Abstract
In this paper, the following new results related to Rayleigh waves in incompressible elastic media under the influence of gravity are presented: (i) the exact formulas for the velocity of Rayleigh waves propagating along the free-surface of an incompressible isotropic elastic half-space under the gravity are derived, and (ii) two approximate formulas for the velocity of the Rayleigh waves are established and it is shown that their accuracy is very high. To derive the exact formulas, we use the theory of cubic equation, and to establish the approximate formulas, we employ the best approximate second-order polynomials of the cubic power. The obtained formulas are powerful tools for analyzing the effect of gravity on the propagation of Rayleigh waves and for solving the inverse problem.
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