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An efficient approach of the pseudospectral method for modelling of geometrically symmetric seismic wavefield


The pseudospectral method is a high-accuracy numerical modelling technique that requires less computer memory and computation time than the traditional techniques such as the finite-difference method. These advantages of the pseudospectral method have enabled us to practically apply this method to modelling realistic problems that have complex structure and source models. However, a major drawback of such numerical schemes for discrete grid models is that even for rather a simple structural model they require as much computational requirements (e.g. computation time and memory) as for an entirely complex structural model with the same size of the simple one. We actually need to employ idealised simple models, such as a model with geometrical symmetry, to investigate basic phenomena of seismic waves, to develop new techniques, or to choose optimal values of some computational parameters for more complex modelling. In this paper we propose an efficient approach of an economical pseudospectral method for calculation of wavefields in models symmetric with respect to a vertical plane or two orthogonal vertical planes. Using this approach, the wavefields only need to be computed in a half or quarter domain of the models, so that the computer memory and computation time can be reduced ideally by half or quarter, respectively, as compared with the calculation of the entire models.


  • Boore, D. M., Finite-difference methods for seismic wave propagation in heterogeneous materials, in Methods in Computational Physics, vol. 11, edited by B. A. Bolt, 310pp., Academic Press, New York, 1972.

    Google Scholar 

  • Cerjan, C., D. Kosloff, R. Kosloff, and M. Reshef, A non-reflecting boundary condition for discrete acoustic and elastic wave equations, Geophysics, 50, 705–708, 1985.

    Article  Google Scholar 

  • Daudt, C. R., L. W. Brail, R. L. Nowack, and C. S. Chiang, A comparison (34) of finite-difference and Fourier method calculations of synthetic seismo-grams, Bull. Seism. Soc. Am., 79, 1210–1230, 1989.

    Google Scholar 

  • Fornberg, B., The pseudospectral method: Comparisons with finite differences for the elastic wave equation, Geophysics, 52, 483–501, 1987.

    Article  Google Scholar 

  • Furumura, T. and K. Koketsu, Specific distribution of ground motion during the 1995 Kobe earthquake and its generation mechanism, Geophys. Res. Lett., 25, 785–788, 1998.

    Article  Google Scholar 

  • Furumura, T. and H. Takenaka, A stable method for numerical differentiation of data with discontinuities at end-points by means of Fourier transform-Symmetric differentiation, Butsuri-Tansa (J. SEGJ), 45, 303–309, 1992 (in Japanese with English abstract).

    Google Scholar 

  • Furumura, T., B. L. N. Kennett, and H. Takenaka, Parallel 3-D pseudospectral simulation of seismic wave propagation, Geophysics, 63, 279–288, 1998.

    Article  Google Scholar 

  • Kosloff, D., M. Reshef, and D. Loewenthal, Elastic wave calculations by the Fourier method, Bull. Seism. Soc. Am., 74, 875–891, 1984.

    Google Scholar 

  • Reshef, M., D. Kosloff, M. Edwards, and C. Hsiung, Three-dimensional elastic modeling by the Fourier method, Geophysics, 53, 1184–1193, 1988.

    Article  Google Scholar 

  • Saatcilar, R. and S. Ergintav, Solving elastic wave equation with the Hartley method, Geophysics, 56, 274–278, 1991.

    Article  Google Scholar 

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Correspondence to Hiroshi Takenaka.

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Takenaka, H., Wang, Y. & Furumura, T. An efficient approach of the pseudospectral method for modelling of geometrically symmetric seismic wavefield. Earth Planet Sp 51, 73–79 (1999).

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