Sedimentary stratigraphic uncertainty: A quantitative analysis framework based on information theory and stochastic processes

Sedimentary stratigraphic uncertainty: A quantitative analysis framework based on information theory and stochastic processes | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Research Article Sedimentary stratigraphic uncertainty: A quantitative analysis framework based on information theory and stochastic processes Zhicheng Lei, Dezhi Yan, Bo Xu, Ping Lei, Songze Li, Yanli Wang This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-4844758/v1 This work is licensed under a CC BY 4.0 License Status: Posted Version 1 posted You are reading this latest preprint version Abstract Sedimentary stratigraphic sequences are crucial archives of Earth's geological history, providing significant insights into paleoenvironments, climate changes, tectonic activities, and hydrocarbon reservoirs. However, the complexity of subsurface conditions and incomplete knowledge often introduce substantial uncertainty into stratigraphic interpretations. This paper proposes a comprehensive framework for quantifying, communicating, and analyzing stratigraphic uncertainty by incorporating principles from information theory and stochastic processes. Our methodology integrates Markov chains, Poisson processes, and Markov pure-jump processes to mathematically represent the stochastic nature of stratigraphic units, boundaries, and sequences. We also formulate entropy models aligned with these stochastic processes, establishing a robust foundation for addressing uncertainty. Through detailed case studies across diverse sedimentary environments—such as marine sandstones, braided river deltas, and meandering river systems—our findings reveal several key insights: (1) Stratigraphic states within a sequence can be accurately predicted using the Markov chain model, with entropy and entropy rate serving as effective metrics for gauging sequence predictability; (2) The asymptotic equipartition property theorem indicates that the number of stratigraphic sequences increases exponentially with entropy and sequence length, underscoring the stochastic complexity inherent in stratigraphic sequences; (3) Entropy and entropy rate values allow us to quantitatively distinguish between various sedimentary environments. Additionally, the stationary probability of the Markov pure-jump process aids in quantitatively assessing differences among stratigraphic sequences within similar sedimentary contexts; (4) Quantifying the uncertainty associated with stratigraphic states and their thicknesses provides valuable geological insights, aiding geologists in making informed decisions. We also present a sensitivity analysis of our approach and outline directions for future research. The insights gained from this study underscore the potential of our methodology in enhancing the understanding of stratigraphic sequence uncertainty, facilitating more informed decision-making in related disciplines. This research paves the way for a more quantitative approach to stratigraphy. Petroleum Geology Economic Geology Stratigraphic uncertainty Uncertainty quantification Entropy Stochastic processes Full Text Additional Declarations The authors declare no competing interests. Cite Share Download PDF Status: Posted Version 1 posted You are reading this latest preprint version Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. As a division of Research Square Company, we’re committed to making research communication faster, fairer, and more useful. We do this by developing innovative software and high quality services for the global research community. Our growing team is made up of researchers and industry professionals working together to solve the most critical problems facing scientific publishing. Also discoverable on Platform About Our Team In Review Editorial Policies Advisory Board Help Center Resources Author Services Accessibility API Access RSS feed Manage Cookie Preferences © Research Square 2026 | ISSN 2693-5015 (online) Privacy Policy Terms of Service Do Not Sell My Personal Information {"props":{"pageProps":{"initialData":{"identity":"rs-4844758","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":334960933,"identity":"65a050ec-4f8a-4800-8ec5-3b91f7f9416f","order_by":0,"name":"Zhicheng 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However, the complexity of subsurface conditions and incomplete knowledge often introduce substantial uncertainty into stratigraphic interpretations. This paper proposes a comprehensive framework for quantifying, communicating, and analyzing stratigraphic uncertainty by incorporating principles from information theory and stochastic processes. Our methodology integrates Markov chains, Poisson processes, and Markov pure-jump processes to mathematically represent the stochastic nature of stratigraphic units, boundaries, and sequences. We also formulate entropy models aligned with these stochastic processes, establishing a robust foundation for addressing uncertainty. 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