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APPLIED GEOPHYSICS  2015, Vol. 12 Issue (1): 101-110    DOI: 10.1007/s11770-014-0476-2
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Variable-coordinate forward modeling of irregular surface based on dual-variable grid
Huang Jian-Ping1, Qu Ying-Ming1, Li Qing-Yang1, Li Zhen-Chun1, Li Guo-Lei2, Bu Chang-Cheng2, and Teng Hou-Hua2
1. Department of Geophysics, School of Geosciences, China University of Petroleum, Qingdao 266555, China.
2. Shengli Geophysical Research Institute of SINOPEC, Dongying 257022, China.
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Abstract The mapping method is a forward-modeling method that transforms the irregular surface to horizontal by mapping the rectangular grid as curved; moreover, the wave field calculations move from the physical domain to the calculation domain. The mapping method deals with the irregular surface and the low-velocity layer underneath it using a fine grid. For the deeper high-velocity layers, the use of a fine grid causes local oversampling. In addition, when the irregular surface is transformed to horizontal, the flattened interface below the surface is transformed to curved, which produces inaccurate modeling results because of the presence of ladder-like burrs in the simulated seismic wave. Thus, we propose the mapping method based on the dual-variable finite-difference staggered grid. The proposed method uses different size grid spacings in different regions and locally variable time steps to match the size variability of grid spacings. Numerical examples suggest that the proposed method requires less memory storage capacity and improves the computational efficiency compared with forward modeling methods based on the conventional grid.
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Huang Jian-Ping
Qu Ying-Ming
Li Qing-Yang
Li Zhen-Chun
Li Guo-Lei
Bu Chang-Cheng
Key wordsmapping   irregular surface   boundary   grid   forward modeling     
Received: 2014-11-12;
Fund:

This study work was financially supported by the National Natural Science Foundation of China (Nos. 41104069 and 41274124), the National 973 Project (Nos. 2014CB239006 and 2011CB202402), the Shandong Natural Science Foundation of China (No. ZR2011DQ016) and Fundamental Research Funds for Central Universities (No. R1401005A).

Cite this article:   
Huang Jian-Ping,Qu Ying-Ming,Li Qing-Yang et al. Variable-coordinate forward modeling of irregular surface based on dual-variable grid[J]. APPLIED GEOPHYSICS, 2015, 12(1): 101-110.
 
[1] Alterman, Z., and Karal, F. C., 1968, Propagation of elastic waves in layered media by finite difference methods: Bulletin of the Seismological Society of America, 58(1), 367-398.
[2] Chu, C. L., and Wang, X. T., 2005, Seismic modeling with a finite-difference method on irregular triangular grids: Periodical of Ocean University of China, 35(1), 43-48.
[3] Crase, E., 1990, High-order (space and time) finite-difference modeling of the elastic equation: 69th SEG Annual International Meeting, Expanded Abstracts, 987-991.
[4] Dong, C., and Dong, L. G., 2009, High-order finite-difference method in seismic wave simulation with variable grids and local time-steps: Chinese J. Geophys. (in Chinese), 52(1), 176-186.
[5] Dong, L. G., 2005, Numerical simulation of seismic wave propagation under complex near surface conditions: Progress in Exploration Geophysics, 28(3), 187-194.
[6] Fornberg, B., 1988a, Generation of finite difference formulas on arbitrary spaced grids: Mathematics of Computation, 51, 699-706.
[7] Fornberg, B., 1988b, The pseudospectral method: accurate representation of interfaces in elastic wave calculations, Geophysics, 53(5), 625-637.
[8] Falk, J., Tessmer, E., and Gajewski, D., 1996, Tube wave modeling by the finite-difference method with varying grid spacing: Prospecting, 148, 77-93.
[9] Falk, J., Tessmer, E., and Gajewski, D., 1998, Efficient finite-difference modelling of seismic waves using locally adjustable time steps: Geophysical Journal International, 46(6), 603-616.
[10] Hayashi, K., Burns, D. R., and Toksöz, M. N., 2001, Discontinuous-grid finite-difference seismic modeling including surface topography: Bull. Seism. Soc. Am, 91(6), 1750-1764.
[11] Hestholm, S. O., and Ruud, B. O., 1994, 2D finite-difference elastic wave modelling including surface topography: Geophysical Prospecting, 42(5), 371-390.
[12] Hestholm, S. O., and Ruud, B. O., 1998, 3D finite-difference elastic wave modelling including surface topography: Geophysics, 63(2), 613-622.
[13] Hestholm, S.O., and Ruud, B. O., 2000, 2D finite-difference viscoelastic wave modelling including surface topography: Geophysical Prospecting, 48(2), 341-373.
[14] Huang, Z. P., Zhang, M., Wu, W. Q., and Dong, L. G., 2004, A domain decomposition method for numerical simulation of the elastic wave propagation: Chinese J. Geophys. (in Chinese), 47(6), 1094-1100.
[15] Jastram, C., and Behle, A., 1992, Acoustic modeling on a vertically varying grid: Geophysical Prospecting, 40(2), 157-169.
[16] Jastram, C., and Tessmer, E., 1994, Elastic modeling on a grid with vertically varying spacing: Geophysical Prospecting, 42(4), 357-370.
[17] Levander, A. R., 1988, Fourth-order finite-difference P-SV seismograms: Geophysics, 53(11), 1425-1436.
[18] Li, S. J., Sun, C. Y., and Ni, C. K., 2007, Acoustic equation numerical modeling on a grid of varying spacing: Chinese Journal of Engineering Geophysics, 4(3), 207-212.
[19] Li, Z. C., Zhang, H., and Zhang, H., 2008, Variable-grid high-order finite-difference numeric simulation of first-order elastic wave equation: Oil Geophysical Prospecting, 43(6), 711-716.
[20] Ma, D. T., and Zhu, G. M., 2004, Hybrid method combining finite difference and pseudospectral method for solving the elastic wave equation: Journal of Earth Sciences and Environment, 26(1), 61-64.
[21] Madariaga, R., 1976, Dynamics of an expanding circular fault. Bull. Seismol. Soc. Am., 66(3), 639-666.
[22] Rao, D. Z., 1994, Wave equation numerical modeling of hexagonal sample by Fourier method: Chinese Journal of Computational Physics, 11(1), 101-106.
[23] Robertsson, J. O. A., and Holliger, K., 1996, Modeling of seismic wave propagation near the earth’s surface: Physics of the Earth and Planetary Interiors, 104, 193-211.
[24] Sun, C. Y., Li, S. J., and Ni, C. K., 2008, Wave equation numerical modeling by finite difference method with varying grid spacing: Geophysical Prospecting for Petroleum, 47(2), 123-128.
[25] Sun, W. T., Yang, H. Z., and Shu, J. W., 2004, Finite difference method of irregular grid for elastic wave equation in heterogeneous media: Chinese Journal of Computational Mechanics, 21(2), 135-141.
[26] Tessmer, E., Kosloff, D., and Behle, A., 1992, Elastic wave propagation simulation in the presence of surface topography: Geophysical Journal International, 108(2), 621-632.
[27] Tessmer, E., and Kosloff, D., 1994, 3D elastic modelling with surface topography by a Chebychev spectral method: Geophysics, 59(3), 464-473.
[28] Tessmer, E., 2000, Seismic finite-difference modeling with spatially varying time steps: Geophysics, 65(4), 1290-1293.
[29] Thomas, Ch., Igel, H., Weber, M., and Scherbaum, F., 2000, Acoustic simulation of P-wave propagation in a heterogeneous spherical earth: numerical method and application to precursor waves to PKPdf: Geophysical Journal International, 141(2), 307-320.
[30] Virieux, J., 1984, SH-wave propagation in heterogeneous media: velocity-stress finite-difference method: Geophysics, 49(11), 1933-1957.
[31] Virieux, J., 1986, P-SV wave propagation in heterogeneous media: velocity-stress finite-difference method: Geophysics, 51(4), 889-901.
[32] Wang, X. C., and Liu, X. W., 2005, Downward Continuing the Seismic record of topography using coordination transformated method: Progress in Geophysics, 20(3), 677-680.
[33] Zhang, H., and Li, Z. C., 2011, Seismic wave simulation method based on dual-variable grid: Chinese J. Geophys. (in Chinese), 54(1), 77-86.
[34] Zhang, J. F., 1998, Non-orthogonal grid finite-difference method for numerical simulation of elastic wave propagation: Chinese J. Geophys. (in Chinese), 41(S1), 357-366.
[35] Zhao, H. B., and Wang, X. M., 2007, An optimized variable staggered grid finite difference method and its application in crosswell acoustic wave: Chinese Science Bulletin (in Chinese), 52(12), 1387-1395.
[36] Zhao, J. X., Zhang, S. L., and Sun, P. Y., 2003, Pseudospectral method on curved grid for 2-D forward modeling: Geophysical Prospecting for Petroleum, 42(1), 1-5.
[37] Zhu, S. W., Qu, S. L., and Wei, X. C., 2007, Numeric simulation by grid-various finite-difference elastic wave equation: Oil Geophysical Prospecting, 42(6), 634-639.
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