TOWARDS A DIRECT STRUCTURAL-ANALYSIS OF AN IRF-K

The automatic structure recognition o an Intrinsic Random Function of order k (IRF-k) is the solution that is available today and fully implemented for modeling the Generalized Covariance (GC). However, in many cases, still working in the frame of IRF-k, it could be interesting to be able to infer the GC directly. This paper proposes a way for the direct modeling of an IRF-k based on the identification of particular authorized measures. These measures are such that the variances of the consequent experimental generalized increments, in accordance with the usual elementary polynomial models of GC, could be expressed as functions of only one parameter. Hence, it is possible to try to model the GC practically like the stationary case where the experimental variogram is plotted versus the distance h. Any such particular measure can be identified by solving one non-linear system. This paper presents the formalism of methodology, then provides some comparisons for different cases of GC modeling, by automatic recognition and by the proposed direct modeling.