Simulation of acoustic waves horizontal refraction using a three-dimensional parabolic equation model

Youngnam Na; Su-Uk Son; Jooyoung Hahn; Keunhwa Lee

doi:10.7776/ASK.2022.41.2.131

All Issue

2022 Vol.41, Issue 2 Preview Page Next Page

Research Article

Simulation of acoustic waves horizontal refraction using a three-dimensional parabolic equation model 3차원 포물선방정식을 이용한 음파의 수평굴절 모의

31 March 2022. pp. 131-142

PDF XML

Abstract

In order to examine the possibility of horizontal simulations of acoustic waves on the environments of big water depth variations, this study introduces a 3-dimensional model based on the pababolic equation. The model gives approximated solutions by separating the cross- and non cross-terms in the equation. Assuming artificial bathymetry (25 km × 4 km) with a source frequency 75 Hz, the simulations give clear horizontal refractions on the transmission loss distributions. The degree of refractions shows non-linear increase along the propagating range and proportional increase with water depth along the cross range. Another simulations with the real bathymetry (25 km × 8 km) also give clear horizontal refractions. The horizontal distributions present little difference with the depth resolution variations of the same data source because the model gives interpolations over the depth data before simulations. Meanwhile, the horizontal distributions show big difference with those of different data sources.

Keywords

Parabolic equation

Cross-term

Horizontal refraction effects

3-dimensional low-frequency modeling

본 연구에서는 동해 수심변화가 큰 해양환경 하에서 음파의 수평굴절 모의 가능성을 고찰하고자 포물선방정식 기반의 3차원 모델을 도입한다. 이 모델은 상관항과 비상관항을 분리함으로써 근사적 해를 제공한다. 가상 수심분포(25 km × 4 km)에 대해 주파수 75 Hz인 음원을 가정하여 모의한 결과는 전달손실의 수평분포 상 분명한 수평굴절을 보인다. 이 굴절 정도는 전파 거리에 비선형적으로 증가하고 횡방향 수심 경사도에 비례하여 증가한다. 실제 수심분포(25 km × 8 km)에 대한 모의 결과도 이러한 수평굴절을 잘 보인다. 수평굴절은 동일 자료 내에서는 해상도별로 수평 음장분포가 크게 변하지 않는데, 이는 모델이 모의 전 수심자료에 대해 내삽을 하기 때문이다. 반면, 수심자료 종류가 다를 경우 수평음장 분포는 크게 달라진다.

키워드

포물선방정식

상관항

수평굴절효과

3차원 저주파모델링

References

F. B. Jensen, W. A. Kuperman, M. B. Porter, and H. Schmidt, Computational Ocean Acoustics, 2nd ed (Springer, NY, 2011), pp. 1-612. 10.1007/978-1-4419-8678-8_1

K. Lee, "A study on the 3D low-frequency acoustic propagation model for the development of an integrated ocean surveillance system," ADDR-415-193072, The 3rd year final Rep., 2019.

K. Lee, W. Seong, and Y. Na, "Three-dimensional Cartesian parabolic equation model with higher-order cross-terms using operator splitting, rational filtering, and split-step Padé algorithm," J. Acoust. Soc. Am. 146, 2041-2049 (2019). 10.1121/1.512542831590535

K. Lee, W. Seong, and Y. Na, "Split-step Pada' solver for three-dimensional Cartesian acoustic parabolic equation in stair-step representation of ocean environment," J. Acoust. Soc. Am. 146, 2050-2057 (2019). 10.1121/1.512559231590520

Y. Lin and T. F. Duda, "A higher-order split-step Fourier parabolic equation sound propagation solution scheme," J. Acoust. Soc. Am. 132, EL61-EL-67 (2012). 10.1121/1.473032822894317

K. B. Smith, "Convergence, stability, and variability of shallow water acoustic predictions using a split- step Fourier parabolic equation model," J. Comput. Acoust. 9, 243-285 (2001). 10.1142/S0218396X01000401

D. Yevick and D. Thomson, "A hybrid split-step/ finite- difference PE algorithm for variable-density media," J. Acoust. Soc. Am. 101, 1328-1335 (1997). 10.1121/1.418160

K. Lee and W. Seong, "Full 3D one-way parabolic equation algorithm" (in Korean), J. Acoust. Soc. Kr. 25, 67-68 (2006).

K. Lee and W. Seong, "The perfectly matched layer applied to the split-step Padé PE solver in an ocean waveguide," J. Acoust. Soc. Kr. 25, 131-136 (2006).

Y. Zhnag, J. Cohen, and J. D. Owens, "Fast trigonal solvers on the GPU," Proc. 15th ACM SIGPLAN Symp. on PPoPP. 127-136 (2010). 10.1145/1837853.1693472

K. Stowe, Ocean Science, 2nd Ed (John Wiley & Sons, NY, 1983), pp. 1-673.

Y. Na, S. U. Son, and Y. Hahn, "The development results on the submarine acoustic information management system (SAIMS3)," ADDR-415-201878, The 3rd year Rep., 2020.

Information

Publisher :The Acoustical Society of Korea
Publisher(Ko) :한국음향학회
Journal Title :The Journal of the Acoustical Society of Korea
Journal Title(Ko) :한국음향학회지
Volume : 41
No :2
Pages :131-142
Received Date : 2022-01-05
Revised Date : 2022-02-03
Accepted Date : 2022-02-28
DOI :https://doi.org/10.7776/ASK.2022.41.2.131

The Journal of the Acoustical Society of Korea ISSN:1225-4428(Print) 2287-3775(Online) 한국음향학회지

All Issue