| In this thesis,analytical general solutions of the inhomogeneous spherically symmetric problem and the spatial axisymmetric problem are given respectively.The elastic earth hierarchical structure model is constructed by the simple functional relationship between the physical and mechanical parameters of the earth,and elastic mechanics solutions of the earth model is given.For the study of inhomogeneous spherically symmetric problems,the displacement control equations for them are derived in the beginning.Firstly,considering the case that Young’s modulus is distributed exponentially with the radius,and the analytical solutions of the problem are given.Secondly,considering Young’s modulus changes with the radius of the general linear rule,the series solutions of the problem are given by the power series method of the ordinary differential equation.In this thesis,the distribution of spherically symmetric universal gravitation is calculated,assuming that the density function is exponentially distributed along the radial direction,and analytical displacement solutions of the non-homogeneous equation with body force are given.For the heterogeneous spatial axisymmetric problem,considering the most general distribution of Young’s modulus,the elastic stress solution method is used to solve the axisymmetric stress equilibrium equations in cylindrical coordinate system,analytical general solutions without body force are given,and the expression method and solving procedure of axisymmetric sphere problems are discussed in the cylindrical coordinates.The internal structure model of the earth is discussed as an application of the inhomogeneous sphere problems.The functional relationships of seismic wave velocity within the earth are obtained by fitting the existing geophysical measurement data at first,then the functions of elastic constants distribution along the depth are obtained in the earth’s interior,and the mechanical model of the elastic earth is constructed.The hierarchical spherical symmetry problem for given boundary conditions is calculated by Runge-Kutta numerical method,in which the Young’s modulus is quadratic polynomial distribution along the depth,and the elastic numerical solutions are obtained when considering the universal gravitation and not considering body force respectively.At the same time,the internal structure model of elastic earth is verified from several different aspects,including the earth’s mass,moment of inertia and the of seismic wave velocities,density distribution in each layer.The procedure and method of constructing the axisymmetric earth model by considering the axisymmetric self-steering force are discussed.At the same time,several practical applications of the earth’s internal structure model and some improving aspects are also discussed in the paper. |
