Technischer Bericht NTB 93-19

Inverse Modellierung in geklüfteten Grundwasserträgern

An inverse modeling scheme is presented which allows the estimation of model parameters of saturated groundwater flow from measurements made on the system response as well as from prior information on the parameters. An indirect approach to the inverse problem is applied determining the hydro- and hydrogeological parameters of a numerical model by repeated solution of the transient flow equation. This so-called direct problem is solved numerically by the Finite Element Method. The three-dimensional model is especially designed for dealing with fractured media so that elements of lower dimension than the overall model can be included in order to model fault zones. Spatially distributed parameters are considered alternatively by conventional zonation or pointwise definition in connection with a kriging interpolation technique.

The inverse problem is formulated in the statistical framework of the maximum-likelihood estimation method which enables one to account for errors of the measurements and for errors of model output. The resulting objective function is minimized by alternative mathematical optimization algorithms where a sequential combination of a gradient method and a Gauss-Newton method has been found to perform best in many cases. With respect to the computational efficiency of the nonlinear optimization problem, the exact gradient (of the numerical problem) as well as the Jacobian matrix, i.e. the partial derivatives of the performance measures, are computed by the adjoint-state method or by direct derivation of the FE-equations, respectively.

In addition to potential head measurements which are conventionally used to calibrate flow models, flow rates measured at model boundaries can be considered. Some basic examples illustrate that such incorporation of flow rate data improves the identifiability problem in many instances. Finally, two case studies of international validation projects are investigated. The hydrogeological characterization of a highly heterogeneous fracture plane as well as the calibration of a three-dimensional fracture-matrix-system aim at testing the specific features of the model applying it to real data.