Application of the WKB method to calculating the group velocities and attenuation coefficients of normal waves in the arctic underwater waveguide

Abstract

Algorithms based on the WKB approximation are proposed for the fast and accurate calculation of the group time delays and effective attenuation coefficients of normal waves in the deep-water sound channel of the Arctic Ocean. These characteristics of the modes are determined in the adiabatic approximation by integrating the local group velocity and attenuation coefficient over the horizontal distance between the ends of the propagation path. According to the WKB method, the local group velocity is the ratio of two quantities. The first one is the sum of the length of the ray corresponding to the mode and the side displacement of the ray at the reflection by the ice cover. The second one is the sum of the travel time of the sound signal along the ray cycle and the time delay caused by the side displacement. The grazing angle of the ray is determined from the condition of quantization for the phase integral. According to the WKB method, the local attenuation coefficient of the mode is specified as the ratio of the squared modulus of the coherent reflection coefficient at the lower boundary of the ice cover and the sum of the cycle length and the side displacement of the ray. Simple recurrent relations are proposed to estimate, with fair accuracy and short calculating time, the phase integral, the integral that describes the cycle length, and the related local group velocities and attenuation coefficients. The capacity and efficiency of the algorithms are confirmed by the comparison of the aforementioned mode characteristics calculated by using the proposed relations and the precise computer code. The calculations are performed with the sound speed profiles obtained from the temperature and salinity measurements during the SEVER and SCICEX-1995 expeditions.