  An acoustic wave equation for pressure accounting for viscoelastic
attenuation is derived from viscoelastic equations of motion. It is assumed
that the relaxation moduli are completely monotonic. The acoustic equation
differs significantly from the equations proposed by Szabo (1994) and in
several other papers. Integral representations of dispersion and attenuation
are derived. General properties and asymptotic behavior of attenuation and
dispersion in the low and high frequency range are studied. The results are
compatible with experiments. The relation between the asymptotic properties of
attenuation and wavefront singularities is examined. The theory is applied to
some classes of viscoelastic models and to the quasi-linear attenuation
reported in seismology.
