Thomas L. Szabo
Imaging Systems, Hewlett-Packard, 3000 Minuteman Rd., Andover, MA 01810
The effects of phase velocity dispersion accompanying attenuation can alter both the shape and time delay of finite length acoustic pulses. For attenuation described by a frequency power law with an exponent y, a time causal theory [T. L. Szabo, J. Acoust. Soc. Am. 93, 2277 (A) (1993)] has shown that dispersion is greatest [in the range (0(less than or equal to)y(less than or equal to)2) when y=1 and is zero for y=0 and y=2. These results are in contrast to the approximate nearly local Kramers--Kronig theory [M. O'Donnell et al., J. Acoust. Soc. Am. 69, 696--701 (1981)] which predicts increasing dispersion as y increases from 0 to 2. The consequences of dispersion from the two theories are compared for simulated finite-length pulses for different values of y. For values of y=1, where the theories agree, the effects of bandwidth on pulse shape and delay are illustrated. An approximate general scaling law for pulses propagating in lossy media is presented.