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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.

The analysis results of the type surface and vegetation changes in the Exclusion Zone of Chornobyl Nuclear Power Plant, for the period after accident in 1986 until 2017 are presented. In the article it is shown that after the Chornobyl accident in 1986, the largest changes occurred with vegetation on agricultural lands. Analysis of the current state of vegetation showed that the area of restored forest plantations on uncultivated lands amounted to –31% of the Chornobyl NPP Exclusion Zone. Studies have shown that fires cause great damage to the forest ecosystems. Forests and woody vegetation of natural regeneration damaged by the fire in the Chornobyl NPP Exclusion Zone as of 2017 amounted to 41.3 km2, which is about 4% of the area of forest vegetation. It is noted that the movement of certain volumes of radioactive waste from temporary storage points affect changes in the levels of pollution of environmental components in the Chornobyl NPP Exclusion Zone. Cartographic calculations showed that the areas allocated for the enterprises of the main and auxiliary cycle in the Chornobyl NPP Exclusion Zone occupy an area of about 56 km2 , of which 42% is covered with woody vegetation. The condition of such forested areas affects fire safety on stationary and temporary areas intended for localization of radioactive waste. It is stated about the expediency of organizing mineralized strips, conducting timely measures to care for plantations around such areas. Such measures are — felling of damaged stands, clearing the area of dead parts of trees, planting forests on burned areas. Maps obtained after the analysis and assessment of spatial heterogeneity of the territory are presented in the article. The maps show the location of areas of enterprises that may be sources of radioactive contamination and natural complexes that was changed. It created a set of digital raster and vector maps which reflect the structure of the study area for different periods. Vector maps were developed based on remote sensing data and fairly accurately reflect the modern structure of the territory, capture processes occurring within the territory. It concluded that the cartographic classification of objects on the ground surface and types of vegetation may be used for analyzing changes in the Exclusion Zone and unconditional resettlement of Chornobyl NPP, as well as parameterization of the type of underlying surface for assessment of environmental pollution. It is noted that the combination of the created cartographic material with the data of actual surveys of forest ecosystems makes it possible to more accurately determine the amount of bioresources of the Exclusion Zone in areas with high levels of pollution. The obtained cartographic materials make it possible to determine and display the modern spatial structure and characteristics on the Earth’s underlying surface and to calculate the areas in the changed territory.

A wide-angle mode parabolic equation is obtained from the horizontal refraction equation by using the rational-linear approximation of the square-root operator. A finite-difference scheme for the numerical solution of the derived equation is developed. The scheme is based on the standard Crank–Nicolson method and fully-discrete transparent boundary conditions which allow for an accurate simulation of sound propagation on an unbounded domain.

The modelling of sound propagation in the ocean by the solution of mode parabolic equations is discussed. Mode parabolic equations can be obtained as the one-way approximation to horizontal refraction equations for modal amplitudes. Their wide-angle capabilities depend on the order of the Pade approximation of the involved pseudo-differential operators. Various aspects of numerical solution methods for wide-angle mode parabolic equations are considered in detail, including artificial domain truncation and Cauchy initial data for the point source field approximation. The capabilities of the discussed numerical approaches are demonstrated in several important test cases, including the problems of sound propagation in a penetrable wedge and in a sea with an underwater canyon.

Recently a new approach to the modeling of one-way wave propagation in Kerr media was proposed [1]. Within this approach the solution of the nonlinear Helmholtz equation is approximated by a series of solutions of iterative parabolic equations (IPEs). It was also shown that IPEs take the nonparaxial propagation effects into account. In this study we develop an efficient pseudospectral numerical method for solving the system of IPEs. The method is a generalization of an exponential time differencing (ETD) method for the nonlinear Schrodinger equation [2]. The ETD technique is well-suited for the system of IPEs, as it allows to reduce the order of the derivative in the input term.