Progress and prospect of studies on elastic normal modes of Earth's free oscillation

In constructing modern Earth model, Earth's interior layered structure is mainly determined according to seismic data; while the density and elastic parameters of the interior Earth, especially the large-scale structure of the density distribution below the mantle, are mainly determined according to the Earth's free oscillation observations. This paper summarizes the theories and methods of solving the eigenvalues of normal modes of Earth's free oscillation, introduces the expressions of the displacement fields in spheroidal and toroidal modes, and discusses attenuation, splitting and coupling effects of the free oscillation modes. In addition, this paper summarizes the methods of detecting the splitting spectral lines of multiplets and estimating the corresponding splitting parameters, and reviews the main progress and existing problems in researching the constraints and inversion of the seismic moment tensor, three-dimensional (3D) heterogeneous structure of the Earth and inner core's super rotation by using elastic normal modes. Finally, we discuss the future development trend in studying normal modes of Earth's free oscillation.