Virtual source array for estimating the intensity of target noise source in shallow water

The measurement and estimation of source intensity of underwater target noise in shallow water significantly deviate from the value measured in the free field. Aimed at the problem, a method of virtual source array is proposed. Based on the move vertically in the waveguide of the tested target to form a virtual source array, the influences of noise field interference and the depths of the sound source and receiving points on the intensity estimation are eliminated according to the orthogonality of the eigenfunctions, and the estimation intensity closer to the free field measurement is obtained. Theoretical and numerical simulation results show that, the target noise source intensity estimated by this method in shallow water waveguide is close to the preset true value, and has the same results in different shallow water waveguides. The numerical simulations confirm the feasibility of the method and show that, the errors of the estimation intensity in a practical waveguide from the South China Sea in the frequency band above 100 Hz are less than 0.5 dB, less than 1.0 dB in the frequency band between 40 Hz and 100 Hz, and about 3.0 dB at 20 Hz. The standard deviations of noise source intensity estimated in four different waveguide environments are less than 0.5 dB above 30 Hz. The main error sources and the reasons for the larger errors at low frequencies are also analyzed and simulated. The virtual source array method proposed can provide an idea to improve the measurement and estimation accuracy of underwater target noise source intensity, and also a reference for the accurate inversion and estimation of waveguide parameters.