Optimization of pilot points location for geostatistical inversion of groundwater flow

摘要

We investigate the influence of pilot points location on our ability to characterize key parameters describing a randomly heterogeneous porous medium via geostatistical inverse modelling. Our methodology is framed in a Maximum Likelihood (ML) context. We estimate the optimal location of pilot points through a differential evolution method (DEM) which we embed in the inversion of moment equations of groundwater flow. The DEM allows investigating a large number of candidate solutions to select those leading to the minimization of a given objective function through an algorithm that mimics the process of natural evolution. We explore the strength of the methodology by way of a synthetic example and we investigate the effect of the parameters embedded in the algorithm and the ability of model quality criteria such as negative log likelihood, the Bayesian criteria BIC and KIC and information criteria AIC, AICc and HIC to estimate the optimal pilot points locations.