Parameter identi®cation in fresh-saltwater ̄ow based on borehole resistivities and freshwater head data

By means of a series of borehole resistivity measurements and a resistivity±salinity relation, a particular salt-freshwater inversion was found under the shore with semi-diurnal tides at the French±Belgian border. These resistivity data provide valuable information about the vertical variation of the saltwater percentage in di€erent boreholes. At di€erent places and depths ̄uctuations of freshwater heads are observed. A regression modelling procedure is proposed in which the hydraulic parameters for density dependent ̄ow and solute transport can be simultaneously considered with the parameters of the resistivity±salinity relation. The object function comprises resistivity residuals and freshwater head residuals along with saltwater percentage residuals and parameter residuals. First, a synthetic problem is elaborated with this regression modelling procedure. It is followed by the application of the procedure on the observed fresh-saltwater ̄ow problem under the shore. In the synthetic problem the identi®cation of the hydraulic parameters was demonstrated without the inclusion of prior information about these parameters. The resistivity±salinity relation was slightly adjusted in this regression. During the regression modelling of the observations made in one of the shore-normal cross sections, the horizontal and vertical conductivity are identi®ed along with the e€ective porosity and the longitudinal and transverse dispersivity. The optimal values of the dispersivities are very small. Finally, it is shown that the high waters on the back shore forms the main threat of saltwater enchroachment from the sea side of the dunes and that the isolated fresh-brackish lens under the lower part of the shore before the build up area of De Panne can be explained by overexploitation. Ó 1999 Elsevier Science Ltd. All rights reserved