Recent publication have indicated that a significant dependence of the quality factor Q on frequency may occur in the interior of the earth, and thus an analysis of pulse propagation in media with Q dependent on frequency is appropriate. It is shown that a simple scaling law describes the degradation of an initially sharp pulse as it propagates in a linear viscoelastic medium in which Q has a power-law dependence variation of the pulse rise time with path, as this parameter may be useful in estimating the Q structure of the earth.