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
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Czech description
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Classification
Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
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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
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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