The complete decoupled wave equations for ellipsoidal anisotropic media

被引：0
|
作者：
Liang K. [1 ]
Cao D. [1 ]
Sun S. [1 ]
Yin X. [1 ]
机构：
[1] School of Geosciences, China University of Petroleum (East China), Qingdao
来源：
Shiyou Diqiu Wuli Kantan/Oil Geophysical Prospecting | 2021年 / 56卷 / 06期
关键词：
Decoupling; Dispersion relation; Elastic wave; Ellipsoidal anisotropic media; Wave equation;
D O I：
10.13810/j.cnki.issn.1000-7210.2021.06.007
中图分类号：
学科分类号：
摘要：
The decoupling of the wave equation refers to the decoupling of an elastic wave equation into wave equations that can describe the independent propagation of various wave patterns, which plays an important role in numerical simulation of seismic waves, seismic migration, and multi-component seismology. In most anisotropic media, the qP wave and qS wave are generally coupled for propagation without exact decoupling nature, but it is found that the ellipsoidal anisotropic (EA) media are an exception. First, on the basis of the exact dispersion relation equation of the elastic wave in homogeneous EA media, three decoupled dispersion equations are decomposed from this equation by the factorization method and then transformed into the completely and exactly decoupled wave equations of the qP wave, qSV wave, and SH wave in homogeneous EA media by inverse Fourier transform. The theoretical formulas and numerical examples indicate that the qP wave, qSV wave, and SH wave can be completely and exactly decoupled and propagate independently in homogeneous EA media by decoupled wave equations. The wavefront of the qP wave and SH wave is ellipsoidal, and the wavefront of the qSV wave is spherical, independent of anisotropic parameters. The three complete decoupled wave equations are suitable not only for weak anisotropic EA media but also for strong anisotropic EA media. © 2021, Editorial Department OIL GEOPHYSICAL PROSPECTING. All right reserved.
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页码：1254 / 1261
页数：7
相关论文
共 25 条
  • [1] (2002)
  • [2] Alkhalifah T., An acoustic wave equation for anisotropic media, Geophysics, 65, 4, pp. 1239-1250, (2000)
  • [3] Alkhalifah T., An acoustic wave equation for orthorhombic anisotropy, Geophysics, 68, 4, pp. 1169-1172, (2003)
  • [4] Grechka V, Zhang L, Rector J W, Shear waves in acoustic anisotropic media, Geophysics, 69, 2, pp. 576-582, (2004)
  • [5] Zhou H, Zhang G, Bloor R., An anisotropic acoustic wave equation for modeling and migration in 2D TTI media, SEG Technical Program Expanded Abstracts, 25, pp. 194-198, (2006)
  • [6] LIANG Kai, WU Guochen, YIN Xingyao, Et al., Wave equation decomposition in 3-D TTI medium, Oil Geophysical Prospecting, 44, 1, pp. 19-27, (2009)
  • [7] Fowler P J, Du X, Fletcher R P., Coupled equations for reverse time migration in transversely isotropic media, Geophysics, 75, 1, pp. S11-S22, (2010)
  • [8] Duveneck E, Bakker P M., Stable P-wave modeling for reverse time migration in tilted TI media, Geophysics, 76, 2, pp. S65-S75, (2011)
  • [9] Zhang Y, Zhang H, Zhang G., A stable TTI reverse time migration and its implementation, Geophysics, 76, 3, pp. WA3-WA11, (2011)
  • [10] Cheng J B, Kang W., Simulating propagation of separated wave modes in general anisotropic media, Part I: qP-wave propagators, Geophysics, 79, 1, pp. C1-C18, (2014)
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