Matched-field processing in a shallow-water channel with a random bottom

Abstract

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.]