# Application of Waveguide Invariant Theory to Analysis of Interference Phenomenon in Deep Ocean

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Waveguide Invariant Model

## 3. Numerical Simulation

^{3}, and attenuation coefficient of 0.1 dB/λ. The sound speed of the lower half space is 1800 m/s, and density is 2200 kg/m

^{3}. The source depth is 150 m and the hydrophone is located at 4500 m in depth. Note that the critical depth is 4100 m. Frequency bandwidth is 50–350 Hz and source ranges are from 5 to 70 km.

## 4. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 2.**Intensity versus range and frequency. The intensity is divided into three parts, such as zone-a, zone-b, and zone-c, according to artificial observation.

**Figure 3.**Acoustic intensity from all modes. The solid black line is the trajectory of source moving radially from the hydrophone.

**Figure 4.**Transmission loss. (

**a**) Refracted and surface reflected (RSR) modes only, phase speeds are less than sound speed; (

**b**) surface reflected and bottom reflected (SRBR) modes, phase speeds are between the sound velocity at the deepest depth in the water column and half space speed.

**Figure 5.**The dependence of waveguide invariant (WI) on phase speed and frequency. (

**a**) Frequency is 50 Hz; (

**b**) frequency is 150 Hz; (

**c**) frequency is 250 Hz; (

**d**) frequency is 350 Hz.

**Figure 6.**Intensity according to phase speed intervals in Figure 5. (

**a**) Phase speed < 1567.3 m/s; (

**b**) 1567.3 m/s < phase speed < 1600 m/s; (

**c**) 1600 m/s < phase speed < 1800 m/s.

**Figure 7.**Intensity versus range and frequency. According to Figure 6, it is divided into five sections: zone-a2, zone-a1, zone-b, zone-c2 and zone-c1.

**Figure 8.**The intensity varies with different attenuation coefficients. (

**a**) 0 dB/$\lambda $; (

**b**) 0.2 dB/$\lambda $; (

**c**) 0.4 dB/$\lambda $; (

**d**) 0.6 dB/$\lambda $.

**Figure 9.**The WI parameter $\beta $ varies with different attenuation coefficients. (

**a**) 0 dB/$\lambda $; (

**b**) 0.2 dB/$\lambda $; (

**c**) 0.4 dB/$\lambda $; (

**d**) 0.6 dB/$\lambda $.

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**MDPI and ACS Style**

Yao, Y.; Sun, C.; Liu, X.
Application of Waveguide Invariant Theory to Analysis of Interference Phenomenon in Deep Ocean. *Acoustics* **2020**, *2*, 595-604.
https://doi.org/10.3390/acoustics2030031

**AMA Style**

Yao Y, Sun C, Liu X.
Application of Waveguide Invariant Theory to Analysis of Interference Phenomenon in Deep Ocean. *Acoustics*. 2020; 2(3):595-604.
https://doi.org/10.3390/acoustics2030031

**Chicago/Turabian Style**

Yao, Yuan, Chao Sun, and Xionghou Liu.
2020. "Application of Waveguide Invariant Theory to Analysis of Interference Phenomenon in Deep Ocean" *Acoustics* 2, no. 3: 595-604.
https://doi.org/10.3390/acoustics2030031