Abstract
In this paper, a modified warping operator for homogeneous shallow water based on the Beam-Displacement Ray-Mode (BDRM) theory is presented. According to the BDRM theory, the contribution of the beam displacement and the time delay to the group velocity can be easily considered in a shallow water waveguide. A more accurate dispersion formula is derived by using the cycle distance formula to calculate the group velocity of normal modes. The derived dispersion formula can be applied to the homogeneous shallow water waveguide. Theoretically, the formula is related to the phase of the reflection coefficient and suitable for various bottom models. Furthermore, based on the derived dispersion relation, the modified warping operator is developed to obtain linear modal structures. For the Pekeris model, the formulae for the phase of the reflection coefficient are derived in this work. By taking account of the effect of the bottom attenuation on the reflection coefficient, the formula for the phase of the reflection coefficient including the bottom attenuation is obtained for the Pekeris model with a lossy bottom. Performance and accuracy of different formulae are evaluated and compared. The numerical simulations indicate that the derived dispersion formulae and the modified warping operator are more accurate.
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