Extrapolating Green's functions using the waveguide invariant theory.

The broadband interference structure of sound propagation in a waveguide can be described by the waveguide invariant, β, that manifests itself as striations in the frequency-range plane. At any given range (r), there is a striation pattern in frequency (ω) , which is the Fourier transform of the multipath impulse response (or Green's function). Moving to a different range (r + Δ r) , the same pattern is retained but is either stretched or shrunken in ω in proportion to Δ r , according to Δ ω / ω = β (Δ r / r). The waveguide invariant property allows a time-domain Green's function observed at one location, g(r,t), to be extrapolated to adjacent ranges with a simple analytic relation: g (r + Δ r , t) ≃ g (r , α (t − Δ r / c)) , where α = 1 + β (Δ r / r) and c is the nominal sound speed of 1500 m/s. The relationship is verified in terms of range variation of the eigenray arrival times via simulations and by using real data from a ship of opportunity radiating broadband noise (200–900 Hz) in a shallow-water environment, where the steep-angle arrivals contributing to the acoustic field have β ≈ 0.92. [ABSTRACT FROM AUTHOR]