水下音傳之聲線模態法建立

Abstract

淺海地區的地形和水文等海洋環境的變異性易造成聲波的水平折射現象，當內波傳播方向的夾角較大時，會造成聲波在水平方向上的能量因此聚集或散發而形成三維效應，為了透過模組行徑路徑了解水平方向上聲波的折射現象及複雜海洋環境中的三維效應，同時保持計算距離大時相同的計算解析度，本研究建立卡氏座標系統上的三維聲學計算模組，結合垂直向的模組及水平面上的高斯射線群來進行聲場計算，考量高斯射線群法的高頻假設，因此聲線模態法之計算模組(Three-Dimensional acoustic propagation model of horizontal Gaussian Beam and Vertical Normal Mode, 3DGBM-M)主要處理高頻淺海的計算問題，同時改善一般簡正模態法計算時忽略模態耦合效應的缺失。模組驗證係經由Pekeris波導做為二維音傳的比較基準，模擬海洋環境中無三維效應的音傳損耗，計算結果與簡正模態法及高斯射線群法進行比較；另外，底床特徵增加仿沙丘的正弦地形，將聲源配置於波峰處，觀察三維效應下的聲場分布，並與FOR3DW(寬角度版本)比較兩者三維模擬的差異。未來聲線模態法之精進可從初始聲源驗證及模組振幅的演算精進兩方面著手，若能更精準計算各類水文環境及海洋地形時，聲線模態法則能清楚呈現三維效應中的聲場變化並具備高效率的計算優勢。

The bathymetry and strong oceanographic variability in shallow water area can contribute to horizontal refraction. A wavefront obliquely incident upon an ocean front can be refracted in a direction dependent upon the angle of incidence and the modal phase speed which is determined by the horizontal wavenumber of the mode. This refraction on the horizontal plane causes convergence or spreading of acoustic energies and characterizes as the 3D effect. In this thesis, a hybrid underwater acoustic propagation model (Three-Dimensional acoustic propagation model of horizontal Gaussian Beam and Vertical Normal Mode, abbreviated as 3DGBM-M) based on the approach of horizontal rays and vertical modes is developed to interpret the horizontal refraction. The horizontal rays are calculated by the Gaussian beam method, in another word, the Gaussian beam method is used to calculate the modal amplitudes of vertical local modes. The Pekeris waveguide case is used as the benchmark to verify this hybrid model (3DGBM-M) for 2D propagation. The shallow water regions with sand dunes are modelled by adding sinusoidal variation to the ocean bottom in a Pekeris waveguide, and the underwater acoustic propagation in this region are calculated with 3DGBM-M and compared with the results calculated by wide-angle version of FOR3D. This hybrid model, 3DGBM-M, offers an robust solution to three-dimensional underwater acoustic propagation with improvement in spatial resolution, a result of using the Cartesian coordinates instead of the cylindrical coordinates, and high computing efficiency.