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研究生:薛炳彰
研究生(外文):Ping-Chang Hsueh
論文名稱: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
論文名稱(外文):Coherent Reflection of Acoustic Plane Wave From a Rough Seabed With a Random Sediment Layer Overlying an Elastic Basement
指導教授:劉金源劉金源引用關係
指導教授(外文):Jin-Yuan Liu
學位類別:碩士
校院名稱:國立中山大學
系所名稱:海下技術研究所
學門:工程學門
學類:電資工程學類
論文種類:學術論文
論文出版年:2002
畢業學年度:90
語文別:英文
論文頁數:56
中文關鍵詞:粗糙海床平均場反射聲波散射隨機沉積層彈性底床
外文關鍵詞:coherent reflectionrandom sediment layerrough seabedacoustic wave scatteringelastic basement
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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
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