Green’s Function Extrapolation with a Generalized Waveguide Invariant

Green’s function extrapolation provides an efficient framework for predicting acoustic fields at adjacent locations from a reference observation. Conventional formulations of this approach have been developed primarily under the assumption that the waveguide invariant [Formula: see text] equals unity, which is valid for range-independent waveguides with flat bathymetry. This study demonstrates the applicability of Green’s function extrapolation in more general ocean waveguides where [Formula: see text] deviates from unity due to either bathymetry-induced range dependence or sound-speed-induced effects. The extrapolation is formulated as a two-step procedure consisting of a geometric time delay followed by a Doppler-like resampling operation, with the latter governing the dilation or compression of the arrival-time structure. Numerical simulations show that accurate extrapolation cannot be achieved by considering the time delay alone; instead, proper scaling of the arrival structure must be incorporated through the appropriate value of [Formula: see text]. Results are presented for range-independent shallow-water waveguides with flat bathymetry, range-dependent waveguides with linearly sloping and bow-shaped bathymetry, and a deep-water Arctic waveguide characterized by an [Formula: see text]-linear sound speed profile (SSP). While the assumption [Formula: see text] fails in environments where [Formula: see text], close agreement is recovered when the appropriate value of [Formula: see text] is employed. These findings establish the central role of [Formula: see text] in Green’s function extrapolation and extend its applicability to a broad class of realistic ocean waveguides.