臺灣博碩士論文加值系統

本問題為探討平面聲波於具彈性底床與隨機沉積層之粗糙海床上反射問題之研究。海洋聲場中的隨機度來自於海床的粗糙度及沉積層中聲速的隨機攝動現象，兩者所會引發的問題分別為面散射及體散射。利用微小攝動法推導出格林函數以求解沉積層中平均場的解析解。再利用邊界攝動法求解粗糙海床的問題，並架構線性系統以求得反射係數。本論文將對不同的海洋聲學參數加以分析，如：頻率、海床粗糙度、沉積層隨機度、沉積層後度、彈性底床特性。並因此而發現，隨著上述的參數數值之增加反射係數將伴隨降低。

This paper studies is considered the problem of coherent re ection of an acoustic plane
wave from a rough seabed with a randomly inhomogeneous sediment layer overlying a
uniform elastic basement. The randomness of the sound eld is attributable to the rough-
ness of the seabed and the sound-speed perturbation in the sediment layer, resulting in a
joint rough surface and volume scattering problem. An approach based upon perturbation
theory, combined with a derived Green''s function for a slab bounded above and below by
a uid and an elastic half space, respectively, is employed to obtain an analytic solution
for the coherent eld in the sediment layer. Furthermore, a boundary perturbation the-
ory developed by Kuperman and Schmidt [22] is applied to treat the problem of rough
surface scattering. A linear system is then established to facilitate the computation of the
coherent re ection eld. The coherent re ection coe cients for various surface roughness,
sediment randomness, frequency, sediment thickness, and basement elasticity have been
generated numerically and analyzed. It was found that the higher/larger size of surface
and/or medium randomness, frequency, thickness, and shear-wave speed, the lower the
coherent re ection. Physical interpretations of the various results are provided.

Introduction 1
1.1 Main Theme and Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.2 Literature Review and Stand-Point . . . . . . . . . . . . . . . . . . . . . . 2
1.3 Objectives and Approaches . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
1.4 Scope of the Thesis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
Theory 6
2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
2.2 Basic Assumption . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
2.3 Acoustic Wave Equation . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
2.4 Acoustic Wave Propagation in Random Media . . . . . . . . . . . . . . . . 10
2.5 Acoustic Wave Scattering from Rough Surfaces . . . . . . . . . . . . . . . 11
2.5.1 Theory in Rough Surface . . . . . . . . . . . . . . . . . . . . . . . . 12
2.5.2 Unperturbed Boundary . . . . . . . . . . . . . . . . . . . . . . . . . 12
2.5.3 Boundary Perturbation Method and Coherent Field . . . . . . . . . 14
2.6 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
Formulation 20
3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
3.2 Green''s Function . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
3.3 Mean-Field Solution in the Random Sediment Layer . . . . . . . . . . . . . 22
3.4 Boundary Operators for the Present Problem . . . . . . . . . . . . . . . . 25
3.5 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27
Results and Discussion 28
4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28
4.2 E ects of Frequency and Sediment Thickness . . . . . . . . . . . . . . . . . 29
4.3 E ects of Volume and Surface Scattering . . . . . . . . . . . . . . . . . . . 30
4.4 E ects of Elastic Basement . . . . . . . . . . . . . . . . . . . . . . . . . . . 36
4.5 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38
Conclusions and Future Work 39
5.1 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39
5.2 Future Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41
A 46

Bass, F.G. and I.M. Fuks, {it Wave Scattering From Statistically Rough Surfaces} (Pergamon, 1979).Beckmann, P. and A. Spizzichino, {it The Scattering of Electromagnetic Waves From Rough Surfaces} (Pergamon, 1963).Berman, D.H., ''Computing effective reflection coefficients in layered media,'' {it J. Acoust. Soc. Am.}, { f 101}, 741-748 (1997).Berman, D.H., ''Reverberation in waveguides with rough surfaces,'' {it J. Acoust. Soc. Am.}, { f 105}, 672-686 (1999).Boyce, W.E. and R.C. DiPrima, {it Elementary Differential Equations and Boundary Value Problems} (John Wiley, 1997).Brekhovskikh, L.M. and Y.P. Lysanov, {it Fundamentals of Ocean Acoustics} (Springer-Verlag, 1991).Chen, C.-S., {it Effects of elastic seabed and waveguide environment on the ambient noise generated by surface random processes, Master Thesis}, Department of Marine Environment, National Sun Yat-sen University (1996).Chernov, L.A., {it Wave Propagation in a Random Medium} ( McGraw-Hill, 1960).Clay, C.S. and H. Medwin, {it Acoustical Oceanography} (John Wiley, 1977).Dacol, D.K. and D.H. Berman, ''Sound scattering from a randomly rough fluid-solid interface,'' {it J. Acoust. Soc. Am.}, { f 84}, 292-302 (1988).Ewing, W.M., W.S. Jardetzky, and F. Press, {it Elastic Wave in Layered Media} (McGraw-Hill, 1957).Garrison, T., {it Oceanography} (Wadsworth, 1999).Goff, J.A. and T.H. Jordan, ''Stochastic modeling of seafloor morphology: Inversion of Sea Beam data for second-order statistics,'' {it J. Geophys. Res.}, { f 93}, No. B11, 13,589-13,608 (1988).Huang, C.-F., {it Acoustic wave scattering from rough sea surface and seabed, Master Thesis}, Institute of Undersea Technology, National Sun Yat-sen University (1998).Ivakin, A.N. and P. Lysanov, ''Theory of underwater sound scattering by random inhomogeneities of the bottom,'' {it Sov. Phys. Acoust.}, { f 27}, 61-64 (1981).Ishiruma, A., {it Wave Propagation and Scattering in Random Media} Vol. 1 & 2. (Academic Press, 1978).Jensen, F.B., W.A. Kuperman, M.B. Poter, and H. Schmidt, {it Computational Ocean Acoustic} (AIP Press, 1994). Kiorboe, L. and S.A. Petersen, ''Seismic investigation of the Faroe basaltes and their substratum,'' {it Geological Society London}, Special Publications { f 90}, 111-123 (1995).Kuperman, W.A., ''Coherent component of specular reflection and transmission at a randomly rough two-fluid interface,'' {it J. Acoust. Soc. Am.}, { f 58}, 365-370 (1975).Kuperman, W.A. and F. Ingenito, ''Attenuation of the coherent component of sound propagation in shallow water with rough boundaries,'' {it J. Acoust. Soc. Am.}, { f 61}, 1178-1187 (1977).Kuperman, W.A. and H. Schmidt, ''Rough surface elastic wave scattering in a horizontally-stratified ocean,'' {it J. Acoust. Soc. Am.}, { f 79}, 1767-1777 (1986).Kuperman, W.A. and H. Schmidt, ''Self-consistent perturbation approach to rough surface scattering in stratified elastic media,'' { it J. Acoust. Soc. Am.}, { f 86}, 1511-1522 (1989).Liu, J.-Y., {it Seismo-Acoustic Rough Interface Scattering of Surface-Generated Ambient Noise in a Stratified Ocean, Ph.D. Dissertation} at M.I.T (MIT Press, 1993).Liu, J.-Y. and C.-F. Huang, ''Acoustic plane-wave reflection from a rough surface over a random fluid half-space,'' {it Ocean Engineering}, { f 28}, 751-762 (2001).Liu, J.-Y., C.-O. Shen, and H.-H. Chen, ''Coherent reflection of acoustic plane wave from a random sediment layer over an elastic sea floor,'' {it Ocean Engineering}, { f 29}(13), 1701-1714 (2001).Liu, J.-Y., H. Schmidt, and W.A. Kuperman, ''Effect of a rough seabed on the spectral composition of deep ocean infrasonic ambient noise,'' {it J. Acoust. Soc. Am.}, { f 93}, 753-769 (1993).Liu, J.-Y. and J.L. Krolik, ''The spatial correlation of rough seabed scattering of surface-generated ambient noise,'' {it J. Acoust. Soc. Am.}, { f 96}, 2876-2886 (1994).Liu, J.-Y., S.-W. Shyue, and C.-F. Huang, ''Coherent reflection of acoustic plane wave from rough interfaces in a stratified random fluid medium,'' {it J. Marine Science and Technology}, { f 8}(2), 90-100 (2000).Miklowitz, J., {it The Theory of Elastic Waves and Waveguides} (North-Holland, 1978).Ogilvy, J. A., {it Theory of Wave Scattering From Random Rough Surfaces} (Adam Hilger, 1991).Robins, A.J., ''Reflection of a plane wave from a fluid layer with continuously varying density and sound speed,'' {it J. Acoust. Soc. Am.}, { f 89}, 1686-1696 (1991).Schmidt, H. and W.A. Kuperman, ''Spectral representations of rough interface reverberation in stratified ocean waveguides,'' {it J. Acoust. Soc. Am.}, { f 97}, 2199-2209 (1995).Schmidt, H., {it OASES} User Guide And Reference Manual (Department of Ocean Engineering Massachusetts Institute of Technology , 1999).Shiao, T.-J., {it A numerical study on ambient noise generated by surface wind waves, Master Thesis}, Department of Marine Environment, National Sun Yat-sen University (1995).Stark, H. and J.W. Woods, {it Probability and Random Processes with Applications to Signal Processing} (Prentice Hall, 2002).Tang, D.J. and G. Frisk, ''Plane-wave reflection from a random fluid half-space,'' {it J. Acoust. Soc. Am.}, { f 90}, 2751-2756 (1991).Tang, D.J., ''Shallow water reverberation due to sediment volume inhomogenieties.,'' {it J. Acoust. Soc. Am.}, { f 98}(A), 2988 (1991).Tracey, B.H. and H. Schmidt, ''A self-consistent theory for seabed volume scattering,'' {it J. Acoust. Soc. Am.}, { f 106}, 2524-2534 (1999).Uscinski, B.J., {it The Element of Wave Propagation in Random Media} (McGraw-Hill, 1994).Voronovich, A.G.,{it Wave Scattering From Rough Surfaces} (Springer-Verlag, 1994).Wolfram, S., {it The Mathematica Book} (Cambridge University Press, 1996).Yamamoto, T., ''Geoacoustic properties of the seabed sediment critical to acoustic reverberation at 50 to 500 Hz: a preliminary data set,'' {it J. Acoust. Soc. Am.}, Suppl. 1, { f 85} , S86 (1989).