Quasi-reversibility method for data assimilation in models of mantle dynamics
Résumé
Rapid progress in imaging deep Earth structures using seismic tomography and in studies of physical and chemical properties of mantle rocks facilitates research in assimilation of data related to mantle dynamics. In this paper, we present a new numerical approach for data assimilation, which allows for incorporating observations (at present) and unknown initial conditions (in the past) for mantle temperature and flow into a 3-D dynamic model in order to determine the initial conditions. The dynamic model is described by the backward heat, motion and continuity equations. The use of the quasi-reversibility (QRV) method implies the introduction into the backward heat equation of the additional term involving the product of a small regularization parameter and a higher order temperature derivative. The data assimilation in this case is based on a search of the best fit between the forecast model state and the observations by minimizing the regularization parameter. We apply the QRV data assimilation method to restore the evolution of (i) mantle plumes (a synthetic case study) and (ii) the lithospheric slab imaged by teleseismic body-wave tomography in the southeastern Carpathians. For both models the present temperature and mantle flow are assimilated to the geological past, and the prominent features of mantle structures are recovered. We then model the evolution of the mantle structures forward in time starting from the restored state to the present state and estimate the accuracy of the model predictions. The results of the QRV data assimilation are compared to that obtained by the variational (VAR) and backward advection data assimilation. Although the accuracy of the QRV data assimilation is lower than that of the VAR data assimilation, the QRV method does not require any additional smoothing of the input data or filtering of temperature noise as the VAR method does. Based on the results and the comparison of the methods, we consider the QRV method to be a highly promising approach to assimilation of data related to mantle dynamics.
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