Mathematical modeling and computer-aided manufacturing of rough surfaces for experimental study of seafloor scattering

IEEE Journal of Oceanic Engineering

Volumn 32, Issue 4, 2007, Pages 897-914

  Summers, Jason E ^a   Soukup, Raymond J ^a   Gragg, Robert F ^a  

^a NAVAL RESEARCH LABORATORY   (United States)

Author keywords

Acoustic scattering; Computer aided manufacturing (CAM); Fractional Brownian motion; Physical modeling; Power law roughness spectrum; Rough surface scattering

Indexed keywords

ACOUSTIC WAVE SCATTERING; COMPUTER AIDED MANUFACTURING; MATHEMATICAL MODELS; POWER SPECTRAL DENSITY; RANDOM PROCESSES; SURFACE ROUGHNESS; UNDERWATER ACOUSTICS;

ACOUSTICAL OCEANOGRAPHY; FRACTIONAL BROWNIAN MOTION; SEAFLOOR;

OCEANOGRAPHY;

EID: 40749094817     PISSN: 03649059     EISSN: None     Source Type: Journal    
DOI: 10.1109/JOE.2007.906403     Document Type: Article

References (90)

1. A. G. Voronovich, "Small slope approximation in the theory of wave scattering at rough surfaces," Zh. Eksp. Teor. Fiz., vol. 89, pp. 116-125, 1985.
2. R. F. Gragg, D. Wurmser, and R. C. Gauss, "Small-slope scattering from rough elastic ocean floors: General theory and computational algorithm," J. Acoust. Soc. Amer., vol. 110, pp. 2878-2901, 2001.
3. W. A. Kinney, C. S. Clay, and G. A. Sandness, "Scattering from a corrugated surface: Comparison between experiment, Helmholtz-Kirchhoff theory, and the facet-ensemble method," J. Acoust. Soc. Amer., vol. 73, pp. 183-194, 1983.
4. R. S. Keiffer and J. C. Novarini, "A wedge assemblage method for 3-D acoustic scattering from sea surfaces: Comparison with a Helmholtz-Kirchhoff method," in Computational Acoustics, D. Lee, A. Cakmak, and R. Vichnevetsky, Eds. Amsterdam, The Netherlands: Elsevier, 1990, pp. 67-81.
5. J. M. Proud, Jr., R. T. Beyer, and P. Tamarkin, "Reflection of sound from randomly rough surfaces," J. Appl. Phys., vol. 31, pp. 543-552, 1960.
6. C. W. Horton, Sr., S. K. Mitchell, and G. R. Barnard, "Model studies on the scattering of acoustic waves from a rough surface," J. Acoust. Soc. Amer., vol. 41, pp. 635-643, 1967.
7. G. R. Mellema, "Subcritical acoustic scattering across a rough fluid-solid interface," Ph.D. dissertation, Dept. Electr. Eng., Univ. Washington, Seattle, WA, 1999.
8. J. P. Sessarego, "Use of scaled models to study scattering by rough bottoms: Application to sea floor backscattering," in Proc. Boundary Influences in High-Frequency, Shallow Water Acoust., N. G. Pace and P. Blondel, Eds., U.K., Sep. 5-9, 2005, pp. 209-216.
9. J. G. Zornig, "Physical modeling of underwater acoustics," in Ocean Acoustics, J. A. DeSanto, Ed. New York: Springer-Verlag, 1979, ch. 4, pp. 159-186.
10. R. J. Soukup, R. F. Gragg, E. L. Kunz, J. E. Summers, G. Canepa, and E. Pouliquen, "Verification of rough surface scattering predictions using an elastic scale model," in Proc. Boundary Influences in High-Frequency, Shallow Water Acoust., N. G. Pace and P. Blondel, Eds., U.K., Sep. 5-9, 2005, pp. 201-207.
11. R. J. Soukup, J. E. Summers, and R. F. Gragg, "Characterizations of acoustic interactions with a scale model of an elastic ocean bottom using deterministic and stochastic representations of the rough surface," in Proc. U.S./Eur. Union - Baltic Int. Symp., Klaipeda, Lithuania, May 23-25, 2006.
12. R. J. Soukup, G. Canepa, H. J. Simpson, J. E. Summers, and R. F. Gragg, "Small-slope simulation of acoustic backscatter from a physical model of an elastic ocean bottom," J. Acoust. Soc. Amer., vol. 122, pp. 2551-2559, 2007.
13. N. S. Neidell, "Spectral studies of marine geophysical profiles," Geophysics, vol. 31, pp. 122-134, 1966.
14. T. H. Bell, Jr., "Statistical features of sea-floor topography," Deep-Sea Res., vol. 22, pp. 883-892, 1975.
15. R. S. Sayles and T. R. Thomas, "Surface topography as a nonstationary random process," Nature, vol. 271, pp. 431-434, 1978.
16. J. M. Berkson and J. E. Matthews, "Statistical properties of seafloor roughness," in Acoustics of the Sea-Bed, N.G. Pace, Ed. Bath,U.K.: Bath Univ. Press, 1983, pp. 215-223.
17. C. G. Fox and D. E. Hayes, "Quantitative methods for analyzing the roughness of the seafloor," Rev. Geophys., vol. 23, pp. 1-48, 1985.
18. A. Malinverno, "Segmentation of topographic profiles of the seafloor based on a self-affine model," IEEE J. Ocean. Eng., vol. 14, no. 4, pp. 348-359, Oct. 1989.
19. M. D. Richardson, K. B. Briggs, L. D. Bibee, P. A. Jumars, W. B. Sawyer, D. B. Albert, R. H. Bennett, T. K. Berger, M. J. Buckingham, N. P. Chotiros, P. H. Dahl, N. T. Dewitt, P. Fleischer, R. Flood, C. F. Greenlaw, D. V. Holliday, M. H. Hulbert, M. P. Hutnak, P. D. Jackson, J. S. Jaffe, H. P. Johnson, D. L. Lavoie, A. P. Lyons, C. S. Martens, D. E. McGehee, K. D. Moore, T. H. Orsi, J. N. Piper, R. I. Ray, A. H. Reed, R. F. L. Self, J. L. Schmidt, S. G. Schock, F. Simonet, R. D. Stoll, D. Tang, D. E. Thistle, E. I. Thorsos, D. J. Walter, and R. A. Wheatcroft, "Overview of SAX99: Environmental considerations," IEEE J. Ocean. Eng., vol. 26, no. 1, pp. 26-53, Jan. 2001.
20. R. J. Soukup and R. F. Gragg, "Backscatter from a limestone seafloor at 2-3.5 kHz: Measurements and modeling," J. Acoust. Soc. Amer., vol. 113, pp. 2501-2514, 2003.
21. B. B. Mandelbrot, The Fractal Geometry of Nature. New York: W. H. Freeman, 1983.
22. J. A. Ogilvy, Theory of Wave Scattering From Random Rough Surfaces New York: Adam Hilger, 1991.
23. L. E. Gilbert and A. Malinverno, "A characterization of the spectral density of residual ocean floor topography," Geophys. Res. Lett., vol. 15, pp. 1401-1404, 1988.
24. O. I. Yordanov and I. S. Atansov, "Self-affine random surfaces," Eur. Phys. J. B, vol. 29, pp. 211-215, 2002.
25. J. M. Bergin, "Analytical and physical aspects of two-dimensional spectra associated with stationary random processes," U.S. Naval Res. Lab., Washington, DC, NRL/FR/8995, 1986.
26. V. Solo, "Intrinsic random functions and the paradox of 1/f noise," SIAM J. Appl. Math, vol. 52, pp. 270-291, 1992.
27. M. V. Berry, "Diffractals," J. Phys. A, Math. Gen., vol. 12, pp. 781-797, 1979.
28. O. I. Yordanov and K. Ivanova, "Description of surface roughness as an approximate self-affine random structure," Surf. Sci., vol. 331-333, pp. 1043-1049, 1995.
29. E. L. Church, "Fractal surface finish," Appl. Opt., vol. 27, pp. 1518-1526, 1988.
30. R. Dashen, F. S. Henyey, and D. Wurmser, "Calculations of acoustic scattering from the ocean surface," J. Acoust. Soc. Amer., vol. 88, pp. 310-323, 1990.
31. D. Wurmser, "Stochastic cross-sections based on the small slope approximation: Theory," U.S. Naval Res. Lab., Washington, DC, NRL/MR/7140-05-8816, 2005.
32. K. B. Briggs, "Microtopographical roughness of shallow-water continental shelves," IEEE J. Ocean. Eng., vol. 14, no. 4, pp. 360-367, Oct. 1989.
33. J. A. Goff and T. H. Jordan, "Stochastic modeling of seafloor morphology: Inversion of sea beam data for second-order statistics," J. Geophys. Res., vol. 93, pp. 13589-13608, 1988.
34. R. Kant, "Statistics of approximately self-affine fractals: Random corrugated surface and time series," Phys. Rev. E, Stat. Phys. Plasmas Fluids Relat. Interdiscip. Top., vol. 53, pp. 5749-5763, 1996.
35. B. B. Mandelbrot and J. W. V. Ness, "Fractional Brownian motions, fractional noises, and applications," SIAM Rev., vol. 10, pp. 422-437, 1968.
36. G. A. Hunt, "Random Fourier transforms," Trans. Amer. Math. Soc. vol. 71, pp. 38-69, 1951.
37. J. Feder, Fractals. New York: Plenum Press, 1988.
38. N. P. Greis and H. S. Greenside, "Implication of a power-law power-spectrum for self-affinity," Phys. Rev. A, Gen. Phys., vol. 44, pp. 2324-2334, 1991.
39. M. S. Taqqu, "Fractional Brownian motion and long-range dependence," in Theory and Applications of Long-Range Dependence, P. Doukhan, G. Oppenheim, and M. S. Taqqu, Eds. Boston, MA: Birkhäuser, 2003, pp. 5-38.
40. D. J. Whitehouse and J. F. Archard, "The properties of random surfaces of significance in their contact," Proc. R. Soc., vol. A3 16, pp. 97-121, 1970.
41. E. Mainsah, J. A. Greenwood, and D. G. Chetwynd, Eds., "Fractal and surface roughness," in Metrology and Properties of Engineering Surfaces. Boston, MA: Kluwer, 2001, pp. 33-41.
42. T. Gneiting and M. Schlather, "Stochastic models that separate fractal dimension and the Hurst effect," SIAM Rev., vol. 46, pp. 269-282, 2004.
43. G. H. Hardy, "Weierstrass's non-differentiable function," Trans. Amer. Math. Soc., vol. 17, pp. 301-325, 1916.
44. M. V. Berry and J. H. Hannay, "Topography of random surfaces," Nature, vol. 273, pp. 573-573, 1978.
45. P. Flandrin, "On the spectrum of fractional Brownian motion," IEEE Trans. Inf. Theory, vol. 35, no. 1, pp. 197-199, Jan. 1989.
46. P. Flandrin, "Wavelet analysis and synthesis of fractional Brownian motion," IEEE Trans. Inf. Theory, vol. 38, no. 2, pp. 910-917, Mar. 1992.
47. S. Orey, "Gaussian sample functions and Haussdorff dimension of level crossings," Z. Wahrscheinlichskeitstheor, vol. 15, pp. 249-256, 1970.
48. S. R. Brown and C. H. Scholz, "Broad bandwidth study of the topography of natural rock surfaces," J. Geophys. Res., vol. 90, pp. 12575-12582, 1985.
49. S. E. Hough, "On the use of spectral methods for the determination of fractal dimension," Geophys. Res. Lett., vol. 16, pp. 673-676, 1989.
50. J. C. Russ, Fractal Surfaces. New York: Plenum, 1994.
51. D. T. Hristopulos, "Permissibility of fractal exponents and models of band-limited two-point functions for fGn and fBm random fields," Stoch. Environ. Res. Risk Assess., vol. 17, pp. 191-216, 2003.
52. G. Franceschetti, A. lodice, M. Migliaccio, and D. Riccio, "Fractals and the small perturbation scattering model," Radio Sci., vol. 34, pp. 1043-1054, 1999.
53. B. Dubuc, J. F. Quiniou, C. Roques-Carmes, C. Tricot, and S. W. Zucker, "Evaluating the fractal dimension of profiles," Phys. Rev. A, Gen. Phys., vol. 39, pp. 1500-1513, 1989.
54. O. I. Yordanov and N. I. Nickolaev, "Self-affinity of time series with finite domain power-law power spectrum," Phys. Rev. E, Stat. Phys. Plasmas Fluids Relat. Interdiscip. Top., vol. 49, pp. R2517-R2520, 1994.
55. J.-S. Leu, "On estimating the spectral exponent of fractional Brownian motion," IEEE Trans. Inf. Theory, vol. 41, no. 1, pp. 233-244, Jan. 1995.
56. A. R. Mehrabi, H. Rassamdana, and M. Sahimi, "Characterization of long-range correlations in complex distributions and profiles," Phys. Rev. E, Stat. Phys. Plasmas Fluids Relat. Interdiscip. Top., vol. 56, pp. 712-722, 1997.
57. C. Castelnovo, A. Podestà, P. Piseri, and P. Milani, "Fractal analysis of sampled profiles: Systematic study," Phys. Rev. E, Stat. Phys. Plasmas Fluids Relat. Interdiscip. Top., vol. 65, pp. 021601-021601, 2002.
58. E. Mainsah, J. A. Greewood, and D. G. Chetwynd, Eds., "Measuring surfaces," in Metrology and Properties of Engineering Surfaces. Boston, MA: Kluwer, 2001, pp. 59-66.
59. M. V. Berry and Z. V. Lewis, "On the Weierstrass-Mandelbrot fractal function," Proc. R. Soc. Lond. A, Math. Phys. Sci., vol. 370, pp. 459-484, 1980.
60. K. Weierstrass, "Über Continuirliche Functionen Fines Reellen Arguments, Die Für Keinen Werth Des Letzteren Emen Bestimmten Differentialquotienten Besitzen" ("Concerning a continuous function of real arguments that is nowhere differentiable"), presented to the Berlin Academy, Berlin, Germany, Jul. 18, 1872.
61. K. Weierstrass, Mathematische Werke. Berlin, Germany: Mayer & Muller, 1895, vol. 2, pp. 71-74.
62. B. R. Hunt, "The Hausdorff dimension of graphs of Weierstrass functions," Proc. Amer. Math. Soc., vol. 126, pp. 791-800, 1998.
63. H. M. Hastings and G. Sugihara, Fractals: A User's Guide for the Natural Sciences. New York: Oxford Univ. Press, 1993.
64. S. Kumar and G. S. Bodvarsson, "Fractal study and simulation of fracture roughness," Geophys. Res. Lett., vol. 17, no. 6, pp. 701-704, May 1990.
65. A. G. Garcia, "Orthogonal sampling formulas: A unified approach," SIAM Rev., vol. 42, pp. 499-512, 2000.
66. J. S. Lim, Two-Dimensional Signal and Image Processing. Englewood Cliffs, NJ: Prentice-Hall, 1990.
67. J. E. Summers, R. J. Soukup, and R. F. Gragg, "Characterization and fabrication of synthetic rough surfaces for acoustical scale-model experiments," U.S. Naval Res. Lab., Washington, DC, NRL/MR-MM/ 7140-05-8871, 2005.
68. J.-J. Wu, "Simulation of rough surfaces with FFT," Tribol. Int., vol. 33, pp. 47-58, 2000.
69. K. Y. R. Billah and M. Shinozuka, "Numerical method for colored-noise generation and its application to a bistable system," Phys. Rev. A, Gen. Phys., vol. 42, pp. 7492-7495, 1990.
70. M. Rosenblatt, "Some comments on narrow band-pass filters," Quart. J. Appl. Math., vol. 18, pp. 387-393, 1961.
71. E. I. Thorsos, "The validity of the Kirchhoff approximation for rough surface scattering using a Gaussian roughness spectrum," J. Acoust. Soc. Amer., vol. 83, pp. 78-92, 1988.
72. H. Stark and J. W. Woods, Probability and Random Processes With Applications to Signal Processing, 3rd ed. Upper Saddle River, NJ: Prentice-Hall, 2002.
73. J.-J. Sung, G.-S. Kang, and S. Kim, "A transient noise model for frequency-dependent noise sources," IEEE Trans. Comput.-Aided Design Integr. Circuits Syst., vol. 22, no. 8, pp. 1097-1104, Aug. 2003.
74. S. Gautier and D. Gibert, "Scattering from a fractal surface: Acoustical experiments and comparison with near-nadir models," Icarus, vol. 167, pp. 453-463, 2004.
75. Y. Kuga and P. Phu, "Experimental studies of millimeter-wave scattering in discrete random media and from random surfaces," Prog. Electromagn. Res. (PIER), vol. 14, pp. 37-88, 1996.
76. A. Warkentin, P. Hoskins, F. Ismail, and S. Bedi, "Computer aided 5-axis machining," in Systems Techniques and Computational Methods C. Leondes, Ed. Washington, DC: CRC Press, 2001.
77. Z. Dong, H. Li, and G. W. Vickers, "Optimal rough machining of sculptured parts on a CNC milling machine," J. Eng. Ind. - Trans. Amer. Soc. Mech. Eng., vol. 115, pp. 424-431, 1993.
78. E. W. Weisstein, "Evolute," Math World [Online]. Available: http://mathworld.wolfram.com/Evolute.html
79. J. E. Summers, R. F. Gragg, and R. J. Soukup, "Topography measurement of scale-model representations of the rough ocean bottom by touch-trigger probe and its implications for spectral characterization," in Proc. MTS/IEEE OCEANS., Boston, MA, Sep. 2006, pp. 18-22.
80. T. R. Thomas, "Measurement," in Rough Surfaces, T. R. Thomas, Ed. White Plains, NY: Longman, 1982, ch. 2-3, pp. 11-69.
81. F. M. M. Chan, E. J. Davis, T. G. King, and K. J. Stout, "Some performance aspects of a multi-axis touch trigger probe," Meas. Sci. Technol., vol. 8, pp. 837-848, 1997.
82. W. T. Estler, S. D. Phillips, B. Borchardt, T. Hopp, M. Levenson, K. Eberhardt, M. McClain, Y. Shen, and X. Zhang, "Practical aspects of touch-trigger probe error compensation," Precis. Eng., vol. 21, pp. 1-17, 1997.
83. C. Dong, C. Zhang, B. Wang, and G. Zhang, "Prediction and compensation of dynamic errors for coordinate measuring machines," Trans. ASME, J. Manuf. Sci. Eng., vol. 124, pp. 509-514, 2002.
84. Z. Xiong and Z. Li, "Probe radius compensation of workpiece localization," Trans. ASME, J. Manuf. Sci. Eng., vol. 125, pp. 100-104, 2003.
85. J.-J. Wu, "Spectral analysis for the effect of stylus tip curvature on measuring rough profiles," Wear, vol. 230, pp. 194-200, 1999.
86. J.-J. Wu, "Spectral analysis for the effects of stylus tip curvature on measuring isotropic rough surfaces," Meas. Sci. Technol., vol. 13, pp. 720-730, 2002.
87. J.-J. Wu, "Spectral analysis for the effects of stylus tip curvature on measuring fractal profiles," Meas. Sci. Technol., vol. 11, pp. 1369-1376, 2000.
88. S. M. Kay, Modern Spectral Estimation: Theory and Application. Englewood Cliffs, NJ: Prentice-Hall, 1988.
89. R. T. Austin, A. W. England, and G. H. Wakefield, "Special problems in the estimation of power-law spectra as applied to topographical modeling," IEEE Trans. Geosci. Remote Sens., vol. 32, no. 4, pp. 928-939, Jul. 1994.
90. K. B. Briggs, D. Tang, and K. Williams, "Characterization of interface roughness of rippled sand off Fort Walton Beach, Florida," IEEE J. Ocean. Eng., vol. 27, no. 3, pp. 505-514, Jul. 2002.