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 I17, (2009) A.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 And a little bit more

A theory of elastic waves In 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?

All this is trivial. Reflection from interfaces is less trivial

Reflection from a free surface At such a critical angle A Longitudinal Surface wave appears

Calculations of reflection amplitudes

-- angle of incidence

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

Experiments by Lokajicek Tomas, Rudajev Vladimir

steel So, to observe an effect we need a material with c t /c l >0.6

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

All we need is a linear vector algebra

It is important to say that we cannot exclude  by averaging of values over all directions of propagation, because all the values depend on

Polarization of waves

In an anisotropic medium propagate plane waves of only 3 modes transverse with А t ~[k x a] and c t 2 =c t0 (1+  ) quasi transverse with А qt in the plane [k,a] quasi longitudinal with А ql in the plane [k,a] quasi longitudinal quasi transverse transverse

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

 of two reflected waves quasi longitudinal wave becomes surface one at

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

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 c t /c l >0.6 are needed.

Thanks