Bayesian estimation of Andrade rheological parameters and mantle thermodynamic states: Constraints from long-period body tides

Bayesian estimation of Andrade rheological parameters and mantle thermodynamic states: Constraints from long-period body tides | 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 Bayesian estimation of Andrade rheological parameters and mantle thermodynamic states: Constraints from long-period body tides Chuanyi Zou, Hao Ding, Wei Luan This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-8516320/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 Earth's anelastic tidal response is critical for constraining its deep interior structure. The traditional Maxwell model only describes two extreme states (instantaneous elasticity and steady-state viscosity) and fails to capture the broadband anelastic process between them. In contrast, the Andrade model includes two rheological parameters (frequency exponent α and relaxation strength β) and better matches the mechanical response across the entire frequency spectrum. Current Andrade parameters are mostly derived from single-crystal olivine experiments in the seismic frequency band. However, thermodynamic conditions (e.g., grain size, temperature, pressure) differ significantly between laboratories and the real deep Earth, causing controversy over extrapolating (α, β) to planetary-scale anelasticity studies. Here, we use dissipation factors of ten long-period body tides as constraints. By coupling the mantle's real grain size and thermobaric conditions via a pseudo-periodic master variable, we establish a Bayesian inversion framework to estimate Andrade parameters and thermodynamic state. Results show α = 0.190 with a 90% confidence interval (CI) of [0.186, 0.194], significantly smaller than laboratory values; β = 8.04×10-14 (90% CI: [6.82, 9.20]×10-14), an order of magnitude lower than laboratory results. Thermodynamic parameters are grain size d = 5.5×10-3 m (90% CI: [2.6, 8.3]×10-3 m) and temperature T = 2221 K (90% CI: [2164, 2287] K), both consistent with seismological and mineral physics data. Notably, long-period body tides are sensitive to the lower mantle, so inverted parameters reflect its properties and structure, constraining quantitative analysis of deep mantle dynamics. Tidal dissipation Anelastic Andrade rheology Thermodynamics Bayesian estimation Full Text Supplementary Files GraphicalAbstract.jpg 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-8516320","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":581187861,"identity":"aec0e97c-33ea-4d23-af75-a1827745cd9e","order_by":0,"name":"Chuanyi Zou","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAA20lEQVRIiWNgGAWjYDACCTjJfIAZzD5AvBa2BJK0gACPAXFa+Gf3GH4ubLOw55fI+SZd2MYgx3cjgfFzAT5L7pwxlp7ZJsEsOSN3G5DBYCx5I4FZegYeLQYSOQbSvG0SbAY3crfd5m1jSNxwI4GNmQe/FuPfQC08BjdynoG01BOjxQxkiwRQCxtIS4IBIS0SN9LKrHnOSRhI9jwz/w1kGM4887BZGp8W/hnJm2/zlNXZ87MnPzbmKbOR5zuefPAzPi1gwMiGsBXEbSCkAQj+EKFmFIyCUTAKRi4AABfFQcNWHNRiAAAAAElFTkSuQmCC","orcid":"https://orcid.org/0009-0007-3770-9346","institution":"Wuhan University","correspondingAuthor":true,"prefix":"","firstName":"Chuanyi","middleName":"","lastName":"Zou","suffix":""},{"id":581187862,"identity":"fb9442c2-18ec-4a05-b427-d0d567a3e49c","order_by":1,"name":"Hao Ding","email":"","orcid":"https://orcid.org/0000-0002-3058-8197","institution":"Wuhan University","correspondingAuthor":false,"prefix":"","firstName":"Hao","middleName":"","lastName":"Ding","suffix":""},{"id":581187863,"identity":"3e7f468e-8bea-4fa5-8c7b-9c0a56bc3a66","order_by":2,"name":"Wei Luan","email":"","orcid":"https://orcid.org/0000-0002-6197-2917","institution":"Wuhan University","correspondingAuthor":false,"prefix":"","firstName":"Wei","middleName":"","lastName":"Luan","suffix":""}],"badges":[],"createdAt":"2026-01-05 02:57:07","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-8516320/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-8516320/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":105033610,"identity":"0d4dd0e9-b1e4-498c-b4fb-d9f02132b33e","added_by":"auto","created_at":"2026-03-20 07:20:36","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":1784655,"visible":true,"origin":"","legend":"","description":"","filename":"manuscript.pdf","url":"https://assets-eu.researchsquare.com/files/rs-8516320/v1_covered_d23bf95b-ac6f-4e6e-b5b7-fec98a86cf1b.pdf"},{"id":101395094,"identity":"18832e8b-4637-4a29-834f-dbaa458c4394","added_by":"auto","created_at":"2026-01-29 09:02:13","extension":"jpg","order_by":11,"title":"","display":"","copyAsset":false,"role":"supplement","size":125883,"visible":true,"origin":"","legend":"","description":"","filename":"GraphicalAbstract.jpg","url":"https://assets-eu.researchsquare.com/files/rs-8516320/v1/0d11f9128a8c0cea15ebdd47.jpg"}],"financialInterests":"","formattedTitle":"Bayesian estimation of Andrade rheological parameters and mantle thermodynamic states: Constraints from long-period body tides","fulltext":[],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":false,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"hideJournal":true,"highlight":"","institution":"","isAcceptedByJournal":false,"isAuthorSuppliedPdf":true,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":true,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true},"keywords":"Tidal dissipation, Anelastic, Andrade rheology, Thermodynamics, Bayesian estimation","lastPublishedDoi":"10.21203/rs.3.rs-8516320/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-8516320/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"Earth's anelastic tidal response is critical for constraining its deep interior structure. The traditional Maxwell model only describes two extreme states (instantaneous elasticity and steady-state viscosity) and fails to capture the broadband anelastic process between them. In contrast, the Andrade model includes two rheological parameters (frequency exponent α and relaxation strength β) and better matches the mechanical response across the entire frequency spectrum. Current Andrade parameters are mostly derived from single-crystal olivine experiments in the seismic frequency band. However, thermodynamic conditions (e.g., grain size, temperature, pressure) differ significantly between laboratories and the real deep Earth, causing controversy over extrapolating (α, β) to planetary-scale anelasticity studies. Here, we use dissipation factors of ten long-period body tides as constraints. By coupling the mantle's real grain size and thermobaric conditions via a pseudo-periodic master variable, we establish a Bayesian inversion framework to estimate Andrade parameters and thermodynamic state. Results show α = 0.190 with a 90% confidence interval (CI) of [0.186, 0.194], significantly smaller than laboratory values; β = 8.04×10-14 (90% CI: [6.82, 9.20]×10-14), an order of magnitude lower than laboratory results. Thermodynamic parameters are grain size d = 5.5×10-3 m (90% CI: [2.6, 8.3]×10-3 m) and temperature T = 2221 K (90% CI: [2164, 2287] K), both consistent with seismological and mineral physics data. 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