hal-00549622
https://polytechnique.hal.science/hal-00549622
https://polytechnique.hal.science/hal-00549622/document
https://polytechnique.hal.science/hal-00549622/file/10-GJI-SH.pdf
doi:10.1111/j.1365-246X.2010.04688.x
[INSU] INSU - Institut National des Sciences de l'Univers
[UNIV-PARIS7] Université Denis Diderot - Paris VII
[X] Ecole Polytechnique
[INSTITUT-TELECOM] Institut Mines Télécom
[ENSMP] MINES ParisTech
[AFRIQ] HAL-Francophonie, Afrique et océan indien
[CNRS] CNRS - Centre national de la recherche scientifique
[IPGP] Institut de Physique du Globe de Paris
[X-LMS] Laboratoire de Mécanique des Solides (LMS)
[X-DEP] Polytechnique
[X-DEP-MECA] Département de mécanique
[ENSMP_LMS] Mécanique des solides (LMS)
[PARISTECH] ParisTech
[PSL] Université Paris sciences et lettres
[ENSMP_DEP_MM] Département Mécanique et Matériaux
[SORBONNE-UNIVERSITE] Sorbonne Université
[UNIV-PARIS] Université Paris Cité
[ENSMP-PSL] MINES ParisTech - École nationale supérieure des mines de Paris - PSL
[SU-TI] Sorbonne Université - Texte Intégral
[ANR] ANR
[ALLIANCE-SU] Alliance Sorbonne Université
2-D non-periodic homogenization of the elastic wave equation: SH case
Guillot, Laurent
Capdeville, Yann
Marigo, Jean-Jacques
[PHYS.MECA.SOLID] Physics [physics]/Mechanics [physics]/Solid mechanics [physics.class-ph]
[SPI.MECA.SOLID] Engineering Sciences [physics]/Mechanics [physics.med-ph]/Solid mechanics [physics.class-ph]
ART
In the Earth, seismic waves propagate through 3-D heterogeneities characterized by a large variety of scales, some of them much smaller than their minimum wavelength. The costs of computing the wavefield in such media using purely numerical methods, are very high. To lower them, and also to obtain a better geodynamical interpretation of tomographic images, we aim at calculating appropriate effective properties of heterogeneous and discontinuous media, by deriving convenient upscaling rules for the material properties and for the wave equation. To progress towards this goal we extend our successful work from 1-D to 2-D. We first apply the so-called homogenization method (based on a two-scale asymptotic expansion of the field variables) to model antiplane wave propagation in 2-D periodic media. These latter are characterized by short-scale variations of elastic properties, compared to the smallest wavelength of the wavefield. Seismograms are obtained using the 0th-order term of this asymptotic expansion, plus a partial first-order correction. Away from boundaries, they are in excellent agreement with solutions calculated at a much higher computational cost, using spectral elements simulations in the reference media. We then extend the homogenization of the wave equation, to 2-D non-periodic, deterministic media.
2010-05-31
2010-12-22
en
Geophysical Journal International
Oxford University Press (OUP)