Comparison of horizontal post-seismic deformations induced by Maule, Iquique, and Illapel megathrust earthquakes: A clue to a linear asthenospheric viscosity?

Spatial geodesy through GNSS allows to measure with a millimetric precision the displacement of the lithosphere during the seismic cycle. The post-seismic part of this cycle can last for decades, traduced by long-lasting surface deformations. One of the main physical processes involved in the postseismic deformation is the viscoelastic relaxation in the asthenosphere. However, a long term debate persists about the involved rheology of the asthenosphere:  Is the viscosity highly variable from one region to the next and is effective viscosity Newtonian (linear) or non-Newtonian (non linear)? 

To investigate these questions, we compare the horizontal post-seismic deformations induced by three Chilean megathrust earthquakes: Maule Mw8.8 (2010), Illapel Mw8.3 (2015) and Iquique Mw8.1 (2014). For each earthquake, we select permanent GPS stations along profiles perpendicular to the trench, extending as far as 1400 km. We calculate the ratio of the cumulative post-seismic (post) over 5 years and the coseismic (co) displacements for each station. Remarkably, at a given distance to the trench, the post/co ratios from the three earthquakes differ only slightly.

What can be the interpretation of this observation in terms of rheology of the asthenosphere? First we can analyse the response of the asthenosphere in the case of homothetic earthquakes of different magnitude. The post/co ratio obeys simple analytical relationships: For a Newtonian rheology, it is simply a function of the (time/viscosity) ratio. For a non-Newtonian viscosity with a stress exponent n=3, the timescale becomes inversely proportional to M**2, where M is the moment of the earthquake. We show that these relationships are only slightly modified when the earthquakes are no longer homothetic and that the post/co ratio is a good proxy to quantify the strain-rate and stress ratio in the underlying asthenosphere. As a conclusion, the post-seismic deformation following the three Chilean earthquakes reveals very similar viscosity. In particular, a Newtonian, rather than a non-Newtonian, effective viscosity is required to explain the post-seismic deformation process.