A Comparison of Linear and Nonlinear Random Field Estimators

Abstract

The estimation of random fields from limited samples is an important issue in most fields of geophysics, such as Hydrology and Meteorology. Work by Matheron and others at the Paris School of Mines has popularized Kriging techniques to estimate random fields at specified locations or to get areal averages. This work presents the theoretical and practical aspects of both Linear and Nonlinear (Disjunctive) Kriging estimators, and provides a comparison of their performance in estimating point and areal values of generated fields. The experiments performed were designed to closely resemble actual and practical situations. The results show that small sample based inconsistencies lead to a Disjunctive Kriging solution which does not give more accurate estimates than the theoretically less precise Linear Kriging estimator. The results also suggest the use of a multi-realization approach when using these techniques in network design problems.