Properties of the seafloor affecting sound propagation can be inferred from the horizontal wave numbers of bottom-interacting modes of sound propagation. To this end, the modal wave numbers can be extracted from the harmonic sound field recorded by a single hydrophone, when either the source or hydrophone are towed at constant depth, giving in effect a well-sampled synthetic aperture array. This method has been used to determine the bottom properties in a range-independent environment, by first applying a Hankel transform to get a representative wave-number spectrum in which the wave numbers of the dominant modes feature prominantly [S. D. Rajan et al., J. Acoust. Soc. Am.82, 998–1017 (1987)]. In range-dependent environments, however, the modes vary owing to changes in bathymetry and seafloor properties, making it impossible to speak of a single set of range-independent modal wave numbers as the Hankel transform method requires. In this paper, a phase demodulation technique is derived from the adiabatic mode model of sound propagation whereby range-dependent wave numbers can be extracted from data collected in range-dependent environments using the same experimental setup as in range-independent environments.