Approximate decomposition of the dispersion equation at high frequencies and the number of multimodes for Rayleigh waves

Dispersion curves of multimodes are usually obtained in Rayleigh wave exploration. It is important to describe their characteiistics theoretically. In this paper, the approximate decomposition formula of transfer matrix and the approximate decomposition formula of the dispersion equation in high frequencies are present based on the high frequency approximate feature of the transfer matrix. Then, four basic modes (R-mode, S-mode, R-period-modes and S-period-modes) are defined by using these approximate formulas. Based on the period feature of the dispersion equation, the approximate formulas of the average interval of period-modes curves and also the number of roots (i. e. the number of multimodes) at any frequency and velocity are presented. Based on these results, a numerical root searching method for the dispersion equation is given.