Response of the Earth to surface mass redistribution and constraints on the rheology of the Earth's interior over seasonal to decadal time scales

Over the past decades, geodetic observations have provided crucial constraints on the Earth's rheology on time scales of a few years or less, mainly through the study of post-seismic deformation. Here, we review recent advances in determining rheological properties of the mantle by investigating the Earth's response to surface mass redistribution over seasonal to decadal time scales, using new geodetic observables.

First, we discuss constraints on the short-term viscosity of the asthenosphere using geodetic strain induced by seasonal surface loading, derived from the Gravity and Recovery Climate experiment (GRACE). We predict associated geodetic surface displacements for a purely elastic spherical reference Earth ­­and for a variety of viscoelastic Earth models. We compare results to global GNSS observations and place a lower bound of 5.10¹⁷ Pa.s on transient asthenospheric viscosity, suggesting that values reported in some postseismic studies do not hold at the global scale.

Seasonal loading also induces pressure variations down to the mantle transition zone and can then help constraining kinetics of mineralogical phase transformations. Indeed, small pressure variations disrupt the two-phases equilibriums, inducing re-equilibration processes and volume changes. However, including the effect of potential phase transformations for the prediction of seasonal displacements at the Earth's surface does not improve the fit to GNSS observations, suggesting that the occurrence of re-equilibration processes occurs over time-scales longer than a year.

Finally, we investigate the alignment of the Earth's Figure axis and its rotation pole at decadal time scales. We take advantage of the long record (1984-2017) of accurate satellite laser tracking to geodetic spherical satellites to measure the long-term displacement of the Figure axis (degree- 2 order-1 geopotential coefficients) and the pole coordinate time series, derived mainly from GPS and VLBI data, to estimate motion of the rotation pole. By analyzing the behavior of the two time series, driven primarily by surface mass redistribution at the decadal time scales, we attempt at providing a new observable to constrain rheological properties of the Earth's deep mantle.