Abstract

Regional analysis of statistical distributions is a complex subject, which influences and is simultaneously influenced by many disciplines of the earth-system sciences. In particular, the study of magnitude and frequency and coupled relations of earth-system phenomena can be effectively investigated using L-moments and multi-variate L-moments (L-comoments). There is an enormous body of literature on ‘regional analysis’ of hydrometerologic data using L-moments. Much of this literature is unfamiliar to geoscientists and petroleum engineers. This poster demonstrates a form of regional analysis with L-moment and L-comoment statistics.

L-moments are defined through linear combinations of the expected values or order statistics (the statistics of ordered random variables and samples). L-comoments are similar defined through linear combinations of the expected values of concomitants of multi-variate random variables and samples. L-moments are direct analogs and have similar interpretations, but are not numerically equivalent, to the well know product moments (mean, standard deviations, skew, and kurtosis). L-comoments have analogous interpretations to correlation, covariance, co-skewers, and co-kurtosis.

The authors initiated development of algorithms that provide for distinct and highly specialized visualization of L-moments and L-comoments in the context of general discordancy and cluster analysis. For this study, the bivariate data of porosity and permeability of a west Texas oil and gas field (Ford Geraldine) are considered. However, the general application and visualization techniques of L-comoments used here are unknown in the literature, and the application of L-moments and L-comoments in regional analysis or porosity and permeability data is unprecedented. The results of the study show that these statistics can be combined in a framework that results in trend identification of a trend in the Ford Geraldine field that is consistent with that in the literature. Further, the analysis here should enhance the understanding of the coupled relation between porosity and permeability.