Source depth estimation in waveguides

In the present paper an approach to source depth estimation in a waveguide is proposed. The method is based on the mode filtering technique. By using a mode filter, the field sampling data of a vertical array are transformed to a vector which consists of two parts: (1) the eigenfunction of each mode and (2) the modal phase corresponding to the source range. The latter part can be compensated by means of range information extraction proposed in our previous paper [Shang et al., J. Acoust. Soc. Am. Suppl. 1 74, S78 (1983)]. The data vector consisting of a finite number of mode eigenfunctions then becomes ‘‘almost orthogonal’’ and can be used to construct a source depth power estimator. It is well known that the ‘‘closure’’ is a property of a complete, orthonormal set of functions, and because the mathematical expression of ‘‘closure’’ is a correlation type, a correlation operator is a reasonable one for identifying source depth. The resolution is the magnitude of −(H/M), where H is the water depth and M is the effective mode number. Some numerical examples and scale model experimental results are shown.