本論文主要研究目的在藉由地聲模式的參數預估，發展一套反算沉積層聲速剖面的演算法。 環境架構為一連續變化的海洋沉積層，其中密度視為廣義指數函數變化，而聲速則採用較符合真實海床之 inverse-square 連續變化。於正算模式中，假設平面波入射海床，而海床由非均質沉積層與均質彈性底床所組成，計算此環境下之反射場。在預估沉積層聲速剖面的反算過程中，將藉由正算模式環境下，噪音干擾所形成的的反射場進行反算，而環境噪音乃藉由數值模擬方式所產生。反算流程可透過假設的噪音數據，預測參數的不確定性，進而計算出事後機率分布。如此可達到量化反算品質的結果。
進行正算模式時，將針對此環境下的參數敏感度進行初步分析。在進行敏感度分析前，需先求解平面波反射係數，經由海床與底層之邊界條件，建構出一套 線性系統，進而求解平面波聲場的反射係數。本研究所得之反射係數解析解利用 OASES 加以驗證，在確認數值解析解撰寫無誤後，改變反射係數裡的各種參變數，探討其對反射場的影響。經此一步驟後，可約略知道參數之敏感度應與密度或聲速剖面的變動程度有關。而後藉由反射係數定義出敏感度指數，找尋較具敏感度指數之地聲參數。本研究之前期研究已在第九屆水下技術研討會暨國科會成果發表會發表，主要探討為沉積層中地聲參數對平面波反射場的影響及其敏感度問題。 而在敏感度分析過程中可知，高敏感度指數地聲參數皆為沉積層聲速參數，將選定這些地聲參數進行地聲反算。藉由參數於一維邊際機率密度與二維邊際機率密度的不確定性，利用統計方式， 將沉積層聲速剖面於不同沉積層厚度時的 99 % 可靠區間計算出來。並且比較三種影響反算成效的因素：信雜比、量測資料數目及量測數據區域，並針對影響結果進行討論。
本研究藉由反算沉積層聲速的連續變化性質，驗證反算連續層化沉積層的可行性。若能建立更符合真實海床之環境架構，可將參數模式化應用於實海域地聲反算問題上，使地聲反算更臻完美。

The objective of this thesis is to develop and implement an algorithm for inverting the sound speed profile via estimation of the parameters embedded in a geoacoustic model. The environmental model inscribes a continuously-varying marine sediment layer with density and sound speed distributions represented by the generalized-exponential and inverse-square functions, respectively. Based upon a forward problem of plane-wave reflection from a non-uniform sediment layer overlying a uniform elastic basement, an inversion procedure for estimating the sound speed profile from the reflected sound field under the influence of noise is established and numerically implemented. The inversion invokes a probabilistic approach quantified by the posterior probability density for measuring the uncertainties of the estimated parameters from synthetic noisy data. Preliminary analysis on the solution of the forward problem and the sensitivity of the model parameters is first conducted, leading to a determination of the parameters chosen for inversion in the ensuing study. The parameter uncertainties referenced 1-D and 2-D marginal posterior probability densities are then examined, followed by the statistical estimation for the sound speed profile in terms of 99 % credibility interval. The effects of, the signal-to-noise ratio (SNR), the dimension of data vector, the region in which the data sampled, on the statistical estimation of sound speed profile are demonstrated and discussed.

第一章　緒論
　1.1　研究主題與研究動機
　1.2　文獻回顧
　1.3　研究方法
　1.4　論文範疇
第二章　理論模式
　2.1　簡介
　2.2　聲波方程式
　　2.2.1　均勻介質
　　2.2.2　非均勻介質
　　2.2.3　綜合整理
　2.3　以平面波求解聲波方程式
　　2.3.1　均勻介質
　　2.3.2　非均勻介質
　　2.3.3　綜合整理
　2.4　邊界條件
　2.5　機率分布之不確定性
　　2.5.1　貝氏定理
2.5.2 目標函數
2.5.3 邊際分布
2.5.4 信賴區間與可靠區間
2.5.5 最高事後密度與中位數
　2.6　敏感度指數
　2.7　結語
　2.6　結語
第三章　正算模式解：反射場分析
　3.1　平面波反射場之結果驗證
　3.2　地聲參數對反射場之影響
　　3.2.1　沉積層密度之地聲參數
　　3.2.2　沉積層聲速之地聲參數
　3.3　結語
第四章　敏感度分析
　4.1　地聲環境對參數敏感度之影響
　4.2　高敏感度指數地聲參數與地聲反算之關聯性
　　4.2.1　一維之關聯性
4.2.2 二維之關聯性
　4.3　結語
第五章　沉積層聲速之反算
　5.1　反算流程
　5.2　反算結果及其不確定性分析
　　5.2.1　信雜比之影響
5.2.2 量測角度數目之影響
5.2.3 量測角度區域之影響
　5.3　結語
第六章　結論與建議
　6.1　結論
　6.2　建議
附錄A 非均質海床地聲模式參數之敏感度分析
附錄B Inverting Sound Speed Profile Using a Parameterized Geoacoustic Model for Marine Sediment Layer

Berman, D.H., ``Computing effective reflection coefficients in layered media,' J. Acoust. Soc. Am., 101(2), 1997, pp. 741-748.
Boyce, W.E. and R.C. DiPrima, Elementary Differential Equations and Boundary Value Problems (7th ed.), John Wiley, 1997.
Clay, C.S. and H. Medwin, Acoustical Oceanography, John Wiley, 1977.
Collins, M.D., ``A split-step Pade solution for the parabolic equation method,' J. Acoust. Soc. Am., 93(4.1), 1993, pp. 1736-1742.
Dozier, L.B. and F.D. Tappert, ``Statistics of normal mode amplitudes in a random ocean, J. Acoust. Soc. Am., 64(2), 1978, pp. 533-547.
Ewing, W.M., W.S. Jardetzky, and F. Press, Elastic Wave in Layered Media, McGraw-Hill, 1957.
Gerstoft, P., SAGA User Manual 5.1: An Inversion Software Package, Marine Physical Laboratory, Scripps Institution of Oceanography, University of California at San Diego, 2004.
Hamilton, E.L., ``Geoacoustic modeling of the sea floor.' J. Acoust. Soc. Am., 68(5), 1980, pp. 1313-1340.
Holland, C.W., J. Dettmer, and S.E. Dosso, ``Remote sensing of sediment density and velocity gradients in the transition.' J. Acoust. Soc. Am., 118(1), 2005, pp. 163-177.
Huang, C.F. and W.S. Hodgkiss, ``Matched-field geoacoustic inversion of low-frequency source tow data from the ASIAEX East China Sea experiment,' IEEE J. Oceanic Eng., 29(4), 2004, pp. 952-963.
Huang, C.F., P. Gerstoft, and W.S. Hodgkiss, ``Uncertainty analysis in matched-field geoacoustic inversions,' J. Acoust. Soc. Am.}, 119(1), 2006, pp. 197-207.
Huang, C.F., P. Gerstoft, and W.S. Hodgkiss, ``Validation of statistical estimation of transmission loss in the presence of geoacoustic inversion uncertainty,' J. Acoust. Soc. Am., 120(4), 2006, pp. 1932-1941.
Huang, C.F., P. Gerstoft, and W.S. Hodgkiss, ``On the effect o error correlation on matched-field geoacoustic inversion,' J. Acoust. Soc. Am., 121(2), 2007, pp. EL64-EL69.
Jensen, F.B., W.A. Kuperman, M.B. Poter, and H. Schmidt, Computational Ocean Acoustic, AIP Press, 1994.
Kuperman, W.A. and H.Schmidt, ``Rough surface elastic wave scattering in a horizontally-stratified ocean,' J. Acoust. Soc. Am., 79(6), 1986, pp. 1767-1777.
Lekner, J., ``Reflection and transmission of compressible waves: some exact results.' J. Acoust. Soc. Am., 87(6), 1990, pp. 2325-2331.
Liu, J.-Y., C.-C. Wang, S.-H. Tsai, and C.-R. Chu ``Acoustic wave reflection from a rough seabed with a continuously varying sediment layer overlying an elastic basement' J. Sound and Vibration, 275, 2004, pp. 739-755.
Liu, J.-Y. and C.-F. Huang, ``Acoustic plane-wave reflection from a rough surface over a random fluid half-space,' Ocean Engineering, 28, 2001, pp. 751-762.
Liu, J.-Y., I.-C. Lin, and C.-R. Chu, ``Effects of sediment properties on surface-generated ambient noise in a shallow ocean,' Ocean Engineering, 32, 2005, pp. 1887-1905.
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,' J. Marine Science and Technology, 8(2), 2000, pp. 90-100.
Miklowitz, J., The Theory of Elastic Waves and Waveguides, North-Holland, 1978.
Porter, M.B. and E.L. Reiss, ``A numerical method for ocean acoustic normal modes,' J. Acoust. Soc. Am., 76(1), 1984, pp. 244-252.
Porter, M.B., The KRAKEN normal mode program Rep. SM-245, SACLANT Undersea Research Centre, La Spezia, Italy, 1991.
Potty, G.R., J.H. Miller, J.F. Lynch, and K.B. Smith, ``Tomographic inversion for sediment parameters in shallow water,' J. Acoust. Soc. Am., 108(3), 2000, pp. 973-986.
Potty, G.R., J.H. Miller, and J.F. Lynch, ``Inversion for sediment geoacoustic properties at the New England Bight,' J. Acoust. Soc. Am., 114(4), 2003, pp. 1874-1887.
Ranz-Guerra, C. and R. Carbo-Fite, ``Im-pulse response of sediment layers with variable density gradients.' Acoustics and the Sea Bed. Bath U.P., Bath, England, 1983.
Robins, A.J., ``Reflection of plane acoustic waves from a layer of varying density,' J. Acoust. Soc. Am., 87(4), 1990, pp. 1546-1552.
Robins, A.J., ``Reflection of a plane wave from a fluid layer with continuously varying density and sound speed,' J. Acoust. Soc. Am., 89(4), 1991, pp. 1686-1696.
Robins, A.J., ``Exact solutions of the Helmholtz equation for plane wave propagation in a medium with variable density and sound speed,' J. Acoust. Soc. Am., 93(3), 1993, pp. 1347-1352.
Robins, A.J., ``Generation of shear and compression waves in an inhomogeneous elastic medium,' J. Acoust. Soc. Am., 96(3), 1994, pp. 1669-1676.
Rutherford, S.R. and K.E. Hawker, ``Effect of density gradients on bottom reflection loss for a class of marine sediments.' J. Acoust. Soc. Am., 63(3), 1978, pp. 750-757.
Schmidt, H. and W.A. Kuperman, ``Spectral representations of rough interface reverberation in stratified ocean waveguides,' J. Acoust. Soc. Am., 97(4), 1995, pp. 2199-2209.
Schmidt, H., SAFARI: User's Guide, SACLANT Undersea Research Centre, La Spezia, Italy, 1988.
Schmidt, H., OASES: User Guide And Reference Manual, Version 3.1, Department of Ocean Engineering, Massachusetts Institute of Technology, 2002.
Tang, D.J. and G. Frisk, ``Plane-wave reflection from a random fluid half-space,' J. Acoust. Soc. Am., 90(5), 1991, pp. 2751-2756.
Tappert, F.D., ``The parabolic approximation method,' Wave Propagation in Underwater Acoustics, edited by J.B. Keller and J.S. Papadakis, Springer-Verlag, 1977, pp. 224-287.
Tolstoy, I., ``The theory of waves in stratified fluids including the effects of gravity and rota-tion.' Rev. Mod. Phys., 35, 1963, pp. 207-230.
Tolstoy, I., ``Effects of density stratification on sound waves.' J. Geophys. Res., 70(24), 1965, pp. 6009-6015.
Williams, A.O. and D.R. MacAyeal, ``Acoustic reflection from a sea bottom with linearly increasing sound speed,' J. Acoust. Soc. Am., 66(6), 1979, pp. 1836-1841.
Wolfram, S., The Mathematica Book, Cambridge University Press, 1996.
楊士鋒、朱崇銳、劉金源，'非均質海床地聲模式參數之敏感度分析'，第九屆水下技術研討會及國科會成果發表會 論文集，2007，頁 15-24。
劉金源，《水中聲學─水聲系統之基本操作原理》，國立編譯館，民 90。
劉金源，《海洋聲學導論─海洋聲波傳播與粗糙面散射之基本原理》，中山大學出版社，民 91。
國立編譯館編訂，《統計學名詞》，水牛圖書出版事業有限公司，民 86。