| dc.description.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. | |
