Spherical Numerical Manifold Method And Its Application To Crustal Movement

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.