A geostatistical application for resolution of an inverse problem with the differential system method
Abstract
The application considers an aquifer with a statistically inhomogeneous transmissivity field. In this case, the resolution of an inverse problem involves the identification of the geometry of homogeneous areas in spatial domain as well as the distribution of transmissivity values within each area. The Differential System Method (DSM) calculates the transmissivity values with a direct deterministic approach. It requires minimum a priori information (i.e., the transmissivity value in one node at least). Moreover, DSM provides a way to deal with geometry identification by applying geostatistical analysis. The DSM considers the discrete transmissivity gradients between grid nodes; the transmissivity values in each node are calculated along an integration path beginning at the node with known transmissivity value and consisting of segments between adjacent nodes. The uncertainty in the identification of the transmissivity heterogeneous field is due to the uncertainty in defining the integration path as well as to the errors in piezometric heads. If source terms are negligible, the transmissivity gradient field is completely described by defining a spatially distributed parameter depending on piezometric heads only. The geostatistical analysis of this parameter is used in order to identify the geometry of the homogeneous areas. The stability of the solution depends on the errors in hydraulic gradients compared with actual transmissivity gradients. The studied approach was applied for a synthetic example. The aquifer was hydraulically characterised with nine strictly homogeneous areas; the transmissivity values of adjacent areas differ of two orders of magnitude at most. The geometry identification was accurate even where the difference between transmissivity values in adjacent areas was less than one order of magnitude.
- Publication:
-
EGS - AGU - EUG Joint Assembly
- Pub Date:
- April 2003
- Bibcode:
- 2003EAEJA....12875O