Research on the Cross of the Dispersion Curves of Rayleigh Waves and Multi‐Modes Coupling Phenomenon

Abstract

AbstractRayleigh wave, which used to be seen as the interferential wave, can be used in the inversion for 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 in multi‐layered 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 are actually not crossing. 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 S2 mode is analyzed. First, with vertical eigendisplacement 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 and forms a surface wave; while the energy of vibration of S2 mode waves is mainly in the second layer and forms a guide wave. Eigendisplacement curves show that some Rayleigh waves near the ‘cross point' have both the characters of R mode and S2 mode, so they are a kind of coupled mode. From the research with a 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 S2 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 are crossing, 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 for the structure with low velocity layer.