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There are two kinds of definitions for waveguide invariant β. One is defined according to the striation slope of acoustic interference patterns, and the other is defined on the basis of dispersion characteristics of acoustic modes. The first definition is appropriate for engineering applications, while the second is suitable for theoretical analysis. However, the two definitions are not consistent with each other for a waveguide with thermoclines, because modal dispersion in such a waveguide can be very different for different modes and different frequencies. In such cases, the waveguide invariant defined according to modal dispersion can take many different values, which are referred to as the spectrum of waveguide invariant (β spectrum for short) in the paper. Each β spectrum can be related to some interference striation patterns with corresponding striation slopes. The sound field is composed of many modes, so the interference pattern is the summation of many components of different striation slopes and may be very complicated as a result of the diversity of β spectrum. In such a case one single β is not able to describe the complicated interference pattern adequately; instead multiple values of β spectrum are required. From the point of view of engineering application, however, the present β-extracting methods can only give one optimal value, and thus a lot of information is lost. In this paper an algorithm for doing so, called β spectrum separation technique, is proposed. By adopting the concept of integral projection used in digital image processing, the image of acoustic intensity is projected at different angles to separate out the striations of different slopes; and then fast Fourier transform (FFT) is applied to the projected curve in order to isolate striations of different spacing from each other. The values for β spectrum can be computed according to striation slopes, which are also mapped into the positions of their corresponding acoustic modal horizontal wavenumber differences in the wavenumber domain. The applicability of this algorithm for the extraction of β spectrum is tested and verified by simulation results and experiment data. It is shown that the algorithm can separate out each β spectrum of different intensity components from acoustic interference structure. The algorithm maps β spectrum into a two-dimensional plane thereby being able to suppress noise more effectively and work in the condition of low signal-to-noise ratio compared with the already-existing β-extracting algorithms.
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Keywords:
- waveguide invariant spectrum /
- striation slope /
- striation separation distance /
- integral projection
[1] Chuprov S D (Ed. By Brekhovskikh L M and Andreevoi I B) 1982 Ocean Acoustics: Current State (Moscow: Nauka) p71
[2] Brekhovskikh L M, Lysanov Yu P 2002 Fundamentals of Ocean Acoustics (Moscow: AIP Press) pp143-148
[3] Cockrell K L, Schmidt H 2011 J. Acoust. Soc. Am. 130 72
[4] Turgut A, Orr M, Rouseff D 2010 J. Acoust. Soc. Am. 127 73
[5] Cockrell K L, Schmidt H 2010 J. Acoust. Soc. Am. 127 2780
[6] Thode A M, Kuperman W, Dspain G L, Hodgkiss W 2000 J. Acoust. Soc. Am. 107 278
[7] Thode A M 2000 J. Acoust. Soc. Am. 108 1582
[8] Zhao Z D, Wang N, Gao D Z, Wang H Z 2010 Chin. Phys. Lett. 27 064301
[9] Yang T C 2003 J. Acoust. Soc. Am. 113 1342
[10] Tao H, Krolik J L 2008 J. Acoust. Soc. Am. 123 1338
[11] Su X X, Zhang R H, Li F H 2006 Acta Acustica 31 305 (in Chinese) [苏晓星, 张仁和，李风华 2006 声学学报 31 305]
[12] Hodgkiss W S, Song H C, Kuperman W A 1999 J. Acoust. Soc. Am. 105 1597
[13] Kim S, Kuperman W A, Hodgkiss W S, Song H C, Edelmann G F, Akal T 2003 J. Acoust. Soc. Am. 114 145
[14] Shang E C, Wu J R, Zhao Z D 2012 J. Acoust. Soc. Am. 131 3691
[15] Potty G, Miller J, Lynch J, Smith K 2000 J. Acoust. Soc. Am. 108 973
[16] Bonnel J, Gervaise C, Nicolas B, Mars J 2012 J. Acoust. Soc. Am. 131 119
[17] Heaney K D 2004 IEEE J. Ocean. Eng. 29 88
[18] Ren Q Y, Hermand J P 2013 J. Acoust. Soc. Am. 133 82
[19] Lu L C, Ma L 2015 Acta Phys. Sin. 64 024305 (in Chinese) [鹿力成, 马力 2015 物理学报 64 024305]
[20] Bonnel J, Le T G, Nicolas B, Jéróme I M 2013 IEEE Signal Proc. Mag. 30 120
[21] Hough P V C 1962 US Patent No. 3069654
[22] Deans S R 1983 The Radon Transform and Some of Its Applications (New York: Wiley)
[23] Rouseff D 2001 Waves in Random Media 11 377
[24] Rouseff D, Zurk L M 2011 J. Acoust. Soc. Am. 130 76
[25] Zhao Z D, Wu J R, Shang E C 2015 J. Acoust. Soc. Am. 138 223.
[26] Zhang W Z, Chen Q, Du D, Sun Z G 2005 J. Tsinghua Univ. (Sci. & Tech.) 45 1446 (in Chinese) [张文增, 陈强, 都东, 孙振国 2005 清华大学学报 45 1446]
[27] Liu J, Saito Y, Kong X H, Wang H, Wen C, Yang Z G, Nakashima R 2010 Marine Geology 278 54
[28] Zhang J Q 2012 Ph. D. Dissertation (Qingdao: Ocean University of China) (in Chinese) [张军强 2012 博士学位论文 (青岛: 中国海洋大学)]
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[1] Chuprov S D (Ed. By Brekhovskikh L M and Andreevoi I B) 1982 Ocean Acoustics: Current State (Moscow: Nauka) p71
[2] Brekhovskikh L M, Lysanov Yu P 2002 Fundamentals of Ocean Acoustics (Moscow: AIP Press) pp143-148
[3] Cockrell K L, Schmidt H 2011 J. Acoust. Soc. Am. 130 72
[4] Turgut A, Orr M, Rouseff D 2010 J. Acoust. Soc. Am. 127 73
[5] Cockrell K L, Schmidt H 2010 J. Acoust. Soc. Am. 127 2780
[6] Thode A M, Kuperman W, Dspain G L, Hodgkiss W 2000 J. Acoust. Soc. Am. 107 278
[7] Thode A M 2000 J. Acoust. Soc. Am. 108 1582
[8] Zhao Z D, Wang N, Gao D Z, Wang H Z 2010 Chin. Phys. Lett. 27 064301
[9] Yang T C 2003 J. Acoust. Soc. Am. 113 1342
[10] Tao H, Krolik J L 2008 J. Acoust. Soc. Am. 123 1338
[11] Su X X, Zhang R H, Li F H 2006 Acta Acustica 31 305 (in Chinese) [苏晓星, 张仁和，李风华 2006 声学学报 31 305]
[12] Hodgkiss W S, Song H C, Kuperman W A 1999 J. Acoust. Soc. Am. 105 1597
[13] Kim S, Kuperman W A, Hodgkiss W S, Song H C, Edelmann G F, Akal T 2003 J. Acoust. Soc. Am. 114 145
[14] Shang E C, Wu J R, Zhao Z D 2012 J. Acoust. Soc. Am. 131 3691
[15] Potty G, Miller J, Lynch J, Smith K 2000 J. Acoust. Soc. Am. 108 973
[16] Bonnel J, Gervaise C, Nicolas B, Mars J 2012 J. Acoust. Soc. Am. 131 119
[17] Heaney K D 2004 IEEE J. Ocean. Eng. 29 88
[18] Ren Q Y, Hermand J P 2013 J. Acoust. Soc. Am. 133 82
[19] Lu L C, Ma L 2015 Acta Phys. Sin. 64 024305 (in Chinese) [鹿力成, 马力 2015 物理学报 64 024305]
[20] Bonnel J, Le T G, Nicolas B, Jéróme I M 2013 IEEE Signal Proc. Mag. 30 120
[21] Hough P V C 1962 US Patent No. 3069654
[22] Deans S R 1983 The Radon Transform and Some of Its Applications (New York: Wiley)
[23] Rouseff D 2001 Waves in Random Media 11 377
[24] Rouseff D, Zurk L M 2011 J. Acoust. Soc. Am. 130 76
[25] Zhao Z D, Wu J R, Shang E C 2015 J. Acoust. Soc. Am. 138 223.
[26] Zhang W Z, Chen Q, Du D, Sun Z G 2005 J. Tsinghua Univ. (Sci. & Tech.) 45 1446 (in Chinese) [张文增, 陈强, 都东, 孙振国 2005 清华大学学报 45 1446]
[27] Liu J, Saito Y, Kong X H, Wang H, Wen C, Yang Z G, Nakashima R 2010 Marine Geology 278 54
[28] Zhang J Q 2012 Ph. D. Dissertation (Qingdao: Ocean University of China) (in Chinese) [张军强 2012 博士学位论文 (青岛: 中国海洋大学)]
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