On approximate analytic expressions for the velocity of Rayleigh waves

An approximate method is presented to determine the velocity of Rayleigh waves. The least-squares approximation is suggested to transform secular equations to quadratic equations. Several explicit expressions for the Rayleigh wave speeds are obtained, and the accuracy of a given approximation is within 0.14%. This method is further generalized to deal with other secular equations including quartic, quintic, or sextic secular equations. An example is given for an incompressible monoclinic half-space with symmetry plane x3 = 0 corresponding to a quartic secular equation, and approximate analytic expressions for the velocity of surface waves are determined explicitly.