An approach for constraining mantle viscosities through assimilation of paleo sea level data into a glacial isostatic adjustment model

Glacial isostatic adjustment is largely governed by rheological properties of the Earth's mantle. Large mass redistributions in the ocean-cryosphere system and the subsequent response of the visco-elastic Earth have led to dramatic sea level changes in the past. This process is ongoing and in order to understand and predict current and future sea level changes the knowledge of mantle properties such as viscosity is essential. In this study we present a method to obtain estimates of mantle viscosities by assimilation of relative sea level data into a visco-elastic model of the lithosphere and mantle. We set up a particle filter with probabilistic resampling. In an identical twin experiment we show that mantle viscosities can be recovered in a glacial isostatic adjustment model of a simple three layer earth structure consisting of an elastic lithosphere and two mantle layers of different viscosity. In two scenarios we investigate the dependence of the ensemblebehavior on the ensemble initialization and observation uncertainties and show that the recovery is successful if the target parameter values are properly sampled by the initial ensemble probability distribution. This even includes cases in which the target viscosity values are located far in the tail of the initial ensemble probability distribution. We then successfully apply the method to two special cases that are relevant for the assimilation of real observations: 1) using observations taken from a single region only, here Laurentide and Fennoscandia, respectively, and 2) using only observations from the last 10 kyrs.