Data assimilation for a visco-elastic Earth deformation model

We present a data assimilation algorithm for the time-domain spectral-finite element code VILMA. We consider a 1D earth structure and a prescribed  glaciation history ICE5G for the external mass load forcing. We use the Parallel Data Assimilation Framework (PDAF) to assimilate sea level data into the  model in order to obtain better estimates of the viscosity structure of mantle and lithosphere. For this purpose, we apply a particle filter in which an ensemble of models is propagated in time, starting shortly before the last glacial maximum. At epochs when observations are available, each particle's performance is estimated  and they are resampled based on their performance to form a new ensemble that better resembles the true viscosity distribution. In a proof of concept we  show that with this method it is possible to reconstruct a synthetic viscosity distribution from which synthetic data were constructed. In a second step,  paleo sea level data are used to infer an optimised 1D viscosity distribution.