**Modeling of the Acoustic Propagation in Shallow Water
Oceanic Regions Including Effects of Bottom Geometry and Sub-bottom Propagation.**

**Project summary :**

The long term goal of the project is to develop a numerical tool (model) for the study of acoustic propagation in a range and depth dependent shallow water environment, with inclusion of bottom effects (scattering and transmission).

As a first step towards the long term goal of the project, two simplified two-dimensional models were developed to study :

- The effect of abrupt or gradual changes in shallow water bottom topography on the acoustic propagation in an homogeneous water column (semi-analytical approach).
- The effect of arbitrary changes in shallow water bottom topography on the acoustic propagation in an homogeneous water column (numerical Boundary Element approach; BEM)

A Boundary Integral Equation (BIE) approach was used for the representation of the solution in the water and in the bottom region (for porous bottom). Matching was specified between the solution in the interior region (water) and the exterior regions (bottom, lateral radiation regions) along interface boundaries. Eigenfunction expansions of the solution were used in radiation regions. Both analytical (Green's function and eigenfunction expansion approaches) and numerical (BEM) solutions were developed for the interior problem equations, with cross-validation between both approaches.

The first limited numerical model developed in this project will make it possible both to understand and to qualitatively predict acoustic signals measured in some of the recent shallow water experiments. The new physical insight gained will help better select and define the important features and the best approach for a more general model, to be developed at a later stage, that will address the long term goals of this project.

**Background :**

Emphasis is now put in the naval community towards problems of acoustic propagation in shallow water regions. Shallow water acoustic problems bring new challenges due to both the range and depth dependent environment (water stratification, complex bottom topography) and the propagation of acoustic waves into the bottom sediments. For various reasons, all traditional methods for calculating sound waves propagation in an oceanic environment fail to fully address these new challenges (i.e., ray methods, normal mode methods, parabolic equation methods, and existing integral solution methods).

Recent in-situ measurements of low frequency acoustic propagation in shallow water over irregular bottom show significant differences in the received signal, depending on source frequency and location. Most existing theoretical or numerical methods for modeling acoustic propagation cannot address such problems. There is thus a need for a more general method of analysis for acoustic propagation in a range and depth dependent shallow water environment, with inclusion of bottom effects, that could help interpreting and understanding such observations.

**Funding history :**

- 1994-95 : Grant No. N-00014-94-I-0565 (PI with P. Stepanishen, $36,022)
of the DOD Office of Naval Research (ONR) Ocean Acoustics Division, to
support the : .Modeling of the Acoustic Propagation in Shallow Water Oceanic
Regions Including Effects of Bottom Geometry and Sub-bottom Propagation.

**Key personnel at URI :**

- S.T. Grilli : Ph.D, Associate Professor in OE, Principal investigator.
- P.R. Stepanishen: Ph.D, Professor in OE, Co-Principal investigator
- T. Pedersen: graduate MS student in OE, 1994-

**Publications :**

- Grilli, S.T., Stepanishen, P., Pedersen, T., and Badiey, M. 1995 A hybrid DR-BEM model for underwater acoustic propagation in inhomogeneous media. Presented at the IABEM95 Intl. Symposium (Mauna Lani, Hawaii, August 1995).
- Grilli, S.T., Pedersen, T.and P., Stepanishen
1998 A Hybrid Boundary Element Method for Shallow Water Acoustic Propagation
over Irregular Bottom.
*Engineering Analysis with Boundary Elements*,**21**(2), 131-145. [abstract] [compressed postcript] (365K) - Stepanishen, P., Grilli, S.T., and Pedersen, T. An analytical
method for shallow water acoustic propagation over irregular bottom.
*J. Sound and Vibrations*(in preparation).

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