Analysis of various amounts charactering scattering phenomena for the elastic surface waves

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The aim of this research is analyzing the more detailed character of a surface wave based on the formulation of scattering theory to the surface wave by the research representatives of this research. One of the quantity which describes the scattering phenomena of elastic surface waves is in the component of the physical quantity called a "scattering kernel. " Existence of a scattering kernel is shown and the representation formula of it is obtained. The representation formula obtained above is represented by using the generalized eigenfunctions to a free system and a perturbed system. From this formula, the concrete representation of the part describing the scattering phenomena of an elastic surface wave among scattering kernels is obtained. By using this representation, how to interpret scattering of a surface wave as the scattering problem of the hyperbolic equation on an boundary surface is considered. The obtained results in this research are as follows:(1) The concrete representat … More ion linking directly to the phenomenon of propagation of surface waves is given.(2) An approximate solution of the Rayleigh wave for pulling out the information about the singularity of a scattering kernel is constructed.(3) Study for pulling out the information about singularities of the scattering kernel is performed by using the approximate solution. The similarity from a viewpoint of the influence which the singularity of waves has on a scattering kernel is shown among various scattering theories for hyperbolic equations.(4) In steps performing (3), oscillatory integrals of more complicated forms than those appeared in the previous work appeared. About this, more precise estimates than those in the previous works are obtained.The "representation formula of the scattering kernel" obtained in this research includes the contents which renew interpretation of the similar formulae obtained until now. Moreover, through analyzing (1)--(4), it become clear that analysis peculiar to scattering of an elastic surface wave is needed. Less