洪淑蕙臺灣大學：地質科學研究所彭振謙Peng, Cheng-ChienCheng-ChienPeng2007-11-262018-06-282007-11-262018-06-282006http://ntur.lib.ntu.edu.tw//handle/246246/54845Plate kinematics on the surface of the Earth has been described successfully by the Eulerian rotation without intraplate deformation. It is, however, difficult to specify the kinematics of the lithosphere subduction. Connected with the surface plate velocity across the pivot axis, the trench, the velocity vector field of the subducted slab had been conventionally defined by simply rotating the surface Eulerian kinematics with respect to the local strike onto the slab surface. It usually results in unrealistic in-plane deformation rates within the slab surface. Alternatively, the flow field as well as the observed slab geometry can be shown to be natural consequences of attaining the kinematic field with the minimum dissipation power. The dependence of the deformation rates, associated with such flow field as defined following the minimization, upon the intrinsic geometry of the non-Euclidean surface is, however, implicit and opaque. We derive, in this study, the fundamental compatibility equation of the strain-rates tensor for the subduction flow field to highlight the fundamental dependency. There are two factors; one is associated with the variation of the Gaussian curvature along the stream lines. The other is the local compressibility amplified by the in situ Gaussian curvature. We discuss the implications of these factors and point out that to delineate the potential membrane deformation rates of the subducted slab, unambiguous information on the subduction kinematics is essential in addition to mapping the Gaussian curvature variation of the subducted slab.目錄 I 圖目錄 II 摘要 III 第一章 序論 1.1運動學與幾何空間 ……………………………………………………………1 1.2應變的相容方程式 ……………………………………………………………3 第二章 基本理論 2.1對於隱沒板塊的假設 …………...…………………………………………….7 2.2 薄板變形與撓曲變形 ……………...…………………………………………8 2.3 薄板變形率：順推問題 ……..……………………………………………….9 2.3.1 薄板變形率張量……………………………………………………………9 2.3.2 投影算符(Projection operator) ….…………………………………………10 2.3.3 將三維問題簡化至二維 …………………………………………………13 2.4 薄板變形率：逆推問題 ……….. …………………………………………..14 2.4.1 總應變率功率 ……………………………………………………………14 2.4.2逆推隱沒流場 …………………………………….………………………15 2.4.2.a牛頓流體的線性逆推問題 .…………………………………………...15 2.4.2.b 指數率流體的非線性逆推問題 ……………...………………………..15 第三章 西北太平洋實驗 3.1 西北太平洋地震活動與板塊幾何 …....…………………………………….17 3.2 前人實驗 …………………………………………………………………….18 3.3 西北太平洋實驗 …………………………………………………………….23 第四章 非歐空間中的應變率相容方程式 4.1 共變微分(Covariant derivative)與平行性(Parallelism) ………….....……….27 4.2高斯理論(Gauss theorem egregium) …….………………..………..…………29 4.3 應變相容方程式……......………………….…..…………………..………….29 4.4 應變相容方程式回顧 …………………………………………..……………30 4.5 非歐空間中的應變率相容方程式 …………………………..………………31 第五章 結論與討論 ……………………………………………..……………….33 參考資料 ………………………………………………………..………………...34 附錄一推導非歐空間中的應變相容方程式 ……………….……………………37 附錄二 推廣的應變相容方程式在橢圓面上的應用 …….….………………….39926300 bytesapplication/pdfen-US隱沒板塊應變相容方程式高斯曲率subductioncompatibility equationsGaussian curvaturethesishttp://ntur.lib.ntu.edu.tw/bitstream/246246/54845/1/ntu-95-R93224209-1.pdf