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Normal mode separation and information extraction are popular topics in marine acoustics. The extraction of modal wavenumbers and modal depth functions using the data of a vertical line array is beneficial to various applications. In this paper, we systematically introduce a normal mode separation method based on the consistency restraint of the horizontal wavenumber, obtain the modal depth functions using the singular value decomposition (SVD) method, determine the vertical distribution of the horizontal wavenumber, and determine the SVD accuracy by the consistency of modal wavenumbers on the vertical direction. Moreover, this method can be used to determine the SVD accuracy without true depth functions. When the degeneracy problem leads to a poor SVD effect, the linear relation between the degenerate and true modes is obtained, and the minimum standard deviation of the vertical distribution of the modal wavenumbers is taken as the loss function, thus optimizing the SVD result and improving the accuracy of modal wavenumber estimation. The proposed method is validated using simulated data. In addition, the modes are successfully extracted from ambient noise.

Normal Mode Separation Method Based on the Consistency Constraint of the Horizontal Wavenumber