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

Abstract

The pressure and horizontal particle velocity combined descriptions in the very low frequency acoustic field of shallow water integrated with the concept of effective depth of Pekeris waveguide is proposed, especially the active component of the pressure and horizontal particle velocity cross-spectrum, also called horizontal complex cross acoustic intensity, when only two normal modes are trapped in the waveguide. Both the approximate theoretic 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.

Performance Analysis of Target Depth Classification Algorithm Based on Sea Experiment Data

“…Based on the above theory which have already been published in [22,23], we can conclude that the value of critical depth changes with different receiving depth, source frequency, sound velocity profile, and seabed. The reason why these factors affect algorithm performance has never been researched.…”

“…The cross-spectrum calculation is performed using signals acquired by a single 3D vector sensor [20,21] or two 2D vector sensors [22,23], and the target depth classification can be achieved based on the characteristics of the crossspectrum signals. However, most of the above algorithms are theoretical studies [20][21][22][23], and the actual performance of the algorithm is rarely analyzed through the analysis of experiment data processing results [24,25]. Based on the sea experiment data processing results, this paper analyzes the influence of the ideal receiving depth concept on the performance of the algorithm while verifying the feasibility of the target depth classification algorithm.…”

A Three-Dimensional Target Depth-Resolution Method with a Single-Vector Sensor

“…In order to solve the problem of target depth resolution in the very low frequency field, many scholars like Hui and Yu et al [ 27 , 28 , 29 , 30 , 31 ] proposed a cross-spectrum (between pressure and velocity) signal-processing algorithm to distinguish the surface targets and the underwater targets. Both the active component of the horizontal interactive complex acoustic intensity and the reactive component of the vertical interactive complex acoustic intensity in the low-frequency field can be used to identify target depth.…”

Application and Extension of Vertical Intensity Lower-Mode in Methods for Target Depth-Resolution with a Single-Vector Sensor

“…For an acoustic vector sensor lying in an emitter’s near-field, the methods for three-dimensional localization has been developed by Wong and Wu et al [ 40 , 41 , 42 , 43 ]. Many scholars like Hui and Yu et al [ 44 , 45 , 46 , 47 , 48 , 49 ] have proposed a method for target depth classification using vertical intensity signals.…”

“…Some of these methods offer rather high accuracies of localization and angle estimation, but have high complexity in the actual calculation [ 40 , 41 , 42 , 43 ]. Others are based on normal mode theory in the case of exciting only the first two normal modes [ 44 , 45 , 46 , 47 , 48 , 49 ], although these methods are of low complexity. When the frequency of research object can only excite the first two normal modes, the working band of the investigable object is greatly limited.…”