Siberian Federal University

The problem of the Rayleigh wave scattering on a three-dimensional deterministic near- surface mass density inhomogeneity of isotropic solid is solved in the Rayleigh-Born approximation of the perturbation theory in inhomogeneity amplitude. The new topological laws of the long-wavelength scattering are established by means of the Rayleigh series arbitrary number of terms zeroing for intensity of the scattered Rayleigh wave due to topological characteristics zeroing, i.e., through the inhomogeneity structure special form selection. In the result the frequency dependence of intensity can have the next form I ∼ !5+2n, where n = 0; 1; 2; : : : . It is found,that topological laws, i.e., inhomogeneity structures topology, create the basis of the linear independent amplitudes of scattering, and so strongly influence as well the scattering angular distribution form in the Rayleigh limit. The scattering, satisfying these laws, violating and expanding the Rayleigh law and conception of scattering, when n = 0, is named meta-Rayleigh scattering in the present work. The new, as compared to scattering on a roughness, physical phenomenon of meta-Rayleigh modulation of the boundary conditions on a free surface by a vertical structure of inhomogeneity is obtained as well as meta-Rayleigh modulation of the frequency dependence of scattering, caused by the Rayleigh wave surface localization. This phenomenon, but not the localization, enables to create one or two arbitrary forbidden angles of scattering, symmetrical with respect to the direction of incident wave propagation, or to zero of the arbitrary number of the Rayleigh series first terms, if the number of the forbidden angles of scattering, defined beforehand, is more than two. So, violating and manipulating the Rayleigh angular isotropy of scattering and the angular spectrum modelling is possible due to vertical structure of inhomogeneity, while the wave-vector, transmitted in a scattering, as well as plane of kinematics of scattering, is orthogonal to its direction. It is obtained, that inhomogeneity topological symmetry dimension strongly influences the laws of the Rayleigh wave long- wavelength scattering. Topological properties of the Prouhet-Thue-Morse sequence, as inhomogeneity structure, are obtained first