地球变形近似解析解的构建及应用

It is of great scientific importance in high precision geodesy and geophysics to theoretically model the Earth′s deformation. We first review the commonly used theory and methods in theoretical modeling of the Earth′s deformation. For the Runge-Kutta method as an example, the numerical difficulties and the ways to overcoming them are both described. We explain why Runge-Kutta method is useless for high harmonic degrees. Then, we introduce a new method to construct the analytical solution by making use of some reasonable assumptions on the Earth model. Finally the new method is applied to compute the dislocation Love numbers. As an example, the deformation due to a shallow explosion is modeled. The results validate that the method is both efficient and stable. This method can produce the asymptotic dislocation Love numbers which guarantees the convergence of the corresponding Green′s functions.