Volume 12, Issue 2
On the Comparison of Properties of Rayleigh Waves in Elastic and Viscoelastic Media

Yangyang He, Jinghuai Gao & Zhangxin Chen

Int. J. Numer. Anal. Mod., 12 (2015), pp. 254-267

Published online: 2015-12

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  • Abstract
Dispersion properties of Rayleigh-type surface waves are widely used in environmental and engineering geophysics to image and characterize a shallow subsurface. In this paper, we numerically study the Rayleigh-type surface waves and their properties in 2D viscoelastic media. A finite difference method in a time-space domain is proposed, with an unsplit convolutional perfectly matched layer (C-PML) absorbing boundary condition. For two models that have analytical expressions of wave fields/dispersion curves, we calculate their wave fields and compare the analytical and numerical solutions to demonstrate the validity of this method. For the case where a medium has a high Poisson's ratio, say 0.49, traditional finite difference methods with a PML boundary condition are not stable when modeling Rayleigh waves but the proposed method is stable. For a laterally heterogeneous viscoelastic media model (Model 1) and a two-layer viscoelastic media model (Model 2) with a cavity, we use this method to obtain their corresponding Rayleigh waves. For several quality factors, the dispersion properties of these Rayleigh waves are analyzed. The results of Model 1 show that in a shallow subsurface, the phase velocity of a fundamental mode of the Rayleigh waves increases considerably with a quality factor Q decreasing; the phase velocity increases with Poisson's ratio increasing. The results of Model 2 indicate that the energy of higher modes of the Rayleigh waves become strong when Q decreases.
  • Keywords

Rayleigh waves elastic and viscoelastic media convolutional perfectly matched layer stability finite difference method

  • AMS Subject Headings

35R35 49J40 60G40

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COPYRIGHT: © Global Science Press

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@Article{IJNAM-12-254, author = {Yangyang He, Jinghuai Gao and Zhangxin Chen}, title = {On the Comparison of Properties of Rayleigh Waves in Elastic and Viscoelastic Media}, journal = {International Journal of Numerical Analysis and Modeling}, year = {2015}, volume = {12}, number = {2}, pages = {254--267}, abstract = {Dispersion properties of Rayleigh-type surface waves are widely used in environmental and engineering geophysics to image and characterize a shallow subsurface. In this paper, we numerically study the Rayleigh-type surface waves and their properties in 2D viscoelastic media. A finite difference method in a time-space domain is proposed, with an unsplit convolutional perfectly matched layer (C-PML) absorbing boundary condition. For two models that have analytical expressions of wave fields/dispersion curves, we calculate their wave fields and compare the analytical and numerical solutions to demonstrate the validity of this method. For the case where a medium has a high Poisson's ratio, say 0.49, traditional finite difference methods with a PML boundary condition are not stable when modeling Rayleigh waves but the proposed method is stable. For a laterally heterogeneous viscoelastic media model (Model 1) and a two-layer viscoelastic media model (Model 2) with a cavity, we use this method to obtain their corresponding Rayleigh waves. For several quality factors, the dispersion properties of these Rayleigh waves are analyzed. The results of Model 1 show that in a shallow subsurface, the phase velocity of a fundamental mode of the Rayleigh waves increases considerably with a quality factor Q decreasing; the phase velocity increases with Poisson's ratio increasing. The results of Model 2 indicate that the energy of higher modes of the Rayleigh waves become strong when Q decreases.}, issn = {2617-8710}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/ijnam/487.html} }
TY - JOUR T1 - On the Comparison of Properties of Rayleigh Waves in Elastic and Viscoelastic Media AU - Yangyang He, Jinghuai Gao & Zhangxin Chen JO - International Journal of Numerical Analysis and Modeling VL - 2 SP - 254 EP - 267 PY - 2015 DA - 2015/12 SN - 12 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/ijnam/487.html KW - Rayleigh waves KW - elastic and viscoelastic media KW - convolutional perfectly matched layer KW - stability KW - finite difference method AB - Dispersion properties of Rayleigh-type surface waves are widely used in environmental and engineering geophysics to image and characterize a shallow subsurface. In this paper, we numerically study the Rayleigh-type surface waves and their properties in 2D viscoelastic media. A finite difference method in a time-space domain is proposed, with an unsplit convolutional perfectly matched layer (C-PML) absorbing boundary condition. For two models that have analytical expressions of wave fields/dispersion curves, we calculate their wave fields and compare the analytical and numerical solutions to demonstrate the validity of this method. For the case where a medium has a high Poisson's ratio, say 0.49, traditional finite difference methods with a PML boundary condition are not stable when modeling Rayleigh waves but the proposed method is stable. For a laterally heterogeneous viscoelastic media model (Model 1) and a two-layer viscoelastic media model (Model 2) with a cavity, we use this method to obtain their corresponding Rayleigh waves. For several quality factors, the dispersion properties of these Rayleigh waves are analyzed. The results of Model 1 show that in a shallow subsurface, the phase velocity of a fundamental mode of the Rayleigh waves increases considerably with a quality factor Q decreasing; the phase velocity increases with Poisson's ratio increasing. The results of Model 2 indicate that the energy of higher modes of the Rayleigh waves become strong when Q decreases.
Yangyang He, Jinghuai Gao & Zhangxin Chen. (1970). On the Comparison of Properties of Rayleigh Waves in Elastic and Viscoelastic Media. International Journal of Numerical Analysis and Modeling. 12 (2). 254-267. doi:
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