Recursive wavefield extrapolation methods in the space-frequency domain are popular because they are powerful in handling strong lateral velocity variations. However, one of the problems of these methods is the instability of the extrapolation operator. Unstable operators tend to amplify the extrapolated wavefield at each depth step.
The Hale's method can design stable extrapolation operators. One of the advantages of Hale's extrapolator is that it is fairly stable where it does not amplify the extrapolated wavefield at each depth step. The impulse response of Hale's extrapolator and the poststack migration of Marmousi dataset show that it can handle lateral velocity variations but not the steeply dipping events. Hale's extrapolator may be a good candidate for data that have moderate dips, but probably not for steeply dipping events.
Some applications of Hale's extrapolator in prestack depth migration with different imaging conditions are shown. The different imaging conditions give different amplitudes of the same reflector. Only the deconvolution imaging condition can preserve the amplitude of the reflector.
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