Signals propagating in waveguides can be decomposed into normal modes that exhibit dispersive characteristics. Based on the dispersion analysis, the warping transformation can be used to improve the modal separability. Different from the warping transformation defined using an ideal waveguide model, an improved warping operator is presented in this paper based on the beam-displacement ray-mode (BDRM) theory, which can be adapted to low-frequency signals in a general shallow water waveguide. For the sake of obtaining the warping operators for the general waveguides, the dispersion formula is first derived. The approximate dispersion relation can be achieved with adequate degree of accuracy for the waveguides with depth-dependent sound speed profiles (SSPs) and acoustic bottoms. Performance and accuracy of the derived formulas for the dispersion curves are evaluated by comparing with the numerical results. The derived warping operators are applied to simulations, which show that the non-linear dispersion structures can be well compensated by the proposed warping operators.