{
  "abstract": "Large explosive eruptions and earthquakes excite atmospheric oscillations near 3.7 and 4.4\\,mHz that couple to the solid Earth. For vertically propagating linear acoustic--gravity waves in a hydrostatic ideal-gas atmosphere, the travel-time formulation gives a Klein--Gordon equation with a potential $Q(τ)$. We establish three main results. First, for every potential admitting a positive zero-energy solution, the corresponding atmospheric profiles are constructed explicitly by quadrature; this extends the known reflectionless profiles of constant $Q$. Second, Darboux--Crum potentials give a smooth atmosphere that reproduces the U.S. Standard Atmosphere between 11 and 100\\,km to within 3\\,K and is exactly transparent to vertical waves above its cut-off; it supports no damped overtone near 4.4\\,mHz, and its ground-confined mode below the cut-off is perfectly trapped. The observed spectrum therefore requires a cut-off barrier of finite thickness connecting the lower atmosphere to the thermosphere. Third, a Rosen--Morse barrier gives an exactly solvable atmosphere with a closed-form hypergeometric resonance condition. Its resonances at 3.76 and 4.37\\,mHz, with leakage quality factors 173 and 20, explain the different damping of the two oscillations: the fundamental lies below the top of the mesospheric cut-off barrier and leaks by tunnelling, whereas the overtone lies above it. Full-wave computations for event-specific atmospheres reproduce the reported 3.7--3.8\\,mHz fundamental oscillation in all six events, of seven considered, in which such a mode was identified.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.07073",
  "author_total": 1,
  "authors": [
    {
      "name": "O. V. Kaptsov"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/dsccsf9hr38qt.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.07073",
  "fulltext_url": null,
  "id": "dsccsf9hr38qt",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.07073",
  "language": null,
  "licence": "CC0-1.0",
  "licence_label": "CC0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/publicdomain/zero/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math-ph"
    ],
    [
      "arxiv",
      "math.MP"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2610.07073",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-05",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/dsccsf9hr38qt.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:27:22Z",
      "native_id": "2610.07073",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.07073"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math-ph",
      "subfield": "mathematical-physics"
    }
  ],
  "title": "Inverse construction of exact atmospheric models and the 3.7--4.4\\,mHz acoustic resonances",
  "title_text": "Inverse construction of exact atmospheric models and the 3.7--4.4\\,mHz acoustic resonances",
  "type": "preprint",
  "updated_at": "2026-10-30T12:27:26Z",
  "url": "https://research.draconitic.com/paper/dsccsf9hr38qt",
  "venue": "arXiv",
  "versions": []
}