### ASA 126th Meeting Denver 1993 October 4-8

## 2pUW4. Complex effective depth and mode eigenvalues for a layered elastic
waveguide.

**C. T. Tindle
N. R. Chapman
**

**
**
*Defence Res. Establishment Pacific, FMO Victoria, BC V0S 1B0, Canada
*

*
*
The complex effective depth [Z. Y. Zhang and C. T. Tindle, J. Acoust. Soc.
Am. 93, 205--213 (1993)] has been investigated for a shallow water waveguide
with a layered elastic bottom. For multiple layers, both the complex effective
depth and the reflection coefficient for the bottom have oscillatory structure
as a result of resonant effects in the layers of the sediment. Under these
conditions and for elastic layers, some of the normal mode eigenvalues can be
difficult to find, as a simple mode counting procedure is not available. The
complex effective depth leads to a formulation of a eigenvalue problem in terms
of a phase integral. The phase integral is a function of complex wave number
and a normal mode exists whenever it is a multiple of (pi). A path exists in
the complex plane along which the phase integral is real and monotonic. The
path passes through all eigenvalues for both trapped and leaky modes and these
can be found systematically. [Work supported by DND.]