| Widely reading the papers with respect to mantle convection throughout the world, we found that mantle convection is an effective way to transport quantity of heat and transform it into the kinetic energy of plate motion, and causes the anomalies of surface observed fields, e.g. geoid anomalies, gravity anomalies, surface topography and stress field anomalies within the lithosphere. It is also the main reason of the secular variations of sea level, the formation of continental erogenic zone and oceanic basin as well as the seismic and volcanic activity all over the world. However, a few aspects still deserve on study at present, e.g. the mechanism of toroidal component of plate motion, how to deal with mantle viscosity and use observations. These problems above are studied and some new results are obtained in my Ph.D. thesis. The main contributions are as follows.1) Setting up a high-order model. In order to understand further the patterns of thermal free convection with thermodynamic parameter- Rayleigh number and spherical-harmonic order m in a spherical shell, Zero-order model is developed into high-order model expanded the scalar poloidal and fluctuating temperature fields into Legendre polynomials with degree / = 6 and order m - 0, 1, 2, ..., l but not m = 0 only. Compared with zero-order model (degree 1 = 6 and order m = 0), from which only 2-D southerly (r) profiles can be obtained, high-order model can provide a series of southerly (r), easterly (r and radial velocity profiles. With Rayleigh number increasing, the convective motion becomes stronger, thermal convection becomes the main way of heat transportation, the hotter plume zone becomes wider, and the convection cells increases. With the addition of order m, the number of the fluctuating zone in temperature profiles increases, which causes the convective cell increase and its aspect ratio larger.2) Setting up a variable viscosity model with one-dimensional viscosity fluctuations. A constant viscosity mantle convection model is developed into a variable viscosity model assumed a latitude-dependent viscosity with small fluctuations on the basis of a constant background value. The features of toroidal field are studied for different boundary conditions, Rayleigh numbers and depths. It is found that the energy of toroidal field mainly concentrates in the middle and upper parts of the shell, and the ratio, hardly dependent on Rayleigh number, of toroidal to total velocities amounts to only a few percents. Rayleigh number has great effects on the convection patterns of toroidal field. The convection patterns and velocities of toroidal field have distinct differences in latitudinal direction.3) Setting up a variable model with 3-D viscosity fluctuations and introducing 3-D seismic wave velocity into the model. One-dimensional variable viscosity is developed into 3-D viscosity variations and the corresponding solution is presented. The seismic wave velocity is transformed into fluctuating temperature field and viscosity variations within the mantle, then the poloidal and toroidal fields are solved.4) Discussing the relationships of the velocity field and surface tectonics, and getting some new results. In the shallow part of the mantle, not only the convergent and divergent zones in poloidal velocity profile are well consistent with plate boundaries, but the profile shows (1) the movingdirection and velocity of each main plate; (2) that the southern, northwestern, and eastern margins of Eurasian continent are collided and compressed by the northward moving Indian plate, the southeastward moving Atlantic plate and the northwest-westward moving Pacific plate, respectively. Therefore, the large erogenic zone and subduction zone occur in its southern and eastern margins. However, there are no these tectonics in its northwestern margin since the rate and direction of Atlantic plate is consistent with that of Eurasian plate; (3) There is a divergent zone in northeast Africa, which probably causes the East African Rift Valley; (4) It is possible that...
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