Wang Jian1, Meng Xiao-Hong1, Liu Hong2, Zheng Wan-Qiu1, and Gui Sheng2
1. School of Geophysics and Information Engineering, China University of Geosciences, Beijing 100083, China.
2. Key Laboratory of Petroleum Resources Research, Institute of Geology and Geophysics, Chinese Academy of Sciences, Beijing 100029, China.
Abstract The numerical dispersion and computational cost are high for conventional Taylor series expansion staggered-grid finite-difference forward modeling owing to the high frequency of the wavelets and the large grid intervals. In this study, the cosine-modulated binomial window function (CMBWF)-based staggered-grid finite-difference method is proposed. Two new parameters, the modulated time and modulated range are used in the new window function and by adjusting these two parameters we obtain different characteristics of the main and side lobes of the amplitude response. Numerical dispersion analysis and elastic wavefield forward modeling suggests that the CMBWF method is more precise and less computationally costly than the conventional Taylor series expansion staggered-grid finite-difference method.
This work was supported by the National Major Research Equipment Development Projects (No. ZDYZ2012-1-02-04 ) and the National Natural Science Foundation of China (No. 41474106).
Alterman, Z., and Karal, F. C., 1968, Propagation of seismic wave in layered media by finite difference methods: Bulletin of Seismological Society of America, 58, 367−398.
[2]
Carcione, J. M., Kosloff, D. D., Behle, A., and Seriani, G., 1992, A spectral scheme for wave propagation simulation in 3-D elastic-anisotropic media: Geophysics, 57, 1593−1607.
[3]
Chu, C. L., and Stoffa, P. L., 2012, Determination of finite-difference weights using scaled binomial windows: Geophysics, 77, W17−W26.
[4]
Dablain, M. A., 1986, The application of high-order differencing to the scalar wave equation: Geophysics, 51, 54−66.
[5]
Diniz, P. S. R., Da Silva, E. A. B., and Netto, S. L., 2012, Digital signal processing system analysis and design: China Machine Press, Beijing.
[6]
Fornberg, B., 1987, The pseudo spectral method: Comparisons with finite differences for the elastic wave equation: Geophysics, 52, 483−501.
[7]
Gazdag, J., 1981, Modeling of the acoustic wave equation with transform methods: Geophysics, 46, 854−859.
[8]
Igel, H., Mora, P., and Riollet, B., 1995, Anisotropic wave propagation through finite-difference grids: Geophysics, 60(4), 1203−1216.
[9]
Kelly, K. R., Ward, R. W., Treitel, S., et al., 1976, Synthetic seismograms: A finite-difference approach: Geophysics, 41(1), 2−27.
[10]
Kosloff, D. D., and Baysal, E., 1982, Forward modeling by a Fourier method: Geophysics, 47(10), 1402−1412.
[11]
Liu, Y., and Sen, M. K., 2009, A new time-space domain high-order finite-different method for the acoustic wave equation: Journal of Computational Physics, 228, 8779-8806.
[12]
Liu, Y., and Sen, M. K., 2010, Acoustic VTI modeling with a time-space domain dispersion-relation-based finite-difference scheme: Geophysics, 75, A11-A17.
[13]
Li, Z., Zhang, H., and Liu, Q., 2007, Elastic wave staggered grid high-order finite difference method for numerical simulation of wavefield separation: Oil Geophysical Prospecting, 42(5), 510-515.
[14]
Marfurt, K. J., 1984, Accuracy of finite-difference and finite-element modeling of the scalar and elastic wave equations: Geophysics, 49, 533−549.
[15]
Saenger, E. H., and Shapiro, S., 2002, An effective velocities in fractured media; A numerical study using the rotated staggered finite- difference grid: Geophysical Prospecting, 50, 183−194.
[16]
Saenger, E. H., and Thomas, B., 2004, Finite-difference modeling of viscoelastic and anisotropic wave propagation using the rotated staggered grid: Geophysics, 69(2), 583−591.
Weiss, R. M., and Shragge, J., 2013, Solving 3D anisotropic elastic wave equations on parallel GPU devices: Geophysics, 78, F7-F15.
[19]
Yan, H., and Liu, Y., 2013a, Visco-acoustic pre-stack reverse-time migration based on the time-space domain adaptive high-order finite-difference method: Geophysical Prospecting, 61, 941-954.
[20]
Yan, H., and Liu, Y., 2013b, Pre-stack reverse-time migration based on the time-space domain adaptive high-order finite-difference method in acoustic VTI medium: Journal of Geophysics and Engineering, 10, 1-10.
[21]
Yang, L., Yan, H. Y., and Liu, H., 2014, Least squares staggered-grid finite-difference for elastic wave modeling: Exploration Geophysics, 45, 255-260.
[22]
Zhao, J. G., and Shi, R. Q., 2013, A perfectly matched layer absorbing boundary condition for the finite-element time-domain modeling of elastic wave equation: Applied Geophysics, 10(3), 323−336.
[23]
Zhao, J. G., Shi, R. Q., Chen, J. Y., et al., 2014, An matched Z-transform perfectly matched layer absorbing boundary in the numerical modeling of viscoacoustic wave equations: Chinese Journal of Geophysics (in Chinese), 57(4), 1284−1291.
[24]
Zhou, B., and Greenhalgh, S. A., 1992, Seismic scalar wave equation modeling by a convolutional differentiator: Bulletin of the Seismological Society of America, 82(1), 289−303.
2017, Vol. 14 
