Determination of the Andrade Rheological Model Parameters for the Earth’s Mantle from the Love Numbers of Ten Tidal Components

Abstract

The rheology of the Earth’s mantle is studied on the basis of data on the Love numbers for ten tidal components (M2, Mqm, Msqm, Mtm, Mstm, SN, Mf, Msf, Mm, and Msm). An adaptation of the Preliminary Reference Earth Model (PREM) is used to model the internal structure of the Earth, while the inelasticity is modeled using the Andrade rheology. The Andrade model depends on two empirical parameters (α and ζ) that are unknown for mantle minerals at high pressures and temperatures and very slow deformations. As a result, in various problems of planetary geophysics where inelasticity in the interior of planets or satellites must be taken into account, authors are often faced with the difficulty of which values of the Andrade rheology parameters to use. To address this issue, an Earth-based calibration of the rheology was performed. The Love numbers of the Earth were calculated at ten tidal frequencies for two viscosity distributions and for 1530 different combinations of the parameters α and ζ. The comparison of the model values with the observed ones allowed us to determine a set of values for α and ζ that are suitable for describing the inelasticity of the Earth’s mantle.