Based on the relationship between the horizontal wavenumber difference of two modes and the waveguide invariant in a range-independent shallow water waveguide, a frequency-warping operator is proposed for the autocorrelation function of the received signal. This operator can transform the cross-correlation functions of two different modes in the signal autocorrelation function into separable impulsive sequences. With a guide source providing the dispersive characteristics of the waveguide, the source range can be extracted from the relative delay time of the impulsive sequence using a single hydrophone. The availability of the waveguide-invariant-warping operator in the passive source range estimation is verified by simulated and experimental data.