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

作者：Fan You Hua^*; Chen Xiao Fei; Liu Xue Feng; Liu Jia Qi; Chen Xiao Hong

来源：Chinese Journal of Geophysics, 2007, 50(1): 233-239.

• Rayleigh waves
• dispersion
• multilayered media
• multimode

Dispersion curves of multimodes are usually obtained in Rayleigh wave exploration. It is important to describe their characteristics 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.

• 出版日期2007-1
• 单位中国石油大学（北京）; 哈尔滨工业大学; 北京大学