Spatial averages for linear elements for two-parameter random field

The paper deals with the modelling of the soil medium as a random field. The necessity of using local random averages in numerical and analytical stochastic calculations are the main interest. The paper concentrates on linear elements and on the calculation of the variances and covariances of local random variables averaged over these elements. Several equations are derived by analytical integration, both for isotropic and anisotropic random fields. These should be useful for calculation, analysis and a better understanding of the influence of the geometry of elements and the value of parameters of random fields on the covariances of local averages.