Tracing real-valued reference rays in anisotropic viscoelastic media

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F22%3A10452103" target="_blank" >RIV/00216208:11320/22:10452103 - isvavai.cz</a>

Výsledek na webu

<a href="https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=KErrzdo2_5" target="_blank" >https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=KErrzdo2_5</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1007/s11200-022-0906-6" target="_blank" >10.1007/s11200-022-0906-6</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Tracing real-valued reference rays in anisotropic viscoelastic media

Popis výsledku v původním jazyce

The eikonal equation in an attenuating medium has the form of a complex-valued Hamilton-Jacobi equation and must be solved in terms of the complex-valued travel time. A very suitable approximate method for calculating the complex-valued travel time right in real space is represented by the perturbation from the reference travel time calculated along the real-valued reference rays to the complex-valued travel time defined by the complex-valued Hamilton-Jacobi equation. The real-valued reference rays are calculated using the reference Hamiltonian function. The reference Hamiltonian function is constructed using the complex-valued Hamiltonian function corresponding to a given complex-valued Hamilton-Jacobi equation. The ray tracing equations and the corresponding equations of geodesic deviation are often formulated in terms of the eigenvectors of the Christoffel matrix. Unfortunately, a complex-valued Christoffel matrix need not have all three eigenvectors at an S-wave singularity. We thus formulate the ray tracing equations and the corresponding equations of geodesic deviation using the eigenvalues of a complex-valued Christoffel matrix, without the eigenvectors of the Christoffel matrix. The resulting equations for the real-valued reference P-wave rays and the real-valued reference common S-wave rays are applicable everywhere, including S-wave singularities.

Název v anglickém jazyce

Tracing real-valued reference rays in anisotropic viscoelastic media

Popis výsledku anglicky

The eikonal equation in an attenuating medium has the form of a complex-valued Hamilton-Jacobi equation and must be solved in terms of the complex-valued travel time. A very suitable approximate method for calculating the complex-valued travel time right in real space is represented by the perturbation from the reference travel time calculated along the real-valued reference rays to the complex-valued travel time defined by the complex-valued Hamilton-Jacobi equation. The real-valued reference rays are calculated using the reference Hamiltonian function. The reference Hamiltonian function is constructed using the complex-valued Hamiltonian function corresponding to a given complex-valued Hamilton-Jacobi equation. The ray tracing equations and the corresponding equations of geodesic deviation are often formulated in terms of the eigenvectors of the Christoffel matrix. Unfortunately, a complex-valued Christoffel matrix need not have all three eigenvectors at an S-wave singularity. We thus formulate the ray tracing equations and the corresponding equations of geodesic deviation using the eigenvalues of a complex-valued Christoffel matrix, without the eigenvectors of the Christoffel matrix. The resulting equations for the real-valued reference P-wave rays and the real-valued reference common S-wave rays are applicable everywhere, including S-wave singularities.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10500 - Earth and related environmental sciences

Projekt

<a href="/cs/project/GA20-06887S" target="_blank" >GA20-06887S: Seismické vlny v nehomogenních anizotropních viskoelastických prostředích</a><br>

Návaznosti

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

Rok uplatnění

2022

Kód důvěrnosti údajů

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

Název periodika

Studia Geophysica et Geodaetica

ISSN

0039-3169

e-ISSN

1573-1626

Svazek periodika

66

Číslo periodika v rámci svazku

3-4

Stát vydavatele periodika

CZ - Česká republika

Počet stran výsledku

21

Strana od-do

124-144

Kód UT WoS článku

000883430500003

EID výsledku v databázi Scopus

2-s2.0-85141995162