  It is shown that the dispersion and attenuation functions in a linear
viscoelastic medium with a positive relaxation spectrum can be expressed in
terms of a positive measure. Both functions have a sublinear growth rate at
very high frequencies. In the case of power law attenuation positive relaxation
spectrum ensures finite propagation speed. For more general attenuation
functions the requirement of finite propagation speed imposes a more stringent
condition on the high-frequency behavior of attenuation. It is demonstrated
that superlinear power law frequency dependence of attenuation is incompatible
with finite speed of propagation and with the assumption of positive relaxation
spectrum.
