Acta Mechanica Sinica

, Volume 20, Issue 3, pp 299–306 | Cite as

Seismic propagation simulation in complex media with non-rectangular irregular-grid finite-difference

  • Sun Weitao
  • Yang Huizhu


This paper presents a finite-difference (FD) method with spatially non-rectangular irregular grids to simulate the elastic wave propagation. Staggered irregular grid finite difference operators with a second-order time and spatial accuracy are used to approximate the velocity-stress elastic wave equations. This method is very simple and the cost of computing time is not much. Complicated geometries like curved thin layers, cased borehole and nonplanar interfaces may be treated with non-rectangular irregular grids in a more flexible way. Unlike the multi-grid scheme, this method requires no interpolation between the fine and coarse grids and all grids are computed at the same spatial iteration. Compared with the rectangular irregular grid FD, the spurious diffractions from “staircase” interfaces can easily be eliminated without using finer grids. Dispersion and stability conditions of the proposed method can be established in a similar form as for the rectangular irregular grid scheme. The Higdon's absorbing boundary condition is adopted to eliminate boundary reflections. Numerical simulations show that this method has satisfactory stability and accuracy in simulating wave propagation near rough solid-fluid interfaces. The computation costs are less than those using a regular grid and rectangular grid FD method.

Key Words

seismic propagation non-rectangular grid finite-difference 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Alterman Z, Karal FC Jr. Propagation of elastic waves in layered media by finite difference methods.Bulletin of the Seismological Society of America, 1968, 58(1): 367–398Google Scholar
  2. 2.
    Boore DM. Finite difference methods for seismic wave propagation in heterogeneous materials. In: Bolt BA ed. Method in Computational Physics. Academic Press, Inc, 1972Google Scholar
  3. 3.
    Alford RM, Kelly KR, Boore DM. Accuracy of finite-difference modeling of the acoustic wave equation.Geophysics, 1974, 39: 834–842CrossRefGoogle Scholar
  4. 4.
    Kelly KR, Ward RW, Treitel S, et al. Synthetic seismograms, a finite difference approach.Geophysics, 1976, 41: 2–27CrossRefGoogle Scholar
  5. 5.
    Virieux J. SH-wave propagation in heterogeneous media: velocity-stress finite-difference method.Geophysics, 1984, 49: 1933–1942CrossRefGoogle Scholar
  6. 6.
    Virieux J. I-SV wave propagation in heterogeneous media. velocity-stress finite-difference method.Geophysics, 1986, 51: 889–901CrossRefGoogle Scholar
  7. 7.
    Levander Alan R. Fourth-order finite-difference P-SV seismograms.Geophysics, 1988, 53: 1425–1436CrossRefGoogle Scholar
  8. 8.
    Dablain MA. The application of high-order differencing to the scalar wave equation.Geophysics, 1986, 51: 54–66CrossRefGoogle Scholar
  9. 9.
    Graves RW. Simulating seismic wave propagation in 3D elastic media using staggered-grid finite differences.Bulletin of the Seismological Society of America, 1996, 86: 1091–1106MathSciNetGoogle Scholar
  10. 10.
    Shortley GH, Weller R. Numerical solution of Laplace's equation.J Appl Phys, 1938, 9: 334–348MATHCrossRefGoogle Scholar
  11. 11.
    Jastram C, Tessmer E. Elastic modeling on a grid with vertically varying spacing.Geophys Prosp, 1994, 42: 357–370CrossRefGoogle Scholar
  12. 12.
    Falk J, Tessmer E, Gajevski D. Tube wave modeling by the finite-differences method with varying grid spacing.Pageoph, 1996, 14: 77–93CrossRefGoogle Scholar
  13. 13.
    Tessmer E, Kosloff D, Behle A. Elastic wave propagation simulation in the presence surface topography.Geophys J Internat, 1992, 108: 621–632Google Scholar
  14. 14.
    Hestholm SO, Ruud BO. 2-D Finite-difference elastic wave modeling including surface topography.Geophys Prosp, 1994, 42: 371–390CrossRefGoogle Scholar
  15. 15.
    Mufti IR. Large-scale three-dimensional seismic models and their interpretive significance.Geophysics, 1990, 55(9): 1166–1182CrossRefGoogle Scholar
  16. 16.
    Oprsal I, Zahradnik J. Elastic finite-difference method for irregular grids.Geophysics, 1999, 64(1): 240–250CrossRefGoogle Scholar
  17. 17.
    Pitarka A. 3D elastic finite-difference modeling of seismic motion using staggered grids with nonuniform spacing.Bulletin of the Seismological Society of America, 1999, 89(1): 54–68MathSciNetGoogle Scholar
  18. 18.
    Nordström J,m Carpenter MH. High-order finite difference methods, multidimensioinal linear problems and curvilinear coordinates.Journal of Computational Physics, 2001, 173: 149–174MATHMathSciNetCrossRefGoogle Scholar
  19. 19.
    Higdon RL. Absorbing boundary conditions for difference approximations to the multidimensional wave equation.Math Comp, 1986, 47: 437–459MATHMathSciNetCrossRefGoogle Scholar

Copyright information

© Chinese Society of Theoretical and Applied Mechanics 2004

Authors and Affiliations

  • Sun Weitao
    • 1
    • 2
  • Yang Huizhu
    • 1
  1. 1.Department of Engineering MechanicsTsinghua UniversityBeijingChina
  2. 2.Department of Computer Science & TechnologyTsinghua UniversityBeijingChina

Personalised recommendations