【作者】 陈庭；

【导师】 刘经南； 许才军；

【作者基本信息】 武汉大学 ， 大地测量学与测量工程， 2005， 博士

【摘要】 以甚长基线干涉测量（VLBI）、卫星激光测距（SLR）、全球定位系统（GPS）和差分合成孔径雷达干涉（D-InSAR）等新兴的空间对地观测技术为代表的现代大地测量为监测和研究地壳运动提供了新途径。大地测量参与地壳形变的主要技术GPS可以10^-9的精度监测点距几十至几百公里不同尺度范围的地壳地表运动和形变,用VLBI和SLR技术可以测定相距数千里的全球板块运动;现代精密重力仪可以微伽的精度测定重力场的变化。通过这些运动信息的数据处理,可以直观地描述地壳运动规律。然而地表的地壳运动是地球深部动力学过程的一种表象,研究地壳运动,需要结合地质、地球物理等资料,探讨构造运动的动力学机制,研究构造运动的力源。 地球物理、地质等学科的观测结果提供的是几十年至上百万年的空间上不连续的资料;虽然GPS观测网络越来越多,但相对于广袤的的大陆来说测站数仍严重不足,同时由于GPS观测主要以地震监测和预报为目的,测站分布多位于一些主断裂或构造活跃地区,地理分布极不均匀,许多地域受观测条件限制而成为观测盲区。因此,要获得特定块体或区域的地壳位移场和应力场的连续图像,必须要借助数理方法,由已知测站的观测得来的速度或位移来推求未被GPS观测覆盖地区的形变位移,并进而作应力分析。 在已有数值模拟工具当中,有限元法因其适用性广、解算过程规范而得到广泛的应用,已成为解决数值正反演问题的主要工具。非连续变形分析方法（DDA）中所有单元是被不连续缝所包围的隔离块体,对每个块体允许有位移和变形,块体间允许有滑移。非连续变形分析方法侧重于处理不连续的问题,它要求区域内所有块体都是被完全分割开的。 本文提出了利用数值流形方法进行地壳形变的数值模拟。数值流形方法是利用现代数学“流形”的有限覆盖技术建立起来的。有限覆盖是由物理覆盖和数学覆盖组成,通过它可以处理连续问题和非连续问题,解决了有限元只能计算连续和非连续变形分析方法侧重于不连续问题的不足,这两种方法都是数值流形方法的特例。 本文最主要的工作是将数值流形方法从平面扩展到了球面,以适应模拟大范围地壳运动和形变的要求。更多还原

【Abstract】 With the rapid progress of Very Long Baseline Interferometry（VLBI）, Satellite Laser Ranger, Global Positioning System （GPS） and Differential Interferometry Synthetic Aperture Radar（D-InSAR）, modern geodesy provides wholly new ways to monitor and research crustal movement. The relative accuracy 10^-9 of baseline measurement can be achieved between GPS stations several hundred kilometers apart. Techniques such as VLBI and SLR are used to monitor global plate’s movement. The results from GPS, VLBI and SLR can directly describe the crustal movement very well. However, if we want to explore the geodynamic mechanism and the driving forces of the plates, related geological and geophysical materials should be combined with geodetic data.Results from geophysical and geological data are in terms of hundred years and millions years respectively. They can not provide continuous current crustal movement field. The coverage of GPS stations is not enough compared with the big area of plate and block. For the observation networks are mainly set up to monitor earthquake and tectonic activity, GPS stations are mostly deployed along faults. So the distribution of GPS stations is not as even as desired. In order to map the velocity field and stress field of crustal movement, numerical tools are used to simulate the movement and deformation of the district without geodetic data and geophysical observation. Among the simulation tools Finite Element Method, which is based on the idea of dividing a complicated domain into small and manageable pieces, has been used in many fields. It can deal with continuous deformation very well. Discontinuous Deformation Analysis is capable of dealing with discontinuity, it requires that all blocks be totally separated by faults.In this dissertation Numerical Manifold Method is proposed to simulate crustal deformation. Here, the most important work is developing spherical Numerical Manifold Method from plane Numerical Manifold Method. A set of formulae is deduced in order that large scale crustal movement could be properly simulated with this method.Main research work is as following:1) The advantage and disadvantage of formerly used numerical simulation techniques are well discussed. FEM and DDA are good at dealing with continuum and discontinuity respectively. They are two special cases of NMM, which incorporate continua and discontinuity in a single model.2) Spherical numerical manifold method is firstly developed from NMM in order that it can deal with large scale crustal movement. Mathematical cover, physical cover and manifold element for general finite covers are explained; the usual forms of displacement function on physical cover are presented. The global displacement function is the weighted averages of local independent cover functions on the common part of several covers.3) Based on the simplified relation formula of displacement and strain in the spherical coordinate system, all relative formulae for spherical general finite covers are deduced. The relation equation of the manifold elements on spherical surface is established according to the theory of least Potential Energy. The potential energy expressions are separately worked out, including stiffness stress, initial stress, point loading, body force loading, inertia matrix, velocity matrix and fixed point matrix. By differentiating the above expressions, the correspondent coefficient sub-matrix are deduced and added to the equilibrium equation.4) The kinematics equation of the manifold elements system is established. A local plane projection coordinate system is set up in order to simplify the calculation of spherical invasion distance and so on. Normal contact matrix, shear contact matrix and friction force matrix for general finite covers are deduced in details.5) Based on the simplified relation formulation of displacement and strain in the spherical coordinate system, all relative formulations for spherical triangle finite covers are deduced. The relation equation of the manifold elements on spherical surface is established according to the theory of least Potential Energy. The potential energy expressions are separately worked out, including the stiffness stress, initial stress, point loading, body force loading, inertia matrix, velocity matrix and fixed point loading. By differentiating the above expressions, the correspondent coefficient sub-matrix are deduced and added to the equilibrium equation.6) Normal Contact matrix, Shear Contact matrix and friction force matrix for triangle mesh covers are deduced. They help to connect the individual discontinuous boundaries into a system.7) To meet the needs of simulating crustal movement, Spherical Numerical Manifold Method software is developed with VC++ language. Time step based on large displacement analysis, open-close iterations and others are introduced as well.8) Spherical numerical manifold method and Spherical discontinuous deformation analysis are used to calculate models with one and three faults respectively. The results indicate that the SNMM can deal with Continua and discontinuity very well.9) GPS station velocities relative to Euroasia plate in Chuandian district are derived from twice observations of Crustal Movement Observation Network of China and NUVEL1A model. The main faults framework is established according to Chuandian’s geological materials. The fields of velocity, maximum and minimum stress change and maximum shear stress change of whole Chuandian district are simulated with spherical numerical manifoldmethod. Finally result analysis is fully made.更多还原