A reduced-order model for dual state-parameter geostatistical inversion

Abstract. To properly account the subsurface heterogeneity, geostatistical inverse models usually permit enormous amount of spatial correlated parameters to interpret the collected states. Several reduced-order techniques for the brick domain are investigated to leverage the memory burden of parameter covariance. Their capability to irregular domain is limited. Furthermore, due to the over fitting of states, the estimated parameters usually diverge to unreasonable values. Although some propriate tolerances can be used to eliminate this problem, they are presumed and heavily rely on the personal judgement. To address these two issues, we present a model reduction technique to the irregular domain by singular value decomposition (SVD). Afterward, the state errors and parameters are sequentially updated to leverage the over fitting. The computational advantages of the proposed reduced-order dual state-parameter inverse algorithm are demonstrated through two numerical experiments and one case study in a catchment scale field site. The investigations suggest that the stability of convergence dramatically improves. The estimated parameter values stabilize to reasonable order of magnitude. In addition, the memory requirement significantly reduces while the resolution of estimate preserves. The proposed method benefits multi-discipline scientific problems, especially useful and convenient for assimilating different types of measurements.