Modeling the Uncertainty in Geologic Volumes: The Log-Normal Case

Abstract

The aim of the study is to develop a methodology that allows the quantification of the uncertainty in an arbitrary volume conditioned by sampling data, without the use of the traditional geostatistical simulation, which is time consuming and hard to manage, specially for large grid sizes. For this, we have studied the behavior of simulations when the variable is distributed according to a log-normal distribution. We have successfully found a formulation that makes the uncertainty in the arbitrary volume dependent on the values within the volume, the spatial correlation and conditioning data. Without the use of geostatistical simulation, and only with a Kriging of the Gaussian values, we are able to obtain local means, full conditional local distributions, covariances and correlations.