Vector-phase characteristics of acoustic fields: Statistical analysis and measurement algorithms

Statistical characteristics of an acoustic field that are based on the data of simultaneous measurements of pressure and acoustic velocity vector are investigated. Conditions of the formation of vector-phase characteristics of acoustic field are formulated in relation to the dispersion properties of the medium. Crosscorrelation functions of the components of the vector field are presented. Expressions for the characteristic functionals of vector-phase relationships in acoustic fields and, in particular, for the acoustic energy flux are derived with the use of functional methods. Algorithms of space-time processing of the energy flux vector and the optimum measurement algorithm for a Gaussian vector-phase field are considered. The signal-to-noise ratio is determined as the quality index of vector reception algorithms, and its relation to the corresponding parameter of scalar pressure field measurements is revealed. Indices of relative efficiency of vector algorithms are determined depending on the dispersion characteristics of the medium (the flux algorithm) and the dimension of the input vector of observations (the optimum algorithm).