Migration and random noise
Figure 4.6-32 shows a section that contains band-limited random noise uncorrelated from trace to trace and its migration using the phase-shift method. Velocity increases linearly from 2000 m/s at the top to 4000 m/s at the bottom of the section. The amplitude and frequency characteristics of the input section in Figure 4.6-32 are virtually unchanged in the interior portion of the migrated section. However, note the smearing of amplitudes at the bottom and side boundaries after migration.
Figure 4.6-33 (a) A deeper portion of a CMP-stacked section with significant noise level, (b) the same portion after migration.
Ambient noise commonly dominates the deep portion of a stacked section where velocities are high. Therefore, organization of random noise caused by migration generally is more severe in the deeper part of a stacked section. A field data example is shown in Figure 4.6-33. In addition to smearing effects, the migrated section also has smiles, which are caused by sparsely distributed bursts of amplitude in the input section. Keep in mind that a single spike on the time section migrates to a semicircle on the depth section.
We already have seen the adverse effect of an improper choice of aperture width in Kirchhoff summation (Figure 4.2-7). A narrow aperture can introduce strong smearing as spurious, nearly horizontal events. A similar effect occurs for all types of migration algorithms if the maximum dip to migrate is severely restricted (Figure 4.5-4). It is a misconception to imagine that migration attenuates random noise and improves signal-to-noise ratio. Instead, one must keep in mind that migration organizes random noise, it does not attenuate it. A dip-limited migration algorithm acts upon the random noise like a dip filter and removes the noise energy beyond the dip limit much like shown in Figure 6.2-2. The dip-limited algorithm also attenuates unaliased linear noise with a dip steeper than the dip limit.
Figure 4.2-7 Tests for aperture width in Kirchhoff migration: Input to migration is a section (a) that contains band-limited random noise uncorrelated from trace to trace. Note the spurious horizontal events in the deeper part of the section after migration using small aperture (60 traces); these gradually disappear at increasingly larger apertures.
Figure 6.2-2 (a) A synthetic CMP gather with band-limited random noise uncorrelated from trace to trace; the same gather after f − k filtering with different pass-fans with dip bands: (b) (+2,-2) ms/trace, and (c) (+4,-4) ms/trace. The f − k spectra are shown at the bottom of each panel. Note that random noise in t − x domain maps onto a rectangular zone in the f − k domain, with its top and base corresponding to the low- and high-frequency end of the passband.