By defining anelastic effects through the superposition of relaxation mechanisms, and incorporating them into the wave equation in terms of memory variables, the time-domain computation of responses of viscoelastic media with arbitrary spatial variations is feasible. This approach is applied to simulation of the effects of realistic distribution of compressional and shear wave quality factors (Qp and Qs) in a sequence of viscoelastic models of increasing complexity from a homogeneous medium, to a fault zone, a near-surface attenuating zone, and inclusions with anomalous Qp and Qs values. Comparisons of elastic and viscoelastic responses for both surface and borehole recordings show pronounced Q-dependent attenuation; analysis of data from viscoelastic media using elastic, rather than a viscoelastic, model may result in misleading or erroneous interpretations.

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