STOCHASTIC SOLUTION TO INVERSE PROBLEM IN-GROUND WATER

A solution to the inverse problem in groundwater is presented with a g eostatistical framework, using Kalman filtering and a nonlinear gradie nt-based search technique. The Kalman filtering recursions are based o n a newly developed and linear state-space equation that relates aquif er head perturbations to stochastic perturbations of log-aquifer prope rties and effective recharge. The Davidon-Fletcher-Powell (DFP) search algorithm is used to identify the mean and the variance of log-aquife r transmissivity and storativity, by minimizing the joint negative log -likelihood function of the innovations (prediction errors). Applicati on to a numerical experiment indicates that the methodology performs w ell for log-transmissivity integral scale smaller than aquifer dimensi ons. The results underline the need for conditioning on point measurem ents of transmissivity and storativity, if the objective is to estimat e the variance parameters. While head measurements are instrumental fo r estimating the geometric means (large-scale parameters), they, howev er, may not be sufficient for inferring the variance of log-aquifer pr operties (small-scale parameters).