分层半空间中Love表面波的精细方法(英文)

Precise method for Love surface waves in layered half-space

精细积分法是求解线性常微分方程两端边值问题和初值问题的精细算法．应用精细积分法(PIM)和扩展Wittrick-Williams(W-W)算法求解了横观各向同性、分层半空间中的Love表面波问题．岩层是由分层介质置于半无限空间上组成．Love表面波对应于波数-频率域线性常微分方程的本征值问题．利用本征值计数技术,扩展W-W算法可以不遗漏地找到所有本征值,得到计算机精度意义下的精确解．

The PIM (precise integration method) is a precise method for solving the linear ODEs (ordinary differential equations) with two-point boundary value conditions or initial value conditions. The Love surface waves propagating in a transversely isotropic and layered half-space is studied by using the PIM and the extended Wittrick-Williams (W-W) algorithm. The solid is multi-layered and located above a semi-infinite space. The solution of Love surface waves is an eigenvalue problem of ODEs in the frequency-wavenumber domain. And by means of the eigenvalue counting technique, the extended W-W algorithm can be developed to find all eigenvalues without missing anyone. The method presented is exact in the sense so that it depends only on the precision of the computer used.