Study on Range-Dependent Evolution of the Mode Eigenvalue by Using the Wigner Distribution Function

In an attempt to obtain the eigenvalues of local modes in a range-dependent ocean environment, the Wigner distribution function (WDF) is exploited in the range-wavenumber domain, instead of in the time-frequency domain, in analogy with time-dependent signal processing. In the first place, it is confirmed that the WDF can extract the exact eigenvalues for the acoustic field simulated in a horizontally stratified environment. Then, the WDF is applied to a range-dependent field simulated using the parabolic equation model. Consequently, the WDF peaks are recognized to evolve laterally in the same manner as local modes; however, some of the small peaks are difficult to identify due to the affection of false images generated in the WDF. As a result of applying a technique to enhance the amplitude of those peaks, their identification can be improved.