Dispersion analysis of generalized wave equations under the single-parameter second-order strain gradient theory

Dispersion analysis of generalized wave equations under the single-parameter second-order strain gradient theory | 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 Dispersion analysis of generalized wave equations under the single-parameter second-order strain gradient theory CHAOPU CHEN, WENLEI BAI, HONG LIU, ZHIYANG WANG, YOUMING LI This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-4447955/v1 This work is licensed under a CC BY 4.0 License Status: Published Journal Publication published 09 Jan, 2025 Read the published version in Pure and Applied Geophysics → Version 1 posted 8 You are reading this latest preprint version Abstract The construction of wave equations describing the wave propagation in real medium is a critical problem to be solved for oil and gas seismic exploration. Researches show that the microstructural interactions by different scales will trigger the heterogeneous response of the medium, which in turn has an impact on the mechanical behavior of macro-scales. The heterogeneous response triggered by microstructural interactions in the medium is portrayed by introducing higher-order spatial derivatives of the strain and additional parameters of the characteristic scale of the medium under the framework of the generalized continuum mechanics theory (GCMT). When considering the heterogeneous responses triggered by microstructural interactions of the medium, seismic waves propagate in a dispersion manner. In this paper, we introduce the generalized wave equations under the single-parameter second-order strain gradient theory (SSSGT) by considering the nonlocal effects, give the decoupled generalized wave equations using the Helmholtz decomposition theorem, and derive the expression of the phase-velocity of the P- and S-wave to analyze the theoretical dispersion. Combined with numerical modeling, we further investigate the dispersion in the propagation of P- and S-wave triggered by the microstructural interactions. Numerical modeling and dispersion analysis indicate that the wave propagation is affected by the characteristic scale of the micropore of the medium and the frequency, and the dispersion of P- and S-wave is prominent increasingly with the frequency and the characteristic scale of the micropore increasing. Numerical modeling Generalized continuum mechanics theory Generalized wave equations Dispersion analysis f-k transform method Full Text Additional Declarations No competing interests reported. Cite Share Download PDF Status: Published Journal Publication published 09 Jan, 2025 Read the published version in Pure and Applied Geophysics → Version 1 posted Editorial decision: Revision requested 28 Oct, 2024 Reviews received at journal 02 Oct, 2024 Reviewers agreed at journal 23 Sep, 2024 Reviewers agreed at journal 23 Sep, 2024 Reviewers invited by journal 23 Sep, 2024 Editor assigned by journal 20 May, 2024 Submission checks completed at journal 20 May, 2024 First submitted to journal 20 May, 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. 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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-4447955","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":307962379,"identity":"47d9203c-af22-4a9d-9a18-dec1d5bfe6f4","order_by":0,"name":"CHAOPU CHEN","email":"","orcid":"","institution":"Institute of Geology and Geophysics","correspondingAuthor":false,"prefix":"","firstName":"CHAOPU","middleName":"","lastName":"CHEN","suffix":""},{"id":307962381,"identity":"f64ab952-6b97-4563-abd1-03584cc58606","order_by":1,"name":"WENLEI BAI","email":"","orcid":"","institution":"Institute of Geology and 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