In prestack depth migration using explicit extrapolators, the attenuation and dispersion of the seismic wave has been neglected so far. We present 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 absorption macro models are used in the wavefield extrapolation. In a model with medium to high absorption, the images obtained are superior to those obtained using extrapolators without compensation for absorption.