Abstract: In regularly layered elastic media where the shear velocity of layer increases with increasing layer depth, the surface wave-fields are dominated by Rayleigh waves of the fundamental mode. Thus, it is very important for calculation of the dispersion curve of the fundamental mode in the surface wave tests. The matrix methods are often used to calculate the dispersion curves of Rayleigh waves in the layered elastic media. The dispersion curves could be obtained from the determinant of the matrix. However, the determinant must be solved using root searching techniques. To avoid the complex algorithm, based on the expression for calculation of the fundamental mode dispersion(Aki & Richards), the phase velocity is assumed to be the root-mean square of the shear wave velocity and/or Rayleigh wave velocity of layer weighted by the integral of the displacement shape functions of the fundamental mode. It can be known that the displacement shape functions of the fundamental mode in regularly layered media are highly correlated to those in the homogenous half space with the properties equal to the first layer. The displacement shape functions in the regularly layered media can be evaluated by calibrating the displacement shape functions in the homogenous half space with the shear wave velocity contrasts between layers. It is shown from the results that the algorithm of the proposed approach is simple compared to the matrix methods, and the accuracy is higher than that of the empirical half wavelength method.

Key words: Rayleigh wave, fundamental mode, half wavelength method, displacement shape function, dispersion