Pressure and velocity cross-spectrum of normal modes in low-frequency acoustic vector field of shallow water and its application

The pressure and horizontal particle velocity combined descriptions in the very low frequency acoustic field of shallow wa- ter integrated with the concept of effective depth of Pekeris wave- guide is proposed, especially the active component of the pressure and horizontal particle velocity cross-spectrum, also called ho- rizontal complex cross acoustic intensity, when only two normal modes are trapped in the waveguide. Both the approximate theo- retic analysis and the numerical results show that the sign of the horizontal complex cross acoustic intensity active component is independent of the range when vertically deployed receiving dual sensors are placed in appropriate depths, the sum of which is equal to the waveguide effective depth, so it can be used to tell whether the sound source is near the surface or underwater; while the range rate is expected to be measured by utilizing the sign distribution characteristic of the reactive component. The further robustness analysis of the depth classification algorithm shows that the existence of shear waves in semi infinite basement and the change of acoustic velocity profiles have few effects on the application of this method, and the seabed attenuation will limit the detection range, but the algorithm still has a good robustness in the valid detection range.