## Te YTj4eMy22

j where the basis function (p* is chosen in such a way that it equals 1 at the particular node j and 0 at all other nodes on the element (e). Other interpolation methods for approximating the transmissivity distribution include simple polynomial approximation, cubic spline, and kriging.

### Stochastic Method

In this approach, the unknown parameter is treated as a random field, characterized by its first two moments, the mean (or drift) and the covariance function. A common approach is to assume that the logarithm of the hydraulic conductivity, Y = log K, is normally distributed (Freeze, 1975; Hoeksema, 1985a). Also, the random field is represented by a constant mean and an isotropic, exponential covariance (Dagan, 1985; Hoeksema and Kitanidis, 1985b; Wagner and Gorelick, 1989):

where a\ = log hydraulic conductivity variance lY = log hydraulic conductivity correlation scale ¿¡J = distance between points xt and Xj

The hydraulic conductivity can thus be estimated by identifying the three statistical parameters pF, rrj-, and ly. In this approach, overparameterization is generally avoided, and the inverse solution obtained by the maximum-likelihood estimate and cokriging is highly stable.

In addition to the traditional approaches for parameterization mentioned above, Sun et al. (1995) suggested a geological parameterization method in which the unknown parameter (hydraulic conductivity) is directly related to the geological materials, and the geological structure of the aquifer is determined by the geostatis-tical method of kriging.

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