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Representation theorem for viscoelastic waves with a non-symmetric stiffness matrix

The result's identifiers

  • Result code in IS VaVaI

    <a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F21%3A10438484" target="_blank" >RIV/00216208:11320/21:10438484 - isvavai.cz</a>

  • Result on the web

    <a href="https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=J.JhDNfr.I" target="_blank" >https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=J.JhDNfr.I</a>

  • DOI - Digital Object Identifier

    <a href="http://dx.doi.org/10.1007/s11200-020-0158-2" target="_blank" >10.1007/s11200-020-0158-2</a>

Alternative languages

  • Result language

    angličtina

  • Original language name

    Representation theorem for viscoelastic waves with a non-symmetric stiffness matrix

  • Original language description

    In an elastic medium, it was proved that the stiffness tensor is symmetric with respect to the exchange of the first pair of indices and the second pair of indices, but the proof does not apply to a viscoelastic medium. In this paper, we thus derive the representation theorem for viscoelastic waves in a medium with a non-symmetric stiffness matrix. The representation theorem expresses the wave field at a receiver, situated inside a subset of the definition volume of the viscoelastodynamic equation, in terms of the volume integral over the subset and the surface integral over the boundary of the subset. For the given medium, we define the complementary medium corresponding to the transposed stiffness matrix. We define the frequency-domain complementary Green function as the frequency-domain Green function in the complementary medium. We then derive the provisional representation theorem as the relation between the frequency-domain wave field in the given medium and the frequency-domain complementary Green function. This provisional representation theorem yields the reciprocity relation between the frequency-domain Green function and the frequency-domain complementary Green function. The final version of the representation theorem is then obtained by inserting the reciprocity relation into the provisional representation theorem.

  • Czech name

  • Czech description

Classification

  • Type

    J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database

  • CEP classification

  • OECD FORD branch

    10500 - Earth and related environmental sciences

Result continuities

  • Project

    <a href="/en/project/GA20-06887S" target="_blank" >GA20-06887S: Seismic waves in heterogeneous anisotropic viscoelastic media</a><br>

  • Continuities

    P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Others

  • Publication year

    2021

  • Confidentiality

    S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Data specific for result type

  • Name of the periodical

    Studia Geophysica et Geodaetica

  • ISSN

    0039-3169

  • e-ISSN

  • Volume of the periodical

    65

  • Issue of the periodical within the volume

    1

  • Country of publishing house

    CZ - CZECH REPUBLIC

  • Number of pages

    6

  • Pages from-to

    53-58

  • UT code for WoS article

    000613192400002

  • EID of the result in the Scopus database

    2-s2.0-85100050429