{
  "abstract": "Subsurface rocks commonly contain fluids and exhibit elastic anisotropy. Fluid substitution in anisotropic media is therefore important in geophysical applications. The general fluid-substitution relation given by Brown and Korringa is expressed in terms of elastic compliance, whereas seismic wave propagation is formulated in terms of stiffness. In this study, a direct stiffness-domain formula for anisotropic fluid substitution is derived using the Sherman–Morrison formula. The undrained stiffness matrix is written as a rank-one update of the frame stiffness matrix. The derived formula is analytically equivalent to the conventional compliance-inversion form, and the singular condition is identified through determinant analysis. Numerical calculations for an anisotropic Berea sandstone model demonstrate that variations in the pore-fluid bulk modulus cause nonlinear and component-dependent stiffness changes. As the singular limit is approached, the undrained compliance matrix becomes increasingly ill-conditioned. The compliance inversion error reaches O (10−6), whereas the error of the direct rank-one expression remains on the order of 10−16 over the tested range. The proposed formula provides a direct stiffness-domain implementation of Brown–Korringa fluid substitution. It improves numerical accuracy over conventional compliance inversion near the singular limit.",
  "abstract_shown": true,
  "affiliations": [
    "School of Geophysics and Information Technology, China University of Geosciences (Beijing), Beijing 100083, China",
    "Department of Geoscience and Petroleum, Norwegian University of Science and Technology, 7491 Trondheim, Norway"
  ],
  "article_type": null,
  "arxiv": null,
  "author_total": 6,
  "authors": [
    {
      "affs": [
        0
      ],
      "name": "Chun Yang"
    },
    {
      "affs": [
        1
      ],
      "name": "Alexey Stovas",
      "orcid": "0000-0002-2294-9626"
    },
    {
      "affs": [
        0
      ],
      "name": "Xuhan Yao"
    },
    {
      "affs": [
        0
      ],
      "name": "Yongli Qiao"
    },
    {
      "affs": [
        0
      ],
      "name": "Yuankang Wang"
    },
    {
      "affs": [
        0
      ],
      "name": "Yiyang Li"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/bnq05e67fz9py.bib",
  "cited_by": 0,
  "doi": "10.3390/math14213865",
  "fulltext_url": null,
  "id": "bnq05e67fz9py",
  "issns": [
    "2227-7390"
  ],
  "landing_url": "https://www.mdpi.com/2227-7390/14/21/3865",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "https://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": null,
  "native_subjects": [
    [
      "openalex",
      "1908|Seismic Imaging and Inversion Techniques"
    ]
  ],
  "openalex": "W7223266628",
  "pdf_url": null,
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-23",
  "publisher": "MDPI AG",
  "ris": "https://research.draconitic.com/paper/bnq05e67fz9py.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:18:29Z",
      "native_id": "10.3390/math14213865",
      "source": "crossref",
      "url": "https://www.mdpi.com/2227-7390/14/21/3865"
    }
  ],
  "subjects": [
    {
      "field": "earth",
      "origin": "openalex:1908|Seismic Imaging and Inversion Techniques",
      "subfield": "geophysics"
    }
  ],
  "title": "Stiffness Formula and Conditioning Analysis for General Brown–Korringa Fluid Substitution",
  "title_text": "Stiffness Formula and Conditioning Analysis for General Brown–Korringa Fluid Substitution",
  "type": "peer-reviewed",
  "updated_at": "2026-10-30T12:18:29Z",
  "url": "https://research.draconitic.com/paper/bnq05e67fz9py",
  "venue": "Mathematics",
  "versions": []
}