Numerical Models of Underwater Acoustic Propagation

  • F. R. DiNapoli
  • R. L. Deavenport
Part of the Topics in Current Physics book series (TCPHY, volume 8)

Abstract

In this chapter an attempt is made to summarize those models of propagation loss in the field of underwater acoustics which have been converted into an automated computer code capable of being executed by someone other than the originator for a wide variety of problems. No single model currently exists which is adequate for all applications. This is perhaps not surprising considering the diversity of the ocean environment and its boundaries, and the concomitant fact that the acoustic frequencies of interest span the regime from less than 10 Hz to greater than 100 kHz. As a result a large number of models, each with its own domain of validity which in many cases is difficult to precisely define, have been developed. Their sheer number makes an exhaustive summary impossible within these limited pages. Thus it was decided to limit consideration to those models which purport to be a solution of the wave equation found in Sect.2.2.1. Fundamentally these models consider the ocean to be a deterministic environment for which the speed of sound is only a function of the spatial coordinates. Non-deterministic effects, if accounted for at all, are included in an ad hoc fashion following the determination of the deterministic propagation loss result. Model development work for the more general problem is required and is in progress. However, this effort has not reached the point where “hands off” computer codes are available. This is due in part to a lack of available experimental/ environmental data and the need for larger and faster computers.

Keywords

Attenuation Propa Explosive Stratification Expense 

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References

  1. 3.1
    F.R. DiNapoli, R.L. Deavenport: “Computer Models of Underwater Acoustic Propagation”; Tech. Rpt. 5867 ( Naval Underwater Systems Center, New London, Conn. 1978 )Google Scholar
  2. 3.2
    H.F. Baker: Proc. London Math. Soc. (Ser. l) 35, 333 (1902)Google Scholar
  3. 3.3
    R.A. Frazer, W.J. Duncan, A.R. Collar: Elementary Matrices ( Cambridge University Press, London 1960 )Google Scholar
  4. 3.4
    F.R. Gantmacher: The Theory of Matrices, Vol. 2 ( Chelsea Publishing, New York 1959 )MATHGoogle Scholar
  5. 3.5
    F. Gilbert, G.E. Backus: Geophys. 31, 326 (1966)CrossRefGoogle Scholar
  6. 3.6
    L.B. Felsen, N. Marcuvitz: Radiation and Scattering of Waves ( Prentice-Hall, Englewood Cliffs, NJ 1973 )Google Scholar
  7. 3.7
    E.A. Coddington, N. Levinson: Theory of Ordinary differential Equations ( McGraw- Hill, New York 1955 )MATHGoogle Scholar
  8. 3.8
    H.W. Marsh, S.R. Elam: Internal Document, Raytheon Company, Marine Research Laboratory, New London, Conn. (1967)Google Scholar
  9. 3.9
    F.R. DiNapoli: “A Fast Field Program for Multilayered Media”; Tech. Rpt. 4103 ( Naval Underwater Systems Center, New London, Conn. 1971 )Google Scholar
  10. 3.10
    F.R. DiNapoli, M.R. Powers: “Recursive Calculation of Products of Cylindrical Functions”, Tech. Memo. PA-83-70 (Naval Underwater Systems Center, New London, Conn. 1970 )Google Scholar
  11. 3.11
    F.R. DiNapoli: “The Collapsed Fast Field Program (FFP)”; Tech. Memo. TA11-317-72 (Naval Underwater Systems Center, New London, Conn. 1972 )Google Scholar
  12. 3.12
    D.C. Stickler: J. Acoust. Soc. Am. 57, 856 (1975)CrossRefADSGoogle Scholar
  13. 3.13
    W.M. Ewing, W.S. Jardetzky, F. Press: Elastic Waves in Layered Media ( McGraw-Hill, New York 1957 )MATHGoogle Scholar
  14. 3.14
    C.L. Bartberger:;AP2 Normal Mode Program, Report, Naval Air Development Center, Warminster, Pa. (1978)Google Scholar
  15. 3.15
    C.L. Pekeris: Geol. Soc. Am. Mem. 27 (1948)Google Scholar
  16. 3.16
    I. Tolstoy: J. Acoust. Soc. Am. 28, 1182 (1956)CrossRefADSGoogle Scholar
  17. 3.17
    S.R. Santaniello, F.R. DiNapoli, R.K. Dullea, P. Herstein: “A Synopsis of Studies on the Interaction of Low Frequency Acoustic Signals with the Ocean Bottom”; Tech. Doc. 5337, Naval Underwater Systems Center, New London, Conn. (1976)Google Scholar
  18. 3.18
    P. Debye: Phys. Z. 9, 775 (1908)Google Scholar
  19. 3.19
    B. Van den Pol, H. Bremmer: Phil. Mag. 24, 141, 825 (1937)MATHGoogle Scholar
  20. 3.20
    D.V. Batorsky, L.B. Felsen: Radio Sci. 6, 911 (1971)CrossRefADSGoogle Scholar
  21. 3.21
    H. Weinberg: J. Acoust. Soc. Am. 58, 97 (1975)CrossRefADSGoogle Scholar
  22. 3.22
    C.W. Spofford: “The FACT Model”; Tech. Rpt. 109, Maury Center for Ocean Science, Washington D.C. (1974)Google Scholar
  23. 3.23
    G.A. Leibiger: “The Acoustic Propagation Model RAYMODE: Theory and Numerical Treatment”; NUSC Tech. Rpt., Naval Underwater Systems Center, New London, Conn. (1978)Google Scholar
  24. 3.24
    M.A. Pedersen, D.F. Gordon: J. Acoust. Soc. Am. 51, 323 (1972)CrossRefMATHADSGoogle Scholar
  25. 3.25
    C. Bartberger: “Normal Mode Solutions and Computer Programs for Underwater Sound Propagation”; Tech. Rpt. NADC-72001-AE, Naval Air Development Center, Warminster, Pa. (1973)Google Scholar
  26. 3.26
    E.C. Titchmarsh: Introduction to the Theory of Fourier Integrals, 2nd ed. ( Oxford University Press, Oxford 1948 )Google Scholar
  27. 3.27
    H. Bremmer: Terrestrial Radio Waves ( Elsevier Publishing, Amsterdam 1949 )Google Scholar
  28. 3.28
    H.M. Nussenzveig: Ann. Phys. 34, 23 (1965)CrossRefADSMathSciNetGoogle Scholar
  29. 3.29
    F. Gilbert: Geophys. J. R. Astr. Soc. 44, 275 (1976)MATHGoogle Scholar
  30. 3.30
    A. Ben-Menahem: Bull. Seis. Soc. Am. 54, 1315 (1964)Google Scholar
  31. 3.31
    C.L. Pekeris: Proa. Symp. Appl. Math., Vol.2 (American Mathematical Society, New York 1950) pp.71–75Google Scholar
  32. 3.32
    D.S. Ahluwalia, J.B. Keller: “Exact and Asymptotic Representations of the Sound Field in a Stratified Ocean”, in Wave Propagation and Underwater Acoustics, ed. by J.B. Keller, J.S. Papadakis, Lecture Notes in Physics, Vol. 70 ( Springer, Berlin, Heidelberg, New York 1977 )Google Scholar
  33. 3.33
    N.A. Haskell: J. Appl. Phys. 157 (1951)Google Scholar
  34. 3.34
    L.M. Brekhovskikh: Sov. Phys. Acoust. 2, 124 (1956)Google Scholar
  35. 3.35
    R.B. Lauer, B. Sussman: “A Methodology for the Comparison of Models for Sonar System Applications”; Vol.1, Naval Sea Systems Command Tech. Rpt. SEA 06H1/036- EVA/M0ST-10, Naval Underwater Systems Center, New London, Conn. (1976)Google Scholar
  36. 3.36
    R.B. Lauer, B. Sussman: “A Methodology for the Comparison of Models for Sonar System Applications—Results for Low Frequency Propagation Loss in the Mediterranean Sea”; Vol.11, Naval Sea Systems Command Tech. Rpt. SEA 06H1/036- EVA/M0ST-11, Naval Underwater Systems Center, New London, Conn. (1978)Google Scholar
  37. 3.37
    D.F. Yarger: “The User’s Guide for the Raymode Propagation Loss Program”; Tech. Memo. 222-10-76, Naval Underwater Systems Center, New London, Conn. (1976)Google Scholar
  38. 3.38
    C.L. Bartberger: “PLRAY, A Ray Propagation Loss Program”; Tech. Rpt. Naval Air Development Center, Warminster, Pa. (1978)Google Scholar
  39. 3.39
    D.F. Gordon: “Normal Mode Computation of Propagation Loss for an Arbitrary Number of Layers”; Tech. Pub. 236, Naval Undersea Center, San Diego, Calif. (1971)Google Scholar
  40. 3.40
    D.W. Hoffman: “LORA, A Model for Predicting the Performance of Long-Range Active Sonar Systems”; Tech. Pub. 541, Naval Undersea Center, San Diego, Calif. (1976)Google Scholar
  41. 3.41
    W.H. Watson, R. McGirr: “Raywave-II, A Propagation Loss Model for the Analysis of Complex Ocean Environments”; Tech. Note 1516, Naval Undersea Center, San Diego, Calif. (1975)Google Scholar
  42. 3.42
    E.B. Wright: “Acoustic Transmission Loss by Single-Profile Ray Tracing, Program RTRACE”; Tech. Rpt. 7815, Naval Research Laboratory, Washington D.C. (1974)Google Scholar
  43. 3.43
    I.M. Blatstein: “Comparisons of Normal Mode Theory, Ray Theory, and Modified Ray Theory for Arbitrary Sound Velocity Profiles Resulting in Convergence Zones”; Tech. Rpt. 74–95, Naval Ordnance Laboratory, White Oak, Silver Spring, Md. (1974)Google Scholar
  44. 3.44
    H. Weinberg: J. Acoust. Soc. Am. 50, 975 (1971)CrossRefADSGoogle Scholar
  45. 3.45
    R.P. Porter, H.D. Leslie: J. Acoust. Soc. Am. 58, 812 (1975)CrossRefADSGoogle Scholar
  46. 3.46
    F.R. DiNapoli: “The Inverse Fast Field Program (IFFP): An Application to the Determination of the Acoustic Parameters of the Ocean Bottom”; Tech. Memo. 771160, Naval Underwater Systems Center, New London, Conn. (1977)Google Scholar
  47. 3.47
    H.W. Kutschale, F.D. Tappert: J. Acoust. Soc. Am. 62, S518 (1977)CrossRefGoogle Scholar
  48. 3.48
    H.W. Kutschale, F.R. DiNapoli: J. Acoust. Soc. Am. S518 (1977)Google Scholar
  49. 3.49
    F.D. Tappert: “The Parabolic Approximation Method”, in Wave Propagation and Underwater Acoustics, ed. by J.B. Keller, J.S. Papadakis, Lecture Notes in Physics, Vol. 70 ( Springer, Berlin, Heidelberg, New York 1977 )Google Scholar
  50. 3.50
    R.H. Hardin, F.D. Tappert: SIAM Rev. 15, 423 (1973)Google Scholar
  51. 3.51
    F.D. Tappert, R.H. Hardin: Proc. 8 Intern. Cong, on Acoustics, Goldcrest, London, Vol. 2, 452 (1974)Google Scholar
  52. 3.52
    R.M. Wilcox: J. Math. Phys. 8, 962 (1967)CrossRefMATHADSMathSciNetGoogle Scholar
  53. 3.53
    F. Jensen, H. Krol: “The Use of the Parabolic Equation Method in Sound Propagation Modeling”; Tech. Rpt. Sm 72, NATO SACLANTCEN, La Spezia, Italy (1975)Google Scholar
  54. 3.54
    J.S. Papadakis, D. Wood: “A Parabolic Decomposition of Helmholtz Equation”; Tech. Rpt., Naval Underwater Systems Center, New London, Conn. (1978)Google Scholar
  55. 3.55
    M.C. Smith: J. Acoust, Soc. Am. 46, 233 (1969)CrossRefADSGoogle Scholar
  56. 3.56
    S.T. McDaniel: J. Acoust. Soc. Am. 58, 1178 (1975)CrossRefADSGoogle Scholar
  57. 3.57
    D. Lee, J.S. Papadakis: “Numerical Solutions of Underwater Acoustic Wave Propagation Problems”; NUSC Tech. Rpt. 5929, Naval Underwater Systems Center, New London, Conn. (1978)Google Scholar
  58. 3.58
    D. Lee: “Nonlinear Multistep Methods for Solving Initial Value Problems in Ordinary Differential Equations”; Ph.D. dissertation, Polytechnic Institute of New York, N.Y. (1977)Google Scholar
  59. 3.59
    P. Henrici: Discrete Variable Methods in Ordinary Differential Equations ( Wiley and Sons, New York 1962 )MATHGoogle Scholar
  60. 3.60
    W.G. Kanabis: “A Shallow Water Acoustic Model for an Ocean Stratified in Range and Depth”; NUSC Tech. Rpt. 4887–1, Naval Underwater Systems Center, New London, Conn. (1975)Google Scholar
  61. 3.61
    W.G. Kanabis: “Computer Programs to Calculate Normal Mode Propagation and Applications to Analysis of Explosive Sound Data in the BIFI Range”; NUSC Tech. Rpt. 4319, Naval Underwater Systems Center, New London, Conn. (1972)Google Scholar
  62. 3.62
    C.W. Spofford, H.M. Garon: “Deterministic Methods of Sound-Field Computation”; in Proc. NATO Conf. on Oceanic Acoustic Modeling„ ed. by W. Bachmann, R.B. Williams (SACLANTCEN, La Spezia, Italy, 1975) pp.40–1 to 43Google Scholar
  63. 3.63
    J.J. Cornyn: “Grass, A Digital-Computer Ray-Tracing and Transmission-Loss-Prediction System”; NRL Rpt. 7621, Vol. 1, Naval Research Laboratory, Washington D.C. (1973)Google Scholar
  64. 3.64
    H.P. Bucker: “The RAVE (Ray Wave) Method”; in Proc. NATO Conf. on Geometrical Acoustics, ed. by B.W. Conolly, R.H. Clark ( SACLANTCEN, La Spezia, Italy 1971 ) pp. 32–36Google Scholar
  65. 3.65
    A.J. Kalinowski: The Shock and Vibration Digest, 11, 12 (March 1979)ADSGoogle Scholar
  66. 3.66
    M.J. Turner, R.W. Clough, H.C. Martin, L.J. Topp: J. Aeronaut. Sci. 23, 805 (1956)MATHGoogle Scholar
  67. 3.67
    J.T. Oden: Finite Elements of Nonlznear Continuum ( McGraw-Hill, New York 1972 )Google Scholar
  68. 3.68
    O.C. Zienkiewicz, Y.K. Cheung: “Finite Elements in the Solution of Field Problems”, The Engineer 220, 507 (1965)Google Scholar
  69. 3.69
    R.H. Gallagher, J.T. Oden, C. Taylor, O.C. Zienkiewicz: Finite Elements in Fluids—Vol.1, Viscous Flow and Hydrodynamics ( Wiley and Sons, New York 1975 )MATHGoogle Scholar
  70. 3.70
    R.H. Gallagher, J.T. Oden, C. Taylor, O.C. Zienkiewicz: Finite Elements in Fluids, Vol.2, Mathematical Foundations3 Aerodynamics and Lubrication ( Wiley and Sons, New York 1975 )Google Scholar
  71. 3.71
    J.T. Oden, O.C. Zienkiewicz, R.H. Gallagher, C. Taylor: Finite Element Methods in Flow Problems (University of Alabama Huntsville Press, Huntsville, Ala. 1974 )Google Scholar
  72. 3.72
    O.C. Zienkiewicz, Y.K. Cheung: The Finite Element Method in Structural and Continuum Mechanics ( McGraw-Hill, New York 1967 )MATHGoogle Scholar
  73. 3.73
    L.J. Segerland: Applied Finite Element Analysis ( Wiley and Sons, New York 1976 )Google Scholar
  74. 3.74
    K.H. Huebner: The Finite Element Method for Engineers ( Wiley and Sons, New York 1975 )Google Scholar
  75. 3.75
    R.D. Cook: Concepts and Applications of Finite Element Analysis ( Wiley and Sons, New York 1974 )Google Scholar
  76. 3.76
    J.T. Oden, J.N. Reddy: An Introduction to the Mathematical Theory of Finite Elements ( Wiley and Sons, New York 1976 )MATHGoogle Scholar
  77. 3.77
    G. Strang, G. Fix: An Analysis of the Finite Element Method (Prentice-Hall, Englewood Cliffs, N.J. 1973 )MATHGoogle Scholar
  78. 3.78
    D. Norrie, Gerard de Vries: Finite Element Bibliography ( IFI/Plenum Data Company, New York 1976 )MATHGoogle Scholar
  79. 3.79
    A.J. Kalinowski: “Fluid-Structure Interaction”, in Shock and Vibration Computer Programs, Review and Summaries, ed. by Pi 1 key and Pi 1 key, SVM-10, The Shock and Vibration Information Center, Washington D.C. (1975)Google Scholar
  80. 3.80
    L.H. Chen, V.M. Pierucci: “Underwater Fluid-Structure Interaction”, Parts I and II, The Shock and Vibration Digest (April issue, pp.23–24; May, pp. 17–21, 1977 )Google Scholar
  81. 3.81
    R.L. Kuhlemeyer, J. Lysmer: J. Soil Mech. Found. Div., ASCE, 99, 421 (1973)Google Scholar
  82. 3.82
    J. Lysmer, R.L. Kuhlemeyer: J. Engr. Mech. Div., ASCE, 95, 859 (1969)Google Scholar
  83. 3.83
    J. Lysmer, L. Drake: “A Finite Element Method for Seismology”, Methods in Computational Physics, ed. by B. Bolt ( Academic Press, New York 1972 )Google Scholar
  84. 3.84
    J.A. Gutierrez: “A Substructure Method for Earthquake Analysis of Structure-Soil Interaction”, Earthquake Enqineering Research Center, Rpt. No. 76–9 (April 1976)Google Scholar
  85. 3.85
    J. Lysmer: Bull. Scism. Soc. Am. 60, 89 (1970)Google Scholar
  86. 3.86
    J. Lysmer, G. Waas: J. Eng. Mech. Div., ASCE, 98, 85 (1972)Google Scholar
  87. 3.87
    E. Kausel, J. Roesset, G. Waas: J. Eng. Mech. Div., ASCE, 101, 679 (1975)Google Scholar
  88. 3.88
    E. Kausel, J. Roesset: J. Eng. Mech. Div., ASCE, 103, 569 (1977)Google Scholar
  89. 3.89
    P. Chakrabarti, A.K. Chopru: Earthquake Engineering and Structural Dynamics 2, 107 (1973)Google Scholar
  90. 3.90
    G.J. Fix, S.P. Marin: “Variational Methods for Underwater Acoustics Problems”, ICASE Rpt. 77–16 (August 1977)Google Scholar
  91. 3.91
    A. Carlson, A.J. Kalinowski, J. Patel: “Solutions of a General Class of Fluid Structure Problems by the Finite Element Method”, Naval Underwater Systems Center TR-5361 (Conf.) (June 1976)Google Scholar
  92. 3.92
    “The NASTRAN User’s Manual”, NASA SP-222(03) (March 1976)Google Scholar
  93. 3.93
    O.C. Zienkiewicz, D.W. Kelly, P. Bettess: International Journal of Numerical Methods in Engineering, 11, 355 (1977)CrossRefMATHMathSciNetGoogle Scholar
  94. 3.94
    C.D. Mote, Jr.: Int. J. Numerical Methods in Engineering, 3, 565 (1971)CrossRefMATHMathSciNetGoogle Scholar
  95. 3.95
    E.A. Rukos: International Journal for Numerical Methods in Engineering, 12, 11 (1978)CrossRefMATHMathSciNetGoogle Scholar
  96. 3.96
    M. Petyt, J. Lea, Koopman: Journal of Sound and Vibration, 45, 495 (1976)CrossRefADSGoogle Scholar
  97. 3.97
    G.J. Fix, M.H. Gunzburger: “On the Use of Modern Numerical Methods in Acoustics”, ICASE Rpt., no dateGoogle Scholar
  98. 3.98
    A.J. Kalinowski: Shock and Vibration Bulletin, 48, 62 (1977)Google Scholar
  99. 3.99
    A.J. Kalinowski: “Application of the Finite Element Method to Acoustic Propagation in the Ocean”; NUSC Tech. Rpt. S891, Naval Underwater Systems Center, New London, Conn. (1979)Google Scholar
  100. 3.100
    R. Dungar, P.J.L. Eledred: Earthquake Eng. Struct. Dynamics 6, 123–138 (1978)CrossRefGoogle Scholar
  101. 3.101
    J.M. Rosset, M.M. Ettouney: International Journal for Numerical and Analytical Methods in Geomechanics, 1, 151 (1977)CrossRefADSGoogle Scholar
  102. 3.102
    R. Kuhlemeyer: “Vertical Vibrations of Footings Embedded in Layered Media”, Ph.D. Thesis, University of Calif., Berkeley (1969)Google Scholar
  103. 3.103
    O.C. Zienkiewicz, R.E. Newton: “Coupled Vibrations of a Structure Submerged in a Compressible Fluid”, Proc. Int. Symp. on Finite Element Techniques (Stuttgart, F.R. Germany 1969 )Google Scholar
  104. 3.104
    P. Bettess, O.C. Zienkiewicz: International Journal for Numerical Methods in Engineering, 11, 1271 (1977)CrossRefMATHMathSciNetGoogle Scholar
  105. 3.105
    P. Bettess: International Journal for Numerical Methods in Engineering, 11, 53 (1977)CrossRefMATHADSGoogle Scholar
  106. 3.106
    O.C. Zienkiewicz, P. Bettess: 2nd Intern. Symp. Computing Meth. Appl. Science and Engng. ( Versailles, France 1975 )Google Scholar
  107. 3.107
    B. Engquist, A. Majda: Mathematical of Computation, 31, 629 (1977)CrossRefMATHADSMathSciNetGoogle Scholar
  108. 3.108
    J.T. Hunt, M. Knittel, C.S. Nichols, D. Barach: J. Acoust. Soc. Am. 57, 287 (1975)CrossRefMATHADSGoogle Scholar
  109. 3.109
    J.T. Hunt, M.P. Knittel, D. Barach: J. Acoust. Soc. Am. 55, 269 (1974)CrossRefADSGoogle Scholar
  110. 3.110
    H.A. Schenck: J. Acoust. Soc. of Am. 44, 41 (1967)CrossRefADSGoogle Scholar
  111. 3.111
    O.C. Zienkiewicz: The Finite Element Method in Engineering Science ( McGraw-Hill, London 1971 )MATHGoogle Scholar
  112. 3.112
    G.C. Everstine, E.M. Schroeder, M.S. Marcus: “The Dynamic Analysis of Submerged Structures”, 4th NASTRAN User’s Colloquium, Langley Research Center, Hampton, Virginia (1975)Google Scholar
  113. 3.113
    D. Shantaram, D.R.J. Owen, O.C. Zienkiewicz: Earthquake Engineering and Structural Dynamics, 4, 561 (1976)Google Scholar
  114. 3.114
    E.P. Sorensen, D.V. Marcal: “A Solid Mechanics Approach to the Solution of Fluid-Solid Vibration Problems by Finite Elements”, Brown University Tech. Rpt. N00014-0007/13 (May 1976)Google Scholar
  115. 3.115
    L. Kiefling, G.C. Feng: AIAA J. 14, 199 (1976)CrossRefMATHADSMathSciNetGoogle Scholar
  116. 3.116
    G.J. Fix, M.D. Gunzburger, R.A. Nicolaides: “On Mixed Finite Element Methods The Kelvin Principle”, ICASE Rpt. ( Dec 1977 )Google Scholar
  117. 3.117
    G.J. Fix, M.D. Gunzburger, R.A. Nicolaides: “On Mixed Finite Element Methods The Least Squares Method”, ICASE Rpt. 77–18 (Dec 1977)Google Scholar
  118. 3.118
    A.J. Kalinowski: “Transmission of Shock Waves into Submerged Fluid Filled Vessels”, in Fluid Structure Interaction Phenomena in Pressure Vessel and Piping Systems, ed. by M. Wang, S.J. Brown (ASME, New York 1977 ) pp. 83–105Google Scholar

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© Springer-Verlag Berlin Heidelberg 1979

Authors and Affiliations

  • F. R. DiNapoli
  • R. L. Deavenport

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