Magnetotelluric impedance consisting of six elements

Magnetotelluric impedance consisting of six elements | 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 Magnetotelluric impedance consisting of six elements Xiaoli WAN, Hisayoshi Shimizu, Peng Yu, Hisashi Utada This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-6073595/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 letter addresses two critical questions concerning the validity of the current formulation of the magnetotelluric (MT) method. The first question pertains to its mathematical formulation: specifically, whether solving the fundamental equations in a Cartesian coordinate system is universally valid. The second question concerns the number of impedance elements. Through a simple theoretical consideration, we found that the MT impedance generally consists of nine elements, which reduces to six at the Earth’s surface, whereas conventional MT studies utilize the impedance consisting of only four elements. Should MT studies adopt the 6-element impedance? Based on three-dimensional (3-D) numerical modeling results in both Cartesian and spherical coordinate systems, along with further theoretical analyses, we derived the following implications: (1) The MT impedance comprising four elements and the tipper are unique response functions only in a Cartesian coordinate system. In a spherical coordinate system, they become non-unique and exhibit significant dependence on the source amplitude. (2) The MT impedance consisting of six elements is a unique response function of the Earth, determinable in a spherical coordinate system but undeterminable in a Cartesian coordinate system under the plane-wave approximation. (3) Consequently, it is inappropriate to invert MT impedances obtained from Earth observations using numerical solvers designed for Cartesian coordinate systems. If these implications are validated, most of the theories and numerical solvers developed for Cartesian coordinate systems will need to be replaced by those adapted for spherical coordinate systems, except for cases involving only the primary field. Magnetotellurics source amplitude coordinate system impedance uniqueness plane-wave approximation flat Earth approximation Full Text Supplementary Files AdditionalFile1.docx GraphAbs.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-6073595","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":424415377,"identity":"0567f150-6d1d-4d7e-97ab-390ec5667dd2","order_by":0,"name":"Xiaoli 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Earth approximation","lastPublishedDoi":"10.21203/rs.3.rs-6073595/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-6073595/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eThis letter addresses two critical questions concerning the validity of the current formulation of the magnetotelluric (MT) method. The first question pertains to its mathematical formulation: specifically, whether solving the fundamental equations in a Cartesian coordinate system is universally valid. The second question concerns the number of impedance elements. Through a simple theoretical consideration, we found that the MT impedance generally consists of nine elements, which reduces to six at the Earth\u0026rsquo;s surface, whereas conventional MT studies utilize the impedance consisting of only four elements. Should MT studies adopt the 6-element impedance? Based on three-dimensional (3-D) numerical modeling results in both Cartesian and spherical coordinate systems, along with further theoretical analyses, we derived the following implications:\u003c/p\u003e \u003cp\u003e(1) The MT impedance comprising four elements and the tipper are unique response functions only in a Cartesian coordinate system. In a spherical coordinate system, they become non-unique and exhibit significant dependence on the source amplitude.\u003c/p\u003e \u003cp\u003e(2) The MT impedance consisting of six elements is a unique response function of the Earth, determinable in a spherical coordinate system but undeterminable in a Cartesian coordinate system under the plane-wave approximation.\u003c/p\u003e \u003cp\u003e(3) Consequently, it is inappropriate to invert MT impedances obtained from Earth observations using numerical solvers designed for Cartesian coordinate systems.\u003c/p\u003e \u003cp\u003eIf these implications are validated, most of the theories and numerical solvers developed for Cartesian coordinate systems will need to be replaced by those adapted for spherical coordinate systems, except for cases involving only the primary field.\u003c/p\u003e","manuscriptTitle":"Magnetotelluric impedance consisting of six elements","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2025-03-20 14:30:42","doi":"10.21203/rs.3.rs-6073595/v1","editorialEvents":[{"type":"communityComments","content":0}],"status":"published","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}}],"origin":"","ownerIdentity":"dc468036-7ab0-404e-b26c-bb6ddc0ca3d1","owner":[],"postedDate":"March 20th, 2025","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"posted","subjectAreas":[],"tags":[],"updatedAt":"2025-08-27T09:21:40+00:00","versionOfRecord":[],"versionCreatedAt":"2025-03-20 14:30:42","video":"","vorDoi":"","vorDoiUrl":"","workflowStages":[]},"version":"v1","identity":"rs-6073595","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-6073595","identity":"rs-6073595","version":["v1"]},"buildId":"XKTyCvWXoU3ODBz1xrDgd","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}