It is shown that in the layered media with weakened interfaces the resonance waves (Kr-waves) are arose. Such waves have the very characteristic frequencies and a lot of other cinematic and dynamic features distinguish them from the well-known Love and Rayleigh type waves. The comparison of the theoretical results with experimental seismic data indicates that Kr-waves can be formed in the real geological section. We show theoretically and numerically that in a sedimentary basin of finite lateral extent horizontal Kr-wave can be trapped and resonate. This wave has a number of interesting properties: wave spectrum has resonance frequency; wave group velocity is equal to an intermediate value between shear and longitudinal velocities; attenuation of wave increases when the frequency varies from the resonance value.


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