CLOSED-FORM SOLUTIONS OF THE 2-DIMENSIONAL TURNING BANDS EQUATION

The turning bands method generates realizations of isotropic Gaussian random fields by means of appropriately summed line processes. For two -dimensional simulations the relation between the isotropic correlatio n function of the random field and the correlation function to be simu lated along the lines is given by an integral equation of Abel type. W e present closed form solutions of this integral equation for almost a ll two-dimensional correlation models encountered in practice and disc uss their numerical implementation. As an additional benefit, our tabl es and illustrations serve as a concise guide to correlation models us eful in geostatistics.