A WKB method based on parabolic cylinder function for very-low-frequency sound propagation in deep ocean

A Wentzel–Kramers–Brillouin (WKB) method is introduced for obtaining a uniform asymptotic solution for underwater sound propagation at very low frequencies in deep ocean. The method utilizes a mode sum and employs the reference functions method to describe the solution to the depth-separated wave equation approximately using parabolic cylinder functions. The conditions for the validity of this approximation are also discussed. Furthermore, a formula that incorporates waveguide effects for the modal group velocity is derived, revealing that boundary effects at very low frequencies can have a significant impact on the propagation characteristics of even low-order normal modes. The present method not only offers improved accuracy compared to the classical WKB approximation and the uniform asymptotic approximation based on Airy functions, but also provides a wider range of depth applicability. Additionally, this method exhibits strong agreement with numerical methods and offers valuable physical insights. Finally, the method is applied to the study of very-low-frequency sound propagation in the South China Sea, leading to sound transmission loss predictions that closely align with experimental observations.