2004-08-012024-05-18https://scholars.lib.ntu.edu.tw/handle/123456789/709682摘要：非歐氏界面上板塊運動的理論推導 近代地體板塊理論之所以能夠精確而簡明的描述相對板塊運動肇因於地球表面近似於理想球面之基本幾何架構。理想球面具有均勻不變的高斯曲度，因此容許藉助免於形變之理想旋轉流場來描述板塊運動。但是相對板塊運動進行的舞台並不侷限於地球表面。例如根據瓦班氏地震帶，我&#20204;知道海洋岩石圈在隱沒進入地幔過程之中維持的形態就是非歐氏二維空間(即具有隨位置變化的高斯曲度)。由於免於形變的剛體旋轉式流場在非歐氏二維空間之中已不可能，是以在這些發生於廣義曲面上的地體活動如何建構其運動流場是理論上必須理解的重要課題。而伴隨著特定流場所衍生的形變在空間分佈的形態、大小與特色以及其可能展現之地球物理觀測(例如地震活動)均是急待瞭解的研究對象。 針對這些重要課題，我們在過去的努力主要在於推演在廣義非歐曲面上形變率張量的數值估算方法，以及根據形變率張量計算，對於特定曲面幾何之最佳流場(亦即形變最小流場)的預測。我們將發展的數值計算方法應用在對於特定隱沒帶幾何之流場建構以致於該隱沒過程中特定質點的傳輸途徑以及可能伴隨之形變估算，提供適當解釋不同隱沒帶若干難以理解觀測現象的<br> Abstract: Theoretical derivation of the plate kinematics on a non-Euclidean surface Simple description of plate kinematics by the Euler’s rotation on the surface of the Earth is the fundamental cornerstone behind the theory of Plate Tectonics. The intrinsic geometric reason that the Earth’s surface is of constant positive Gaussian curvature makes it possible to have a flow field prescribing the plate kinematics to be free from internal deformation. However, plate kinematics is not restricted on the surface of the Earth. The slab of the oceanic lithosphere plunges into the deep mantle during subduction while the slab geometry, portrayed by the Wadati-Benioff seismicity, is clearly not Euclidean (i.e., having variable curvature). It is of fundamental importance to inquire on how plate kinematics during such process be configured since rigid body rotation without internal deformation is no longer possible for non-stationary curvature variation. Specifically, what is the potential deformation regime associated with the optimum subduction flow field and how these intrinsic deformation manifest into observable geophysical processes such as slab earthquakes are of critical geophysical interests. To improve our comprehension on these topics, we have previously devised a numerical scheme that looks for the virtual flow field on non-Euclidean slab surface that bears the minimum membrane deformation rate. The scheme has been applied to model plausible subduction flow fields that show intriguing highlights on deformation regimes and particle paths of subducted slabs with anomalous geometric configurations. A recent application of such non-Euclidean kinematical configuration that yield interesting insights is an attempt to model slip variation of the 1999 Chi-Chi earthquake on the Chelungpu fault. Although these preliminary successes are encouraging, the numerical modeling approach is, however, incapable of identifying the fundamental physics of how the intrinsic geometry of the non-Euclidean interface sets up the basic constraint on the deformation regime and thus the flow kinematics. We intend to start from the compatibility of strain rate tensor on the non-Euclidean surface. It is very likely that the derivation can only be checked analytically on very simple geometry, but working together with our previously built numerical scheme, we intend to establish both the physical and geometrical principle as well as practical algorithm to be able to construct the proper flow field for tectonic transport in general. We believe that this work is not only of theoretical concern but will also have important practical applications.板塊運動非歐氏界面高斯曲度膜面形變Plate kinematicsnon-Euclidean interfaceGaussian curvaturemembrane deformation