{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,10,1]],"date-time":"2026-10-01T18:59:45Z","timestamp":1790881185154,"version":"4.1.0"},"reference-count":45,"publisher":"American Physical Society (APS)","issue":"2","license":[{"start":{"date-parts":[[2026,7,9]],"date-time":"2026-07-09T00:00:00Z","timestamp":1783555200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100012166","name":"National Key Research and Development Program of China","doi-asserted-by":"publisher","award":["2024YFC2207300"],"award-info":[{"award-number":["2024YFC2207300"]}],"id":[{"id":"10.13039\/501100012166","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100003981","name":"Agenzia Spaziale Italiana","doi-asserted-by":"publisher","award":["2025-29-HH.0"],"award-info":[{"award-number":["2025-29-HH.0"]}],"id":[{"id":"10.13039\/501100003981","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100004543","name":"China Scholarship Council","doi-asserted-by":"publisher","award":["202506010256"],"award-info":[{"award-number":["202506010256"]}],"id":[{"id":"10.13039\/501100004543","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100010661","name":"Horizon 2020 Framework Programme","doi-asserted-by":"publisher","award":["101131928"],"award-info":[{"award-number":["101131928"]}],"id":[{"id":"10.13039\/100010661","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["journals.aps.org"],"crossmark-restriction":true},"short-container-title":["Phys. Rev. Lett."],"accepted":{"date-parts":[[2026,5,13]]},"abstract":"<jats:p>The recent success of gravitational-wave (GW) astronomy together with renewed plans for lunar geophysical instrumentation has revived interest in using the Moon as a resonant detector for midfrequency (mHz\u2013Hz) GWs. In realistic observational scenarios, the GW strain amplitude is expected to be constrained independently by networks of GW detectors, which motivates an inverse,  question: to what extent can measurements of the Moon\u2019s seismic response to known GWs be used to infer its internal structure? In this Letter, we develop a first-principles, perturbative framework that maps spherically symmetric perturbations of the elastic and density structure to measurable changes in observables, especially GW-driven modal amplitudes of the Moon. The formalism combines (i)\u00a0a normal-mode representation of the elastic response, (ii)\u00a0first-order perturbation theory for eigenvalues and eigenfunctions, and (iii)\u00a0a linearized observation model that links frequency and amplitude observables to model parameters (bulk and shear moduli, density, and interface locations) and their perturbations. We show that the estimation errors of the Moon\u2019s elastic parameters can be reduced by about an order of magnitude with observations of calibrated GWs.<\/jats:p>","DOI":"10.1103\/3tcp-hqf9","type":"journal-article","created":{"date-parts":[[2026,7,9]],"date-time":"2026-07-09T12:32:09Z","timestamp":1783600329000},"update-policy":"https:\/\/doi.org\/10.1103\/crossmark-policy","source":"Crossref","is-referenced-by-count":1,"title":["Gravitational-Wave Tomography of the Moon: Constraining Lunar Structure with Calibrated Gravitational Waves"],"prefix":"10.1103","volume":"137","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-1320-5243","authenticated-orcid":true,"given":"Han","family":"Yan","sequence":"first","affiliation":[{"id":[{"id":"https:\/\/ror.org\/02v51f717","id-type":"ROR","asserted-by":"publisher"}],"name":"Peking University"},{"name":"Kavli Institute for Astronomy and Astrophysics"},{"id":[{"id":"https:\/\/ror.org\/02v51f717","id-type":"ROR","asserted-by":"publisher"}],"name":"Peking University"},{"id":[{"id":"https:\/\/ror.org\/043qcb444","id-type":"ROR","asserted-by":"publisher"}],"name":"Gran Sasso Science Institute"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-7332-9806","authenticated-orcid":true,"given":"Jan","family":"Harms","sequence":"additional","affiliation":[{"id":[{"id":"https:\/\/ror.org\/043qcb444","id-type":"ROR","asserted-by":"publisher"}],"name":"Gran Sasso Science Institute"},{"id":[{"id":"https:\/\/ror.org\/02s8k0k61","id-type":"ROR","asserted-by":"publisher"}],"name":"INFN, Laboratori Nazionali del Gran Sasso"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"16","published-online":{"date-parts":[[2026,7,9]]},"reference":[{"key":"3tcp-hqf9Cc1R1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRev.117.306","type":"journal-article"},{"key":"3tcp-hqf9Cc2R1","doi-asserted-by":"publisher","DOI":"10.1093\/nsr\/nwad329","type":"journal-article"},{"key":"3tcp-hqf9Cc3R1","volume-title":"LPI Contributions","author":"M.\u2009P. 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However, the importance of amplitude measurement will be even greater.","type":"other"},{"key":"3tcp-hqf9Cc41R1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevD.77.042001","type":"journal-article"},{"key":"3tcp-hqf9Cc42R1","unstructured":"Note: \u03ba=\u03c1(vp2\u221243vs2), \u03bc=\u03c1vs2.","type":"other"},{"key":"3tcp-hqf9Cc43R1","doi-asserted-by":"publisher","DOI":"10.5281\/zenodo.20309657","type":"software"},{"key":"3tcp-hqf9Cc44R1","unstructured":"Previous work [19] has validated the appropriateness of this refinement-and-interpolation procedure.","type":"other"},{"key":"3tcp-hqf9Cc45R1","unstructured":"Since we have a sufficient number of observables, far exceeding the number of model parameters, the specific layer thickness does not have significant influence on the results.","type":"other"},{"key":"3tcp-hqf9Cc46R1","unstructured":"Contributions of higher modes decay rapidly as \u03c9n\u22122.","type":"other"},{"key":"3tcp-hqf9Cc47R1","volume-title":"Origins, Worlds, and Life: Planetary Science and Astrobiology in the Next Decade","year":"2023","type":"book"},{"key":"3tcp-hqf9Cc48R1","doi-asserted-by":"publisher","DOI":"10.1046\/j.1365-246X.2001.00502.x","type":"journal-article"}],"container-title":["Physical Review Letters"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.aps.org\/article\/10.1103\/3tcp-hqf9","content-type":"unspecified","content-version":"vor","intended-application":"syndication"},{"URL":"http:\/\/harvest.aps.org\/v2\/journals\/articles\/10.1103\/3tcp-hqf9\/fulltext","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,10,1]],"date-time":"2026-10-01T18:03:47Z","timestamp":1790877827000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.aps.org\/doi\/10.1103\/3tcp-hqf9"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026,7,9]]},"references-count":45,"journal-issue":{"issue":"2","published-print":{"date-parts":[[2026,7]]}},"URL":"https:\/\/doi.org\/10.1103\/3tcp-hqf9","relation":{"has-preprint":[{"id-type":"doi","id":"10.48550\/arXiv.2605.13960","asserted-by":"subject"}]},"ISSN":["0031-9007","1079-7114"],"issn-type":[{"value":"0031-9007","type":"print"},{"value":"1079-7114","type":"electronic"}],"subject":[],"published":{"date-parts":[[2026,7,9]]},"assertion":[{"value":"2026-01-09","name":"date_received","label":"Date Received","group":{"name":"publication_dates","label":"Publication dates"}},{"value":"Published by the American Physical Society. All rights are reserved, including those for text and data mining, AI training, and similar technologies.","name":"copyright_statement","label":"Copyright statement","group":{"name":"copyright","label":"copyright"}},{"value":"2026","name":"copyright_year","label":"Copyright year","group":{"name":"copyright","label":"copyright"}},{"value":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/","name":"creative_commons_license","label":"Creative Commons license","group":{"name":"licenses","label":"Licenses"}},{"value":"\u00a92026 The authors","name":"copyright_holder","label":"Copyright holder","group":{"name":"copyright","label":"copyright"}}],"article-number":"021409"}}