Inverse modeling of unsaturated flow combined with stochastic simulation using empirical orthogonal functions (EOF)

摘要

A Bayesian maximum likelihood method is used to derive optimal parameters for an unsaturated flow problem. Liquid saturation data can be acquired with high spatial density at low cost by indirect methods, making saturation a potentially useful primary observation type for inverse modeling. However, limited sensitivity of saturation to unsaturated flow parameters makes it necessary to also include a priori information into the inversion procedure. The quality of the estimated parameter set is expressed through a covariance matrix. Impacts of parameter uncertainties are evaluated by conditional stochastic simulations, in which not only the most likely parameters are reproduced, but also the cross-correlation structure between the parameters. Ignoring parameter cross-correlations in the simulation procedure leads to Monte Carlo realizations with unlikely parameter combinations. In this paper, we present a conditional simulation method that utilizes the orthogonal functions derived directly from the estimated covariance matrix.