Fundamental and singular solutions of Lamé equations for media with arbitrary elastic anisotropy

Abstract

Abstract. Fundamental and singular solutions of Lamé equations for media with arbitrary elastic anisotropy are constructed on the basis of multipolar expansions (expansions in spherical harmonics) of symbols and the corresponding operators. Theorems of convergence are formulated. A posteriori error estimates are presented.

Seismic Barriers for Protection Against Surface and Headwaves: Multiple Scatters and Metamaterials

“…Due to the higher requirements for computational resources, spatial models are used much less frequently to solve the Lamb problem with a barrier, see [41]. In the case when it is necessary to take into account the elastic anisotropy of a half-plane or half-space, the methods of boundary integral equations can be used to solve the Lamb problems with the construction of the corresponding fundamental solutions [42][43][44].…”

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“…Introducing N C :D C 0 D C C 1 D c , one readily computes Z where in the first line we used (30), in the second line the G-equivariance of C i was taken into account, and the third line is transformed on the basis of the substitution y D Q T x. Furthermore, the defining Equation (14) forˆE sh S .…”

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