Modal depth function estimation using time-frequency analysis

Acoustic propagation in shallow water is characterized by a set of depth-dependent modes, the modal depth functions, which propagate in range according to their horizontal wavenumbers. For inversion purposes, modal depth function estimation in shallow water is an issue when the environment is not known. Classical methods that provide blind mode estimation rely on the singular value decomposition of the received field at different frequencies over a vertical array of transducers. These methods require that the vertical array spans the full water column. This is obviously a strong limitation for the application of such methods in an operational context. To overcome these shortcomings, this study proposes to replace the spatial diversity constraint by a frequency diversity condition, and thus considers the case of a field emanating from an impulsive source. Indeed, because of the discrete nature of the wavenumber spectrum and due to their dispersive behavior, the modes are separated in the time-frequency domain. This phenomenon enables the design of a modal filtering scheme for signals received on a single receiver. In the case of a vertical receiver array, the modal contributions can be isolated for each receiver even when using a partial water column spanning array. This method thus eliminates the receiving constraints of classical methods of modal depth function estimation, although it imposes the use of an impulsive source. The developed algorithm is benchmarked on numerical simulations and validated on laboratory experimental data recorded in an ultrasonic waveguide. Practical applications are also discussed.