Earth’s Tidal Response for Maxwell, Burgers, Andrade and Sundberg-Cooper rheological models of the mantle

Tidal forces represent a significant external influence on Earth's deformation and have been extensively studied, beginning with Lord Kelvin (W. Thomson, 1862), who first calculated the elastic deformation of a homogeneous, incompressible Earth under tidal forces. Later, Love (1911) extended this work by developing a formalism for a compressible, homogeneous, spherical, non-rotating elastic isotropic Earth (SNREI), introducing the concept of Love numbers to describe tidal effects through dimensionless parameters. The Earth's visco-elastic deformation due to tidal forces is typically modeled using Maxwell, and less frequently, Burgers rheologies in the mantle. In this work, we perform a comparative analysis of four major rheological models—Maxwell, Burgers, Andrade, and Sundberg-Cooper—to evaluate their efficacy in describing Earth's rheological behavior. While Andrade and Sundberg-Cooper models are rarely applied to Earth, they have demonstrated effectiveness in modeling the visco-elastic tidal response of planetary bodies and satellites. We have developed theoretical responses for each of these models from seismic frequencies to very long periods. We first compare the advanced Andrade (1910) and Sundberg-Cooper (2010) models with the more traditional Maxwell and Burgers models. We then focus on tidal responses by comparing predicted gravimetric factors for these models with those observed from long-term gravimetric data collected by superconducting gravimeters within the IGETS (International Geodynamics and Earth Tide Service) network and by SLR (Satellite Laser Ranging).