In prestack depth migration using explicit extrapolators, the attenuat
ion and dispersion of the seismic wave has been neglected so far. We p
resent a method for accommodating absorption and dispersion effects in
depth migration schemes. Extrapolation operators that compensate for
absorption and dispersion are designed using an optimization algorithm
. The design criterion is that the wavenumber response of the operator
should equal the true extrapolator. Both phase velocity and absorptio
n macro models are used in the wavefield extrapolation. In a model wit
h medium to high absorption, the images obtained are superior to those
obtained using extrapolators without compensation for absorption.