An analytical representation of the velocity potential of a point source of sound is constructed for a model of a marine acoustic waveguide with a rigid stepped bottom, where a sound velocity profile varies with depth. Inhomogeneity of the bottom in the form of a cylindrical protrusion is modeled on the basis of the method of partial regions. The sound field is represented in the form of the sum of normal modes to construct the sound velocity potential in each partial region. The continuity of solutions at the boundary of partial regions leads to an infinite system of linear equations with respect to the coefficients under normal modes. In this work, formulas are obtained that describe the energy characteristics of the propagation of each of the normal modes along the waveguide. Examples of numerical modeling are given. An analysis of the excitation coefficients of normal modes is carried out for waveguide parameters are true to type of the Black Sea region.

Keywords: waveguide, normal modes, bottom inhomogeneity, excitation coefficient, partial regions, infinite system of linear equations, asymptotics