Information theory and the analysis of uncertainties in the context of structural geological modelling.

@inproceedings{WellmanGM2013,
 abstract = { The interpretation of uncertainties in a spatial context is of fundamental importance in the context of structural geological models: from questions of mineral exploration, to scientific structural geological studies and fundamental mapping/ geological evaluations.
Structural geological models, here understood as structural representations of the dominant geological units in the subsurface, always contain uncertainties. The evaluation of these uncertainties is intricate as these models are usually constructed on the basis of greatly varying data quality and spatial distribution. Even when a suitable method for the generation of multiple possible model realisations is applied, an important question remains for complex 3-D geological models: what is a meaningful measure to visualise and analyse these uncertainties quantitatively?
Information entropy provides a measure of uncertainty, based on the relative probabilities of potential outcomes of a random variable. To derive a spatially meaningful interpretation, we consider each subspace in a discretised model domain as a random variable. We derive probability mass functions using outcomes from a stochastic geological modelling method and then evaluate the information entropy at each location in the subsurface. Additional measures from information theory, conditional entropy and mutual information, provide intuitive interpretations of structural correlations and reductions of uncertainty and are related to the value of information in a spatial context.
We apply these information theoretic measures to a case study where uncertainties exist about the structure, and shape, of a bounded geological unit at depth. The results yield some, at first, surprising, but very reasonable results for the interpretation of uncertainties. In a next step, the measures are used to analyse and visualise uncertainties in a realistic full 3-D geological model, based on the outcomes of a stochastic implicit geological modelling method. In addition, it is evaluated how average information entropy can be used to estimate the uncertainty of the entire model. The case studies highlights the fact that information theoretic measures provide very intuitive measures of uncertainty. In addition, they provide a way n to answer the important question in many exploration scenarios: where, and by how much, would additional information reduce uncertainties in the model? },
 author = { Wellmann, Florian },
 booktitle = { Proc. 33rd Gocad Meeting, Nancy },
 title = { Information theory and the analysis of uncertainties in the context of structural geological modelling. },
 year = { 2013 }
}