At the present time, proper solutions for absorption modeling are based on wavefield extrapolation techniques which, in some instances, may be considered expensive. Two alternative, low cost, but incomplete solutions exist in the literature. The first models dispersion in the frequency domain in accordance with the Futterman dispersive relations but does not consider attenuation. The second models both attenuation and dispersion in the time domain but assumes a digital minimum-phase formulation that results in an inadequate treatment of the dispersion. We show that this second solution can be adapted to perform attenuation and/or dispersion modeling in agreement with the Futterman attenuation-dispersion relationships thus obviating the shortcoming mentioned above. Synthetic and real data examples are shown to illustrate the performance of the proposed algorithm.