Modes Separation based on Compressive Sensing and Coordinate Transformation

Sound field of a point source can be expressed in terms of discrete normal modes in a shallow water waveguide. Modes' dispersion characteristics can be observed with the splitting curves in the beam domain of low-frequency sound field received by a long horizontal line array (HLA). The frequency-azimuth curves are nonlinear and difficult to separate. A modes separation method based on compressive sensing and coordinate transformation is proposed. The distribution of azimuth spectrum of horizontal longitudinal sound field is estimated with compressive sensing beamforming. The spectra in beam domain are transformed into the vertical wavenumber domain with coordinate transformation, and the modes are separated with the linear boundaries. Vertical wavenumbers of modes are constant in an ideal waveguide and vary slowly with frequency in a non-ideal waveguide. Modes separation in the vertical wavenumber domain is more convenient than that in the beam domain. For simulation, a seafloor deployed 21-element uniform HLA, with aperture of 1 km and element interval of 50 m, is used to receive 20~120 Hz sound field excited by an ideal point pulse sound source at depth 5.7 m and range 100 km. After separation with the proposed method, the modes' complex amplitudes of each frequency can be extracted by summing up values along the vertical wavenumber axis with the boundaries. It is simple and effective. Converting the extracted modes from frequency domain to time domain by inverse Fourier transformation, modes' waveforms can be recovered. The correlation coefficients between the extracted waveforms of different modes and the theoretical ones are greater than 0.99, which verify the effectiveness of the proposed method.