Stochastic Solution to Inverse Problem in Ground Water

Abstract

A solution to the inverse problem in groundwater is presented with a geostatistical framework, using Kalman filtering and a nonlinear gradient-based search technique. The Kalman filtering recursions are based on a newly developed and linear state-space equation that relates aquifer head perturbations to stochastic perturbations of log-aquifer properties and effective recharge. The Davidon-Fletcher-Powell (DFP) search algorithm is used to identify the mean and the variance of log-aquifer transmissivity and storativity, by minimizing the joint negative log-likelihood function of the innovations (prediction errors). Application to a numerical experiment indicates that the methodology performs well for log-transmissivity integral scale smaller than aquifer dimensions. The results underline the need for conditioning on point measurements of transmissivity and storativity, if the objective is to estimate the variance parameters. While head measurements are instrumental for estimating the geometric means (large-scale parameters), they, however, may not be sufficient for inferring the variance of log-aquifer properties (small-scale parameters).