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We study the propagation of transient waves under the action of a verticalstep point load on the surface of a half-space filled by a block medium. Theblock medium is modeled by a square lattice of masses connected by springs inthe directions of the axes x, y, and in the diagonal directions. The problem issolved by two methods. Analytically, we obtain asymptotic solutions in thevicinity of the Rayleigh wave at large time intervals. Numerically, we obtain asolution for any finite time interval. We compare these solutions with eachother and with the solution to the Lamb problem for an elastic medium.

The discrete Lamb problem: Elastic lattice waves in a block medium