杨氏模量和泊松比反射系数近似方程及地震叠前反演
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摘要
杨氏模量和泊松比是表征岩石性质的重要弹性参数;地震叠前反演是获取地下弹性参数最有效的方法之一,其核心是描述地震波反射特点的反射系数方程。针对缺失大入射角的地震数据,经典三项式反射系数方程的反演不稳定性较突出的情况下,拟从减少参数维数入手,提高反演结果的稳健性。首先从Aki-Richards近似方程出发,通过引入密度幂指数经验近似模型拟合密度反射系数,推导得到直接反演杨氏模量和泊松比的两项式反射系数近似方程;然后,从正演与反演角度,利用多个参数化模型对新方程的稳定性与精度进行分析、验证,结果表明该方程具有计算精度高、适用性较强的特点;最后,依据新方程总结了一套适用于含气储层、能够直接反演岩体脆性参数的叠前反演方法,该方法较好地刻画了含气目标,为油气储层含气特征的识别提供了新的手段。
Young's modulus and Poisson ratio are two important rock parameters to indicate rock properties.Seismic prestack inversion is one of the most effective ways to obtain these parameters,and its core is reflection coefficient equation describing characteristics of seismic reflection.This article starts with introducing a variable parameter formula to Aki-Richards approximation equation,derive a new two-term reflection coefficient approximate equation in terms of Young's modulus and Poisson ratio by reasonably fitting density reflection coefficient;and then analyzes the stability and precision of the new equation using different parametric models.Experimental results show that this equation is as accurate as the exact equation,and possesses good applicability.Finally,a new prestack seismic inversion procedure which is applicable to gas-bearing reservoirs is proposed for rock brittleness.Real data tests show that the proposed inversion method can well describe gas-bearing reservoirs.
Young's modulus and Poisson ratio are two important rock parameters to indicate rock properties.Seismic prestack inversion is one of the most effective ways to obtain these parameters,and its core is reflection coefficient equation describing characteristics of seismic reflection.This article starts with introducing a variable parameter formula to Aki-Richards approximation equation,derive a new two-term reflection coefficient approximate equation in terms of Young's modulus and Poisson ratio by reasonably fitting density reflection coefficient;and then analyzes the stability and precision of the new equation using different parametric models.Experimental results show that this equation is as accurate as the exact equation,and possesses good applicability.Finally,a new prestack seismic inversion procedure which is applicable to gas-bearing reservoirs is proposed for rock brittleness.Real data tests show that the proposed inversion method can well describe gas-bearing reservoirs.
引文
[1] 赵波,王赟,芦俊.多分量地震勘探技术新进展及关键问题探讨[J].石油地球物理勘探,2012, 47(3):506-516.ZHAO Bo,WANG Yun,LU Jun.Recent advances of multi-component seismic and some of its key issues[J].Oil Geophysical Prospecting,2012,47(3):506-516.
[2] 王海龙,杨午阳,李海亮,等.塔东古城地区深层油气藏岩溶储层预测[J].石油地球物理勘探,2017,52(增刊2):116-122.WANG Hailong,YANG Wuyang,LI Hailiang,et al.Deep karst reservoir prediction in the Gucheng area,Tarim Basin[J].Oil Geophysical Prospecting,2017,52(S2):116-122.
[3] 任岩,曹宏,姚逢昌,等.吉木萨尔致密油储层脆性及可压裂性预测[J].石油地球物理勘探,2018,53(3):511-519.REN Yan,CAO Hong,YAO Fengchang,et al.Brittleness and fracability prediction for tight oil reservoir in Jimsar Sag,Junggar Basin[J].Oil Geophysical Pro-specting,2018,53(3):511-519.
[4] Sena A,Castillo G,Chesser K,et al.Seismic reservoir characterization in resource shale plays: “Sweet Spot” discrimination and optimization of horizontal well placement[J].SEG Technical Program Expanded Abstracts, 2011,30:1744-1748.
[5] Koefoed O.Reflection and transmission coefficients for plane longitudinal incident waves[J].Geophysical Prospecting,1962,10(3):304-351.
[6] Shuey R T.A simplification of the Zoeppritz-equations[J].Geophysics,1985,50(4):609-614.
[7] Smith G C,Gidlow M.The fluid factor angle and the crossplot angle[C].SEG Technical Program Expanded Abstracts,2003,22:2452.
[8] Vestrum R W,Stewart R R.Joint P and P-SV Inversion:Application and Testing[R].Crewes Research Report,1993,13(5):1-7.
[9] Fatti J L.Detection of gas in sandstone reservoirs using AVO analysis:A 3-D seismic case history using the Geostack technique[J].Geophysics,1994,59(9):1362-1376.
[10] 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 Xiaodong.Approximation of Zoeppritz equation and its application[J].Oil Geophysical Prospecting,1991,26(2):129-144.
[11] Ursenbach C.Two new approximations for AVO inversion[C].2004 CSEG National Convention,2004.
[12] 蔡涵鹏,贺振华,李瑞,等.两项AVO反演研究及应用[J].成都理工大学学报(自然科学版),2011,38(5):581-587.CAI Hanpeng,HE Zhenhua,LI Rui,et al.Study and application of two-term AVO inversion[J].Journal of Chengdu University of Technology,2011,38(5):581-587.
[13] 高刚,贺振华,曹俊兴,等.两项式弹性波阻抗反演方法在深层碳酸盐岩储层预测中的应用[J].石油地球物理勘探,2013,48(3):450-457.GAO Gang,HE Zhenhua,CAO Junxing,et al.The new two-term elastic impedance inversion and its application to predict deep gas-bearing carbonate reserviors[J].Oil Geophysical Prospecting,2013,48(3):450-457.
[14] 宗兆云,印兴耀,张峰,等.杨氏模量和泊松比反射系数近似方程及叠前地震反演[J].地球物理学报,2012, 55(11):3786-3794.ZONG Zhaoyun,YIN Xingyao,ZHANG Feng,et al.Reflection coefficient equation and pre-stack seismic inversion with Young’s modulus and Poisson ratio[J].Chinese Journal of Geophysics,2012,55(11):3786-3794.
[15] 宗兆云,印兴耀,吴国忱.基于叠前地震纵横波模量直接反演的流体检测方法[J].地球物理学报,2012,55(1):284-292.ZONG Zhaoyun,YIN Xingyao,WU Guochen.Fluid identification method based on compressional and shear modulus direct inversion[J].Chinese Journal of Geophysics,2012,55(1):284-292.
[16] 张广智,杜炳毅,李海山,等.页岩气储层纵横波叠前联合反演方法[J].地球物理学报,2014,57(12):4141-4149.ZHANG Guangzhi,DU Bingyi,LI Haishan,et al.The method of joint pre-stack inversion of PP and P-SV waves in shale gas reservoirs[J].Chinese Journal ofGeophysics,2014,57(12):4141-4149.
[17] 苏建龙,屈大鹏,陈超,等.叠前地震反演方法对比分析——焦石坝页岩气藏勘探实例[J].石油地球物理勘探,2016,51(3):581-588.SU Jianlong,QU Dapeng,CHEN Chao,et al.Application of pre-stack inversion technique for shale gas in Jiaoshiba Gas Field[J].Oil Geophysical Prospecting,2016, 51(3):581-588.
[18] 李超,张金淼,朱振宇.深部储层流体因子直接反演方法[J].石油物探,2017,56(6):827-834.LI Chao,ZHANG Jinmiao,ZHU Zhenyu.Direct inversion for fluid factor of deep reservoirs[J].Geophysical Prospecting for Petroleum,2017,56(6):827-834.
[19] Aki K,Richards P G.Quantitative Seismology[M].W.H.Freeman,San Francisco,1980,5-43.
[20] Lu S.Elastic impedance inversion of multichannel seismic data from unconsolidated sediments containing gas hydrate and free gas[J].Geophysics,2004,69(1):164-179.
[21] Gardner G H F,Gardner L W,Gregory A R,et al.Formation velocity and density: The diagnostic basis for stratigraphic traps[J].Geophysics,1974,39(6):777-780.
[22] 朱广生,桂志先,熊新斌,等.密度与纵横波速度关系.地球物理学报[J],1995,38(增刊1):260-264.ZHU Guangsheng,GUI Zhixian,XIONG Xinbin,et al.Relationships between density and P-wave,S-wave velocities[J].Chinese Journal of Geophysics,1995,38(S1):260-264.
[23] 文晓涛,黄德济.礁滩储层地震识别[M].北京: 科学出版社, 2014.
[24] 王家映.地球物理反演理论[M].北京: 高等教育出版社, 2002.
[2] 王海龙,杨午阳,李海亮,等.塔东古城地区深层油气藏岩溶储层预测[J].石油地球物理勘探,2017,52(增刊2):116-122.WANG Hailong,YANG Wuyang,LI Hailiang,et al.Deep karst reservoir prediction in the Gucheng area,Tarim Basin[J].Oil Geophysical Prospecting,2017,52(S2):116-122.
[3] 任岩,曹宏,姚逢昌,等.吉木萨尔致密油储层脆性及可压裂性预测[J].石油地球物理勘探,2018,53(3):511-519.REN Yan,CAO Hong,YAO Fengchang,et al.Brittleness and fracability prediction for tight oil reservoir in Jimsar Sag,Junggar Basin[J].Oil Geophysical Pro-specting,2018,53(3):511-519.
[4] Sena A,Castillo G,Chesser K,et al.Seismic reservoir characterization in resource shale plays: “Sweet Spot” discrimination and optimization of horizontal well placement[J].SEG Technical Program Expanded Abstracts, 2011,30:1744-1748.
[5] Koefoed O.Reflection and transmission coefficients for plane longitudinal incident waves[J].Geophysical Prospecting,1962,10(3):304-351.
[6] Shuey R T.A simplification of the Zoeppritz-equations[J].Geophysics,1985,50(4):609-614.
[7] Smith G C,Gidlow M.The fluid factor angle and the crossplot angle[C].SEG Technical Program Expanded Abstracts,2003,22:2452.
[8] Vestrum R W,Stewart R R.Joint P and P-SV Inversion:Application and Testing[R].Crewes Research Report,1993,13(5):1-7.
[9] Fatti J L.Detection of gas in sandstone reservoirs using AVO analysis:A 3-D seismic case history using the Geostack technique[J].Geophysics,1994,59(9):1362-1376.
[10] 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 Xiaodong.Approximation of Zoeppritz equation and its application[J].Oil Geophysical Prospecting,1991,26(2):129-144.
[11] Ursenbach C.Two new approximations for AVO inversion[C].2004 CSEG National Convention,2004.
[12] 蔡涵鹏,贺振华,李瑞,等.两项AVO反演研究及应用[J].成都理工大学学报(自然科学版),2011,38(5):581-587.CAI Hanpeng,HE Zhenhua,LI Rui,et al.Study and application of two-term AVO inversion[J].Journal of Chengdu University of Technology,2011,38(5):581-587.
[13] 高刚,贺振华,曹俊兴,等.两项式弹性波阻抗反演方法在深层碳酸盐岩储层预测中的应用[J].石油地球物理勘探,2013,48(3):450-457.GAO Gang,HE Zhenhua,CAO Junxing,et al.The new two-term elastic impedance inversion and its application to predict deep gas-bearing carbonate reserviors[J].Oil Geophysical Prospecting,2013,48(3):450-457.
[14] 宗兆云,印兴耀,张峰,等.杨氏模量和泊松比反射系数近似方程及叠前地震反演[J].地球物理学报,2012, 55(11):3786-3794.ZONG Zhaoyun,YIN Xingyao,ZHANG Feng,et al.Reflection coefficient equation and pre-stack seismic inversion with Young’s modulus and Poisson ratio[J].Chinese Journal of Geophysics,2012,55(11):3786-3794.
[15] 宗兆云,印兴耀,吴国忱.基于叠前地震纵横波模量直接反演的流体检测方法[J].地球物理学报,2012,55(1):284-292.ZONG Zhaoyun,YIN Xingyao,WU Guochen.Fluid identification method based on compressional and shear modulus direct inversion[J].Chinese Journal of Geophysics,2012,55(1):284-292.
[16] 张广智,杜炳毅,李海山,等.页岩气储层纵横波叠前联合反演方法[J].地球物理学报,2014,57(12):4141-4149.ZHANG Guangzhi,DU Bingyi,LI Haishan,et al.The method of joint pre-stack inversion of PP and P-SV waves in shale gas reservoirs[J].Chinese Journal ofGeophysics,2014,57(12):4141-4149.
[17] 苏建龙,屈大鹏,陈超,等.叠前地震反演方法对比分析——焦石坝页岩气藏勘探实例[J].石油地球物理勘探,2016,51(3):581-588.SU Jianlong,QU Dapeng,CHEN Chao,et al.Application of pre-stack inversion technique for shale gas in Jiaoshiba Gas Field[J].Oil Geophysical Prospecting,2016, 51(3):581-588.
[18] 李超,张金淼,朱振宇.深部储层流体因子直接反演方法[J].石油物探,2017,56(6):827-834.LI Chao,ZHANG Jinmiao,ZHU Zhenyu.Direct inversion for fluid factor of deep reservoirs[J].Geophysical Prospecting for Petroleum,2017,56(6):827-834.
[19] Aki K,Richards P G.Quantitative Seismology[M].W.H.Freeman,San Francisco,1980,5-43.
[20] Lu S.Elastic impedance inversion of multichannel seismic data from unconsolidated sediments containing gas hydrate and free gas[J].Geophysics,2004,69(1):164-179.
[21] Gardner G H F,Gardner L W,Gregory A R,et al.Formation velocity and density: The diagnostic basis for stratigraphic traps[J].Geophysics,1974,39(6):777-780.
[22] 朱广生,桂志先,熊新斌,等.密度与纵横波速度关系.地球物理学报[J],1995,38(增刊1):260-264.ZHU Guangsheng,GUI Zhixian,XIONG Xinbin,et al.Relationships between density and P-wave,S-wave velocities[J].Chinese Journal of Geophysics,1995,38(S1):260-264.
[23] 文晓涛,黄德济.礁滩储层地震识别[M].北京: 科学出版社, 2014.
[24] 王家映.地球物理反演理论[M].北京: 高等教育出版社, 2002.