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ISSN  2096-3955

CN  10-1502/P

Citation: JinHai Zhang, ZhenXing Yao, 2017: Exact local refinement using Fourier interpolation for nonuniform-grid modeling, Earth and Planetary Physics, 1, 58-62.

2017, 1(1): 58-62. doi: 10.26464/epp2017008

Exact local refinement using Fourier interpolation for nonuniform-grid modeling

Key Laboratory of Earth and Planetary Physics, Institute of Geology and Geophysics, Chinese Academy of Sciences, Beijing 100029, China

Corresponding author: JinHai Zhang,

Received Date: 2017-02-27

Numerical solver using a uniform grid is popular due to its simplicity and low computational cost, but would be unfeasible in the presence of tiny structures in large-scale media. It is necessary to use a nonuniform grid, where upsampling the wavefield from the coarse grid to the fine grid is essential for reducing artifacts. In this paper, we suggest a local refinement scheme using the Fourier interpolation, which is superior to traditional interpolation methods since it is theoretically exact if the input wavefield is band limited. Traditional interpolation methods would fail at high upsampling ratios (say 50); in contrast, our scheme still works well in the same situations, and the upsampling ratio can be any positive integer. A high upsampling ratio allows us to greatly reduce the computational burden and memory demand in the presence of tiny structures and large-scale models, especially for 3D cases.

Key words: local refinement, varying grid, tiny structures, fourier interpolation, nonuniform grid

Chu, C. L., and Stoffa, P. L. (2012), Nonuniform grid implicit spatial finite difference method for acoustic wave modeling in tilted transversely isotropic media, J. Appl. Geophys., 76, 44-49 doi: 10.1016/j.jappgeo.2011.09.027

Etgen, J. T., and O’Brien, M. J. (2007), Computational methods for large-scale 3D acoustic finite-difference modeling: A tutorial, Geophysics, 72(5), SM223-SM230 doi: 10.1190/1.2753753

Falk, J., Tessmer, E., and Gajewski, D. (1998), Efficient finite-difference modelling of seismic waves using locally adjustable time steps, Geophys. Prospect., 46(6), 603-616 doi: 10.1046/j.1365-2478.1998.00110.x

Huang, C., and Dong, L. G. (2009), Staggered-grid high-order finite-difference method in elastic wave simulation with variable grids and local time-steps, Chinese J. Geophys. (in Chinese), 52(11), 2870-2878 doi: 10.3969/j.issn.0001-5733.2009.11.022

Jastram, C., and Behle, A. (1992), Acoustic modelling on a grid of vertically varying spacing, Geophys. Prospect., 40(2), 157-169 doi: 10.1111/j.1365-2478.1992.tb00369.x

Kosloff, D. D., and Baysal, E. (1982), Forward modeling by a Fourier method, Geophysics, 47(10), 1402-1412 doi: 10.1190/1.1441288

Kostin, V., Lisitsa, V., Reshetova, G., and Tcheverda, V. (2015), Local time-space mesh refinement for simulation of elastic wave propagation in multi-scale media, J. Comput. Phys., 281, 669-689 doi: 10.1016/

Liu, Y., and Sen, M. K. (2013), Time-space domain dispersion-relation-based finite-difference method with arbitrary even-order accuracy for the 2D acoustic wave equation, J. Comput. Phys., 232(1), 327-345 doi: 10.1016/

Moczo, P. (1989), Finite-difference technique for SH-wave in 2-D media using irregular grids-application to the seismic response problem, Geophys. J. Int., 99(2), 321-329 doi: 10.1111/j.1365-246X.1989.tb01691.x

Oliveira, S. A. M. (2003), A fourth-order finite-difference method for the acoustic wave equation on irregular grids, Geophysics, 68(2), 672-676 doi: 10.1190/1.1567237

Oppenheim, A. V., Schafer, R. W., and Buck, J. R. (1999). Discrete-Time Signal Processing, 2nd Edition. Prentice-Hall, New York

Sacchi, M. D., Ulrych, T. J., and Walker, C. J. (1998), Interpolation and extrapolation using a high-resolution discrete Fourier transform, IEEE Transac. Signal. Process., 46(1), 31-38 doi: 10.1109/78.651165

Song, G. J., Yang, D. H., Chen, Y. L., and Ma, X. (2010), Non-uniform grid algorithm based on the WNAD method and elastic wave-field simulations, Chinese J. Geophys. (in Chinese), 53(8), 1985-1992 doi: 10.3969/j.issn.0001-5733.2010.08.025

Tan, S., and Huang, L. J. (2014), A staggered-grid finite-difference scheme optimized in the time-space domain for modeling scalar-wave propagation in geophysical problems, J. Comput. Phys., 276, 613-634 doi: 10.1016/

Tessmer, E. (2000), Seismic finite-difference modeling with spatially varying time steps, Geophysics, 65(4), 1290-1293 doi: 10.1190/1.1444820

Yang, D. H., Teng, J. W., Zhang, Z. J., and Liu, E. R. (2003), A nearly analytic discrete method for acoustic and elastic wave equations in anisotropic media, Bull. Seismol. Soc. Am., 93(2), 882-890 doi: 10.1785/0120020125

Zhang, J. F., and Gao, H. W. (2009), Elastic wave modelling in 3-D fractured media: An explicit approach, Geophys. J. Int., 177(3), 1233-1241 doi: 10.1111/j.1365-246X.2009.04151.x

Zhang, J. H., and Yao, Z. X. (2013), Optimized explicit finite-difference schemes for spatial derivatives using maximum norm, J. Comput. Phys., 250, 511-526 doi: 10.1016/

Zhang, Z. G., Zhang, W., Li, H., and Chen, X. F. (2013), Stable discontinuous grid implementation for collocated-grid finite-difference seismic wave modeling, Geophys. J. Int., 192(3), 1179-1188 doi: 10.1093/gji/ggs069

Zhao, H. B., and Wang, X. M. (2008), An optimized staggered variable-grid finite-difference scheme and its application in cross-well acoustic survey, Chinese Sci. Bull., 53(6), 825-835 doi: 10.1007/s11434-008-0042-x


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Exact local refinement using Fourier interpolation for nonuniform-grid modeling

JinHai Zhang, ZhenXing Yao