In a recent letter [Hegewisch and Tomsovic, Europhys. Lett. 97, 34002 (2012)], random matrix theory is introduced for long-range acoustic propagation in the ocean. The theory is expressed in terms of unitary propagation matrices that represent the scattering between acoustic modes due to sound speed fluctuations induced by the ocean's internal waves. The scattering exhibits a power-law decay as a function of the differences in mode numbers thereby generating a power-law, banded, random unitary matrix ensemble. This work gives a more complete account of that approach and extends the methods to the construction of an ensemble of acoustic timefronts. The result is a very efficient method for studying the statistical properties of timefronts at various propagation ranges that agrees well with propagation based on the parabolic equation. It helps identify which information about the ocean environment can be deduced from the timefronts and how to connect features of the data to that environmental information. It also makes direct connections to methods used in other disordered waveguide contexts where the use of random matrix theory has a multi-decade history.

1.
S. M.
Flatté
,
R.
Dashen
,
W. H.
Munk
, and
F.
Zachariasen
,
Sound Transmission Through a Fluctuating Ocean
(
Cambridge University Press
,
Cambridge
,
1979
), pp.
1
320
.
2.
W. H.
Munk
,
P.
Worcester
, and
C.
Wuncsh
,
Ocean Acoustic Tomography
(
Cambridge University Press
,
Cambridge
,
1995
), pp.
1
456
.
3.
P. F.
Worcester
,
B. D.
Cornuelle
,
M. A.
Dzieciuch
,
W. H.
Munk
,
B. M.
Howe
,
J. A.
Mercer
,
R. C.
Spindel
,
J. A.
Colosi
,
K.
Metzger
,
T.
Birdsall
, and
A. B.
Baggeroer
, “
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
(
1999
).
4.
J. A.
Colosi
,
E. K.
Scheer
,
S. M.
Flatté
,
B. D.
Cornuelle
,
M. A.
Dzieciuch
,
W. H.
Munk
,
P. F.
Worcester
,
B. M.
Howe
,
J. A.
Mercer
,
R. C.
Spindel
,
K.
Metzger
,
T.
Birdsall
, and
A. B.
Baggeroer
, “
Comparisons of measured and predicted acoustic fluctuations for a 3250-km propagation experiment in the eastern North Pacific Ocean
,”
J. Acoust. Soc. Am.
105
,
3202
3218
(
1999
).
5.
D.
Makarov
,
S.
Prants
,
A.
Virovlyansky
, and
G. M.
Zaslavksy
,
Ray and Wave Chaos in Ocean Acoustics: Chaos in Waveguides, Vol. 1 of Complexity, Nonlinearity and Chaos
(
World Scientific Publishing Company
,
Singapore
,
2009
), pp.
1
388
.
6.
J.
Simmen
,
S. M.
Flatté
, and
G.-Y.
Wang
, “
Wavefront folding, chaos, and diffraction for sound propagation through ocean internal waves
,”
J. Acoust. Soc. Am.
102
,
239
255
(
1997
).
7.
M. G.
Brown
,
J. A.
Colosi
,
S.
Tomsovic
,
A. L.
Virovlyansky
,
M. A.
Wolfson
, and
G. M.
Zaslavsky
, “
Ray dynamics in long-range deep ocean sound propagation
,”
J. Acoust. Soc. Am.
113
,
2533
2547
(
2003
).
8.
F. J.
Beron-Vera
,
M. G.
Brown
,
J. A.
Colosi
,
S.
Tomsovic
,
A. L.
Virovlyansky
,
M. A.
Wolfson
, and
G. M.
Zaslavsky
, “
Ray dynamics in a long-range acoustic propagation experiment
,”
J. Acoust. Soc. Am.
114
,
1226
1242
(
2003
).
9.
S.
Tomsovic
and
M. G.
Brown
, “
Ocean acoustics: A novel laboratory for wave chaos
,” in
New Directions in Linear Acoustics and Vibration: Random Matrix Theory, Quantum Chaos and Complexity
, edited by
R.
Weaver
and
M.
Wright
(
Cambridge University Press
,
New York, 2010
), pp.
169
187
.
10.
F. D.
Tappert
, “
The parabolic approximation method
,” in
Wave Propagation and Underwater Acoustics, Vol. 70 of Lecture Notes in Physics
, edited by
J. B.
Keller
and
J. S.
Papadakis
(
Springer-Verlag
,
New York, 1977
), pp.
224
287
.
11.
D. R.
Palmer
,
M. G.
Brown
,
F. D.
Tappert
, and
H. F.
Bezdek
, “
Classical chaos in nonseparable wave propagation problems
,”
Geophys. Res. Lett.
15
,
569
572
, doi: (
1988
).
12.
K. B.
Smith
,
M. G.
Brown
, and
F. D.
Tappert
, “
Ray chaos in underwater acoustics
,”
J. Acoust. Soc. Am.
91
,
1939
1949
(
1992
).
13.
K. B.
Smith
,
M. G.
Brown
, and
F. D.
Tappert
, “
Acoustic ray chaos induced by mesocsale ocean structure
,”
J. Acoust. Soc. Am.
91
,
1950
1959
(
1992
).
14.
C. W. J.
Beenakker
, “
Random-matrix theory of quantum transport
,”
Rev. Mod. Phys.
69
,
731
808
(
1997
).
15.
C. M.
Marcus
,
A. J.
Rimberg
,
R. M.
Westervelt
,
P. F.
Hopkins
, and
A. C.
Gossard
, “
Conductance fluctuations and chaotic scattering in ballistic microstructures
,”
Phys. Rev. Lett.
69
,
506
509
(
1992
).
16.
M. A.
Topinka
,
B. J.
LeRoy
,
S. E. J.
Shaw
,
E. J.
Heller
,
R. M.
Westervelt
,
K. D.
Maranowski
, and
A. C.
Gossard
, “
Imaging coherent electron flow from a quantum point contact
,”
Science
289
,
2323
2326
(
2000
).
17.
M. A.
Topinka
,
B. J.
LeRoy
,
R. M.
Westervelt
,
S. E. J.
Shaw
,
R.
Fleischmann
,
E. J.
Heller
,
K. D.
Maranowski
, and
A. C.
Gossard
, “
Coherent branched flow in a two-dimensional electron gas
,”
Nature
410
,
183
186
(
2001
).
18.
M. A.
Wolfson
and
S.
Tomsovic
, “
On the stability of long-range sound propagation through a structured ocean
,”
J. Acoust. Soc. Am.
109
,
2693
2703
(
2001
).
19.
K. C.
Hegewisch
and
S.
Tomsovic
, “
Random matrix theory for underwater sound propagation
,”
Europhys. Lett.
97
,
34002
(
2012
).
20.
K. C.
Hegewisch
, Ph.D. thesis,
Washington State University, Pullman, WA
,
2010
.
21.
R. L.
Weaver
, “
Spectral statistics in elastodynamics
,”
J. Acoust. Soc. Am.
85
,
1005
1013
(
1989
).
22.
E.
Wigner
, “
Characteristic vectors of bordered matrices with infinite dimensions
,”
Ann. Math.
62
,
548
564
(
1955
).
23.
F. J.
Dyson
, “
The threefold way. algebraic structure of symmetry groups and ensembles in quantum mechanics
,”
J. Math. Phys.
3
,
1199
1215
(
1962
).
24.
L. B.
Dozier
and
F. D.
Tappert
, “
Statistics of normal mode amplitudes in a random ocean. I. Theory
,”
J. Acoust. Soc. Am.
63
,
353
365
(
1978
).
25.
L. B.
Dozier
and
F. D.
Tappert
, “
Statistics of normal mode amplitudes in a random ocean. II. Computations
,”
J. Acoust. Soc. Am.
63
,
533
547
(
1978
).
26.
A. K.
Morozov
and
J. A.
Colosi
, “
Stochastic differential equation analysis for sound scattering by random internal waves in the ocean
,”
Acoust. Phys.
53
,
335
347
(
2007
).
27.
J. A.
Colosi
and
A. K.
Morozov
, “
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
(
2009
).
28.
P. A.
Mello
and
N.
Kumar
,
Quantum Transport in Mesoscopic Systems. Complexity and Statistical Fluctuations
(
Oxford University Press
,
Oxford
,
2010
), pp.
1
416
.
29.
W. H.
Munk
, “
Sound channel in an exponentially stratified ocean with applications to SOFAR
,”
J. Acoust. Soc. Am.
55
,
220
226
(
1974
).
30.
J. A.
Colosi
and
M. G.
Brown
, “
Efficient numerical simulation of stochastic internal-wave induced sound-speed perturbation fields
,”
J. Acoust. Soc. Am.
103
,
2232
2235
(
1998
).
31.
K. C.
Hegewisch
,
N. R.
Cerruti
, and
S.
Tomsovic
, “
Ocean acoustic wave propagation and ray method correspondence: Internal waves
,”
J. Acoust. Soc. Am.
117
,
1582
1594
(
2005
).
32.
A. G.
Voronovich
and
V. E.
Ostashev
, “
Low-frequency sound scattering by internal waves in the ocean
,”
J. Acoust. Soc. Am.
119
,
1406
1419
(
2006
).
33.
A. G.
Voronovich
and
V. E.
Ostashev
, “
Coherence function of a sound field in an oceanic waveguide with horizontally isotropic statistics
,”
J. Acoust. Soc. Am.
125
,
99
110
(
2009
).
34.
C. E.
Porter
,
Statistical Theories of Spectra: Fluctuations
(
Academic Press
,
New York
,
1965
), pp.
1
576
.
35.
A.
Pandey
, “
Statistical properties of many-particle spectra: III. Ergodic behavior in 2 random-matrix ensembles
,”
Ann. Phys
.
119
,
170
191
(
1979
).
36.
L. S.
Froufe-Perez
,
M.
Yepez
,
P. A.
Mello
, and
J. J.
Saenz
, “
Statistical scattering of waves in disordered waveguides: From microscopic potentials to limiting macroscopic statistics
,”
Phys. Rev. E
75
,
031113
(
2007
).
37.
L. A.
Chernov
,
Waves in Randomly—Inhomogeneous Media
(
Nauka
,
Moscow
,
1975
) (in Russian).
38.
S. M.
Flatté
, “
Wave propagation through random media: Contributions from ocean acoustics
,”
Proc. IEEE
71
,
1267
1294
(
1983
).
39.
L. J.
van Uffelen
,
P. F.
Worcester
,
M. A.
Dzieciuch
, and
D. L.
Rudnick
, “
The vertical structure of shadow-zone arrivals at long range in the ocean
,”
J. Acoust. Soc. Am.
125
,
3569
3588
(
2009
).
40.
L. J.
van Uffelen
,
P. F.
Worcester
,
M. A.
Dzieciuch
,
D. L.
Rudnick
, and
J. A.
Colosi
, “
Effects of upper ocean sound-speed structure on deep acoustic shadow-zone arrivals at 500- and 1000-km range
,”
J. Acoust. Soc. Am.
127
,
2169
2181
(
2010
).
41.
C. C.
 et al, “
TeraGrid: Analysis of organization, system architecture, and middleware enabling new types of applications, HPC and grids in action
,” in
Advances in Parallel Computing Series
, edited by
Lucio
Grandinetti
(
IOS Press
,
Amsterdam
,
2007
), pp.
225
249
.
42.
C. J. R.
Garrett
and
W. H.
Munk
, “
Internal waves in the ocean
,”
Annu. Rev. Fluid Mech.
11
,
339
369
(
1979
).
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