Formation Characteristics of the Zonal Structure of Acoustic Fields in the Deep Part of the Sea of Japan

The results of modeling the effects of stochastic levels of sound speed on formation of the zonal structure of acoustic fields for the hydrologic and acoustic environment of the deep part of the Sea of Japan. Numerical experiment involved calculation of the vertical structure of acoustic fields at the ranges from 20 to 120 km with discontinuity equal to 50 m in beam zooming for the set values of random component of sound speed field. In accordance with calculation, analytical correlations of changing coordinates of the closest and the furthest borderlines of the first three convergence zones at emitter depth depending on the level of random component of sound speed field were determined. Changes in borderlines of convergence zones occur in accordance with linear law; this said, the closest borderlines shift towards the emitter and the furthest borderlines – away from it. The obtained results of analyzing changes in structure of vertical distribution of acoustic field at the borderlines of convergence zones can be applied for engineering the systems of underwater monitoring for detection of local disruptions of acoustic velocity field of various nature against natural stochastic parameters of water environment in the deep part of the Sea of Japan.


Introduction
Zonal structure of an acoustic field is the interleaved sequence of zones of illumination and shade. It is formed with converging ray tracings and sound focus in convergence zones (CZ) due to refraction and outlet of acoustic beams that propagate in underwater waveguides to the surface. The outstretch of zones depends on the distance from emitter to the axis of underwater acoustic channel and changes with increase of sequential number of the zonehorizontal outstretch of convergence zones increases and the shade zones become smaller.
The results of experimental research of long-range acoustic propagation in the ocean significantly differs from the expected ones that were obtained via smooth profiles of sound speed. Illumination of the acoustic shade zone, the CZ shift, and an earlier arrival of acoustic beams are observed [1][2][3][4]. For instance, position of the closest borderline of the first convergence zone for the regions of the Indian Ocean, the Mediterranean Sea, the Sea of Japan and The Norwegian Sea show differences of experimentally obtained values from expected ones by 0,5-2,5 km [5]. Dependence of shift of the starting part of the first convergence zone towards the sound emitter on the depth in comparison with calculation data was observed in the Atlantic ocean (approximately by 2 km with receiving depth of 190 m and by 2.5-3 km with receiving depth of 880 m); moreover, there was a more significant shift of the second convergence zone in comparison to the first onefor the first zone of convergence it was approximately 3-3.5 km and 4-4.5 kmfor the second one [3]. The difference between numerical mod- eling and experimental data is usually explained with small-scale inconsistency of the sound speed due to temperature and salt-content fluctuations that must be taken into account when modeling acoustic propagation in the ocean [4,6,7].
This work presents results of modeling the influences of small-scale hydrological inhomogeneities on formation of zonal structure of acoustic field for hydrologic and acoustic environment of the deep part of the Sea of Japan in ray approximation. Numerical research of acoustic fields allows to predict correctly the key characteristics of received signals at the channels that are a few thousands of kilometers long. The results obtained via approximation the ray acoustics fairly correlate with both calculations via method of parabolic equation and data of natural experiments [8].
In calculative models of effects of small-scale hydrological inhomogeneities, the sound speed field is represented as where C 0 (x,z) -is the determined component of the acoustic velocity field, which generally smoothly depends on both coordinates, and ∆C ≈ (x,z) -is the random component; this said, C  (x,z)=0, х, zare the coordinates of range and depth accordingly.

Initial data of the numerical experiment
The research of the zonal structure of acoustic field was conducted based on numerical solution of the ray tracing equation in alternate field of sound speed that was obtained from the Fermat's principle. The Monte Carlo method was used for modeling the random component of sound speed field [9,10]. Research that was conducted earlier showed opportunity for determining stochastic level of the sound speed field for a particular region of the ocean through comparison of calculation results that were obtained via this given method of stochastic modeling of effects of small-scale inhomogeneities of sound speed on the acoustic field structure and these experiments for hydrologic environment of the Atlantic Ocean [11].
Zonal structure of the acoustic field in oceanic waveguide and the deep sea at various emitter depths significantly differs, which can be explained with difference of the axis depth of the underwater acoustic channelfor the deep sea it is about couple hundred meters and in oceanic waveguidesit is 1000 -1500 m. Databases of the interdepartmental information system for accessing resources of marine information systems and complex information support of the marine activities were used as initial data (ESIMO) [12], scheme of the region and profile of the vertical profile of the sound speed are represented in Figure 1.
Initial data for the numerical modeling: polygon length -120 km, emitter source is located higher than axis if the underwater acoustic channel at the depth of 50 m. The flare angle of the emitter is 6, which corresponds to the water propagation of ray tracings without multipath propagation from the seafloor and the surface for all selected values of the random component of the sound speed field. Discontinuity of output of ray tracings equals to 0.02. The random component of the sound speed field C  (x, z) was discretely changing from 0 to 0.3 m/s with discontinuity equal to 0.01 m/s. For each value C  (x, z) > 0 there were conducted 1000 experiments.

Results and discussion
The following results were obtained upon the conduct of the numerical experiments on determina-tion of changes of the closest and the furthest borderlines of the convergence zones at the emitter depth with regard to the level of random component. The closest borderlines of the convergence zone shift towards the emitter when the level of the random component increases and the furthest onesaway from it in accordance with linear law.   Based on correlations in Figure 2 it can be concluded that with set values of the level of the random component of sound speed field, the coordinates of the closest borderlines of the convergence zones shift towards the emitter at a longer distance then the furthest ones shift away from the emitter. This said, the higher the sequential number of the convergence zone, the stronger shift of the closest and the furthest borderline coordinates occurs. Figure 3 shows the correlations of changes of the vertical distribution of acoustic field at the closest and the furthest borderlines of the first three convergence zones depending on the level of random component of the sound speed field. As it follows from the presented materials, vertical distribution of the acoustic field have one distinct maximum; with increase in the level of the random component of the sound speed field from 0 to 0.3 m/s, the amplitudes of maximums decrease and their coordinates by depth shift sideways in accordance with linear law (see Table 1). In Table 1, zis the coordinate of depth of the maximum vertical propagation of sound speed field, bis the value of the random component of sound speed field, kis the size coefficient. As it follows from the presented materials, with increase of the sequential number of the convergence zone, the speed of coordinate shifting of the maximum vertical distribution of sound speed by depth at the closest borderlines increases and at the furthest onesdecreases. This said, the coordinates of depths of the maximum vertical distribution of acoustic field at the closest borderlines shift faster than at the furthest ones. Analytical correlations presented in Table 1 are determined via standard MS Excel functions with approximation accuracy equal to R 2 ≥ 0,97.

Conclusion
The results of the numerical experiments on the effects of the random component level of the sound speed field on the zonal structure of acoustic fields in the deep part of the Sea of Japan can be used for the development of experimental and theoretical methods of zoning the aquatoriums by the stochastic level of the water environment and choosing the optimal locations for the underwater monitoring systems that are based on methods of illuminative hydrology.