最优的Zoeppritz方程的简化综述
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摘要
基于Zoeppritz方程的\VO技术是一项利用振幅随炮检距变化特征分析识别岩性和油气藏的地震勘探技术.许多学者在不同的前提条件下对该方程进行了不同的简化,但在不同程度上都影响着反演的精度和可靠性.最优的Zoeppritz方程是一种新的近似,其在某种程度上达到了最优,相比之下,最简化又最精确.是类比与AkiRichards近似形式的一种拟线性近似,因此可以简化的运用到非线性反演中,为实际应用提供更准确的理论基础.
Based on the equation of Zoeppritz the AVO technology uses the amplitude variation with offset for identifying lithology and reservoir.Many scholars have simplified this equation in different conditions, but to different extents the accuracy and reliability of the inversion are influenced.New approximations are developed that are optimal in the sense that they preserve as much accuracy as possible with as much simplicity as possible.In particular, they are expressed in a form that is pseudo-linear after the form of the Aki-Richards approximation.Thus they would be very simple to apply in an essentially exact non-linear inversion and to provide a more accurate theoretial basis for practical applications.
Based on the equation of Zoeppritz the AVO technology uses the amplitude variation with offset for identifying lithology and reservoir.Many scholars have simplified this equation in different conditions, but to different extents the accuracy and reliability of the inversion are influenced.New approximations are developed that are optimal in the sense that they preserve as much accuracy as possible with as much simplicity as possible.In particular, they are expressed in a form that is pseudo-linear after the form of the Aki-Richards approximation.Thus they would be very simple to apply in an essentially exact non-linear inversion and to provide a more accurate theoretial basis for practical applications.
引文
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[39] 孙鹏远,孙建国,卢秀丽.P-SV波AVO方法研究进展[J].地球物理学进展,2003,18(4) :602～607． Sun P Y,SuN J G,Lu X L.Progress in research on the method of P-SV wave AVO[J].Progress in Geophysics,2003,18(4) :602～607．
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[2] 孙鹏远,孙建国,卢秀丽.基于弹性参数的PP波AVO分析[J].石油物探与开发,2004,31(3) :86～88． Sun P Y,Sun J G,Lu X L.PP-Wave AVO analysis with elastic parameters[J].Petroleum Exploration and Development,2004,31(3) :86～88．
[3] 孙鹏远,孙建国,卢秀丽.P-P波AVO近似对比研究:定性分析[J].石油地球物理勘探,2002,37:164～171． Sun P Y,Sun J G,Lu X L.AVO approximation Comparative Study for P-P wave:Qualitative analysis[J].Oil Geophysical Prospecting,2002,37:164～171．
[4] 孙鹏远,孙建国,卢秀丽.P-P波AVO近似对比研究:定量分析[J].石油地球物理物探,2002,37:172～179． Sun P Y,Sun J G,Lu X L.AVO approximation Comparative Study for P P-wave:Quantitative Analysis[J].Oil Geophysical Prospecting,2002,37 :172～179．
[5] 安艺敬一,理查德.定量地震学:理论与方法[M].地震出版社,1980． Aki K,Richards P G.Quantitative Seismology:Theory and Methods[M].Earthquake Press,1980．
[6] Koefoed O.Reflection and transmission coefficients for plane longitudinal incident waves[J].Geophysical Prospecting,1962,10:304～351．
[7] Bortfeld.Approximation to the reflect ion and transmission coefficients of plane longitudinal and transverse waves[J]. Geophysical Prospecting,1961,9:485～502．
[8] Aki K,Richards P G.Quantitative Seismology:Theory and Methods[M].W.H.Freeman,1980．
[9] Shuey R T.A simplification of the Zoeppritz equations[J]. Geophysics,1985,50 :609～614．
[10] Charles P.Ursenbach.Optimal Zoeppritz approximations[J]. CREWES Research Report,2002,14:1～10．
[11] Richards P G,Frasier C W.Scattering of elastic waves from depth-dependent in homogeneities[J].Geophysics,1976,41: 441～458．
[12] 潘仁芳.AVO的内涵与外延[J].石油天然气学报,2006,28 (2) :50～55． Pan R F.Intension and Extension of AVO[J].Journal of Oil and Gas Technology,2006,28(2) .50～55．
[13] Ostrander W J.Plane wave reflection coefficients for gas sands at no normal angles of incidence[J].Geophysics,1984,49:1637～1648．
[14] Knott C G.On the reflect ion and refract ion of elastic wave with seismological application[J].PhilMag 5th ser,1899,48:64～97．
[15] Wang Y H.Approximations to Zoeppritz equations and their use in AVO analysis[J].Geophysics,1999,64 :1920～1927．
[16] Mallick.A simple approximation to the P-wave reflection coefficient and its implication in the inversion of amplitude variation with offset data[J].Geophysics,1993,58,544～ 552．
[17] FattI J L et al.Detection of gas in sandstone reservoirs using AVO analysis[J].Geophysics,1994,59:1362～1376．
[18] Goodway B,Chen T,Downton J.Improved AVO fluid detect ion and litho logy discrimination using Lame petrol physical parameters,“ K”,“ L” and “ K”,from P and S inversions[J].CSEG Expanded Abstracts,1997,148～151．
[19] Castagna J P,Swan H W.Principles of AVO cross plotting [J].The Leading Edge,1997,16:135～171．
[20] 陈天胜,刘洋,魏修成.纵波和转换波联合AVO反演方法研究[J].中国石油大学学报,2006,30(1) :33～37． Chen T S,Liu Y,Wei X C.Joint amplitude versus off set inversion of P-P and P SV seismic data[J].Journal of China University of Petroleum,2006,30(1) :33～37．
[21] 王栋.AVO技术的研究探讨[J].内蒙古石油化工,2007,8:16～19． Wang D.Research and Discussion about AVO[J].Inner Mongolia Petrochemical Industry,2007,8 :16～19．
[22] Eborm D,Sheriff R E.Anisotropy and reservoir development [J].Reservoir Geophysics,1992,7:353～361．
[23] 阴可,杨慧珠.各向异性介质中的AVO[J].石油物探,1997,36(4) :28～37． Yin K,Yang H Z,Dong Y.Reflection coefficient of P wave in anisotropic media[J].Geophysical Pprospecting for Petroleum,1997,36(4) :28～37．
[24] 寻浩,董敏煜,牟永光.横向各向同性介质中的AVO[J].石油地球物理勘探,1997,32(1) :45～56． Xun H,Dong M Y,Mou Y G.AVO in transverse isotropic medium[J].oil Geophysical Prospecting,1997,32(1) :45～56．
[25] Thomsen L.Weak elastic anisotropy[J].Geophysics,1986,51:1954～1966．
[26] Charles P.Ursenbach.Improved approximations for anisotropic reflectivies[J].CERWES Research Report,2004,14:1～5．
[27] Rüger A.Reflection Coefficients and Azimuthally AVO Analysis in Anisotropic Media[M].Ph.D.Thesis,Colorado School of Mines.1996
[28] Carcuz J R.A combined AVO analysis of P-P and P-S reflection data[C].in SEG 2001 Extended Abstracts.2001．
[29] Ramos A C B,Castagna J P.Useful approximations for converted-wave AVO[J].Geophysics.,2001,66:1721～ 1734．
[30] Ursenbach C P.Testing pseudo-linear Zoeppritz approximations:P-wave AVO inversion[J].CREWES 2003 Research Report,2003,15 :13～27．
[31] Ursenbach C P.Testing pseudo-linear Zoeppritz approximations:Multicomponent and joint AVO inversion [J].CREWES 2003 Research Report,2003,15:1～12
[32] 郑晓东.Zoeppritz方程的近似及其应用[J].石油地球物理勘探,1991,26(2) :129～144． Zheng X D.Approximately and application of Zoeppritz equations[J].Oil Geophysical Prospecting,1991,26(2) :129～144．
[33] 杨绍国,周熙襄.Zoeppritz方程的级数表达式及近似[J].石油地球物理勘探,1994,29(4) :399～412． Yang S G,Zhou X X.Zoeppritz series expressions and approximate equations[J].Oil Geophysical Prospecting.1994,29(4) :399～412．
[34] Wang Y H.Approximations to Zoeppritz equations and their use in AVO analysis[J].Geophysics,1999,64:1920～1927．
[35] 尚永生,杨长春,王真理.等.塔里术盆地卡4区块AVO研究[J].地球物理学进展,2007,22(5) :1408～1415． Shang Y S,Yang C C,Wang Z L,et al.AVO research in Ka 4 region of Tarim basin[J].Progress in Geophysics(in Chinese),2007,22(5) :1408～1415．
[36] 孙鹏远,孙建国,卢秀丽.P-SV波反射系数近似及其AVO属性特征[J].地球学报,2006,27(1) :85～89． Sun P Y,Sun J G,Lu X L.P-SV wave reflection coefficient approximations and characteristics of AVO attributes[J].Acta Geoscientica Sinica,2006． 27(1) :85～89．
[37] 孙鹏远,孙建国,卢秀丽.P-SV波AVO分析[J].石油地球物理勘探,2003,38(2) :131～135． Sun P Y,Sun J G,Lu X L.AVO analyses is for P-SV wave[J].Oil Geophysical Prospecting,2003,38(2) :131～135．
[38] John P C,Steven W S.Comparison of AVO indicators:A modeling study[J].Geophysics,1994,59(12) :1849～1855．
[39] 孙鹏远,孙建国,卢秀丽.P-SV波AVO方法研究进展[J].地球物理学进展,2003,18(4) :602～607． Sun P Y,SuN J G,Lu X L.Progress in research on the method of P-SV wave AVO[J].Progress in Geophysics,2003,18(4) :602～607．
[40] 冯晅,舒梦珵,王兆国,刘财,王典,王世煜.P-P波和P-SV波联合AVO反演研究[J].地球物理学进展,2008,23(5) :1556～1559． Feng X,Shu M C,Wang Z G,Liu C,Wang D,Wang S Y.Joint AVO inversion using P P and P-SV seismic data[J].Progress in Geophysics,2008,23(5) :1556～1559
[41] 宋建国,王艳香,乔玉雷,王慧.AVO技术进展[J].地球物理学进展,2008,23(2) :508～514． Song J G,Wang Y X,Qiao Y L,Wang H.Advances in AVO technique[J].Progress in Geophysics,2008,23(2) :508～514．
[42] 雍学善,马海珍,高建虎.双相介质AVO方程及参数简化研究[J].地球科学进展,2006,21(3) :242～249． Yong X S,Ma H Z,Gao J H.A Study of AVO Equation in Dual-phase Medium and Parameter Simplification[J].Advances in Earth Science,2006,21(3) :242～249．
[43]Tarantala A,Velette B.Generalized nonlinear inverse Problems solved using the least squares criteria,Rev[J].GeoPhys.and space physics,1982,20:219～232．
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