Comptes Rendus
no. 1
On the existence of the low-frequency surface waves in a porous medium
[Sur l'existence des ondes de surface basse fréquence en milieux poreux]

Présenté par : Évariste Sanchez-Palencia

Inna Edelman1
1 Weierstrass Institute for Applied Analysis and Stochastics, Mohrenstr. 39, 10117 Berlin, Germany
Comptes Rendus. Mécanique, Volume 332 (2004) no. 1, pp. 43-49.

La nature et la propagation des ondes de surface engendrées par la surface libre d'un milieu poreux sont étudiées en basse fréquence : nous mettons en évidence deux types d'ondes de surface : l'onde de Rayleigh et l'onde de Stoneley. Cette dernière existe pour une gamme limitée de nombres d'onde. Le comportement de bifurcation de l'onde de Stoneley et de l'onde lente de Biot (P2) dépendant du nombre d'onde est mis en évidence. Il est aussi prouvé qu'à l'intérieur du domaine d'existence du nombre d'onde, l'onde de Stoneley ne peut pas apparaı̂tre pour certaines valeurs de paramètres élastiques de la phase solide. Les formules asymptotiques des vitesses de phase des ondes de surface sont également présentées.

The existence and propagation of the surface waves at a vacuum/porous medium interface are investigated in the low frequency range. Two types of surface waves are shown to be possible: the generalized Rayleigh wave, which always exists, and the Stoneley wave, which exists for a limited range of wave numbers. Moreover, within the k-domain of existence the Stoneley wave cannot appear for certain values of elastic parameters of the solid phase. The bifurcation behavior of both the Stoneley wave and the Biot (P2) bulk wave, depending on the wave number, is revealed. The asymptotic formulas for the phase velocities of the surface waves are derived.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crme.2003.11.004
Keywords: Porous media, Waves, Asymptotic analysis, Bifurcation, Interface
Mot clés : Milieux poreux, Ondes, Analyse asymptotique, Bifurcation, Interface
Inna Edelman 1

1 Weierstrass Institute for Applied Analysis and Stochastics, Mohrenstr. 39, 10117 Berlin, Germany 
@article{CRMECA_2004__332_1_43_0,
     author = {Inna Edelman},
     title = {On the existence of the low-frequency surface waves in a porous medium},
     journal = {Comptes Rendus. M\'ecanique},
     pages = {43--49},
     publisher = {Elsevier},
     volume = {332},
     number = {1},
     year = {2004},
     doi = {10.1016/j.crme.2003.11.004},
     language = {en},
}
TY  - JOUR
AU  - Inna Edelman
TI  - On the existence of the low-frequency surface waves in a porous medium
JO  - Comptes Rendus. Mécanique
PY  - 2004
SP  - 43
EP  - 49
VL  - 332
IS  - 1
PB  - Elsevier
DO  - 10.1016/j.crme.2003.11.004
LA  - en
ID  - CRMECA_2004__332_1_43_0
ER  - 
%0 Journal Article
%A Inna Edelman
%T On the existence of the low-frequency surface waves in a porous medium
%J Comptes Rendus. Mécanique
%D 2004
%P 43-49
%V 332
%N 1
%I Elsevier
%R 10.1016/j.crme.2003.11.004
%G en
%F CRMECA_2004__332_1_43_0
Inna Edelman. On the existence of the low-frequency surface waves in a porous medium. Comptes Rendus. Mécanique, Volume 332 (2004) no. 1, pp. 43-49. doi : 10.1016/j.crme.2003.11.004. https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.1016/j.crme.2003.11.004/

[1] Lord Rayleigh On waves propagated along the plane surface of an elastic solid, Proc. London Math. Soc., Volume 17 (1885), pp. 4-11

[2] R. Stoneley Elastic waves at the surface of separation of two solids, Proc. Roy. Soc. London Ser. A, Volume 106 (1924), pp. 416-428

[3] L.M. Brekhovskikh Waves in Layered Media, Academic Press, New York, 1960

[4] P.B. Nagy Acoustics and ultrasonics, Experimental Methods in the Physical Sciences, Academic Press, 1999, pp. 161-221

[5] I. Edelman; K. Wilmanski Asymptotic analysis of surface waves at vacuum/porous medium and liquid/porous medium interfaces, Continuum Mech. Thermodyn., Volume 14 (2002) no. 1, pp. 25-44

[6] M.A. Biot Mechanics of deformation and acoustic propagation in porous media, J. Appl. Phys., Volume 33 (1962) no. 4, pp. 1482-1498

[7] K. Wilmanski Lagrangean model of two-phase porous material, J. Non-Equilib. Thermodyn., Volume 20 (1995), pp. 50-77

[8] I. Edelman Bifurcation of the Biot slow wave in a porous medium, J. Acoust. Soc. Am., Volume 114 (2002) no. 1, pp. 90-97

[9] I. Edelman Waves on boundaries of porous media, Phys. Dokl., Volume 46 (2001), pp. 517-521

[10] I. Edelman, On the bifurcation of the Biot slow wave in a porous medium, WIAS, Preprint 738 (2002).2

Cité par Sources :

Commentaires - Politique

Ces articles pourraient vous intéresser

Is subsurface geophysics as seismic and acoustic investigations a rescue to groundwater flow inversion?

Frederick Delay; Jean-Luc Mari; Gilles Porel; ...

C. R. Géos (2023)

Source distribution of ocean microseisms and implications for time-dependent noise tomography

Sharon Kedar

C. R. Géos (2011)

Azimuthal anisotropy using shear dipole sonic: insights from the AIG 10 well, Corinth Rift Laboratory

Romain Prioul; Thomas Plona; Michael Kane; ...

C. R. Géos (2004)