Graph-Optimized Graphic Correlation: an automated framework for combining stratigraphical data

Quantitative stratigraphical methods include powerful tools for constructing stratigraphical models that maximize predictive power. Among these, Shaw’s Graphic Correlation method stands out as a widely used technique that underpins many automated stratigraphical correlation tools. A key challenge in Graphic Correlation is to determine the line of correlation (LOC) in an objective manner that remains consistent with geological principles such as the law of superposition. In this study, we present a novel, graph-optimized Graphic Correlation (GOGC) approach that can automatically and quantitatively construct the LOC and generate a composite standard (CS). This method follows the qualitative rule of ‘Splitting Tops and Bases’, which favours the LOC that passes through the maximum number of stratigraphical events—referred to as ‘Longest-path LOC’ in this study. We reformulate this LOC estimation as a longest-path problem on a directed graph, which can be efficiently solved using topological sorting and dynamic programming. The results show that Longest-path LOCs are comparable to those produced by a genetic algorithm but are deterministic and more computationally efficient. The CSs derived from the Longest-path LOC exhibit high precision and are similar to those generated by Constrained Optimization (CONOP), a commonly used quantitative stratigraphical method. Additionally, our approach shows promise as a new method for applying CSs in stratigraphical correlation, refining existing CSs, and enabling the automated construction of age-depth models for stratigraphical sections or drill cores, thereby demonstrating great potential for managing large databases and facilitating quantitative stratigraphy.