A Variational Dispersion Mode Decomposition Approach to Extracting Normal-Mode Interference Spectra from Broadband Acoustic Intensity Measurements

The primary objective of separating normal-mode interference spectra (NMISs) is to extract more fine-grained coherent structures between different pairs of modes in a shallow water sound field. However, NMISs generally exhibit nonlinear phase frequency and amplitude frequency relationships in one-dimensional broadband sound intensity measurements, which poses a challenge for effective separation. To address the difficulty arising from the nonlinearity of NMISs, this study presents a variational dispersion mode decomposition (VDMD) method. An innovation of VDMD is to incorporate the physical model of NMISs into the framework of Variational Nonlinear Chirp Mode Decomposition (VNCMD). First, it utilizes the waveguide invariant and the interference frequency factor to characterize the phase function of NMISs. Second, this parameterization of the nonlinear phase function provides an analytical expression for the gradient of the objective function in the variational optimization processing of VNCMD, thereby improving the efficiency of its iterative search and enabling accurate extraction of NMISs. Finally, experimental results from a Yellow Sea trial demonstrate that the separated NMISs agree well with the reference modes, validating the effectiveness of our proposed method.