Abstract
The paper presents a staggered-grid any even-order accurate finite-difference scheme for two-dimensional (2D), three-component (3C), first-order stress-velocity elastic wave equation and its stability condition in the arbitrary tilt anisotropic media; and derives a perfectly matched absorbing layer (PML) boundary condition and its staggered-grid any even-order accurate difference scheme in the 2D arbitrary tilt anisotropic media. The results of numerical modeling indicate that the modeling precision is high, the calculation efficiency is satisfactory and the absorbing boundary condition is better. The wave-front shapes of elastic waves are complex in the anisotropic media, and the velocity of qP wave is not always faster than that of qS wave. The wave-front triplication of qS wave and its events in both reflected domain and propagated domain, which are not commonly hyperbola, is a common phenomenon. When the symmetry axis is tilted in the TI media, the phenomenon of S-wave splitting is clearly observed in the snaps of three components and synthetic seismograms, and the events of all kinds of waves are asymmetric.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Carcinoe J M, Kosloff D, Behle A et al. 1992. A spectral scheme for wave propagation simulation in 3-D elastic anisotropic media [J]. Geophysics, 57(5): 1 593–1 607.
Collino F and Tsogka C. 2001. Application of the perfectly matched absorbing layer model to the linear elastodynamic problem in anisotropic heterogeneous media [J]. Geophysics, 66(1): 294–307.
Crampin S, Bush I, Taylor D B. 1986. Estimating the internal structure of reservoirs with shear-wave VSPs [J]. The Leading Edge, 5(11): 35–39.
Crampin S. 1981. A review of wave motion in anisotropic and cracked elastic media [J]. Wave Motion, 3: 343–391.
Crampin S. 1984. Anisotropy in exploration seismics [J]. First Break, 2(3): 19–21.
HE Qiao-deng and ZHANG Zhong-jie. 1996. Seismic Wave and Its Numerical Simulation in TI Media [M]. Changchun: Jilin University Publishing House (in Chinese).
HOU An-ning and HE Qiao-deng. 1995. Study on characteristics of elastic wave propagation in pseudo-spectral modeling [J]. Oil Geophysical Prospecting, 34(2): 36–45 (in Chinese).
Hudson J A, Liu E, Crampin S. 1996. The mechanical properties of materials with interconnected cracks and pores [J]. Geophy J Int, 124: 105–112.
Igel H, Mora P, Riollet B. 1995. Anisotropic wave propagation through finite-difference grids [J]. Geophysics, 60(4): 1 203–1 216.
Liu Y, Crampin S, Abercrombie R E. 1997. Shear-wave anisotropy from borehole recordings at 2.5 km depth and the stress field at Cajon Pass [J]. Geophy J Int, 129: 439–449.
NIU Bin-hua and SUN Chun-yan. 1995. Numerical simulation for 2.5-D elastic wave fields in crack anisotropic media [J]. Earth Science (Journal of the China University of Geosciences), 20(1): 107–111 (in Chinese).
Okaya D A and McEvilly T. 2003. Elastic wave propagation in anisotropic crustal material possessing arbitrary internal tilt [J]. Geophys J Int, 153: 344–358.
PEI Zheng-lin. 2004. Three-dimensional numerical simulation of elastic wave propagation in 3-D anisotropic media with staggered-grid high-order difference method [J]. Journal of the University of Petroleum, China (Edition of Natural Science), 28(5): 23–29 (in Chinese).
TENG Ji-wen and ZHANG Zhong-jie. 1995. Numerical modeling for three components seismic data by the convolutional derivative operator method in anisotropic media [J]. Oil Geophysical Exploration, 34(3): 14–22 (in Chinese).
TENG Ji-wen, ZHANG Zhong-jie, WANG Ai-wu et al. 1992. Evolution, status and problem of study on anisotropy in elastic media [J]. Progress in Geophysics, 7(4): 14–28 (in Chinese).
Thomsen L. 1986. Weak elastic anisotropy [J]. Geophysics, 51(10): 1 954–1 966.
Thomsen L. 1995. Elastic anisotropy due to aligned cracks in porous rock [J]. Geophysical Prospecting, 43: 805–829.
YANG Ding-hui, TENG Ji-wen, ZHANG Zhong-jie. 1996. An approximately analytic solution to simulate the 3-C seismic wave-fields [J]. Chinese J Geophys, 39(Suppl): 283–291 (in Chinese).
ZHANG Wen-sheng and SONG Hai-bin. 2001. Finite-difference forward modeling of three-component records with high precision in 3-D orthorhombic anisotropic media [J]. Oil Geophysical Prospecting, 36(4): 422–432 (in Chinese).
Author information
Authors and Affiliations
Additional information
Foundation item: Fund Project of Key Lab of Geophysical Exploration of China National Petroleum Corporation (GPR0408).
About this article
Cite this article
Zheng-lin, P., Shang-xu, W. A staggered-grid high-order finite-difference modeling for elastic wave field in arbitrary tilt anisotropic media. Acta Seimol. Sin. 18, 471–482 (2005). https://doi.org/10.1007/s11589-005-0025-9
Received:
Revised:
Accepted:
Issue Date:
DOI: https://doi.org/10.1007/s11589-005-0025-9