Pure and Applied Geophysics

, Volume 175, Issue 10, pp 3419–3439 | Cite as

Simulating Seismic Wave Propagation in Viscoelastic Media with an Irregular Free Surface

  • Xiaobo Liu
  • Jingyi ChenEmail author
  • Zhencong Zhao
  • Haiqiang Lan
  • Fuping Liu


In seismic numerical simulations of wave propagation, it is very important for us to consider surface topography and attenuation, which both have large effects (e.g., wave diffractions, conversion, amplitude/phase change) on seismic imaging and inversion. An irregular free surface provides significant information for interpreting the characteristics of seismic wave propagation in areas with rugged or rapidly varying topography, and viscoelastic media are a better representation of the earth’s properties than acoustic/elastic media. In this study, we develop an approach for seismic wavefield simulation in 2D viscoelastic isotropic media with an irregular free surface. Based on the boundary-conforming grid method, the 2D time-domain second-order viscoelastic isotropic equations and irregular free surface boundary conditions are transferred from a Cartesian coordinate system to a curvilinear coordinate system. Finite difference operators with second-order accuracy are applied to discretize the viscoelastic wave equations and the irregular free surface in the curvilinear coordinate system. In addition, we select the convolutional perfectly matched layer boundary condition in order to effectively suppress artificial reflections from the edges of the model. The snapshot and seismogram results from numerical tests show that our algorithm successfully simulates seismic wavefields (e.g., P-wave, Rayleigh wave and converted waves) in viscoelastic isotropic media with an irregular free surface.


Irregular free surface viscoelastic wavefield simulation convolutional perfectly matched layer 



The authors acknowledge the Faculty Internationalization Grant at The University of Tulsa. The author, Dr. Fuping Liu, also thanks the support for this study from The Beijing City Board of Education Science and Technology Key Project (KZ201510015015), PXM2016_014223_000025, Beijing City Board of Education Science and Technology Project (KM201510015009), and Natural Science Foundation of Beijing (4142016). We appreciate William Sanger (Schlumberger) for English-polishing. Finally, thanks to two anonymous reviewers and to our editor Andrew Gorman for the valuable suggestions and comments.


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Copyright information

© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  • Xiaobo Liu
    • 1
  • Jingyi Chen
    • 1
    Email author
  • Zhencong Zhao
    • 1
  • Haiqiang Lan
    • 2
  • Fuping Liu
    • 3
  1. 1.Seismic Anisotropy Group, Department of GeosciencesThe University of TulsaTulsaUSA
  2. 2.Institute of Geology and GeophysicsChinese Academy of SciencesBeijingChina
  3. 3.Beijing Institute of Graphic CommunicationBeijingChina

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