A PRACTICAL APPROACH TO VALIDATE THE VARIOGRAM REPRODUCTION FROM GEOSTATISTICAL SIMULATION

Abstract

The variogram model is one of the most relevant parameters in geostatistical estimation and simulation methods. The sample variogram is inferred from available data, which may be subject to spatial bias and proportional effect. Over this sample variogram, a licit variogram model is fit and is carried through the process of estimation and/or simulation of the random function usually without regard to its uncertainty. The simulated realizations are required to adequately reproduce this input variogram model. We propose a methodology to test the validity of the output variograms from a suite of realizations computed using a reference variogram model. The test is based on a multivariate Gaussian hypothesis for the resulting variogram values at different lags. Hotelling’s T2 statistic is used to verify the hypothesis that the mean sample variogram vector is equal to the vector of input variogram values for a set of lags. The T2 statistic is distributed as a random variable with Fdistribution with p and n-p degrees of freedom for a given confidence level α. A simple methodology is presented that requires the computation of simple statistics of the output realizations and can be easily implemented. The test can be used to tune the search parameters used for simulation, such as maximum number of samples and previously simulated nodes used for computing the conditional distribution at every node. Two simple examples show the proposed test. The results are discussed with emphasis in the limitations and future research associated to the proposed methodology.