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 A model of the Earthquake surface waves

 A model of the Earthquake surface waves. V.K.Ignatovich. FLNP JINR. STI2011 June 8. This report is along the papers. V.K. Ignatovich and L.T.N. Phan. Those wonderful elastic waves. Am.J.Phys. v. 77, n. 12, pp. 1093-I17, (2009). N. Nikitin, T.I. Ivankina, and V.K. Ignatovich

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 A model of the Earthquake surface waves

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  1.  A model of the Earthquake surface waves V.K.Ignatovich. FLNP JINR STI2011 June 8

  2. This report is along the papers V.K. Ignatovich and L.T.N. Phan. Those wonderful elastic waves. Am.J.Phys. v. 77, n. 12, pp. 1093-I17, (2009) • N. Nikitin, T.I. Ivankina, and V.K. Ignatovich • The Wave Field Patterns of the Propagation • of Longitudinal and Transverse Elastic Waves • in Grain-Oriented Rocks • Physics of the Solid Earth, • 2009, v. 45, n. 5, pp. 424-436 And a little bit more

  3. A theory of elastic wavesIn isotropic media Usually solution of this equation is represented as a sum is a scalar potential is a vector potential however why not to do differently?

  4. All this is trivial. Reflection from interfaces is less trivial

  5. Reflection from a free surface At such a critical angle ALongitudinal Surface wave appears

  6. Calculations of reflection amplitudes

  7. -- angle of incidence

  8. V.K. Ignatovich. A proposal of a UCN experiment to check an earthquake waves model. Europhys. Lett. 92 (69002-p1-4) 2010. Tomas Lokajicek, Vladimir Rudajev

  9. Experiments byLokajicek Tomas, Rudajev Vladimir

  10. steel So, to observe an effect we need a material with ct/cl>0.6

  11. Anisotropic media -- a set of phenomenologocal constants In general 21 constants But anisotropy means a vector and an additional constant. So we can define

  12. All we need is a linear vector algebra

  13. It is important to saythat we cannot exclude xby averaging of values over alldirections of propagation, because all the values depend on

  14. Polarization of waves

  15. In an anisotropic medium propagate plane waves of only 3 modes • transverse with Аt~[kxa] and ct2=ct0(1+x) • quasi transverse withАqt in the plane [k,a] • quasi longitudinal withАql in the plane [k,a] transverse quasi longitudinal quasi transverse

  16. Reflection of a quasi transverse wave from a free surface One can find an analytical solution

  17. f of two reflected waves quasi longitudinal wave becomes surface one at

  18. It seems possible to find such a direction of vector athat for given elastic parameters the amplitude of thesurface longitudinal wave becomes maximal. For instance

  19. Summary • Reflection of elastic waves from free surfaces is accompanied by beam splitting. • At some critical angle of the incident shear wave polarized in the incidence plane a longitudinal surface wave is created. • Its amplitude and energy can be large, and its polarization along the surface is alike to devastating earthquake waves. • For observation of such waves the materials with ratio ct/cl>0.6 are needed.

  20. Thanks

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