Finite-difference Modeling and Wave-field Analysis of Rayleigh Surface Wave in Viscoelastic Media
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摘要: 瑞雷面波经常被用来反演地表浅层横波速度，受到越来越广泛的关注。对瑞雷波的研究一般都基于完全弹性介质，而实际地层更接近黏弹性介质，对黏弹性介质中的瑞雷面波进行模拟更具实际意义。本文采用广义标准线性体模型来描述黏弹性介质，并采用交错网格有限差分法对考虑水平自由表面的黏弹介质进行正演模拟，再与弹性介质中的结果进行对比分析。首先采用非线性最优化算法根据期望常数品质因子直接求取松弛时间来拟合常Q模型，并给出广义标准线性固体的具体算例，实施自由表面条件时采用声学-弹性边界近似法，通过剪切模量不变来考虑自由表面上、下横向应力保持连续的条件。对于非自由表面，采用非分裂的多轴卷积完全匹配层来吸收波场。然后对几种典型的数值模型进行正演模拟计算，数值解与解析解的对比验证了本文方法的准确性与有效性，正演结果的对比表明波场尤其是面波频散会受黏弹性影响，因此有必要在面波勘探中考虑黏弹性因素。Abstract: Rayleigh surface wave has been used to research the character of shallow subsurface widely, and the real geological medium is close to viscoelastic media. This paper models Rayleigh wave in viscoelastic media with planar free surface by using the staggered-grid finite-difference method based on the generalized standard linear body. And we compared the results of the viscoelastic media with the elastic one. In this paper the Levenberg-Marquarat algorithm is adopted to compute the relaxation time to fitting the constant Q model firstly. Acoustic-elastic boundary approximation method is used to implement free surface conditions. The condition that transverse stress on and under the free surface remain continuous is considered by keeping the shear modulus unchanged. And for other boundaries the unsplit multiaxial convolutional perfectly matched layer is chosen to absorb waves. Then the wave fields are calculated in several typical models. The comparisons of numerical and analytical solutions confirm the veracity and validity of the method in this paper. And the computed results indicate that viscoelasticity can influence the surface wave dispersion. So the viscoelastic factors should be considered in the surface wave exploration.
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