Skip to main content


We’d like to understand how you use our websites in order to improve them. Register your interest.

FDM computation of seismic wavefield for an axisymmetric earth with a moment tensor point source


Axisymmetric modeling has been playing an important role in global seismic waveform modeling since it can correctly model geometrical spreading effects in 3-D within computational resources comparable to 2-D modeling. However, in the previous investigations on axisymmetric modeling, seismic sources were restricted to axisymmetric sources such as an explosive source. In this paper, we propose implementation of an arbitrary moment tensor point source to axisymmetric modeling using the finite-difference method (FDM). The validity and efficiency of this technique are demonstrated by comparing synthetic seismograms with analytical solutions for a homogeneous earth model, as well as with the DSM synthetics for a spherically symmetric earth. We also show a numerical example with a subducting slab structure.


  1. Aki, K. and P. G. Richards, Quantitative Seismology, 2nd ed., 700 pp, University Science Books, Sausalito, CA, 2002.

  2. Alterman, Z. S., J. Aboudi, and F. C. Karal, Pulse propagation in a laterally heterogeneous solid elastic sphere, Geophys. J. R. astr. Soc., 21, 243–260, 1970.

  3. Chaljub, E. and A. Tarantola, Sensitivity of SS precursors to topography on the upper-mantle 660-km discontinuity, Geophys. Res. Lett., 24(21), 2613–2616, 1997.

  4. Fukao, Y., S. Widiyantoro, and M. Obayashi, Stagnant slabs in the upper and lower mantle transition region, Rev. Geophys., 39(3), 291–323, 2001.

  5. Igel, H. and O. Gudmundsson, Frequency-dependent effects on travel times and waveforms of long-period S and SS waves, Phys. Earth Planet. Int., 104, 229–246, 1997.

  6. Igel, H. and M. Weber, SH-wave propagation in the whole mantle using high-order finite differences, Geophys. Res. Lett., 22(6), 731–734, 1995.

  7. Igel, H. and M. Weber, P-SV wave propagation in the Earth’s mantle using finite differences: Application to heterogeneous lowermost mantle structure, Geophys. Res. Lett., 23(5), 415–418, 1996.

  8. Kennett, B. L. N. and E. R. Engdahl, Traveltimes for global earthquake location and phase identification, Geophys. J. Int., 105, 429–465, 1991.

  9. Lundgren, P. and D. Giardini, The June 9 Bolivia and March 9 Fiji deep earthquakes of 1994: I. Source processes, Geophys. Res. Lett., 22(16), 2241–2244, 1995.

  10. Pitarka, A., 3D elastic finite-difference modeling of seismic motion using staggered grids with nonuniform spacing, Bull. Seism. Soc. Am., 89(1), 54–68, 1999.

  11. Takenaka, H., Y. Wang, and T. Furumura, An efficient approach of the pseudospectral method for modelling of geometrically symmetric seismic wavefield, Earth Planets Space, 51, 73–79, 1999.

  12. Takenaka, H., H. Tanaka, T. Okamoto, and B. L. N. Kennett, Quasi-cylindrical 2.5D wave modeling for large-scale seismic surveys, Geo-phys. Res. Lett., 30(21), 2086, doi:10.1029/2003GL018068, 2003.

  13. Takeuchi, H. and M. Saito, Seismic surface waves, Meth. comput. Phys., 11, 217–295, 1972.

  14. Takeuchi, N., R. J. Geller, and P. R. Cummins, Highly accurate P-SV complete synthetic seismograms using modified DSM operators, Geophys. Res. Lett., 23(10), 1175–1178, 1996.

  15. Thomas, Ch., H. Igel, M. Weber, and F. Scherbaum, Acoustic simulation of P-wave propagation in a heterogeneous spherical earth: numerical method and application to precursor waves to PKPdf, Geophys. J. Int., 141, 307–320, 2000.

  16. Toyokuni, G., H. Takenaka, Y. Wang, and B. L. N. Kennett,, Geophys. Res. Lett., 32, L09305, doi:10.1029/2004GL022180, 2005.

  17. Wessel, P. and W. H. F. Smith, New version of the generic mapping tools released, EOS Trans. AGU Electron. Suppl., Aug. 15, 1995.

Download references

Author information



Corresponding author

Correspondence to Genti Toyokuni.

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Toyokuni, G., Takenaka, H. FDM computation of seismic wavefield for an axisymmetric earth with a moment tensor point source. Earth Planet Sp 58, e29–e32 (2006).

Download citation

Key words

  • Axisymmetric modeling
  • moment tensor
  • synthetic seismogram
  • finite-difference method (FDM)