A geostatistical approach to an inverse problem: Identification of geometry and estimate of equivalent conductivities for highly heterogeneous porous media with the differential system method

Abstract

A methodology for identifying the geometry of different materials in highly heterogeneous porous media in discrete inverse problems (DIP) is described. It applies a geostatistical approach within the differential system method (DSM). DSM calculates conductivity values along an integration path beginning at a point with known conductivity. In aquifers with zero source terms, DSM completely describes the conductivity field through a spatially distributed parameter depending on hydraulic head gradients and integration path. A factor analysis of the structural components of this parameter (i.e. coregionalisation analysis) was carried out to identify the geometry of different materials, corresponding to distinct statistically homogeneous areas. The equivalent conductivity values for homogeneous areas were estimated. This approach was applied for a synthetic aquifer. The identification of geometry was accurate and the estimates of equivalent parameters were good, compared with reference values. The accuracy of the results depended on errors in hydraulic gradients, compared with conductivity gradients.