Skip to main content
Log in

Application of the double absorbing boundary condition in seismic modeling

  • Published:
Applied Geophysics Aims and scope Submit manuscript

Abstract

We apply the newly proposed double absorbing boundary condition (DABC) (Hagstrom et al., 2014) to solve the boundary reflection problem in seismic finite-difference (FD) modeling. In the DABC scheme, the local high-order absorbing boundary condition is used on two parallel artificial boundaries, and thus double absorption is achieved. Using the general 2D acoustic wave propagation equations as an example, we use the DABC in seismic FD modeling, and discuss the derivation and implementation steps in detail. Compared with the perfectly matched layer (PML), the complexity decreases, and the stability and flexibility improve. A homogeneous model and the SEG salt model are selected for numerical experiments. The results show that absorption using the DABC is considerably improved relative to the Clayton-Engquist boundary condition and nearly the same as that in the PML.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  • Bécache, E., Givoli, D., and Hagstrom, T., 2010, Highorder absorbing boundary conditions for anisotropic and convective wave equations: Journal of Computational Physics, 229(4), 1099–1129.

    Article  Google Scholar 

  • Bérenger, J. P., 1994, A perfectly matched layer for the absorption of electromagnetic waves: Journal of Computational Physics, 114, 185–200.

    Article  Google Scholar 

  • Bécache, E., Fauqueux, S., and Joly, P., 2003, Stability of perfectly matched layers, group velocities and anisotropic waves: Journal of Computational Physics, 188(2), 399–433.

    Article  Google Scholar 

  • Cerjan, C., Kosloff, D., Kosloff, R., and Moshe, R., 1985, A non-reflection boundary condition for discrete acoustic and elastic wave equation: Geophysics, 50(4), 705–708.

    Article  Google Scholar 

  • Clayton, R., and Engquist, B., 1977, Absorbing boundary conditions for acoustic and elastic wave equations: Bulletin of the Seismological Society of America, 67(6), 1529–1540.

    Google Scholar 

  • Collino, F., 1993, High order absorbing boundary conditions for wave propagation models: Straight line boundary and corner cases: Proceedings of the 2nd International Conference on Mathematical and Numerical Aspects of Wave Propagation, 161–171.

    Google Scholar 

  • Collino, F., and Tsogka, C., 2001, Application of the perfectly matched absorbing layer model to the linear elastodynamic problem in anisotropic heterogeneous media: Geophysics, 66(1), 294–307.

    Article  Google Scholar 

  • Gedney, S. D., 1996, An anisotropic perfectly matched layer-absorbing medium for the truncation of FDTD lattices: Antennas and Propagation, IEEE Transactions on, 44(12), 1630–1639.

    Article  Google Scholar 

  • Givoli, D., Neta, B., 2004, High-order non-reflecting boundary scheme for time-dependent waves: Journal of Computational Physics, 186(1), 24–46.

    Article  Google Scholar 

  • Hagstrom, T., Givoli, D., Rabinovich, D., and Bielak, J., 2014, The Double Absorbing Boundary method: Journal of Computational Physics, 259, 220–241.

    Article  Google Scholar 

  • Higdon, R. L., 1987, Numerical absorbing boundary conditions for the wave equation: Mathematics of Computation, 49(179), 65–90.

    Article  Google Scholar 

  • Komatitsch, D. and Tromp, J., 2003, A perfectly matched layer absorbing boundary condition for the second-order seismic wave equation: Geophysical Journal International, 154(1), 146–153.

    Article  Google Scholar 

  • Liu, Y., and Sen, M. K., 2010, A hybrid scheme for absorbing edge reflections in numerical modeling of wave propagation: Geophysics, 75(2), A1–A6.

    Article  Google Scholar 

  • Liu, Y., and Sen, M. K., 2012, A hybrid absorbing boundary condition for elastic staggered-grid modeling: Geophysical Prospecting, 60(6), 1114–1132.

    Article  Google Scholar 

  • Rabinovich, D., Givoli, D., and Bécache, E., 2010, Comparison of high-order absorbing boundary conditions and perfectly matched layers in the frequency domain: International Journal for Numerical Methods in Biomedical Engineering, 26(10), 1351–1369.

    Article  Google Scholar 

  • Roden, J. A., and Gedney S. D., 2000, Convolutional PML (CPML): An efficient FDTD implementation of the CFS-PML for arbitrary media: Microwave and Optical Technology Letters, 27(5), 334–339.

    Article  Google Scholar 

  • Song J. Y., Zheng X. D., Zhang Y., Xu J. Q., Qin Z., and Song X. J., 2011, Frequency domain wave equation forward modeling using gaussian elimination with static pivoting: Applied Geophysics, 8(1), 60–68.

    Article  Google Scholar 

  • Yan, H. Y., and Liu Y., 2013a, Visco-acoustic prestack reverse-time migration based on the time-space domain adaptive high-order finite-difference method: Geophysical Prospecting, 61, 941–954.

    Article  Google Scholar 

  • Yan, H. Y., Liu Y., 2013b, Acoustic VTI modeling and prestack reverse-time migration based on the time-space domain staggered-grid finite-difference method: Journal of Applied Geophysics, 90, 41–52.

    Article  Google Scholar 

  • Zhao, J. G., and Shi, R. Q., 2013, Perfectly matched layer-absorbing boundary condition for finite-element time-domain modeling of elastic wave equations: Applied Geophysics, 10(3), 323–336.

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Xiang-Yang Li.

Additional information

This research is supported by the National Nature Science Foundation of China (Grant No. U1262208) and the Important National Science & Technology Specific Projects (Grant No. 2011ZX05019-008).

Liu Yang is a PhD student in the Department of Geological Resources and Geological Engineering, China University of Petroleum (Beijing). Her research interests are high-precision numerical modeling, physical modeling of rugged topography, and seismic processing.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Liu, Y., Li, XY. & Chen, SQ. Application of the double absorbing boundary condition in seismic modeling. Appl. Geophys. 12, 111–119 (2015). https://doi.org/10.1007/s11770-014-0463-z

Download citation

  • Received:

  • Revised:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11770-014-0463-z

Keywords

Navigation