负荷勒夫数渐近值解析表达式

The Earth's deformation due to surface mass loading is an important issue in geodesy and geophysics. Computing load Love numbers and constructing the convergent load Green's functions are the fundamentals in simulating the Earth's deformation due to surface mass loading, in which the analytical asymptotic load Love numbers for the harmonic degree at infinity play an important role. In this paper, the boundary value problem for the surface mass loading is introduced first. The three methods proposed before by other scholars to derive the asymptotic values are then briefly reviewed. Finally a new novel approach is proposed. The new way applies the analytical method, which is used to solve the boundary value problem for Earth's deformation, and an efficient and powerful propagator matrix method to link the boundary conditions on the Earth's surface and the high-degree load Love numbers. In this way, new exact closed-form asymptotic expressions of the load Love numbers are obtained. The analytical asymptotic expressions of the load Love numbers are able to more accurately describe the asymptotic characteristics of the load Love numbers. The new approach is simple in theory and is easy to understand, which only involves the solution base of the ordinary differential equations with constant coefficients and some primary matrix algebras.