Abstract:Making use of the normal mode theory of the Earth, this paper studies the variations of the displacement field in the Earth’s interior and of the gravity field in the Earth’s exterior due to deformation caused by different external forces, including body and surface ones for a spherically symmetric, non-rotating, elastic and isotropic (SNREI) Earth. The operational formulas, indicating the intrinsic relation between normal modes and Love numbers, are derived to compute the Love numbers of various deformation problems of the Earth, such as tide, surface loading, as well as those due to pressure and shear forces. The numerical results demonstrate that the calculated Love numbers are in good agreement with the values derived by the numerical integration method, which validates the derived operational formulas.