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A multidomain approach of the Fourier pseudospectral method using discontinuous grid for elastic wave modeling

Abstract

Pseudospectral method is an efficient and high-accuracy numerical modeling technique that has been applied to the simulation of seismic wavefields in realistic models with complex structures such as sedimentary basin. However, if the sedimentary layers are included in the model, high velocity contrasts arise because of the very low S-wave velocities of the sediments as compared with the bedrock. The grid spacing then has to be very small, which leads to spatial oversampling in regions with higher velocities. As a result, we also have to use very small time interval for time marching, so that the computation requires much CPU time. A treatment of this problem is use of a multidomain approach that can employ different grid spacings in different regions, i.e. “discontinuous grid”. In this study, we propose a scheme for the Fourier pseudospectral method using discontinuous grid, which uses an interpolation by the FFT. This scheme can reduce the computation time and the required computer memory as compared with the conventional one. The accuracy and efficiency of this approach are demonstrated in the present paper through examples of 2-D elastic wave modeling.

References

  • Aoi, S. and H. Fujiwara, 3D finite-difference method using discontinuous grids, Bull. Seis. Soc. Am., 89, 918–930, 1999.

    Google Scholar 

  • Bouchon, M. and K. Aki, Discrete wave-number representation of seismic-source wave fields, Bull. Seis. Soc. Am., 67, 259–277, 1977.

    Google Scholar 

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

    Article  Google Scholar 

  • Daudt, C., L. Braile, R. Nowack, and C. Chiang, A comparison of finite-difference and Fourier method calculations of synthetic seismogram, Bull. Seis. Soc. Am., 79, 1210–1230, 1989.

    Google Scholar 

  • Falk, J., E. Tessmer, and D. Gajewski, Tube wave modeling by the finite-difference method with varying grid spacing, Pageoph, 148, 77–93, 1996.

    Article  Google Scholar 

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

    Article  Google Scholar 

  • Fornberg, B., The pseudospectral method: accurate representation of interfaces in elastic wave calculations, Geophysics, 53, 625–637, 1988.

    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., H. Takenaka, and K. Koketsu, Numerical 3-D modeling of seismic waves by the pseudospectral method, Butsuri-Tansa (J. SEGJ), 49, 536–548, 1996 (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, 1998a.

    Article  Google Scholar 

  • Furumura, T., B. L. N. Kennett, and M. Furumura, Seismic wavefield calculation for laterally heterogeneous whole earth models using the pseudospectral method, Geophys. J. Int., 135, 645–860, 1998b.

    Google Scholar 

  • Graves, R. W., Simulating realistic earthquake ground motions in regions of deep sedimentary basins, Proc. of the 11th World Conference on Earthquake Engineering, Acapulco, Mexico, 1996.

  • Herrmann, R. B., SH-wave generation by dislocation source—a numerical study, Bull. Seis. Soc. Am., 69, 1–15, 1979.

    Google Scholar 

  • Hung, S. H. and D. W. Forsyth, Modelling anisotropic wave propagation in oceanic inhomogeneous structures using parallel multidomain pseudospectral method, Geophys. J. Int., 133, 726–740, 1998.

    Article  Google Scholar 

  • Jastram, C. and A. Behle, Acoustic modeling on a grid of vertically varying spacing, Geophys. Prosp., 40, 157–170, 1992.

    Article  Google Scholar 

  • Jastram, C. and E. Tessmer, Elastic modelling on a grid with vertically varying spacing, Geophys. Prosp., 42, 357–370, 1994.

    Article  Google Scholar 

  • Kosloff, D. and E. Baysal, Forward modeling by a Fourier method, Geophysics, 47, 1402–1412, 1982.

    Article  Google Scholar 

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

    Google Scholar 

  • Moczo, P., Finite-difference technique for SH-waves in 2-D media using irregular grids—application to the seismic response problem, Geophys. J. Int., 99, 321–329, 1989.

    Article  Google Scholar 

  • Moczo, P. and P.-Y. Bard, Wave diffraction, amplification and differential motion near strong lateral discontinuities, Bull. Seis. Soc. Am., 83, 85–106, 1993.

    Google Scholar 

  • Moczo, P., P. Labák, J. Kristek, and F. Hron, Amplification and differential motion due to an antiplane 2D resonance in the sediment valleys embedded in a layer over the half-space, Bull. Seis. Soc. Am., 86, 1434–1446, 1996.

    Google Scholar 

  • Moczo, P., E. Bystrický, J. Kristek, J. M. Carcione, and M. Bouchon, Hybrid modeling of P-SV seismic motion at inhomogeneous viscoelastic topographic structures, Bull. Seis. Soc. Am., 87, 1305–1323, 1997.

    Google Scholar 

  • Olsen, K. B. and R. J. Archuleta, Three-dimensional simulation of earthquakesonthe Los Angeles fault system, Bull. Seis. Soc. Am., 86, 575–596, 1996.

    Google Scholar 

  • Olsen, K. B., R. J. Archuleta, and J. R. Matarese, Magnitude 7.75 earthquake on the San Andreas fault: three-dimensional ground motion in Los Angeles, Science, 270, 1628–1632, 1995.

    Article  Google Scholar 

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

    Google Scholar 

  • Sato, T., R. W. Graves, P. G. Somerville, and S. Kataoka, Estimates of regional and local strong motions during the great 1923 Kanto, Japan, earthquake (MS 8.2), part 1: forward simulation of seismograms using variable slip rupture models and estimation of near fault long period ground motions, Bull. Seis. Soc. Am., 88, 206–227, 1998.

    Google Scholar 

  • Wang, Y. B., H. Takenaka, and T. Furumura, Modelling seismic wave propagation in a 2-D cylindrical whole earth model using the pseudospectral method, Geophys. J. Int., 2001 (in press).

    Google Scholar 

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Correspondence to Yanbin Wang.

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Wang, Y., Takenaka, H. A multidomain approach of the Fourier pseudospectral method using discontinuous grid for elastic wave modeling. Earth Planet Sp 53, 149–158 (2001). https://doi.org/10.1186/BF03352372

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Keywords

  • Grid Point
  • Grid Spacing
  • Coarse Grid
  • Uniform Grid
  • Synthetic Seismogram