Thomas L. Szabo
Imaging Systems, Hewlett Packard, 3000 Minuteman Rd., Andover, MA 01810
The classic parabolic time domain wave equation describes acoustic propagation in a medium in which absorption is a quadratic function of frequency. For the general case of power law absorption, (alpha)((omega))=(alpha)[sub 0]|(omega)|[sup y], where (alpha)[sub 0] and y are arbitrary real positive constants and (omega) is angular frequency, generalized time domain parabolic wave equations are presented. The differential loss operator in the original classic parabolic equation is replaced by a single propagation convolution operator that accounts for both absorption and dispersion. These operators, based on new time causal relations, have different forms for y as an even or odd integer or noninteger. The new equations are compared to those in the literature corresponding to the cases y=0.5 (acoustic duct), y=1.0 (medical and underwater applications), and y=0 or 2 (classic forms).