{
  "abstract": "The main difficulty in 3D gravity inversion is that surface observations lack vertical wavenumber information, making the problem underdetermined and depth resolution poor. Building on the author's spectral-domain pseudo-inverse theory for unitary diagonalizable systems, this paper presents a true 3D inversion method. Surface data are analytically continued upward via Laplace's equation to form a 3D data volume, providing the vertical wavenumber sampling for the 3D Fourier transform. A general analytical expression for the half-space spectrum is derived, separating the horizontal spectrum from the vertical propagation kernel. The Green's function of the 3D Poisson equation is unitarily diagonalized, yielding the forward spectral response $λ(\\kk) = -i 4πG k_z / K^2$, and a stable inverse filter $q_α(λ) = \\barλ/(|λ|^2 + α)$ is constructed. This filter is proved to have bounded stability and consistency (reducing to the exact inverse as $α\\to 0^+$). Validation with a homogeneous sphere model shows correct recovery of the anomaly location and singular behavior at the source. The contributions are twofold: (1) upward continuation constructs a 3D volume from 2D surface data, which does not add physical observations but unfolds the 3D spatial variation information (data innovation) derived through the governing physical equation; (2) the inversion is reduced to one forward 3D Fourier transform, one spectral scaling, and one inverse transform. The framework extends to any linear potential-field inverse problem with a translation-invariant forward operator, including magnetic inversion.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2608.11014",
  "author_total": 1,
  "authors": [
    {
      "name": "Shengchang Chen"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/bx33n9jhn036w.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2608.11014",
  "fulltext_url": null,
  "id": "bx33n9jhn036w",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2608.11014",
  "language": null,
  "licence": "CC-BY-NC-SA-4.0",
  "licence_label": "CC BY-NC-SA 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by-nc-sa/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "cs.NA"
    ],
    [
      "arxiv",
      "math.NA"
    ],
    [
      "arxiv",
      "physics.geo-ph"
    ],
    [
      "openalex",
      "1908|Geophysical and Geoelectrical Methods"
    ]
  ],
  "openalex": "W7202281974",
  "pdf_url": "https://arxiv.org/pdf/2608.11014",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-13",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/bx33n9jhn036w.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:29:11Z",
      "native_id": "2608.11014",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2608.11014"
    }
  ],
  "subjects": [
    {
      "field": "earth",
      "origin": "arxiv:physics.geo-ph",
      "subfield": "geophysics"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.NA",
      "subfield": "numerical-analysis"
    }
  ],
  "title": "A Spectral-Domain Pseudo-Inverse Method for True 3D Gravity Inversion",
  "title_text": "A Spectral-Domain Pseudo-Inverse Method for True 3D Gravity Inversion",
  "type": "preprint",
  "updated_at": "2026-10-30T12:29:19Z",
  "url": "https://research.draconitic.com/paper/bx33n9jhn036w",
  "venue": "arXiv",
  "versions": []
}