3. Love and Shida Numbers

When the mass distribution on the surface of the Earth varies, the solid Earth deforms both elastically and inelastically. This deformation has three distinct components:

1. a vertical (radial) displacement of the surface

2. a horizontal (tangential) displacement of the surface

3. a change in the gravitational potential

The magnitude of each individual component can be characterised by a dimensionless scaling factor [47, 61]. These factors are collectively known as Love/Shida Numbers, and are defined for each spherical harmonic degree.

Symbol	Name
\(h_l\)	Love number (vertical)
\(k_l\)	Love number (potential)
\(l_l\)	Shida number (horizontal)

3.1. Load Love Numbers

Load Love numbers describe the deformation of the solid Earth in response to a change in surface mass load. The loading change acts upon the surface of the Earth [78].