Modeling and simulation analysis of hydroacoustic field under ice

In order to study the effect of polar ice on sound propagation in seawater, the finite element method was used to establish a seawater sound propagation model with and without ice, and the influence of the presence of ice on the seawater sound propagation law was analyzed. The simulation results show that the energy of sound propagation in seawater has a certain loss when there is an ice layer compared with the case of no ice layer. Through frequency domain analysis, the propagation process of sound energy in seawater can be clearly seen. Normally, the sound energy generated by a point source at a suitable location will return to the seawater after passing through the sea surface, while after the addition of the ice layer, part of the sound energy generated by the point source will be lost to the air through the ice layer, resulting in a reduction of the acoustic energy returned to the seawater. As a result, there is less acoustic energy in the seawater than in the ice-free case.


Introduction
The Arctic is a barren land of extreme cold, covered in snow and ice all year round, but due to its special geographic location and the melting of sea ice brought about by increasing global warming, the value of the Arctic as an important shipping lane is constantly rising [1].Meanwhile, the strategic significance of exploring the Arctic under-ice acoustic field is also huge due to the large amount of fossil and ore resources in the Arctic.Modelling and simulation of the under-ice acoustic field is a prerequisite for large-scale exploration of the polar regions [2].Domestic research on the under-ice acoustic field started late, and only in 2016 did the Institute of Acoustics of the Chinese Academy of Sciences (CAS) carry out experiments related to polar under-ice acoustic propagation [3].
Foreign scholars carried out systematic experiments on polar hydroacoustic as early as the last century.The U.S. Navy used a nuclear submarine to do a comprehensive sampling of the Arctic ocean basin in 1993, which included tests related to Arctic under-ice sound propagation, and W.A kuperman et al. used a variety of perturbation methods to simulate the loss of under-ice sound propagation [4].Nevertheless, hardware and computational power limitations have made it difficult for past researchers to compute complex under-ice sound propagation processes using sound field modelling [5].The simple normal mode model represents the hydroacoustic field characteristics by superimposing discrete simple normal modes of different orders obtained by separating the variables, and Hardin et al. applied the parabolic equation method to hydroacoustic studies, relying on the standard parabolic equation form of the fluctuation equations obtained by narrow-angle approximation in the solution derivation process [6].However, although the above methods can explain the currently known hydroacoustic phenomena, they all need to make some approximations to the inhomogeneous properties of the ocean, resulting in a not very wide range of application.With the continuous development of the computer level and the improvement of the accuracy and complexity of the calculation results in the field of hydroacoustic, the finite element analysis method has begun to show its prominence [7].
FEA is to discretize the domain into a finite number of units connected by nodes, and then rely on the correlation between the units to form a series of finite element equations to get the solution, so the complex margin problem can be converted into a system of equations, so in the practical application of hydroacoustic field modeling, FEA is not limited by the complexity of the situation [8].In this paper, the acoustic field model in the polar ice environment is established and the propagation of acoustic waves in the underwater acoustic field under ice is simulated using the finite element method.

Construction of sound field model
Aiming at the sound propagation characteristics under the ice, this paper designs the sound field calculation model under the polar ice environment in the column coordinate system, according to the physical characteristics of the ice layer, seawater layer and seabed layer, respectively, using elastic medium, fluid medium and fluid medium to describe the acoustic characteristics of each layer, and establishes the calculation model of the ocean sound field under the polar ice including "air-ice layerwater layer-seabed layer", as shown in figure 1.
The horizontal scale is 4km and the vertical scale is 202m, of which the air layer is 50m, the ice layer is 2m, the water layer is 100m and the seabed layer is 50m.The sound velocity of the air is 343m/s and the density is 1.29kg/m 3 .The ice layer is in the middle of the air and water layers.Take the longitudinal wave speed of the ice layer as 3593.4m/s, the transverse wave speed as 1819.8m/s,and the density of the ice as 917 kg/m 3 .The density of the ice is 917 kg/m 3 .The speed of sound in water is 1500 m/s and the density of seawater is 1000 kg/m 3 .The longitudinal wave velocity at the bottom of the sea is 2400 m/s, the transverse wave velocity is 1200 m/s and the density of the sea is 1500 kg/m 3 .To simulate the absorption of the sound wave as it propagates away from the source, perfectly matched layers are placed on the right side of the model and on the bottom of the model.Finally, a point source is placed in a suitable location.

Application of basic theories
Since the circumferential derivative in column coordinates is zero when the data have axial symmetry, the Helmholtz equation for hydroacoustic propagation in the column coordinate system can be simplified to a two-dimensional axisymmetric form: where P is the sound pressure, ρ is the density, k is the wave number, r is the horizontal axis, and z is the vertical axis [9].
Due to the existence of the sea ice layer, there is a fluid-solid interface in the model, and the interaction between the two phases of the medium, the ice layer will deform or move under the action of seawater.The deformation or movement in turn affects the seawater movement, thus changing the distribution and magnitude of the seawater load, so it is necessary to use the fluid-solid coupling equation, the definition of the domain at the same time there is a fluid domain and the solid domain [10].
At the same time, because the acoustic energy flow diagram compared to the traditional sound pressure study more intuitive to show the uniformity of sound propagation in seawater, so this paper adopts the acoustic energy flow diagram as the basis of analysis, the definition of the equation is: where Ir is the acoustic energy propagated in the horizontal direction, Iz is the acoustic energy propagated in the vertical direction, and Iref is the reference value of acoustic energy.

Simulation and analysis
This research paper investigates the variances in sound transmission within seawater affected by polar ice by analysing the simulation results of the aqueous acoustic field in two different scenarios: one without ice and another with ice. Figure 2 illustrates the acoustic energy flow diagrams of the aqueous acoustic field model in the case without ice, whilst Figures 3 and 4 display the acoustic energy flow diagrams of the aqueous acoustic field model in the ice-covered scenarios (ice thicknesses of 1m and 4m without attenuation coefficients).

Figure 2. Energy flow diagram of the hydroacoustic field in the absence of ice
In the usual case of ice-free environment, the acoustic energy flow diagram of the hydroacoustic field is shown in figure 2, where the lighter color represents the higher energy.It can be seen that the acoustic energy emitted by the point source is reflected back into the seawater as it is transmitted to the sea surface-air boundary, and in the seawater, it is further diffused to the seafloor layer according to a certain law, which gradually decreases with increasing distance.The study maintained all other conditions while increasing the thickness of the polar ice sheet from 1m to 4m by simulating an underwater acoustic field model with 1m and 4m ice layers.The acoustic energy flow diagrams are provided in Figures 3 and 4, respectively.It is noteworthy that these diagrams clearly display substantial energy losses to the air, which explains the decrease in energy that returns to the seawater relative to the ice-free case, with slightly less energy returning in the case of thicker ice.The findings also reveal more energy loss to the air in the latter case.To facilitate accurate quantitative analysis of the hydroacoustic field models in the three different cases, the data was exported to the simulation software and further analysed using MATLAB.The resulting three comparative diagrams are displayed in Figure 5, illustrating the loss of acoustic energy in the absence of ice (blue curves), with 1 metre of ice (red curve), and with 4 metres of ice (black curve).A clear reduction in acoustic energy is observed in the first 100 meters of the ice case, in comparison to the hydroacoustic field present in the ice-free case.This reduction strongly suggests that a notable part of the energetic acoustics are lost to the air with increasing ice thickness.Additionally, it aligns with the conclusions derived from the acoustic energy flow diagrams.

Conclusion
Developing acoustic propagation models in both iced and ice-free seawater, gathering acoustic observations under varying conditions, and elucidating the dissimilarities in sound propagation in iced and ice-free seawater establish the foundation for future issues, namely acoustic inversion and the requirement for investigating the polar marine environment.The paper establishes an acoustic field model for a two-dimensional column coordinate system, both with and without ice, from a frequency domain perspective.
The results of the analysis indicate that the propagation of acoustic energy in seawater is affected under particular conditions of different parameters when ice is present on the sea surface.When ice is present, some of the acoustic energy produced by a point source at a suitable location is lost to the air via the ice, causing less acoustic energy to be returned to the seawater than when ice is not present.This effect is more pronounced as the thickness of the ice increases.Upon closer examination, it becomes evident that the initial energy loss during sound energy propagation is greatest when ice is present and decreases as the distance increases.

Figure 1 .
Figure 1.Under-ice water sound field model

Figure 3 .Figure 4 .
Figure 3. Energy flow diagram of the hydroacoustic field for an ice thickness of 1 m

Figure 5 .
Figure 5. Energy loss curves of the hydroacoustic field for three cases