Irregular surface seismic forward modeling by a body-fitted rotated–staggered-grid finite-difference method
Cheng Jing-Wang1,2, Fan Na1, Zhang You-Yuan1, and Lü Xiao-Chun3
1. Geophysics and Oil Resource Institute, Yangtze University, Wuhan 430100, China.
2. Key Laboratory of Exploration Technologies for oil and Gas Resources, Ministry of Education, Yangtze University, Wuhan 430100, China.
3. College of Resources and Environment, North China University of Water Resources and Electric Power, Zhengzhou 450011, China.
Abstract Finite-difference (FD) methods are widely used in seismic forward modeling owing to their computational efficiency but are not readily applicable to irregular topographies. Thus, several FD methods based on the transformation to curvilinear coordinates using body-fitted grids have been proposed, e.g., stand staggered grid (SSG) with interpolation, nonstaggered grid, rotated staggered grid (RSG), and fully staggered. The FD based on the RSG is somewhat superior to others because it satisfies the spatial distribution of the wave equation without additional memory and computational requirements; furthermore, it is simpler to implement. We use the RSG FD method to transform the first-order stress–velocity equation in the curvilinear coordinates system and introduce the high-precision adaptive, unilateral mimetic finite-difference (UMFD) method to process the free-boundary conditions of an irregular surface. The numerical results suggest that the precision of the solution is higher than that of the vacuum formalism. When the minimum wavelength is low, UMFD avoids the surface wave dispersion. We compare FD methods based on RSG, SEM, and nonstaggered grid and infer that all simulation results are consistent but the computational efficiency of the RSG FD method is higher than the rest.
This research was supported by the National Nature Science Foundation of China (Nos. 41504102 and 41604037) and National Science and Technology Major Project (No. 2016ZX05015-006) and Yangtze University Youth Found (No. 2015cqn32).
Cite this article:
. Irregular surface seismic forward modeling by a body-fitted rotated–staggered-grid finite-difference method[J]. APPLIED GEOPHYSICS, 2018, 15(3-4): 420-431.
[1]
Appelo, D., and Petersson, N. A., 2009, A Stable Finite Difference Method for the Elastic Wave Equation on Complex Geometries with Free Surfaces: Communications in Computational Physics, 5(1), 84−107.
[2]
Rojas, O., Otero, B., Castillo, J. E., and Day, S. M., 2014, Low dispersive modeling of Rayleigh waves on partly staggered grids: Computational Geosciences, 18(1), 29−43.
[3]
Bogey, C., and Bailly, C., 2004, A family of low dispersive and low dissipative explicit schemes for flow and noise computations: Journal of Computational Physics, 194(1), 194−214.
[4]
Saenger, E. H., and Bohlen, T., 2004, Finite-difference modeling of viscoelastic and anisotropic wave propagation using the rotated staggered grid: Geophysics, 69(2), 583−591.
[5]
Bohlen, T., and Saenger, E. H., 2006, Accuracy of heterogeneous staggered-grid finite-difference modeling of Rayleigh waves: Geophysics, 71(4), T109−T115.
[6]
Saenger, E. H., Gold, N., & Shapiro, S. A., 2000, Modeling the propagation of elastic waves using a modified finite-difference grid: Wave Motion, 31(1), 77−92.
[7]
Castillo, J. E., Hyman, J. M., Shashkov, M., and Steinberg, S., 2001, Fourth- and sixth-order conservative finite difference approximations of the divergence and gradient: Applied Numerical Mathematics, 37(1−2), 171−187.
[8]
Tarrass, I., Giraud, L., and Thore, P., 2011, New curvilinear scheme for elastic wave propagation in presence of curved topography: Geophysical Prospecting, 59(5), 889-906.
[9]
Chaljub, E., Komatitsch, D., and Vilotte, J. P., 1998, The spectral element method: An efficient tool to simulate the seismic response of 2D and 3D geological structures: Bulletin of the Seismological Society of America, 88(2), 368−392.
[10]
Chen, H., Wang, X., and Zhao, H., 2006, A rotated staggered grid finite-difference with the absorbing boundary condition of a perfectly matched layer: Chinese Science Bulletin, 51(19), 2304−2314.
[11]
Thompson, J. F., Warsi, Z. U. A., and Mastin, C. W., 1985, Numerical grid generation: foundations and applications: Elsevier Science Publishing Co Inc, North-Holland, 1−300.
[12]
Yan, H. Y., and Liu, Y., 2012, High-Order Finite-Difference Numerical Modeling of Wave Propagation in Viscoelastic TTI Media Using Rotated Staggered Grid: Chinese Journal of Geophysics, 55(2), 252−265.
[13]
Fan, N., Zhao, L. F., Xie, X. B., Ge, Z., and Yao, Z. X., 2016, Two-dimensional time-domain finite-difference modeling for viscoelastic seismic wave propagation: Geophysical Journal International, 206(3), 1539−1551.
[14]
Hestholm, S., 2003, Elastic wave modeling with free surfaces: Stability of long simulation: Geophysics, 68(1), 314−321.
[15]
Yang, Y., Huang, J. P., Lei, J. S., Li, Z. C., Tian, K., and Li, Q. Y., 2016, Numerical simulation of Lebedev grid for viscoelastic media with irregular free-surface: Oil Geophysical Prospecting, 51(4), 698−706.
[16]
Hestholm, S., and Ruud, B., 1998, 3-D finite-difference elastic wave modeling including surface topography: Geophysics, 63(2), 613−622.
[17]
Zhang, W., and Chen, X., 2006, Traction image method for irregular free surface boundaries in finite difference seismic wave simulation: Geophysical Journal International, 167(1), 337−353.
[18]
Zhang, W., Zhang, Z., and Chen, X., 2012, Three-dimensional elastic wave numerical modelling in the presence of surface topography by a collocated-grid finite-difference method on curvilinear grids: Geophysical Journal International, 190(1), 358−378.
[19]
Huang, J. P., Qu, Y. M., Li, Q. Y., Li, Z. C., Li, D. L., and Bu, C. C., 2015,Variable-coordinate forward modeling of irregular surface based on dual-variable grid: Applied Geophysics, 12(1), 101−110.
[20]
Komatitsch, D., and Tromp, J., 1999, Introduction to the spectral element method for three-dimensional seismic wave propagation: Geophysical Journal of the Royal Astronomical Society, 139(3), 806−822.
[21]
Zhang, Y., Ping, P., and Zhang, S. X., 2017, Finite-difference modeling of surface waves in poroelastic media and stress mirror conditions: Applied Geophysics, 14(1), 105−114.
2018, Vol. 15 
