Research on the cross of the dispersion curves of Rayleigh waves and multi-modes coupling phenomenon
LIU Xue-Feng~1 , FAN You-Hua~(1,*), CHEN Xiao-Fei~21 Harbin Institute of Technology Shenzhen Graduate School,Shenzhen 518055, China2 School of Earth and Space Sciences , University of Science and Technology of China , Hefei 230026, China
Rayleigh wave, which used to be seen as the interferential wave, can be used in the inversion of the structure near the surface. It is also very meaningful in geophysical exploration, oil exploration and so on. There will be some dispersion curves that seem to cross each other for multilayered medium containing a low velocity layer. However, there is no systematic research about the phenomenon. In fact, it can be seen that some seemingly crossing dispersion curves do not actually cross. Changing the thickness and the S-wave velocity of the low velocity layer, we found that the more evident the low velocity is (i. e. the low velocity layer is thicker or has a lower S-wave velocity) , the harder the dispersion curves to cross. Fan et al found that there are four basic modes of Rayleigh wave dispersion curves, so there are two different modes in the area that dispersion curves seem to cross. In this paper, the 'cross' phenomenon in the area that has both R mode and S_2 mode is analyzed. First, with vertical eigen displacement curves, it can be found that the energy of vibration of R mode wave is mainly near the surface of the medium and decreases quickly with depth, forms surface wave while the energy of vibration of S_2 mode waves is mainly in the second layer, forms guide wave. Eigen displacement curves show that some Rayleigh waves near the 'cross point' have both the characters of R mode and S_2 mode, so that is a kind of coupled mode. From the research of given model, we found that in the area near the 'cross point', if the two dispersion curves do not cross, transformation between R mode and S_2 mode via coupled mode happens to the mode on each curve, we call the phenomenon 'coupling phenomenon' of Rayleigh wave mode in this paper. If the two dispersion curves cross, the mode corresponding to the same dispersion curve is almost the same, though there is some coupled mode very close to the cross point, we say the modes do not couple. The content of this paper can be used as a reference in the inversion of the structure with low velocity layer.