Adiabatic transforms for spectral analysis and synthesis of weakly range‐dependent shallow ocean Green’s functions

Range‐independent (separable) ocean waveguide Green’s functions can be synthesized by applying exact transform theorems to the range variables and thereby reducing the two‐ or three‐dimensional problem to a one‐dimensional problem for the depth‐dependent portion. The resulting spectral integral representations are useful for determining alternative forms of the total direct Green’s function and also, by inversion applied to given data, for recovery of spectral plane‐wave reflection coefficients that contain information about the bottom structure [G. V. Frisk, J. F. Lynch, and J. A. Doutt, in Ocean Seismo‐Acoustics, edited by T. Akal and J. M. Berkson (Plenum, New York, 1986)]. Exact transform theory fails in the presence of range dependence (nonseparability). When such dependence is weak, adiabatic spectral invariants deduced from the properties of the adiabatic modes may be invoked to adapt the spectral integrals approximately to these generalized conditions [A. Kamel and L. B. Felsen, J. Acoust. Soc. Am...