Second order mode statistics as a function of range and source depth are presented from the Long Range Ocean Acoustic Propagation EXperiment (LOAPEX). During LOAPEX, low frequency broadband signals were transmitted from a ship-suspended source to a mode-resolving vertical line array. Over a one-month period, the ship occupied seven stations from 50 km to 3200 km distance from the receiver. At each station broadband transmissions were performed at a near-axial depth of 800 m and an off-axial depth of 350 m. Center frequencies at these two depths were 75 Hz and 68 Hz, respectively. Estimates of observed mean mode energy, cross mode coherence, and temporal coherence are compared with predictions from modal transport theory, utilizing the Garrett–Munk internal wave spectrum. In estimating the acoustic observables, there were challenges including low signal to noise ratio, corrections for source motion, and small sample sizes. The experimental observations agree with theoretical predictions within experimental uncertainty.
REFERENCES
1.
Andrew
, R.
, Zarnetske
, M.
, Howe
, B.
, and Mercer
, J.
(2010
). “Ship-suspended acoustical transmitter position estimation and motion compensation
,” IEEE. J. Ocean. Eng.
35
, 797
–810
.2.
Chandrayadula
, T. K.
, and Wage
, K. E.
(2008
). “Interpolation methods for vertical linear array element localization
,” in OCEANS
2008
, pp. 1
–5
.3.
Colosi
, J. A.
, and Brown
, M. G.
(1998
). “Efficient numerical simulation of stochastic internal wave-induced sound-speed perturbation fields
,” J. Acoust. Soc. Am.
103
, 2232
–2235
.4.
Colosi
, J. A.
, Chandrayadula
, T. K.
, Voronovich
, A. G.
, and Ostashev
, V. E.
(2013
). “Coupled mode transport theory for sound transmission through an ocean with random sound speed perturbations: Coherence in deep water environments
,” J. Acoust. Soc. Am.
134
, 3119
–3133
.5.
Colosi
, J. A.
, Duda
, T. F.
, and Morozov
, A. K.
(2012
). “Statistics of low-frequency normal-mode amplitudes in an ocean with random sound-speed perturbations: Shallow-water environments
,” J. Acoust. Soc. Am
131
, 1749
–1761
.6.
Colosi
, J. A.
, and Flatté
, S. M.
(1996
). “Mode coupling by internal waves for multimegameter acoustic propagation in the ocean
,” J. Acoust. Soc. Am
100
, 3607
–3620
.7.
Colosi
, J. A.
, and Morozov
, A. K.
(2009
). “Statistics of normal mode amplitudes in an ocean with random sound-speed perturbations: Cross-mode coherence and mean intensity
,” J. Acoust. Soc. Am
126
, 1026
–1035
.8.
Dozier
, L.
, and Tappert
, F.
(1978a
). “Statistics of normal mode amplitudes in a random ocean. 1. Theory
,” J. Acoust. Soc. Am.
63
, 353
–365
.9.
Dozier
, L.
, and Tappert
, F.
(1978b
). “Statistics of normal mode amplitudes in a random ocean. 2. Computations
,” J. Acoust. Soc. Am.
64
, 533
–547
.10.
Ewart
, T. E.
(1980
). “A numerical simulation of the effects of oceanic finestructure on acoustic transmission
,” J. Acoust. Soc. Am.
67
, 496
–503
.11.
Ewart
, T. E.
, Macaskill
, C.
, and Uscinski
, B.
(1983
). “Intensity fluctuations. Part 2: Comparison with the Cobb Experiment
,” J. Acoust. Soc. Am.
74
, 1484
–1499
.12.
Ferris
, R. H.
(1972
). “Comparison of measured and calculated normal-mode amplitude functions for acoustic waves in shallow water
,” J. Acoust. Soc. Am.
52
, 981
–988
.13.
Fisher
, R. A.
(1915
). “Frequency distribution of the value of the correlation coefficient in samples from an indefinitely large population
,” Biometrika
10
, 507
–521
.14.
Fisher
, R. A.
(1921
). “On the ‘probable error’ of a coefficient of correlation deduced from a small sample
,” Metron
1
, 1
–32
.15.
Fisher
, R. A.
(1990
). Statistical Methods, Experimental Design, and Scientific Inference
(Oxford University Press
, New York, NY
), Chap. 6, pp. 177
–212
.16.
Flatté
, S. M.
(1983
). “Wave propagation through random media: Contributions from Ocean Acoustics
,” Proc. IEEE
71
, 1267
–1294
.17.
Garrett
, C.
, and Munk
, W.
(1972
). “Space-time scales of internal waves
,” Geophys. Fluid. Dyn.
2
, 225
–264
.18.
Garrett
, C.
, and Munk
, W.
(1975
). “Space-time scales of internal waves: A progress report
,” J. Geophys. Res
80
, 291
–297
.19.
Hotelling
, H.
(1953
). “New light on the correlation coefficient and its transforms
,” J. R. Stat. Soc. B
15
, 193
–232
.20.
Ingenito
, F.
(1973
). “Measurements of mode attenuation coefficients in shallow water
,” J. Acoust. Soc. Am.
53
, 858
–863
.21.
Jensen
, F. B.
, Kuperman
, W. A.
, Porter
, M. B.
, and Schmidt
, H.
(1994
). Computational Ocean Acoustics
(American Institute of Physics
, Melville, NY
), Chap 5, pp. 281
–295
.22.
Levitus
, S.
, and Boyer
, T.
(1994
). World Ocean Atlas 1994 Volume 4: Temperature
, NOAA Atlas NESDIS 4 (NOAA
, Washington, DC
).23.
Levitus
, S.
, Burgett
, R.
, and Boyer
, T.
(1994
). World Ocean Atlas 1994 Volume 3: Salinity
, NOAA Atlas NESDIS 3 (NOAA
, Washington, DC
).24.
Mercer
, J. A.
, Colosi
, J. A.
, Howe
, B. M.
, Dzieciuch
, M. A.
, Stephen
, R.
, and Worcester
, P. F.
(2009
). “LOAPEX: The Long-Range Ocean Acoustic Propagation EXperiment
,” IEEE. J. Ocean. Eng.
34
, 1
–11
.25.
Munk
, W. H.
, Worcester
, P. F.
, and Wunsch
, C.
(1995
). Ocean Acoustic Tomography
(Cambridge University Press
, New York, NY
), Chap. 5, pp. 183
–197
, 218–221.26.
Priestley
, M. B.
(1992
). Spectral Analysis and Time Series
, Volume 1
(Academic
, San Diego, CA
), Chap. 5, pp. 318
–320
, 330–337.27.
Voronovich
, A. G.
, Ostashev
, V. E.
, and Colosi
, J. A.
(2011
). “Temporal coherence of acoustic signals in a fluctuating ocean
,” J. Acoust. Soc. Am.
129
, 3590
–3597
.28.
Wage
, K. E.
(2000
). “Broadband modal coherence and beamforming at megameter ranges
,” Ph.D. thesis, Massachusetts Institute of Technology/Woods Hole Oceanographic Institution
.29.
Wage
, K. E.
, Baggeroer
, A. B.
, and Preisig
, J. C.
(2003
). “Modal analysis of broadband acoustic receptions at 3515-km range in the North Pacific using short-time Fourier techniques
,” J. Acoust. Soc. Am.
113
, 801
–817
.30.
Wage
, K. E.
, Dzieciuch
, M. A.
, Worcester
, P. F.
, Howe
, B. M.
, and Mercer
, J. A.
(2005
). “Mode coherence at megameter ranges in the North Pacific Ocean
,” J. Acoust. Soc. Am.
117
, 1565
–1581
.31.
Worcester
, P. F.
, Cornuelle
, B. D.
, Dzieciuch
, M. A.
, Munk
, W. H.
, Howe
, B. M.
, Mercer
, J. A.
, Spindel
, R. C.
, Colosi
, J. A.
, Metzger
, K.
, Birdsall
, T. G.
, and Baggeroer
, A. B.
(1999
). “A test of basin-scale acoustic thermometry using a large-aperture vertical array at 3250-km range in the eastern North Pacific Ocean
,” J. Acoust. Soc. Am.
105
, 3185
–3201
.32.
Worcester
, P. F.
, Howe
, B. M.
, Mercer
, J. A.
, Dzieciuch
, M. A.
, and the Alternate Source Test (AST) Group (2000
). “A comparison of long-range acoustic propagation at ultra-low (28 Hz) and very-low (84 Hz) frequencies
,” in Proceedings of the US–Russia Workshop on Experimental Underwater Acoustics
, edited by V.
Talnov
(Institute of Applied Physics, Russian Academy of Science
, Nizhny Novgorod
), pp. 93
–104
.33.
Worcester
, P. F.
, and Spindel
, R. C.
(2005
). “North Pacific Acoustic Laboratory
,” J. Acoust. Soc. Am.
117
, 1499
–1510
.34.
Yang
, T. C.
(2008
). “Temporal coherence of sound transmission in deep water revisited
,” J. Acoust. Soc. Am.
124
, 113
–127
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2013
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