A Robust Numerical Framework for Ultrasonic Wave Characterization in Complex Petrophysical Environments

A Robust Numerical Framework for Ultrasonic Wave Characterization in Complex Petrophysical Environments | 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 Short Report A Robust Numerical Framework for Ultrasonic Wave Characterization in Complex Petrophysical Environments Ujjal Mandal This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-9293893/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 Characterizing internal rock heterogeneities, such as pores, vugs, and micro-fractures, represents a fundamental challenge in petrophysics and reservoir engineering. This study presents a robust numerical framework based on the k-space pseudospectral method (k-Wave) to model 1 MHz ultrasonic wave propagation within complex petrophysical environments. A heterogeneous rock model was developed, consisting of a fluid-saturated host matrix with a longitudinal velocity of 2500 m/s, embedded with five discrete circular inclusions assigned a lower velocity of 350 m/s to simulate high-contrast impedance mismatches typical of vuggy porous media. The wave propagation was excited using a 51-element linear source array, and the resulting steady-state acoustic field was analyzed using a 16384-point Fast Fourier Transform (FFT). The simulation results revealed significant scattering effects, wavefront distortions, and the formation of pronounced acoustic shadow zones behind inclusion clusters. Quantitative evaluation was performed using several key metrics, including a Contrast Ratio (CR) of 3.51 dB and an effective attenuation coefficient of 421.95 dB/m, which reflect the combined influence of intrinsic absorption and extrinsic scattering. The stability of the framework was further enhanced by integrating the Convergent Born Series (CBS) protocol and fractional viscoacoustic modeling to account for frequency-dependent power-law absorption. Crucially, a comparative validation between the k-Wave results and the Modified Born Approach (MBA) showed a numerical discrepancy of less than $1\%$, confirming the high precision of the proposed model. This framework provides an accurate and computationally efficient tool for interpreting ultrasonic testing data, facilitating the non-destructive estimation of porosity and inclusion density in heterogeneous porous media. Geophysics Petrophysics Ultrasonic Testing k-Wave Simulation Scattering Potential Rock Heterogeneity k-space Pseudospectral Method 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-9293893","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Short Report","associatedPublications":[],"authors":[{"id":616065561,"identity":"af4c00d8-b5bc-4763-8ce7-2f83831b8957","order_by":0,"name":"Ujjal Mandal","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAA80lEQVRIie3RMWsCMRTA8SfCuTy49R0V+xWeZGgX8askHDil0NFJToSjm6v9Fo4dA0JvuQ/gmEOwSwu6KYg0Kd3Eu7p1yB+yhPcjIQEIhf5nLSvHhFFnZozk3z1ZT9q8Kx97Mb5LR/hPJEpe87FIFtqPc/2s72Fe2DuMSC3Xem/s8+keOisL1dt10l1rFoiOlF9Lf7F+hiMGVV4nRAgpkiPF0w9pZaABVF5D4sKukB0x2noyzOLPBgKyP11IEsmLBk9URk2nkBawM+QfmR0RaU5bNg0X+zio88R/5WZ/OPUG8zitqmMNuSxyy9wCQqFQKHTZN+J8U4I+YsfkAAAAAElFTkSuQmCC","orcid":"https://orcid.org/0009-0008-3559-0502","institution":"University of Gour Banga","correspondingAuthor":true,"prefix":"","firstName":"Ujjal","middleName":"","lastName":"Mandal","suffix":""}],"badges":[],"createdAt":"2026-04-01 15:37:14","currentVersionCode":1,"declarations":{"humanSubjects":true,"vertebrateSubjects":true,"conflictsOfInterestStatement":false,"humanSubjectEthicalGuidelines":true,"humanSubjectConsent":true,"humanSubjectClinicalTrial":false,"humanSubjectCaseReport":false,"vertebrateSubjectEthicalGuidelines":true},"doi":"10.21203/rs.3.rs-9293893/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-9293893/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":106093969,"identity":"d3e7a449-d5b0-4da8-be57-2f2f218287ef","added_by":"auto","created_at":"2026-04-03 11:40:23","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":645900,"visible":true,"origin":"","legend":"","description":"","filename":"ARobustNumericalFrameworkforUltrasonicWaveCharacterizationinComplexPetrophysicalEnvironments.pdf","url":"https://assets-eu.researchsquare.com/files/rs-9293893/v1_covered_e06f282f-600b-4c86-9c9b-9e7c82e80aa7.pdf"}],"financialInterests":"The authors declare no competing interests.","formattedTitle":"\u003cp\u003eA Robust Numerical Framework for Ultrasonic Wave Characterization in Complex Petrophysical Environments\u003c/p\u003e","fulltext":[],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":false,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":true,"hideJournal":true,"highlight":"","institution":"University of Gour Banga","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":"Petrophysics, Ultrasonic Testing, k-Wave Simulation, Scattering Potential, Rock Heterogeneity, k-space Pseudospectral Method","lastPublishedDoi":"10.21203/rs.3.rs-9293893/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-9293893/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eCharacterizing internal rock heterogeneities, such as pores, vugs, and micro-fractures, represents a fundamental challenge in petrophysics and reservoir engineering. This study presents a robust numerical framework based on the k-space pseudospectral method (k-Wave) to model 1 MHz ultrasonic wave propagation within complex petrophysical environments. A heterogeneous rock model was developed, consisting of a fluid-saturated host matrix with a longitudinal velocity of 2500 m/s, embedded with five discrete circular inclusions assigned a lower velocity of 350 m/s to simulate high-contrast impedance mismatches typical of vuggy porous media. The wave propagation was excited using a 51-element linear source array, and the resulting steady-state acoustic field was analyzed using a 16384-point Fast Fourier Transform (FFT). The simulation results revealed significant scattering effects, wavefront distortions, and the formation of pronounced acoustic shadow zones behind inclusion clusters. Quantitative evaluation was performed using several key metrics, including a Contrast Ratio (CR) of 3.51 dB and an effective attenuation coefficient of 421.95 dB/m, which reflect the combined influence of intrinsic absorption and extrinsic scattering. The stability of the framework was further enhanced by integrating the Convergent Born Series (CBS) protocol and fractional viscoacoustic modeling to account for frequency-dependent power-law absorption. Crucially, a comparative validation between the k-Wave results and the Modified Born Approach (MBA) showed a numerical discrepancy of less than $1\\%$, confirming the high precision of the proposed model. 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