On the characteristics of high-frequency Rayleigh waves in stratified half-space

Abstract

SUMMARY The Rayleigh wave is dispersive in a stratified half-space. The modes of Rayleigh waves in a stratified half-space are usually defined by the order of the dispersion curves, such as fundamental mode, first higher mode, etc. However, the propagation characteristics of the same mode can be essentially different (e.g. surface wave and trapped wave) at different frequencies, and there is no rule to explain which parts of dispersion curves correspond to the surface wave or trapped wave. Actually, when the frequency is high, by decomposition of dispersion equation, three basic modes (R mode, R-period mode and S-period mode) of Rayleigh waves can be defined, and the mode can be further named by the phase velocities such as R1 mode, R1∼2 mode, etc. By the new definition, the dispersion curves can be divided into several velocity zones, and the modes can then be determined. In this paper, with generalized R/T coefficient method, the eigendisplacements of the three basic modes at high frequencies are studied. The study shows the physical advantage of the new definition of modes: Rayleigh waves of the same mode share the similar characteristics, and the main eigendisplacement characteristics of one mode remain the same when the medium is changed. With the definition of modes, the study makes it possible to know the basic eigendisplacement characteristics of high-frequency Rayleigh waves at different parts of the dispersion curves immediately. Especially, it presents a rule to explain which parts of dispersion curves correspond to the surface wave or trapped wave. Besides, based on the new definition, the modes in the vicinity of the osculation points are analysed. The ‘coupled modes’ that show the characteristics of two different modes simultaneously are found. It is found that the two neighbouring dispersion curves can exchange their corresponding modes of Rayleigh waves sometimes: one mode changes into another one gradually via coupled modes on each dispersion curve. The mode conversion can happen not only between surface wave mode and trapped wave mode, but also between two different trapped wave modes. However, when there is only one mode in the vicinity of the osculation points, there will be no mode conversion.