SEISMIC CONSTANT-VELOCITY REMIGRATION

When a seismic common midpoint (CMP) stack or zero-offset (ZO) section is depth or time migrated with different (constant) migration velocit ies, different reflector images of the subsurface are obtained. If the migration velocity is changed continuously, the (kinematically) migra ted image of a single point on the reflector, constructed for one part icular seismic ZO reflection signal, moves along a circle at depth, wh ich we call the Thales circle. It degenerates to a vertical line for a nondipping event. For all other dips, the dislocation as a function o f migration velocity depends on the reflector dip. In particular for r eflectors with dips larger than 45 degrees, the reflection point moves upward for increasing velocity. The corresponding curves in a time-mi grated section are parabolas. These formulas will provide the seismic interpreter with a better understanding of where a reflector image mig ht move when the velocity model is changed. Moreover, in that case, th e reflector image as a whole behaves to some extent like an ensemble o f body waves, which we therefore call remigration image waves. In the same way as physical waves propagate as a function of time, these imag e waves propagate as a function of migration velocity. Different migra ted images can thus be considered as snapshots of image waves at diffe rent instants of migration velocity. By some simple planewave consider ations, image-wave equations can be derived that describe the propagat ion of image waves as a function of the migration velocity. The Thales circles and parabolas then turn out to be the characteristics or ray trajectories for these image-wave equations.