Analysis of Surface Waves in Saturated Layered Poroelastic Half-Spaces Using the Thin Layer Method

Abstract

There are multiple modes of surface waves in saturated layered poroelastic half-spaces. The phase velocity and the attenuation of the modes are frequency dependent. The frequency behaviour of the modes can be studied using the layer transfer, stiffness and the transmission/reflection matrix methods. However, it is very difficult to find the complex roots of the determinants because the entries of the matrices involve the complex exponential functions of the wavenumber and the thickness of layer. To overcome this difficulty, the entries in the matrix are expressed in the form of algebraic functions using the thin layer method. Thus, the eigenvalues and eigenvectors can be easily solved using the matrix decomposition techniques instead of the root-searching ones. Some of the eigenvalues correspond to the wavenumbers of the surface waves, and can be picked out based on the characteristics of the surface waves. The frequency behaviour, variations of the pore pressure and the skeleton’s displacements with the depth can be then investigated from the corresponding eigenvalues and eigenvectors, respectively. The method is verified by comparing the analytical and the discrete results in the saturated poroelastic half-space with the permeable surface. The method is applied to appreciate the effects of an impermeable surface on Rayleigh waves (R-waves) and the existence of Stoneley waves in the poroelastic half-space. The frequency behaviour of Rayleigh waves in three typical layered poroelastic half-spaces is also analyzed.