ELASTIC-WAVES IN DISCONTINUOUS MEDIA - 3-DIMENSIONAL SCATTERING

This report contains an exact study of elastic wave propagation and it s scattering in discontinuous media where hard reflectors are onionlik e sets of surfaces. In order to reformulate the problem as a finite se t of boundary integral equations, the wave motion between reflectors i s represented by means of elastic potentials which involve vectorial d ensities on the surfaces. In the external medium, an outgoing asymptot ic condition generalizes the Silver-Muller (and the Sommerfeld) condit ion to the case of coupled waves (S and P waves) moving with different velocities. The uniqueness of the Green's function, which guarantees the uniqueness of the direct problem solution, is proven. For any inci dent wave and arbitrary number of surfaces, the transmission and scatt ering problems are studied, with and without the simplification obtain ed by assuming constant Poisson ratios. According to the parameter ran ges, the equations which are obtained are well posed, either as second kind Fredholm equations, or because they reduce to the inverse of the sum of the identity operator and a ''small norm'' bounded operator. T he results can be used to describe rigorously the three-dimensional sc attering of elastic waves in the frequency domain for any kind of inci dent wave function (P,S,...) as well as the response to a localized so urce.