Extraction of Acoustic Normal Mode Depth Functions Using Range-Difference Method with Vertical Linear Array Data

Data-derived normal mode extraction is an effective method for extracting normal mode depth functions in the absence of marine environmental data. However, when the corresponding singular vectors become nonunique when two or more singular values obtained from the cross-spectral density matrix diagonalization are nearly equal, this results in unsatisfactory extraction outcomes for the normal mode depth functions. To address this issue, we introduced in this paper a range-difference singular value decomposition method for the extraction of normal mode depth functions. We performed the mode extraction by conducting singular value decomposition on the individual frequency components of the signal's cross-spectral density matrix. This was achieved by using pressure and its range-difference matrices constructed from vertical line array data. The proposed method was validated using simulated data. In addition, modes were successfully extracted from ambient noise.