—A review of modern methods of modeling acoustic fields based on their representation as a superposition of normal modes is presented. Most of the described methods are based on an approach to calculating mode amplitudes by solving parabolic equations of various types, both narrow-angle and wide-angle. We also consider two-dimensional methods for calculating acoustic fields, to which the above-mentioned three-dimensional approaches are reduced in the absence of dependence of the field and medium parameters on one of the horizontal coordinates. The computation of both time-harmonic acoustic fields and pulsed sound signals is discussed. A number of numerical examples are considered in which such calculations are performed taking into account three-dimensional sound propagation effects. For the first time within the framework of this approach, the calculation of particle accelerations at the pulse signal reception points, as well as the calculation of the energy density flux of the vector field were performed.

A description of a program for computation of acoustic fields in 3D shallow-water waveguides of arbitrary form is presented. This program is a C++ implementation of a numerical solver of wide-angle mode parabolic equations. The user can specify sound speed distribution, bottom relief, and the structure of bottom layers via configuration files when performing acoustic field simulation. The output of the program consists of one or several horizontal cut planes of the acoustic pressure field at specified depths. One of the main advantages of the implemented method is its high computational efficiency. The developed program is open-source and available online. It can be of interest for specialists in different areas of ocean acoustics who perform the modeling of sound propagation in course of the solution of various practical problems.