层状介质中瑞雷面波的频散研究

Research on the dispersion of rayleigh waves in multilayered media

为了提高计算的速度和稳定性以及发现不同算法之间的联系 ,将位移应力矢量的传递矩阵 T 的元素表示为实数量及无量纲量的形式 ,发现柱面瑞雷面波与平面瑞雷面波的频散方程形式可以完全一样 ;将Menke方法的传递矩阵F表示为三个五阶矩阵的乘积 ,发现Menke方法与δ矩阵法的频散方程形式可以完全一样 ;最后提出了一种快速稳定的标量传递算法 ,此算法进一步提高了计算速度 .

The elements of transfer matrix T of the displacement-stress vector is written with real and dimensionless quantities, to improve the speed and stability of the computation and to discover the relationship of some algorithms, by which it is then discovered that plane Rayleigh wave and cylindrical Rayleigh wave have exactly the same dispersion equation. The transfer matrix of F of Menke-method is written as the product of three five-order matrixes, and it is then discovered that Menke-method and δ-method have exactly the same dispersion equation; A fast and stable algorithm named scalar-transfer algorithm is deduced to further improve the computational speed.