Fig. 6 Shallow water model
The whole space in Fig. 6 can be divided into three parts. Part I includes the upper surface layer of the ocean in which the sound speed changes rapidly due to the sunlight, wind, etc. Part III includes the bottom half-space. Part II includes the water column in which the sound speed changes slowly, so the eigenfunction in this part can be expressed by the generalized phase integral (WKBZ) approximation. The division between Part I and Part II will not affect the calculation of sound field. The eigen-equation of the normal mode can be expressed as

The sound field can thus be calculated by solving this equation.
To illustrate the computational speed and accuracy of BDRM theory, shallow water sound transmission losses for two bottom models are calculated. The sound speed profile in water column for these two models is shown in Fig.7(a)