Quasi-Reversibility Method and Its Applications

Abstract

In this chapter, we introduce a quasi-reversibility (QRV) approach to data assimilation, which allows for incorporating observations (at present) and unknown initial conditions (in the past) for physical parameters (e.g., temperature and flow velocity) into a three-dimensional 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 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 present the application of the QRV method to two case studies: evolution of (i) mantle plumes and (ii) a relic lithospheric slab.