Quantifying and Analyzing the Uncertainty in Fault Interpretation Using Entropy

Abstract

Fault interpretation in geology inherently involves uncertainty, which has driven the need to develop methods to quantify and analyze this uncertainty. This paper introduces a novel framework for this task by integrating graph theory, entropy, and random walk. The proposed approach employs graph theory to mathematically represent a fault network in both map-view and profile sections. By integrating the theory of two-dimensional random walk, the stochastic nature of the fault growth process can be effectively characterized, enabling the development of tailored probability formulations for the fault network through weighted graph theory. In addition, entropy models tailored to the fault network are formulated, providing a solid foundation for uncertainty quantification and analysis. Furthermore, the proposed method employs the principle of increase of entropy to quantitatively assess the uncertainty involved in comparing different fault networks. A case study is presented to demonstrate the practical application in addressing the challenges associated with quantifying, communicating, and analyzing the uncertainty in fault interpretation. The findings obtained in this study suggest that (1) entropy serves as a reliable metric for measuring and communicating the uncertainty in fault interpretation; (2) entropy can be used to estimate the potential numbers of evolutionary paths available for a fault network; and (3) the growth process of a fault network adheres to the principle of increase of entropy, enabling us to utilize entropy to measure the complexity of the fault network and subsequently compare the differences between various fault networks. The results obtained highlight the potential of this approach not only for understanding the geological meaning of uncertainty in fault interpretation but also for enhancing decision-making in related fields.