广义反射-透射系数算法的无量纲化

Making the calculation of generalized reflection-transmission coefficients dimensionless

水平层状介质中瑞利波频散曲线的计算一直是受关注的问题.陈晓非提出的广义反射-透射系数方法虽然具备很好的精确性和稳定性,但是算法中起决定作用的矩阵E存在有量纲元素,并且不同元素之间的数量级差异很大.本文作者通过把广义反射-透射系数算法无量纲化,得到了简洁的瑞利波频散函数的公式体系.分别计算了改进后算法和原算法中矩阵E的最大模元素与最小模元素的比值ε,发现前者的矩阵E中最大模元素与最小模元素最多只相差1个数量级,而后者的矩阵E中最大模元素与最小模元素之间最大达11个数量级的差异,尽管后者可以通过选取变量的单位减小ε的值,但新算法精度更高,从而完善了利用广义反射-透射系数方法求解瑞利波频散曲线问题的理论和算法.

The calculation of dispersion curves of Rayleigh wave in horizontal multilayered medium has been a concerned subject. Chen＇s generalized reflection-transmission coefficient method has good accuracy and stability, but in the calculation of matrix E, which plays a decisive role in the algorithm, has dimensional elements, and the different elements have an order of magnitude difference. By making the generalized reflection-transmission coefficient calculation dimensionless, we obtained a more concise formula system for computing the dispersion function of Rayleigh wave. We calculated the ratio e of the largest element over the smallest in the matrix E using the improved and the original algorithm, respectively. We found that in the improved algorithm the elements of matrix E have at most one order of magnitude difference, while in the original algorithm the difference reaches to eleven orders. This indicates that the improved approach has higher accuracy. It is expected that the improved generalized reflection-transmission coefficient method is more applicable to the computation of Rayleigh wave dispersion.