Jeffrey L. Krolik
Dept. of Elec. Eng., Duke Univ., Box 90291, Durham, NC 27708
Kevin D. LePage
Bolt Beranek and Newman, Inc., Cambridge, MA 01238
An important source of uncertainty in shallow-water propagation models used for minimum variance (MV) matched-field processing is bottom roughness or irregular bathymetry. A perturbative solution to the Helmholtz equation which gives the point source field in a shallow-water waveguide with rough boundaries has been derived in [W. Kuperman and H. Schmidt, J. Acoust. Soc. Am. 86, 1511--1522 (1989)]. This formulation yields an expression for the point-source wave front correlation matrix which is determined by the coherent field and a scattered field generated by random secondary sources at the bottom interface. Alternatively, adiabatic normal modes and first-order perturbation of the horizontal modal wave numbers also provides a solution for the wave front correlation matrix in terms of the second-order statistics of the random bottom depth. In this paper, matched-field source localization performance under both these models is evaluated for several MV beamforming approaches. Minimum variance beamforming with environmental perturbation constraints [J. L. Krolik, J. Acoust. Soc. Am. 92, 1408--1418 (1992)] is demonstrated to be an approach which can exploit these random propagation models to achieve robust matched-field source localization. [Work supported by ONR.]