Gravitational potential changes of a spherically symmetric earth model caused by a surface load

Abstract

We define load Love numbers and derive expressions of Green's functions for calculating the vertical displacement, potential and gravity changes for any r. Numerical calculations are carried out for the 1066A earth model. Load Love numbers are obtained for three depths: r = a, r = 6334.4 km and r = 3484 km. The results show that the load Love numbers inside the earth decrease very fast as n increases. The smaller the radial distance r, the faster is the decrease of the load Love numbers with n. The load Love numbers inside the earth for degrees 2 and 20 indicate that a low degree load Love number has a global contribution and varies gently in magnitude along the radius, while a high degree load Love number reflects a regional or even a local contribution and it decreases very fast as the depth increases. The Green's functions of vertical displacement, potential and gravity changes for above mentioned three depths are also numerically calculated. All the Green's functions show that a deformation in near field is much larger than that in far field and the whole earth deforms under a surface mass load.