For sound speed profiles which vary only in depth, a method has been developed whereby the scattered field data in frequency (or k-space) can be related to the sound speed profile correction (from an assumed profile guess input) as a quasi-Fourier transform pair. The inversion is straightforward. The method uses a Fourier-Bessel representation of the acoustic field, a Born approximation on the depth dependent part of the Green’s function, a WKB representation for the wave functions and asymptotics and linearization to derive the transform pair. Small perturbations about the main profile trend are recovered very accurately if the background slope is assumed known.