures lead to better lateral resolution medium. For small aperture widths, migration
in the migration output. On the other hand, the is ineffective to suppress the diffraction hyper-
run time of the algorithm also significantly bola. A migration with a small aperture, how-
increases as the aperture width increases. Unnec- ever, acts as a dip filter and removes steeply
essarily high apertures require too much compu- dipping events from the data, because the steep
tational time and hence may not be economical. flanks of the hyperbolas are ignored in the dif-
Therefore, an optimum migration aperture, fraction summation process for small apertures.

FIG. 11.12 Kirchhoff migration is effective in a conical area on the input data (shaded zone) because the theoretical diffrac-
tion hyperbolas, along which the summation is performed, widen towards the deeper parts of the section due to the vertically
increasing velocity.