Relationship between the reflection coefficient of Arctic ice and dispersion of Lamb waves

To obtain the relationship between the reflection coefficients of the Arctic ice layer and Lamb waves, the transfer matrix method is applied, and the real and imaginary parts, modulus range and dispersion of the free Lamb waves and leaky Lamb waves are analyzed. The corresponding relationship between the dispersion curves of the free Lamb waves in the ice layer and the reflection coefficients is obtained. In response to the phenomenon that the vibration mode of the leaky Lamb wave cannot be identified when the phase velocity of the leaky Lamb wave is greater than the longitudinal wave velocity of the ice layer, the improved dispersion equation of the leaky Lamb wave is obtained by adjusting the coupling conditions of the ice water interface. The relationship between the vibration mode and reflection coefficient of the leaky Lamb wave in the ice layer under small angle incidence is obtained, and verified by the data from the cross-ice detection experiment in the Arctic. The results indicate that acoustic waves in the frequency band with reflection coefficients less than 1 excite the Lamb waves in the corresponding frequency band of the ice layer. In addition, based on the improved leaky Lamb wave dispersion equation, the dispersion curves of multi-layer ice layer leaky Lamb waves are further obtained.