Rayleigh波的频散方程高频近似分解和多模式激发数目

对于在Rayleigh波勘探中经常提取到的多模式频散曲线，如何在理论上对其特征进行描述是一个很有意义的问题. 本文根据Rayeigh波频散方程中传递矩阵具有的高频近似特征，提出了传递矩阵的高频近似分解公式，据此导出了频散方程的高频近似分解公式，并在此基础上，定义了Rayleigh波的4种基本模式(R模、S模、R型周期模和S型周期模). 根据频散方程具有的周期性特征，给出了周期模频散曲线之间的平均间隔近似公式，以及在任意频率和相速度段内频散方程根的数目（即多模式的激发数目）的预测公式. 在这些结果的基础上，本文最后提出了频散方程数值搜根的一种新方法.

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 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.