A method of range and depth estimation by modal decomposition

Abstract

Normal mode amplitudes are definite functions of depth and have a characteristic phase as a function of source range rs [i.e., exp(−ikirs), where ki is the ith mode wavenumber]. The range and depth of an acoustic source in the ocean can then be determined by decomposing array data and beamforming on the mode amplitudes. In particular, the product of the normal mode amplitudes with the steering vector Ui [where Ui=exp(ikir) ] is maximum for the true source range (r=rs). Similarly, the correlation of the measured (decomposed) mode amplitudes with the theoretically calculated mode amplitudes is maximum at the source depth. Accurate range and depth estimation with this approach, however, requires reliable estimates of the mode amplitudes. In this article, an eigenvector decomposition technique is used to extract the mode amplitudes for data received on a long (1-km) vertical array. Range and depth are successfully estimated both for simulated data and for data from the 1982 FRAM IV experiment in the Arctic Ocean. The effect of the number of modes on the estimates is also illustrated.