An interpretation experiment on eddies’ role in sound propagation in the ocean using ray model

The relationship between mesoscale eddies and ambient acoustic propagation under different conditions were studied using high resolution ocean reanalysis products in South China Sea, which was summarized by a linear-equation representing the convergence zone change with respect to eddy signatures and source positions. Beyond the experiments scales, warm eddies “dragged” the sound propagation and cold eddies “squeezed” that in contrast, and the acoustic amplifying mechanism can be summarized as stronger(eddies), nearer(eddies) and deeper(source).


Introduction
Research on sound propagation in the ocean has significant implications for various applications, including underwater communication and ocean environmental monitoring.Mesoscale eddies are vortices with diameters ranging from tens to hundreds of kilometers in the ocean, and have significant dynamic characteristics and special ecological environments, which, as a typical thermo structure in the ocean, have a significant impact on sound propagation.The study in different impact modes and the influence extent of mesoscale eddies on sound propagation dependent on eddy attributes such as size, intensity and polarity etc., were conducted in-depth using modeling and interpretation, in order to advance the interpretation and application of numerical products related to mesoscale eddies and enhance research on hydroacoustic applications.
This study is organized as follows: First, by collecting and organizing on-site observation data, we understand the characteristics of mesoscale eddies such as their shapes, polarity, intensity, and spatial distribution.Then, using the ray tracing model, the impact of different vortex properties (such as types, intensity, radius, core position etc.) and relative position between source and eddies(in/on/out of eddy) on sound propagation and analyzed possible mechanism were explored and convergence zone is examined as a key variable.Finally, based on the qualitative analysis results of the convergence zone, linear regression is utilized as the interpretation method to proposed an indexation scheme as guidance to quickly obtain the drift of convergence zone under position-ascertained source and features-aware eddy conditions.

Acoustic ray tracing Model
The theoretical basis for underwater acoustic field modeling is the wave equation, including the commonly used methods like ray tracing algorithm, normal modes (NM), parabolic equation (PE), fast field (FFP) algorithms etc..With clear physical meaning and faster computational speed and more intuitive results, ray tracing methods are suitable for calculating high-frequency short-range sound fields.However, traditional ray tracing methods have limitations in calculating low-frequency and shadow zone sound fields, which was improved by introducing the Gaussian approximation method from seismology into underwater sound field calculations in the 1980s, [1].The BELLHOP model proposed in 1987 [2] has been selected by the US Navy as the standard model for sound propagation in the 10-100 kHz range [3], which is also currently one of the commonly used acoustic modeling methods , thus suitable for this study as well.

Mesoscale Eddy Model
Due to the difficulty in collecting a large amount of mesoscale eddy observation data, this experiment adopts the Gaussian eddy model [4] to describe the propagation characteristics of sound in the ocean mesoscale eddy environment.The sound velocity distribution is determined by the following mathematical expression [5]: Where, DC is the vortex intensity, which represents the maximum sound speed difference between the vortex core and the outer edge of the vortex.When there are cold vortexes, DC is negative and when there are warm vortexes, DC is positive.Re is the horizontal position of the vortex core, DR is the horizontal radius of the vortex, DZ is the vertical radius of the vortex, and Ze is the vertical position of the vortex core.
Using Gaussian algorism, when cold eddies exist, the isopleths distribute horizontally in an oval shape, and the core of cold eddies has an area of minimal acoustic velocity; When warm eddies exist, the ambient sound velocity significantly increases.As the vortex radius increases, the influence range of vortex on sound velocity increases as well.It can be concluded that the Gaussian vortex model can be used to reproduce the basic features of the sound velocity distribution of the mesoscale eddies.

Experiment Settings
Mesoscale eddies are widely distributed in the world's oceans.Over the past few decades, extensive research on the statistical characteristics of mesoscale eddies in the ocean were carried out [6][7][8], revealing the typical eddies reaching out to a diameter of 150km and a depth of 1000m.Thus to make the experiment representative, the eddy attributes in this study are set as follows: the eddy radius DR is set to 50, 75, 100, 125, and 150 kilometers and the eddy intensity DC is set to 40, 20, -20, and -40, respectively.The core depth Ze is 500 meters, and the vertical radius DZ is 500 meters.To understand the influence of the relative position between the sound source and the eddy core on sound propagation, the background sound field of the eddy was shifted to reflect changes in their horizontal relative position.The horizontal distance Re of the eddy core was set to DR+5km (upstream of the eddy), DR (on the edge), 1/2DR (interior of the eddy), and 0km (at the core), and the 100Hz sound source of depth was placed at depths of 100m, 200m, 300m, and 400m vertically.Background temperature data used as the none-eddy control run is constructed from smoothed reanalysis data and the temperature fields from Gaussian model is added depending on different experiment setting.

Simulation results
The effects of the horizontal/vertical position of the sound source and the attributes of the eddies on sound propagation were discussed in detail by setting the sound source frequency to 100Hz at depths of 100m, 200m, 300m, and 400m, the receivers spacing to 100 meters and the depth of the sea bed to 5000m.

Horizontal position of the sound source
The influence of the relative position between the horizontal position of the sound source and eddy cores on the shift of convergence zone was experimented.Figure 1a-h show the sound loss maps for an eddy radius of 50km, with the sound source located at the core, midpoint of the vortex radius, vortex edge, and 5km outside the vortex, i.e., the distance from the sound source to the vortex core is 0, 25, 50, and 55km, respectively.The sound source depth is 100m, and the vortex intensity DC is 40 and -40. Figure 2i represents the case when DC=0, i.e., no eddy exists.The results show that as the relative distance between the sound source and the vortex core decreases, compared to the case without a vortex, the convergence zone exhibits a small rearward shift and a significant increase in the inversion depth under a warm eddy condition, which means the convergence effect is gradually strengthened, producing a "magnification" effect.When a cold eddy exists, as the distance between the sound source and the vortex core decreases, the convergence zone exhibits a forward shift and a significant decrease in the inversion depth, resulting in a "compression" effect on the convergence zone.
A simulation with the same setting of Figure 2 except for the sound source depth is 400m is carried out as well.The results show that compared with the case when the sound source depth is 100m, with the decrease of the relative distance between the sound source and the vortex core, when a warm eddy exists, the convergence zone exhibits a more obvious rearward shift, and the inversion depth increases more significantly.At a closer distance to the vortex core, the sound field structure changes greatly, and the "magnification" effect is more obvious.When a cold eddy exists, as the distance between the sound source and the vortex core decreases, the convergence zone exhibits a more significant forward shift and a decrease in the inversion depth, also with an enhanced "compression" effect.

Source depth
This section mainly discusses the influence of sound source depth on the convergence zone.Figure 2 show the sound propagation loss maps for a warm/none/cold vortex radius of 50km, with the sound source located at the vortex edge, i.e., 50km from the vortex core, at a depth of 100m(left panels) and 400m(right panels), and with vortex intensity DC of 40, 0, and -40.The results show that regardless of the presence of a mesoscale eddy, the inversion depth of the convergence zone decreases with the source depth increases, and the distinction between the convergence zone and shadow zone are weaker when source is deeper with an eddy background.

Eddy size
The sound propagation loss maps were drawn but bot shown for vortex radius of 50 and 150km, with the sound source located at the vortex edge, i.e., 50 and 150km from the vortex core, at a depth of 100m, and with vortex intensity DC of 40 and -40.The results show that with the increase of vortex radius, regardless of cold eddies or warm eddies, the position, width, and structure of the first convergence zone do not produce significant changes.When a warm eddy exists, the width of the convergence zones following the first one increases, the position shifts rearward, and the structure becomes more scattered.When a cold eddy exists, the width of the convergence zones following the first one decreases, the position shifts forward, and the structure becomes more concentrated.

Eddy intensity
The sound propagation loss maps were drawn but not shown here for a vortex radius of 50km, with the sound source located at the vortex edge at a depth of 100m, i.e., 50km from the vortex core.The vortex intensity DC are 40, 20, -20, and -40.The results show that under the current conditions, when a warm eddy exists, the position of the convergence zone will shift rearward and increase the inversion depth, while maintaining a relatively complete convergence zone structure.The characteristics of the shadow zone will weaken, and these effects are more pronounced with increasing eddy intensity.When a cold eddy exists, with increasing eddy intensity, the position of the convergence zone shifts forward and becomes more scattered, while reducing the inversion depth.

Conclusions and discussions
Based on the previous results, it can be concluded that the source location and depth, eddy radius and intensity can all shift the convergence zone to different degrees.Figure 3 summarize the statistics of the first convergence zone position when the sound source is located at the vortex core, midpoint of the vortex radius, vortex edge, and 5km outside the vortex, and the sound source depth is set to 100m, 200m, 300m, and 400m, the vortex radius DR is 100km, and for simplification, only the maximum vortex intensity DC ±40 is shown.The overall statistical results show that as the intensity of warm(cold) eddies increases, the distance of the first convergence zone gradually increases(decreases); as the sound source approaches the vortex core, the influence degree of the vortex on the distance of the first convergence zone gradually increases; and as the sound source depth enhanced the shift of the first convergence zone.Beyond the experiments scales, warm eddies "dragged" the sound propagation and cold eddies "squeezed" that in contrast, and the acoustic amplifying mechanism can be summarized as stronger(eddies), nearer(eddies) and deeper(source).The detailed conclusions can be drawn as follows: (1) The relative distances of warm eddies are mostly positive and those of cold eddies are negative, indicating that warm eddies tend to increase the distance of the convergence zone, while cold eddies tend to decrease it.Moreover, the impact of cold eddies on the distance of the convergence zone is greater than that of warm eddies.
(2) When the depth of the sound source increases, regardless of the presence of mesoscale eddies, the inversion depth of the convergence zone decreases, and the presence of eddies weakens the difference of the convergence and shadow zone.
(3) Changes in the vortex radius have a relatively small impact on the position of the first convergence zone and mainly affect the structure of subsequent convergence zones.
(4) Cold eddies cause the convergence zone to shift forward and increase the inversion depth, while warm eddies cause the convergence zone to shift rearward and deepen the inversion depth.The stronger the vortex is, the greater the magnitude of the shift of the inversion depth and the convergence zone.

Figure 3 .
Figure 3. Statistical relationship between the distance of the first convergence zone from the source and different source and eddy attributes.Legend show the case name in form of DC/Zs, where Zs is source depth and the sign of DC is the type of eddies, ie.positive/negative DC represents warm/cold eddies.