Skip to main content
Log in

2d and 3D elastic wave propagation by a pseudo-spectral domain decomposition method

  • Published:
Journal of Seismology Aims and scope Submit manuscript

Abstract

A new numerical method is presented for propagating elastic waves in heterogeneous earth media, based on spectral approximations of the wavefield combined with domain decomposition techniques. The flexibility of finite element techniques in dealing with irregular geologic structures is preserved, together with the high accuracy of spectral methods. High computational efficiency can be achieved especially in 3D calculations, where the commonly used finite-difference approaches are limited both in the frequency range and in handling strongly irregular geometries. The treatment of the seismic source, introduced via a moment tensor distribution, is thoroughly discussed together with the aspects associated with its numerical implementation. The numerical results of the present method are successfully compared with analytical and numerical solutions, both in 2D and 3D.

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

  • Abramowitz, M. and Stegun, I. A. (eds), 1966, Handbook of Mathematical Functions, Dover, New York.

  • Aki K. and Richards, P., 1980, Quantitative Seismology. Theory and Methods, Freeman, San Francisco.

    Google Scholar 

  • Bernardi, C. and Maday, Y., 1992, Approximations Spectrales de Problèmes aux Limites Elliptiques, SpringerVerlag, Paris.

    Google Scholar 

  • Boyd, J. P., 1989, Chebyshev and Fourier Spectral Methods, SpringerVerlag, Berlin.

    Google Scholar 

  • Canuto, C., Hussaini, M., Quarteroni, A. and Zang, T., 1988, Spectral Methods in Fluid Dynamics, SpringerVerlag, New York.

    Google Scholar 

  • Clayton, R. and Engquist, B., 1977, Absorbing boundary conditions for acoustic and elastic wave equations, B.S.S.A. 67, 1529–1540.

    Google Scholar 

  • Davis, P. and Rabinowitz, P., 1984, Methods of Numerical Integration, 2nd edn., Academic Press, Orlando.

    Google Scholar 

  • Faccioli, E., Maggio, F., Quarteroni, A. and Tagliani, A., 1996, Spectraldomain decomposition methods for the solution of acoustic and elastic wave equations, Geophysics 61, 1160-1174.

    Google Scholar 

  • Frankel, A. and Vidale, J., 1992, A three-dimensional simulation of seismic waves in the Santa Clara Valley, California, from a Loma Prieta aftershock, B.S.S.A. 82, 2045–2074.

    Google Scholar 

  • Frankel, A., 1993, Three-dimensional simulations of ground motions in the San Bernardino Valley, California, for hypothetical earthquakes on the San Andreas fault, B.S.S.A. 83, 1020–1041.

    Google Scholar 

  • Garvin, W., 1956, Exact transient solution of the buried line source problem, Proc. Royal Soc. London, Series A 234, 528–541.

    Google Scholar 

  • Graff, K. F., 1975, Wave Motion in Elastic Solids, Oxford University Press, London.

    Google Scholar 

  • Graves, R., 1996, Simulating seismic wave propagation in 3D elastic media using staggered-grid finite differences, B.S.S.A. 86, 1091–1106.

    Google Scholar 

  • Kosloff, D., Reshef, M. and Loewenthal, D., 1984, Elastic wave calculations by the Fourier method. B.S.S.A. 74, 875–891.

    Google Scholar 

  • Kosloff, R. and Kosloff, D., 1986, Absorbing boundaries for wave propagation problems, J. Comp. Phys. 63, 363–376.

    Google Scholar 

  • Lahaye, D., Maggio, F. and Quarteroni, A., 1997, Hybrid spectral element finite element methods for wave propagation problems. To appear in East–West J. Num. Math..

  • Madariaga, R., 1983, Earthquake source theory: a review. In: Proc. Int. School of Physics “E. Fermi”, Course 85, Varenna, Italy, 1–44, North-Holland, Amsterdam.

  • Maggio, F. and Quarteroni, A., 1994, Acoustic wave simulation by spectral methods. East–West J. Num. Math. 2, 129–150.

    Google Scholar 

  • Olsen, K., Pechmann, J. and Schuster, G., 1995a, Simulation of 3D elastic wave propagation in the Salt Lake Basin, B.S.S.A. 85, 1688–1710.

    Google Scholar 

  • Olsen, K., Archuleta, R. and Matarese, J., 1995b, Three-dimensional simulation of a magnitude 7.75 earthquake on the San Andreas fault, Science 270, 1628–1632.

    Google Scholar 

  • Olsen, K., Pechmann, J. and Schuster, G., 1996, An analysis of simulated and observed blast records in the Salt Lake basin, B.S.S.A. 86, 1061–1076.

    Google Scholar 

  • Rodríguez-Zúñiga, J. L., Sánchez-Sesma, F. J. and Pérez-Rocha, L. E., 1995, Seismic response of shallow alluvial valleys: the use of simplified models, B.S.S.A. 85, 890–899.

    Google Scholar 

  • Sánchez-Sesma, F. J. and Campillo, M., 1991, Diffraction of P, SV, and Rayleigh waves by topographic features: a boundary integral formulation, B.S.S.A. 81, 2234–2253.

    Google Scholar 

  • Sánchez-Sesma, F. J. and Luzon, F., 1995, Seismic response of three-dimensional alluvial valleys for incident P, S, and Rayleigh waves, B.S.S.A. 85, 269–284.

    Google Scholar 

  • Sánchez-Sesma, F. J., 1996, Written personal communication.

  • Stacey, R., 1988, Improved transparent boundary formulations for the elastic-wave equation, B.S.S.A. 78, 2089–2097.

    Google Scholar 

  • Zienkiewicz, O. C. and Taylor, R. L., 1989, The Finite Element Method, Vol. 1, McGraw-Hill, London.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

About this article

Cite this article

Faccioli, E., Maggio, F., Paolucci, R. et al. 2d and 3D elastic wave propagation by a pseudo-spectral domain decomposition method. Journal of Seismology 1, 237–251 (1997). https://doi.org/10.1023/A:1009758820546

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1023/A:1009758820546

Keywords

Navigation