CONSTANT Q-WAVE PROPAGATION AND ATTENUATION

A linear model for attenuation of waves is presented, with Q, or the portion of energy lost during each cycle or wavelength, exactly independent of frequency. The wave propagation is completely specified by two parameters, e.g., Q and co, a phase velocity at an arbitary reference frequency wo. A simple exact derivation leads to an expression for the phase velocity c as a function of frequency: c/co = (w/wo), where gamma = (1/pi) tan-1 (1/Q). Scaling relationships for pulse propagation are derived and it is shown that for a material with a given value of Q, the risetime or the width of the pulse is exactly proportional to travel time. The travel time for a pulse resulting from a delta function source at x = 0 is proportioal to xbeta, where beta = 1/(1 - gamma). On the basis of this relation it is suggested that the velocity dispersion associated with anelasticity may be less ambiguously observed in the time domain than in the frequency domain. -Author