Integrating probabilistic graphical models, information theory, and the principle of increase of entropy for quantifying and analyzing the uncertainty in fault interpretation

Fault interpretation in geology inherently involves uncertainty, and there is a growing need to develop methods to quantify and analyze this uncertainty. In this paper, we propose a novel framework that integrates Markov chains, graph theory, information theory, and the principle of increase of entropy to comprehensively analyze uncertainty in fault interpretation and its geological implications. Our framework provides a more complete and quantitative approach compared to traditional methods, we show how entropy can quantify the uncertainty in fault interpretation and kinematic analysis results, be interpreted for faulting analysis, and analyze fault network evolution using the principle of increase of entropy. Our findings suggest that entropy can be used as a metric to compare different fault networks, and it provides a measure of the total available evolutionary paths for a fault network, enabling quantification of uncertainty in fault kinematic analysis results. The integration of these tools provides a powerful approach for quantifying and analyzing the uncertainty in fault interpretation, which can enhance our understanding of the geological implications of uncertainty and enable geologists to analyze fault networks in a more quantitative manner.