Theoretical Model for Correlation Function of Wideband Signal Received by Two Vertical Arrays and Retrieval of Modal Dispersion Curves in Shallow Water

The paper presents the results of theoretical modeling and numerical calculations of the cross-correlation function from a broadband source, both deterministic and random (for example, ship noise) in a shallow water waveguide. The signal is received by two synchronized vertical linear arrays (VLAs) located at some distance d from each other. The parameters of the problem correspond to the conditions of experiments carried out earlier by the authors in Lake Kinneret (Israel): depth 40 m, distance between the moving source and receiving antennas ~ 500-1500 m, source spectrum in the low-frequency region (30-300 Hz). An important feature of this area is the presence of a gas-saturated layer of sediments with a thickness ~1 m The CCF of the problem in this case is constructed in coordinates (wave number, frequency) and allows us to estimate dispersion curves for waveguide modes, including modes, trapped in the narrow gassy layer. Taking into account that receiving system is set of hydrophones and the corresponding expressions for CCF should be written in the matrix form. Analysis of CCF allows us to estimate parameters of sediment, more specifically thickness of gassy layer and gas concentration.