Contemporary high-resolution sonar systems use broadband pulses and long arrays to achieve high resolution. It is important to understand effects that high-resolution sonar systems might have on quantitative measures of the scattered field due to the seafloor. A quantity called the broadband scattering cross section is defined, appropriate for high-resolution measurements. The dependence of the broadband scattering cross section, σbb, and the scintillation index, SI, on resolution was investigated for one-dimensional rough surfaces with power-law spectra and backscattering geometries. Using integral equations and Fourier synthesis, no resolution dependence of σbb was found. The incoherently averaged frequency-domain scattering cross section has negligible bandwidth dependence. SI increases as resolution increases, grazing angle decreases, and spectral strength increases. This trend is confirmed for center frequencies of 100 and 10 kHz, as well as for power-law spectral exponents of 1.5, 2, and 2.5. The hypothesis that local tilting at the scale of the acoustic resolution is responsible for intensity fluctuations was examined using a representative model for the effect of slopes (inspired by the composite roughness approximation). It was found that slopes are responsible in part for the fluctuations, but other effects, such as multiple scattering and shadowing may also play a role.
References
1.
Abraham
, D. A.
, and Lyons
, A. P.
(2002
). “Novel physical interpretations of K-distributed reverberation
,” IEEE J. Ocean Eng.
27
, 800
–813
.2.
Abraham
, D. A.
, and Lyons
, A. P.
(2004
). “Reverberation envelope statistics and their dependence on sonar bandwidth and scattering patch size
,” IEEE J. Ocean Eng.
29
, 126
–137
.3.
Abramowitz
, M.
, and Stegun
, I. A.
(1972
). Handbook of Mathematical Functions
(Dover
, Mineola, NY)
, p. 297
.4.
Anderson
, E.
, Bai
, Z.
, Bischof
, C.
, Blackford
, S.
, Demmel
, J.
, Dongarra
, J.
, Croz
, J. D.
, Greenbaum
, A.
, Hammarling
, S.
, McKenney
, A.
, and Sorensen
, D.
(1999
). LAPACK Users' Guide
, 3rd ed. (SIAM
, Philadelphia, PA
).5.
Atkinson
, K.
(1997
). The Numerical Solution of Integral Equations of the Second Kind
(Cambridge University Press
, Cambridge, UK
).6.
Bachmann
, W.
(1973
). “A theoretical model for the backscattering strength of a composite-roughness sea surface
,” J. Acoust. Soc. Am.
54
(3
), 712
–716
.7.
Bellettini
, A.
, and Pinto
, M.
(2009
). “Design and experimental results of a 300-kHz synthetic aperture sonar optimized for shallow-water operations
,” IEEE J. Ocean Eng.
34
(3
), 285
–293
.8.
Blacknell
, D.
, Blake
, A. P.
, Oliver
, C. J.
, and White
, R. G.
(1992
). “A comparison of SAR multilook registration and contrast optimisation autofocus algorithms applied to real SAR data
,” in 92 International Conference on Radar
, pp. 363
–366
.9.
Brown
, D. C.
, Johnson
, S. F.
, and Olson
, D. R.
(2017
). “A point-based scattering model for the incoherent component of the scattered field
,” J. Acoust. Soc. Am.
141
(3
), EL210
–EL215
.10.
Callow
, H. J.
(2003
). “Signal processing for synthetic aperture sonar image enhancement
,” Ph.D. thesis, University of Canterbury
, Christchurch, New Zealand.11.
Dillon
, J.
(2018
). “Real-time interferometric SAS processing with ultra-low power consumption
,” in OCEANS 2018 MTS/IEEE Charleston
, pp. 1
–6
.12.
Fossum
, T. G.
, Sæbø
, T. O.
, Langli
, B.
, Callow
, H.
, and Hansen
, R. E.
(2008
). “HISAS 1030—High resolution interferometric synthetic aperture sonar
,” in Proceedings of the Canadian Hydrographic Conference
, Victoria BC, Canada.13.
Frigo
, M.
, and Johnson
, S. G.
(2005
). “The design and implementation of FFTW3
,” Proceedings of the IEEE
93
(2
), 216
–231
.14.
Fritsch
, F. N.
, and Carlson
, R. E.
(1980
). “Monotone piecewise cubic interpolation
,” SIAM J. Numer. Anal.
17
(2
), 238
–246
.15.
Galusha
, A. P.
, Keller
, J. M.
, Zare
, A.
, and Galusha
, G.
(2018
). “A fast target detection algorithm for underwater synthetic aperture sonar imagery
,” in Detection and Sensing of Mines, Explosive Objects, and Obscured Targets XXIII
, edited by J. C.
Isaacs
and S. S.
Bishop
, SPIE
.16.
Gradshteyn
, I.
, and Rhyzik
, I.
(2007
). Table of Integrals
, Series, and Products
, 7th ed. (Elsevier Academic Press
, Burlington, MA
).17.
Hackbusch
, W.
(2015
). Hierarchical Matrices: Algorithms and Analysis
, 1st ed. (Springer Publishing Company
, Berlin
).18.
Harris
, F. J.
(1978
). “On the use of windows for harmonic analysis with the discrete Fourier transform
,” Proc. IEEE
66
(1
), 51
–83
.19.
Hefner
, B. T.
(2015
). “Inversion of high frequency acoustic data for sediment properties needed for the detection and classification of UXOs
,” final report, https://www.serdp-estcp.org/content/download/34593/333838/file/MR-2229-FR.pdf (Last viewed 21 December 2020).20.
Hellequin
, L.
, Boucher
, J. M.
, and Lurton
, X.
(2003
). “Processing of high-frequency multibeam echo sounder data for seafloor characterization
,” IEEE J. Ocean Eng.
28
(1
), 78
–89
.21.
Ishimaru
, A.
(1978
). Wave Propagation and Scattering in Random Media
(Academic
, New York
), Vol. 2
, p. 437
.22.
Jackson
, D.
, and Olson
, D. R.
(2020
). “The small-slope approximation for layered, fluid seafloors
,” J. Acoust. Soc. Am.
147
(1
), 56
–73
.23.
Jackson
, D. R.
, Baird
, A. M.
, Crisp
, J. J.
, and Thomson
, P. A. G.
(1986a
). “High-frequency bottom backscatter measurements in shallow water
,” J. Acoust. Soc. Am.
80
(4
), 1188
–1199
.24.
Jackson
, D. R.
, and Ivakin
, A. N.
(1998
). “Scattering from elastic sea beds: First-order theory
,” J. Acoust. Soc. Am.
103
, 336
–345
.25.
Jackson
, D. R.
, and Richardson
, M. D.
(2007
). High-Frequency Seafloor Acoustics
, 1st ed. (Springer
, New York, NY
).26.
Jackson
, D. R.
, Winebrenner
, D. P.
, and Ishimaru
, A.
(1986b
). “Application of the composite roughness model to high-frequency bottom backscattering
,” J. Acoust. Soc. Am.
79
, 1410
–1422
.27.
Jakeman
, E.
(1980
). “On the statistics of K-distributed noise
,” J. Phys. A: Math. Gen.
13
, 31
–48
.28.
Kur'yanov
, B.
(1963
). “The scattering of sound at a rough surface with two types of irregularity
,” Sov. Phys. Acoust.
8
(3
), 252
–257
.29.
Kwon
, H.
, and Nasrabadi
, N.
(2005
). “Kernel RX-algorithm: A nonlinear anomaly detector for hyperspectral imagery
,” IEEE Trans. Geosci. Remote Sens.
43
(2
), 388
–397
.30.
Landau
, L. D.
, and Lifshitz
, E. M.
(1987
). Fluid Mechanics
, 2nd ed. (Butterworth Heinemann
, New York
), p. 255
.31.
Li
, H.
, and Johnson
, J. T.
(2017
). “On the amplitude distributions of bistatic scattered fields from rough surfaces
,” IEEE Trans. Geosci. Remote Sens.
55
(12
), 6883
–6892
.32.
Liu
, Y.
(2009
). Fast Multipole Boundary Element Method: Theory and Applications in Engineering
(Cambridge University Press
, Cambridge, UK
).33.
Lupien
, V.
(1999
). “The role of scale structure in scattering from random rough surfaces
,” J. Acoust. Soc. Am.
105
, 2187
–2202
.34.
Lyons
, A.
, Olson
, D. R.
, and Hansen
, R.
(2016
). “Quantifying the effect of random seafloor roughness on high-frequency synthetic aperture sonar image statistics
,” in Acoustic and Environmental Variability, Fluctuations, and Coherence
, Institute of Acoustics
, Cambridge, UK, Vol. 38
, pp. 151
–158
.35.
Lyons
, A. P.
, Abraham
, D. A.
, and Johnson
, S. F.
(2010
). “Modeling the effect of seafloor ripples on synthetic aperture sonar speckle statistics
,” IEEE J. Ocean Eng.
35
(2
), 242
–249
.36.
Lyons
, A. P.
, Johnson
, S. F.
, Abraham
, D. A.
, and Pouliquen
, E.
(2009
). “High-frequency scattered envelope statistics of patchy seafloors
,” IEEE J. Ocean Eng.
34
, 451
–458
.37.
Lysanov
, Y. P.
(1973
). “A property of the scattering coefficient in the Fraunhofer zone
,” Sov. Phys. Acoust.
18
(4
), 505
–506
.38.
Marston
, T. M.
, and Plotnick
, D. S.
(2015
). “Semiparametric statistical stripmap synthetic aperture autofocusing
,” IEEE Trans. Geosci. Remote Sens.
53
(4
), 2086
–2095
.39.
McDaniel
, S. T.
, and Gorman
, A. D.
(1983
). “An examination of the composite-roughness scattering model
,” J. Acoust. Soc. Am.
73
, 1476
–1486
.40.
Moccia
, A.
, and Renga
, A.
(2011
). “Spatial resolution of bistatic synthetic aperture radar: Impact of acquisition geometry on imaging performance
,” IEEE Trans. Geosci. Remote Sens.
49
(10
), 3487
–3503
.41.
Ng
, E. W.
, and Geller
, M.
(1969
). “A table of integrals of the error functions
,” J. Res. Natl. Bureau Stand. B: Math. Sci.
73B
(1
), 1
–20
.42.
Olson
, D. R.
, Lyons
, A. P.
, Abraham
, D. A.
, and Sæbø
, T. O.
(2019
). “Scattering statistics of rock outcrops: Model-data comparisons and Bayesian inference using mixture distributions
,” J. Acoust. Soc. Am.
145
(2
), 761
–774
.43.
Olson
, D. R.
, Lyons
, A. P.
, and Sæbø
, T. O.
(2016
). “Measurements of high-frequency acoustic scattering from glacially eroded rock outcrops
,” J. Acoust. Soc. Am.
139
(4
), 1833
–1847
.44.
Pierce
, A. D.
(1994
). Acoustics: An Introduction to its Physical Principles and Applications
(Acoustical Society of America
, New York
), p. 19
.45.
Pinto
, M.
(2011
). “Interferometric synthetic aperture sonar design optimized for high area coverage shallow water bathymetric survey
,” in Proceedings of the 4th International Conference and Exhibition on Underwater Acoustics Measurements
, Kos, Greece, pp. 505
–512
.46.
Sauter
, S. A.
, and Schwab
, C.
(2011
). Boundary Element Methods
(Springer-Verlag
, Heidelberg
).47.
Sternlicht
, D. D.
, Fernandez
, J. E.
, Prater
, J. L.
, Weaver
, J. N.
, Isaacs
, J. C.
, Montgomery
, T. C.
, Loeffler
, C. M.
, and Purcell
, M.
(2016
). “Advanced sonar technologies for high clearance rate mine countermeasures
,” in OCEANS 2016 MTS/IEEE Monterey
, pp. 1
–8
.48.
Tatarski
, V. I.
(1961
). Wave Propagation in a Turbulent Medim
(Dover Reprint
, New York
).49.
Thorsos
, E. I.
(1988
). “The validity of the Kirchhoff approximation for rough surface scattering using a Gaussian roughness spectrum
,” J. Acoust. Soc. Am.
83
, 78
–92
.50.
Thorsos
, E. I.
, and Jackson
, D. R.
(1989
). “The validity of the perturbation approximation for rough surface scattering using a Gaussian roughness spectrum
,” J. Acoust. Soc. Am.
86
, 261
–277
.51.
Thorsos
, E. I.
, and Jackson
, D. R.
(1991
). “Studies of scattering theory using numerical methods
,” Waves Random Media
1
(3
), S165
–S190
.52.
Toporkov
, J.
, Marchand
, R.
, and Brown
, G.
(1998
). “On the discretization of the integral equation describing scattering by rough conducting surfaces
,” IEEE Trans. Ant. Propag.
46
(1
), 150
–161
.53.
Urick
, R. J.
(1954
). “The backscattering of sound from a harbor bottom
,” J. Acoust. Soc. Am.
26
, 231
–235
.54.
Urick
, R. J.
(1983
). Principles of Underwater Sound
, 3rd ed. (Peninsula
, Los Altos Hills, CA
).55.
Valenzuela
, and Liang
(1971
). “On the statistics of sea clutter
,” U.S. Naval Research Laboratory, Report No. 7349.56.
Wang
, Z.
, and Bovik
, A. C.
(2002
). “A universal image quality index
,” IEEE Sign. Process. Lett.
9
(3
), 81
–84
.57.
Williams
, D. P.
(2015
). “Fast unsupervised seafloor characterization in sonar imagery using lacunarity
,” IEEE Trans. Geosci. Remote Sens.
53
(11
), 6022
–6034
.58.
Williams
, D. P.
(2018
). “The Mondrian detection algorithm for sonar imagery
,” IEEE Trans. Geosci. Remote Sens.
56
(2
), 1091
–1102
.59.
Williams
, K.
, Jackson
, D.
, Thorsos
, E.
, Tang
, D.
, and Briggs
, K.
(2002
). “Acoustic backscattering experiments in a well characterized sand sediment: Data/model comparisons using sediment fluid and Biot models
,” IEEE J. Ocean Eng.
27
, 376
–387
.60.
Winebrenner
, D.
, and Ishimaru
, A.
(1986
). “On the far-field approximation for scattering from randomly rough surfaces
,” IEEE Trans. Ant. Propag.
34
(6
), 847
–849
.61.
Wu
, T. W.
(2000
). Boundary Element Acoustics: Fundamentals and Computer Codes
(WIT Press
, Southampton, UK
).62.
Yang
, C. C.
, and McDaniel
, S. T.
(1991
). “Fourth moments of acoustic waves forward scattered by a rough ocean surface
,” Waves Random Media
1
(4
), 419
–439
.2021
U.S. Government
You do not currently have access to this content.
