—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.

The features of propagation of low-frequency tonal and pulsed acoustic signals generated at sea to land have been experimentally and theoretically studied. The accuracy in determining signals characteristics and, in particular, transmission losses using relatively simple measuring instruments (a hydrophone placed in a small water-filled container) is shown. The results of the calculating estimates for the sound field parameters on the coast formed by a source operating in the water layer are demonstrated. The calculations done by a program that uses a parabolic equation in the horizontal plane and vertical waveguide modes.

The paper presents the results of field measurements of acoustic fields generated in autumn hydrological conditions of the Sea of Japan shelf by a TON-320Hz autonomous signal emitter, moored in the sea at a depth of 34 m, as well as by a low-frequency pulsed pneumoemitter lowered from from a ship to a horizon of 10 m. Reception was via a hydrophone moored at a depth of 41 m from a digital radio-hydroacoustic buoy and the hydrophone of an autonomous acoustic recorder lowered together with an autonomous hydrological sonde from a drifting ship. Sound propagation from these sources was simulated by a wide-angle parabolic equation taking into account the elastic properties of rocks making up the bottom, as well as by a 3-D mode parabolic equation in the adiabatic approximation for a “fluid” bottom.

Приводятся результаты натурных измерений акустических полей, формируемых в осенних гидрологических условиях шельфа Японского моря автономным излучателем сигнала ТОН-320Гц, установленным в море глубиной 34 м, и низкочастотным импульсным пневмоизлучателем, опускаемым с борта судна на горизонт 10 м. Прием осуществлялся с помощью гидрофона, установленного на глубине 41 м цифрового радиогидроакустического буя и гидрофона автономного акустического регистратора, опускаемого вместе с автономным гидрологическим зондом с борта дрейфующего судна. Моделирование распространения звука от данных источников проведено с помощью широкоугольного параболического уравнения с учетом упругих свойств пород, слагающих дно, и 3-D модового параболического уравнения в адиабатическом приближении для “жидкого” дна.

A statistical analysis of fluctuations of the intensity and phase of underwater 315 Hz-sound signals measured on the fixed propagation paths oriented across the shelf of the Sea of Sapan was carried out. The spectra of fluctuations of the parameters of sound signals are compared with the power spectrum of internal waves measured in the same region. Typical dependences of the spectra of fluctuations of the sound signal intensity and phase upon the path length are established. The results of a computer simulation of the effect of a linear internal wave of the first mode propagating over the inclined bottom on the sound field are presented. Hydrological parameters and geometry of the experimental path are used as input data in the computer simulation.