Relation of different type Love-Shida numbers determined with the use of time-varying incremental gravitational potential

The time-varying gravitational potential was determined in case of deformation generated by tide, tidal, load and potential free load with the use of the Love and Shida numbers in case of a symmetric non-rotating isotropic elastic model Earth (SNREI). The Love-Shida numbers are determined in this case by the radial profiles of elastic Lamé parameters and density. Due to the mass conservation in case of elastic deformation the incremental mass density was inferred from the divergence of the product of initial mass density and the vertical displacement field.

With the use of gravitational field derived in this way an integral relation was obtained which relates Love-Shida numbers h, l, h’, l’, h” and l” and Love numbers k, k’ and k”, where ‘ denotes load numbers and “ potential free load numbers. There are different equations to describe relations between different classes of Love-Shida numbers (Molodensky, Saito, Varga, Okubo & Saito, and Merriam). The relation obtained in frame of present study is the only relation which holds for every type of Love-Shida parameters and does not follow from the sixth-order differential equation system of motion usually applied to calculate the Love-Shida numbers.

This research was completed during research stay of P. Varga at the Department of Geodesy and Geoinformatics,, Stuttgart University supported by the Alexander Humboldt Foundation.