Deformation Response of a Snrei Earth to Surface Loads and Tidal Forces

Abstract

AbstractBased on the preliminary reference Earth model (PREM), we use the deformation theory for a spherically stratified and non‐rotating Earth with perfectly elastic and isotropic structural relation (SNREI Earth) to investigate the deformation characteristics under different forces exerting on the Earth. The 4th order Runge‐Kutta numerical integration technique is utilized to solve the motion equations of the Earth's displacement field. The numerical solutions for the deformation and gravitational potential perturbation within the Earth interior and on the surface under the surface loads and luni‐solar tidal force, as well as the Love numbers for surface loads and body tides are obtained. The results indicate that deformation within the solid inner core is very small. The variation of displacement at low spherical harmonic degrees (n < 10) with radius is relatively complicated within the liquid outer core. While the loading degree is larger than 10, the deformation and the gravitational potential perturbation in the core, including both the inner and outer core, are significantly little. As a result, the Earth's response is mainly expressed as the radial displacement in the elastic mantle and decreases rapidly with increasing depth. The higher the loading degree is, the more rapidly this response decreases. The frequency‐dependence of Love numbers for the surface loads and body tides is very weak for a SNREI Earth. In the computation of Love numbers for the body tides, the motion equations for a SNREI Earth are also adopted. Meanwhile, the additional pressure on the core mantle boundary (CMB) is taken into account due to the Earth's rotation and ellipticity. The final results, obtained with this approximate procedure, are in good agreement with the tidal gravity observations on the Earth surface.