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The extra roots of the Rayleigh equation for an elastic<br />halfspace contribute to the solution only for large enough values of the<br />Poisson coefficient (a > 0.309). One of them corresponds to leaking modes<br />with the phase velocity less than the velocity of the longitudinal wave.<br />A similar wave with distinct dispersion may exists in the case where an<br />elastic halfspace is covered by a thin layer with lower velocities of elastic<br />waves. The thickness of a layer should be not too small in comparison<br />with the wave length.