Geostatistical Solution for the Classification Problem with an Application to Oil Prospecting

Abstract

Mathematically modeled thematic maps can relate productivity to geology and display the probability of occurrence of mineral deposits. Stochastic simulation, a geostatistical technique that regards a surface as an outcome of a random function, is used for nonparametric characterization of the uncertainty involved in the estimation of the Mahalanobis’ distances at unsampled locations. This avoids overly smooth maps and precludes the need for distributional assumptions to assess misclassification probabilities, problems encountered in earlier studies that described the relations between multivariate observations and rock type by distances and treated them as univariate variables.

In the stochastic approach, discriminant analysis is used to simultaneously partition the multidimensional space occupied by the observations and select the most informative geological variables. Clusters are identified by regarding each observation as a point in space with as many dimensions as variables. Mahalanobis’ distances to the cluster centroids at all geographic locations are estimated using sequential Gaussian simulation. By generating multiple realizations of the distances, the most likely distances and their estimation uncertainties can be assessed. Finally, using Bayesian relations, probabilities are adjusted for misclassification and sampling bias. The technique is used to demonstrate that results of stochastic simulation agree well with actual distributions of fields in an oil-producing area in western Kansas, USA; the map of probability of drilling a producing well corresponds with previous results using kriging to map Mahalanobis’ distances.