### ASA 125th Meeting Ottawa 1993 May

## 1pPA8. Causal time domain parabolic wave equations for power law
absorption.

**Thomas L. Szabo
**

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*Imaging Systems, Hewlett Packard, 3000 Minuteman Rd., Andover, MA 01810
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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).