Delayed van der Pol Model for Fault Dynamics under Hydrological Loading: Application to the GERD Reservoir

Delayed van der Pol Model for Fault Dynamics under Hydrological Loading: Application to the GERD Reservoir | 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 Delayed van der Pol Model for Fault Dynamics under Hydrological Loading: Application to the GERD Reservoir M. A. Elfouly This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-7049901/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 This study introduces a nonlinear delayed Van der Pol model to investigate the evolution of fault slip behavior under the combined influence of periodic and hydromechanical forcing. The model incorporates nonlinear friction, dual delayed tectonic feedback, and pore-pressure coupling, enabling a unified representation of diverse fault slip regimes—fast slip, slow slip, silent earthquakes, and fault creep. Structurally, the model extends the classical Van der Pol oscillator to include geophysically meaningful time delays that represent short- and long-term tectonic memory, alongside external loading from reservoir impoundment and cyclic stress. The behavior is governed by two synergistic control parameters: the hydromechanical coupling coefficient, representing fault sensitivity to pore pressure, and the reservoir fill rate, capturing the temporal intensity of hydrological loading. Bifurcation and time-domain analyses reveal that small increases in either parameter can induce a transition from steady creep to dynamic rupture through stability and chaotic attractors—especially under resonance conditions. Conversely, slower reservoir filling significantly enlarges the stability domain and delays critical transitions, highlighting its importance as a mitigation strategy. Phase-space and delay-embedding projections illustrate the shift from organized to disordered attractors with increasing coupling strength and loading speed. Temporal evolution of displacement amplitude confirms that rapid impoundment leads to high-frequency oscillations and instability, even in previously stable regimes. The findings emphasize that fault destabilization is driven not only by fluid presence but also by the temporal structure and resonance alignment of anthropogenic loading. The proposed delay-based Van der Pol model offers a predictive and physically grounded tool for assessing induced seismicity and guiding safer reservoir operations in tectonically sensitive regions. Geophysics Applied Mathematics Mathematical Physics Seismology Hydrology Delay Differential Equations van der Pol oscillator Nonlinear dynamics Bifurcation analysis Fault Dynamics 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-7049901","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":480907216,"identity":"b84bf5f5-45a3-4de6-8b3a-905075c6c0e2","order_by":0,"name":"M. A. 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Conversely, slower reservoir filling significantly enlarges the stability domain and delays critical transitions, highlighting its importance as a mitigation strategy. Phase-space and delay-embedding projections illustrate the shift from organized to disordered attractors with increasing coupling strength and loading speed. Temporal evolution of displacement amplitude confirms that rapid impoundment leads to high-frequency oscillations and instability, even in previously stable regimes. The findings emphasize that fault destabilization is driven not only by fluid presence but also by the temporal structure and resonance alignment of anthropogenic loading. 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