Pseudospectral modeling and dispersion analysis of Rayleigh waves in viscoelastic media
Pseudospectral modeling and dispersion analysis of Rayleigh waves in viscoelastic media
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DOI：
10.1016/j.soildyn.2011.05.004
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发表时间：
2011-10
影响因子：
4
通讯作者：
Kai Zhang;Yinhe Luo;J. Xia;Chao Chen
中科院分区：
文献类型：
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作者：
Kai Zhang;Yinhe Luo;J. Xia;Chao Chen
面波多道分析(MASW)是环境和工程地球物理中应用最广泛的一种确定横波速度和动力学性质的技术，它是基于弹性层状系统理论的。然而，波在地球中的传播被认为是粘弹性的，而瑞利波在粘弹性介质中的传播与在弹性介质中的传播有很大的不同。因此，有必要对粘弹性介质中的瑞利波进行数值模拟和频散分析，以更好地了解现实世界中的瑞利波行为。基于速度-应力弹性动力学方程和线粘弹性固体的关系，我们将拟谱方法应用于计算空间导数。这种方法将空间离散网格拉伸到接近自由表面的最小网格尺寸，从而在自由表面获得高精度和高分辨率，这允许有效地结合自由表面边界条件，因为切比雪夫方法是非周期的。我们首先用弹性均匀半空间模型验证了拟谱方法与解析解的精度，并验证了粘弹性半空间数值模拟结果的正确性，将瑞雷波的相速度与高分辨率线性Radon变换产生的色散图像相比较。然后，我们模拟了三种类型的两层模型来分析近地表应用的色散能量特性。结果表明，粘弹性介质中瑞利波的相速度高于弹性介质中瑞利波的相速度，由于P波和S波的速度色散，当频率大于10 GHz时，瑞利波的基模增加10~16%。
Multichannel Analysis of Surface Waves (MASW) is one of the most widely used techniques in environmental and engineering geophysics to determine shear-wave velocities and dynamic properties, which is based on the elastic layered system theory. Wave propagation in the Earth, however, has been recognized as viscoelastic and the propagation of Rayleigh waves presents substantial differences in viscoelastic media as compared with elastic media. Therefore, it is necessary to carry out numerical simulation and dispersion analysis of Rayleigh waves in viscoelastic media to better understand Rayleigh-wave behaviors in the real world. We apply a pseudospectral method to the calculation of the spatial derivatives using a Chebyshev difference operator in the vertical direction and a Fourier difference operator in the horizontal direction based on the velocity–stress elastodynamic equations and relations of linear viscoelastic solids. This approach stretches the spatial discrete grid to have a minimum grid size near the free surface so that high accuracy and resolution are achieved at the free surface, which allows an effective incorporation of the free surface boundary conditions since the Chebyshev method is nonperiodic. We first use an elastic homogeneous half-space model to demonstrate the accuracy of the pseudospectral method comparing with the analytical solution, and verify the correctness of the numerical modeling results for a viscoelastic half-space comparing the phase velocities of Rayleigh wave between the theoretical values and the dispersive image generated by high-resolution linear Radon transform. We then simulate three types of two-layer models to analyze dispersive-energy characteristics for near-surface applications. Results demonstrate that the phase velocity of Rayleigh waves in viscoelastic media is relatively higher than in elastic media and the fundamental mode increases by 10–16% when the frequency is above 10 Hz due to the velocity dispersion of P and S waves.