P wave reflection coefficient approximation of viscoelastic medium
Wang Xiaojie1,2,3, Luan Xiwu1,2,3, Zheng Jingjing4
1. The Key Laboratory of Marine Hydrocarbon Resources and Environmental Geology, Ministry of Land and Resources, Qingdao, Shandong 266071, China;
2. Function Laboratory for Marine Mineral Resource Geology and Exploration, Qingdao National Laboratory for Marine Science and Technology, Qingdao, Shandong 266071, China;
3. Qingdao Institute of Marine Geology, Qingdao, Shandong 266071, China;
4. Shengli Geophysical Research Institute of SINOPEC, Dongying, Shandong 257022, China
Abstract：We propose in this article a method for P wave reflection coefficient approximation. Based on the accurate Zoeppritz equation of viscoelastic medium and the viscoelastic medium, we use the approximation of weak viscoelastic medium and similar medium to derive reflection coefficient approximate formula of viscoelastic medium according to the theory of decomposition of medium. The approximate formula is divided into real part and imaginary part. The elastic and viscoelastic terms are all in the real part, which more accurately reflects the wave propagation in the actual formation. In particular, when the quality factor is infinite and the attenuation angel is zero, the reflection coefficient approximate formula is completely consistent with the reflection coefficient approximate formula in the elastic medium(Aki-Richards approximate formula), which proves the rationality of the formula. Finally, the validity of the reflection coefficient approximate formula of viscoelastic medium is verified with the four kinds of AVO models and different viscoelastic parameters. The results show that the P-wave reflection coefficient approximate formula with the background of viscoelastic medium has higher precision than Aki-Richards approximate formula.
Wang Xiaojie, Yin Xingyao, Wu Guochen. Estimation of layer quality factors from pre-stack seismic data. OGP, 2011, 46(3):423-428.
[3]
Buchen P W. Reflection, transmission, and diffrac-tion of SH-waves in linear viscoelastic solids.Geophysical Journal of the Royal Astronomical Society, 1971a, 25(3):97-113.
[4]
Borcherdt R D. Reflection and refraction of type-Ⅱ S waves in elastic and anelastic media. Bulletin of the Seismological Society of America, 1977, 67(4):43-67.
[5]
阎贫, 何樵登.横向各向同性粘弹性介质中的地震波.石油物探, 1992, 31(4):23-34.
Yan Pin, He Qiaodeng.Seismic waves in transversely isotropic viscoelasticmedium.GPP, 1992, 31(4):23-34.
[6]
范家参.粘弹性介质中的地震波.地震研究, 2001, 24(4):358-362.
Fan Jiashen. Seismic waves in viscoelastic medium.Journal of Seismological Research, 2001, 24(4):358-362.
Guo Zhiqi, Liu Cai, Zhang Fengqin.Reflection and transmission problem of SH waves in layered viscoelastic medium.Journal of Jilin University(Earth Science Edition), 2005, 35(S1):57-61.
Yin Chen, He Zhenhua, Huang Deji.The research and the application of the seismic attenuation theory based on the wave equation. Computing Techniques for Geophysical and Geochemical Exploration, 2008, 30(5):353-357.
Shen Zhanghong, Wang Xiaojie.The approximation of P waves reflection and transmission coefficient in viscoelastic medium and comparative analysis. Progress in Geophysics, 2013, 28(1):257-264.
Zhang Yuhua.The AVO Forward Modeling Based on Rock Physics[D], China University of Petroleum(East China), Dongying, Shandong, 2007, 64-68.
[13]
Ren J X, Gangi A F.Reflection and transmissions of plane waves on an interface between dissimilar fluid-saturated porous media.SEG Technical Program Expanded Abstracts, 1994, 13:1167-1170.
[14]
Wang Y H. Approximations to the Zoeppritz equa-tions and their use in AVO analysis. Geophysics, 1999, 64(6):1920-1927.
[15]
Shuey R T. A simplification of the Zoeppritz equa-tions.Geophysics, 1985, 50(4):609-614.
[16]
Ostrander W J. Plane wave reflection coefficients for gas sands at nonnormal angles of incidence.Geophy-sics, 1984, 49(10):1637-1648.
Liu Yang, Li Chengchu, Mu Yongguang.Reflection and transmission of plane wave on an interface between dissimilar two-phase, transversely isotropic media. Chinese Journal of Geophysics, 2000, 43(5):691-698.
[18]
Carcione J M and Tinivella U.Bottom-simulating reflectors:seismic velocities and AVO effects.Geophysics, 2000, 65(1):54-67.
[19]
Xu Y.AVO Developments Applied to Blackfoot 3C-2D Broadband Line[D].University of Calgary, 1999.
[20]
Rutherford S R and Williams Robert H. Amplitude-versus-offset variations in gas sands.Geophysics, 1989, 54(6):680-688.
