层状黏弹性介质中Rayleigh波频散曲线“交叉”现象分析

Rayleigh波勘探方法在探测近地表横波速度、动力学特征等环境与工程地球物理领域获得了广泛应用.这种方法以弹性层状介质理论为基础,然而实际介质具有黏弹性,研究面波在层状黏弹性介质中的传播特征,将为近地表面波勘探提供有益帮助.在某些弹性层状介质模型中,例如存在低速夹层和强波阻抗差异地层模型,Rayleigh波相邻两条频散曲线彼此会非常靠近,产生看似彼此"交叉"的现象,即"osculation"现象,但对于黏弹性介质中的这种现象并没有进行相关的研究.本文利用Muller法计算层状黏弹性介质Rayleigh波频散方程,基于层状介质模型中Rayleigh波频散和衰减曲线连续的性质,结合本征位移曲线特征,分析二层黏弹性介质模型中Rayleigh波频散曲线"交叉"现象以及"交叉"点附近的波动特性.结果表明:与弹性介质相比,黏弹性介质中Rayleigh波的波动特性存在明显差异,随着介质对地震波的损耗越来越强,将导致Rayleigh波频散曲线发生"交叉"现象.

Analysis on the cross of Rayleigh-wave dispersion curves in viscoelastic layered media

The Rayleigh-wave method, which is based on the elastic layered system theory, is one of the most widely used techniques in environmental and engineering geophysics to determine shear-wave velocities and dynamic properties. Wave propagation in the Earth, however, has been recognized as viscoelastic. Therefore, it is important to study propagation characteristics of Rayleigh waves in viscoelastic layered media to improve surface wave exploration in the field. It is well known as the osculation phenomenon which causes two adjacent dispersion curves to get very close to each other in certain types of elastic layered models(e.g. in presence of low-velocity layers and strong impedance contrasts).However, there is no related research about this phenomenon in viscoelastic layered media. We introduce the Muller method to calculate the Rayleigh secular function in viscoelastic layered media. Based on the continuity of Rayleigh-wave dispersion and attenuation curves in layered media, we analyze the cross of Rayleigh-wave dispersion curves in normally dispersive two-layer models. Then we study the oscillation characteristics of Rayleigh-wave dispersion curves in the vicinity of "cross" points by eigendisplacement curves. Results demonstrate that the oscillation characteristics of Rayleigh waves have substantial differences in viscoelastic media compared with elastic media. Rayleigh-wave dispersion curves cross each other even in some normal models due to the effects of the increasingly strong dissipation in viscoelastic media, which does not occur in the elastic case.