广义反射-透射系数算法的无量纲化

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.

Making the calculation of generalized reflection-transmission coefficients dimensionless

The calculation of dispersion curves of Rayleigh wave in horizontal multilayered medium has been a concerned subject. Chen's generalized reflec-tion-transmission coefficient method has good accuracy and stability, but in the calculation of matrix E, which plays a decisive role in the algorithm, has dimen-sional elements, and the different elements have an order of magnitude differ-ence. 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 ε of the largest el-ement over the smallest in the matrix E using the improved and the original al-gorithm, 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 im-proved approach has higher accuracy. It is expected that the improved general-ized reflection-transmission coefficient method is more applicable to the compu-tation of Rayleigh wave dispersion.