Journal of Seismology

, Volume 13, Issue 2, pp 209–217 | Cite as

Elastic wave modelling method based on the displacement–velocity fields: an improving nearly analytic discrete approximation

Original article
First Online:
Received:
Accepted:
  • 110 Downloads

Abstract

In this paper, we present an improvement to our previously published nearly analytic discrete method (NADM) to solve acoustic and elastic wave equations. We compare the numerical errors of the improved NADM with the original NADM and also the fourth-order Lax–Wendroff correction and present examples of three-component wave fields in 2D transversely isotropic media with strong velocity contrasts. Comparing with the original NADM, we find that the improved method requires significantly less storage space and can increase the time accuracy from second order of the original NADM to fourth order, while the space accuracy remains the same as that of the original one. Theoretical analyses and numerical results suggest that our improved NADM is suitable for large-scale numerical modelling as it can effectively suppress numerical dispersion and source-generated noises caused by discretising wave equations when too-coarse grids are used.

Keywords

Nearly analytic discrete approximation Numerical dispersion Wave-field modelling  Wave equations Finite-difference method 
This is a preview of subscription content, log in to check access.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Aboudi J (1971) Numerical simulation of seismic sources. Geophysics 36:810–821CrossRefGoogle Scholar
  2. Dablain MA (1986) The application of higher-order differencing to the scalar wave equation. Geophysics 51:54–66CrossRefGoogle Scholar
  3. Faria EL, Stoffa PL (1994) Finite-difference modelling in transversely isotropic media. Geophysics 59:282–289CrossRefGoogle Scholar
  4. Fei T, Larner K (1995) Elimination of numerical dispersion in finite-difference modelling and migration by flux-corrected transport. Geophysics 60:1830–1842CrossRefGoogle Scholar
  5. Konddoh Y, Hosaka Y, Ishii K (1994) Kernel optimum nearly analytical discretization algorithm applied to parabolic and hyperbolic equations. Computers Math Appl 27:59–90CrossRefGoogle Scholar
  6. Kosloff D, Baysal E (1982) Forward modelling by a Fourier method. Geophysics 47:1402–1412CrossRefGoogle Scholar
  7. Mizutani H, Geller RJ, Takeuchi N (2000) Comparison of accuracy and efficiency of time-domain schemes for calculating synthetic seismograms. Phys Earth Planet Int 119:75–97CrossRefGoogle Scholar
  8. Sei A, Symes W (1994) Dispersion analysis of numerical wave propagation and its computational consequences. J Sci Comput 10:1–27CrossRefGoogle Scholar
  9. Vlastos S, Liu E, Main IG, Li XY (2003) Numerical simulation of wave propagation in media with discrete distributions of fractures: effects of fracture sizes and spatial distributions. Geophys J Int 152:649–668CrossRefGoogle Scholar
  10. Wang SQ, Yang DH, Yang KD (2002) Compact finite difference scheme for elastic equations. J Tsinghua Univ (Sci & Tech) 42:1128–1131Google Scholar
  11. Yang DH, Liu E, Zhang ZJ, Teng J (2002) Finite-difference modelling in two-dimensional anisotropic media using a flux-corrected transport technique. Geophys J Int 148:320–328CrossRefGoogle Scholar
  12. Yang DH, Teng JW, Zhang ZJ, Liu E (2003) A nearly-analytic discrete method for acoustic and elastic wave equations in anisotropic media. Bull Seism Soc Am 93:882–890CrossRefGoogle Scholar
  13. Yang DH, Lu M, Wu RS, Peng JM (2004) An optimal nearly-analytic discrete method for 2D acoustic and elastic wave equations. Bull Seism Soc Am 94:1982–1992CrossRefGoogle Scholar
  14. Yang DH, Peng JM, Lu M, Terlaky T (2006) Optimal nearly analytic discrete approximation to the scalar wave equation. Bull Seism Soc Am 96:1114–1130CrossRefGoogle Scholar
  15. Yang DH, Song GJ, Lu M (2007) Optimally accurate nearly-analytic discrete scheme for wave-field simulation in 3D anisotropic media. Bull Seism Soc Am 97:1557–1569CrossRefGoogle Scholar
  16. Zahradnik J, Moczo P, Hron T (1993) Testing four elastic finite-difference schemes for behavior at discontinuities. Bull Seism Soc Am 83:107–129Google Scholar
  17. Zhang ZJ, Wang GJ, Harris JM (1999) Multi-component wave-field simulation in viscous extensively dilatancy anisotropic media. Phys Earth Planet Inter 114:25–38CrossRefGoogle Scholar
  18. Zheng HS, Zhang ZJ, Liu E (2006) Non-linear seismic wave propagation in anisotropic media using the flux-corrected transport technique. Geophys J Int 165:943–956.CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media B.V. 2008

Authors and Affiliations

  • Dinghui Yang
    • 1
  • Enru Liu
    • 2
    • 4
  • Guojie Song
    • 1
    • 3
  • Nian Wang
    • 1
  1. 1.Department of Mathematical SciencesTsinghua UniversityBeijingChina
  2. 2.British Geological SurveyEdinburghUK
  3. 3.College of SciencesSouthwest Petroleum UniversityChengduChina
  4. 4.ExxonMobilHoustonUSA

Personalised recommendations