Toward quantitative characterization of simulated earthquake- cycle complexities

Toward quantitative characterization of simulated earthquake- cycle complexities | 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 Article Toward quantitative characterization of simulated earthquake- cycle complexities Shiqi Wang This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-4139966/v1 This work is licensed under a CC BY 4.0 License Status: Published Journal Publication published 21 Jul, 2024 Read the published version in Scientific Reports → Version 1 posted 9 You are reading this latest preprint version Abstract Earthquake cycle simulations based on the rate-and-state friction formulation are evolutions of nonlinear dynamical systems (NDS). The term “cycle” implies an overall stable structure that is a phase-space attractor naturally traced out by trajectories of NDS as it evolves. Quantitatively characterizing these attractors should be a basis for measuring complexities of the simulated earthquake cycles, i.e. to determine if and how regular or chaotic they are. I first revisit the textbook-standard quasi-dynamic spring-slider system from an NDS perspective, explicitly showing the attractors, their relationship with the parameters of the NDS, and how they can be characterized taken advantage of their low-dimensionality while aiming to extend the analysis to high-dimensionality. I evaluate two approaches, computing the Lyapunov exponents (LEs) and measuring correlation dimensions, with the simple spring-slider and earthquake-cycle examples whose phase-space attractors can be visually verified. I conclude LEs are too inconvenient and computationally expensive to use whereas measuring correlation dimensions is an easy and effective approach even with highly non-uniform time sampling present in all simulations. For earthquake-cycle simulations, an attractor reconstruction is performed based on Taken’s theorem to corroborate my correlation-dimension results. The current method is limited in its ability to detect chaos in a dichotomous manner, which illuminates the direction for future study. An improving ability to quantitatively characterize earthquake-cycle simulations as an overall stable structure offers new opportunities to understand exotic seismic observations such as slow-slip events and enables more informative comparison with real data, particularly from paleoseismology, which could have far-reaching implications in earthquake forecasting. Earth and environmental sciences/Solid earth sciences/Geophysics Earth and environmental sciences/Solid earth sciences/Seismology rate-state spring slider earthquake cycle simulations phase-space attractor nonlinear dynamics Full Text Additional Declarations No competing interests reported. Supplementary Files EQComplexityShiqiWang2024Supplementary.docx Cite Share Download PDF Status: Published Journal Publication published 21 Jul, 2024 Read the published version in Scientific Reports → Version 1 posted Editorial decision: Revision requested 20 Jun, 2024 Reviewers agreed at journal 21 Apr, 2024 Reviews received at journal 19 Apr, 2024 Reviewers agreed at journal 08 Apr, 2024 Reviewers invited by journal 08 Apr, 2024 Editor assigned by journal 08 Apr, 2024 Editor invited by journal 29 Mar, 2024 Submission checks completed at journal 29 Mar, 2024 First submitted to journal 20 Mar, 2024 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. 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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-4139966","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Article","associatedPublications":[],"authors":[{"id":286708889,"identity":"5ded29b3-8512-4b6b-a047-8e7febc3fe3c","order_by":0,"name":"Shiqi Wang","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAA9klEQVRIiWNgGAWjYHACxgMgkh/MtgFiIFeCkB6wFskGZiCZRooWgwPEauGfkXzgME/NHbvN588f/FyQYJPPd4D54G0ePFokzhxLOMxz7FnythvJzNIzEtIsZx5gS7bGp4XheI/B4Ry2w8lmN5gZpHl/HDYwOMBjJo1Pi/xh/g+Hc/4dTjbuP8z8mycBpIX/G14tBsd7GA7nth22M2BIZpOGaOFhw6vF8Mwxg8N/+w4nSNxINrPmSUgzkDzMZmw5B48WuRvJDx/O+HbYnr//4OPbPAk2BnzHmx/eeIPP+1CQ2ABnMhOhHATsiVQ3CkbBKBgFIxEAAGuSUgb87QtYAAAAAElFTkSuQmCC","orcid":"","institution":"Stanford University","correspondingAuthor":true,"prefix":"","firstName":"Shiqi","middleName":"","lastName":"Wang","suffix":""}],"badges":[],"createdAt":"2024-03-21 01:29:15","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-4139966/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-4139966/v1","draftVersion":[],"editorialEvents":[{"content":"https://doi.org/10.1038/s41598-024-67685-4","type":"published","date":"2024-07-22T00:28:15+00:00"}],"editorialNote":"","failedWorkflow":false,"files":[{"id":60858209,"identity":"e11481a1-0473-402c-b2cd-9c00fef1e891","added_by":"auto","created_at":"2024-07-23 00:28:21","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":858624,"visible":true,"origin":"","legend":"","description":"","filename":"EQComplexityShiqiWang2024.pdf","url":"https://assets-eu.researchsquare.com/files/rs-4139966/v1_covered_238ec31a-8d28-48db-9a78-db65da265e37.pdf"},{"id":54023124,"identity":"fbb4119f-8a33-40ae-8407-d42c74163467","added_by":"auto","created_at":"2024-04-03 14:10:51","extension":"docx","order_by":1,"title":"","display":"","copyAsset":false,"role":"supplement","size":15793215,"visible":true,"origin":"","legend":"","description":"","filename":"EQComplexityShiqiWang2024Supplementary.docx","url":"https://assets-eu.researchsquare.com/files/rs-4139966/v1/2112de084e5c073dc616a48c.docx"}],"financialInterests":"No competing interests reported.","formattedTitle":"Toward quantitative characterization of simulated earthquake- cycle complexities","fulltext":[],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":false,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"hideJournal":false,"highlight":"","institution":"","isAcceptedByJournal":true,"isAuthorSuppliedPdf":true,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":true,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"scientific-reports","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"scirep","sideBox":"Learn more about [Scientific Reports](http://www.nature.com/srep/)","snPcode":"","submissionUrl":"","title":"Scientific Reports","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"stoa","reportingPortfolio":"Scientific Reports","inReviewEnabled":true,"inReviewRevisionsEnabled":true},"keywords":"rate-state spring slider, earthquake cycle simulations, phase-space attractor, nonlinear dynamics","lastPublishedDoi":"10.21203/rs.3.rs-4139966/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-4139966/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eEarthquake cycle simulations based on the rate-and-state friction formulation are evolutions of nonlinear dynamical systems (NDS). The term \u0026ldquo;cycle\u0026rdquo; implies an overall stable structure that is a phase-space attractor naturally traced out by trajectories of NDS as it evolves. Quantitatively characterizing these attractors should be a basis for measuring complexities of the simulated earthquake cycles, i.e. to determine if and how regular or chaotic they are. I first revisit the textbook-standard quasi-dynamic spring-slider system from an NDS perspective, explicitly showing the attractors, their relationship with the parameters of the NDS, and how they can be characterized taken advantage of their low-dimensionality while aiming to extend the analysis to high-dimensionality. I evaluate two approaches, computing the Lyapunov exponents (LEs) and measuring correlation dimensions, with the simple spring-slider and earthquake-cycle examples whose phase-space attractors can be visually verified. I conclude LEs are too inconvenient and computationally expensive to use whereas measuring correlation dimensions is an easy and effective approach even with highly non-uniform time sampling present in all simulations. For earthquake-cycle simulations, an attractor reconstruction is performed based on Taken\u0026rsquo;s theorem to corroborate my correlation-dimension results. The current method is limited in its ability to detect chaos in a dichotomous manner, which illuminates the direction for future study. An improving ability to quantitatively characterize earthquake-cycle simulations as an overall stable structure offers new opportunities to understand exotic seismic observations such as slow-slip events and enables more informative comparison with real data, particularly from paleoseismology, which could have far-reaching implications in earthquake forecasting.\u003c/p\u003e","manuscriptTitle":"Toward quantitative characterization of simulated earthquake- cycle complexities","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2024-04-03 14:10:34","doi":"10.21203/rs.3.rs-4139966/v1","editorialEvents":[{"type":"communityComments","content":0},{"type":"decision","content":"Revision requested","date":"2024-06-20T06:50:53+00:00","index":"","fulltext":""},{"type":"reviewerAgreed","content":"04bea5b5-7d26-45e0-8e27-0e3335452d43","date":"2024-04-21T21:30:54+00:00","index":"hide","fulltext":""},{"type":"editorInvitedReview","content":"","date":"2024-04-19T08:29:14+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"6116a491-f182-46bd-af8f-07ba57e10559","date":"2024-04-09T00:26:19+00:00","index":"hide","fulltext":""},{"type":"reviewersInvited","content":"","date":"2024-04-08T09:47:15+00:00","index":"","fulltext":""},{"type":"editorAssigned","content":"","date":"2024-04-08T09:40:11+00:00","index":"","fulltext":""},{"type":"editorInvited","content":"","date":"2024-03-29T10:44:53+00:00","index":"","fulltext":""},{"type":"checksComplete","content":"","date":"2024-03-29T10:33:27+00:00","index":"","fulltext":""},{"type":"submitted","content":"Scientific Reports","date":"2024-03-21T01:19:23+00:00","index":"","fulltext":""}],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"scientific-reports","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"scirep","sideBox":"Learn more about [Scientific Reports](http://www.nature.com/srep/)","snPcode":"","submissionUrl":"","title":"Scientific Reports","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"stoa","reportingPortfolio":"Scientific Reports","inReviewEnabled":true,"inReviewRevisionsEnabled":true}}],"origin":"","ownerIdentity":"75d6b3ea-fe8e-4a80-9cd3-f181c15da159","owner":[],"postedDate":"April 3rd, 2024","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"published-in-journal","subjectAreas":[{"id":30178823,"name":"Earth and environmental sciences/Solid earth sciences/Geophysics"},{"id":30178824,"name":"Earth and environmental sciences/Solid earth sciences/Seismology"}],"tags":[],"updatedAt":"2024-07-23T00:28:15+00:00","versionOfRecord":{"articleIdentity":"rs-4139966","link":"https://doi.org/10.1038/s41598-024-67685-4","journal":{"identity":"scientific-reports","isVorOnly":false,"title":"Scientific Reports"},"publishedOn":"2024-07-22 00:28:15","publishedOnDateReadable":"July 22nd, 2024"},"versionCreatedAt":"2024-04-03 14:10:34","video":"","vorDoi":"10.1038/s41598-024-67685-4","vorDoiUrl":"https://doi.org/10.1038/s41598-024-67685-4","workflowStages":[]},"version":"v1","identity":"rs-4139966","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-4139966","identity":"rs-4139966","version":["v1"]},"buildId":"qtupq5eGEP_6zYnWcrvyt","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}