基于YPD-Zoeppritz方程的杨氏模量和泊松比直接反演方法
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摘要
为解决非常规油气勘探中"甜点"的有效识别问题,开展了杨氏模量和泊松比直接反演方法研究。针对Zoeppritz近似方程精度有限的问题,对精确Zoeppritz方程进行重新推导,建立了以杨氏模量、泊松比和密度的自然对数为未知参数的YPD-Zoeppritz方程;在此基础上,结合广义线性反演和贝叶斯理论,引入一阶差分矩阵和三变量柯西分布,构建更为合理的反射系数稀疏约束项,提高了广义线性反演的适定性;引入低频软约束项进一步稳定反演结果的低频成分,提高了反演剖面的横向连续性。模型数据和实际数据试算结果表明,该方法反演精度较高,而且能够逐步压缩子波旁瓣,使反演结果呈现明显的"块化"效果,降低了子波旁瓣对反演结果的影响。基于YPD-Zoeppritz方程的杨氏模量和泊松比直接反演方法适定性强,具有较好的稳定性。
To effectively identify the dessert areas in unconventional oil and gas exploration,a direct inversion method of Young's modulus and Poisson's ratio was developed.First,by re-deriving the exact Zoeppritz equation,the YPD-Zoeppritz equation with the natural logarithm of Young's modulus,Poisson's ratio,and density as unknown parameters was established.Next,based on generalized linear inversion and Bayesian theory,the first-order differential matrix and the three-variable Cauchy distribution were used to construct a more reasonable sparse constraint term of reflection coefficient,to improve the fitness of generalized linear inversion.Moreover,the low-frequency soft constraint term was introduced for stable inversion of the low-frequency component,to improve the lateral continuity of inversion profile.Testing on both model data and field data indicated that the inversion method could reduce the influence of wavelet side lobes on the inversion results by gradually compressing the wavelet side lobes,thus making the inversion results show an obvious "blocking" effect.The proposed direct inversion method is well-posed and stable.
To effectively identify the dessert areas in unconventional oil and gas exploration,a direct inversion method of Young's modulus and Poisson's ratio was developed.First,by re-deriving the exact Zoeppritz equation,the YPD-Zoeppritz equation with the natural logarithm of Young's modulus,Poisson's ratio,and density as unknown parameters was established.Next,based on generalized linear inversion and Bayesian theory,the first-order differential matrix and the three-variable Cauchy distribution were used to construct a more reasonable sparse constraint term of reflection coefficient,to improve the fitness of generalized linear inversion.Moreover,the low-frequency soft constraint term was introduced for stable inversion of the low-frequency component,to improve the lateral continuity of inversion profile.Testing on both model data and field data indicated that the inversion method could reduce the influence of wavelet side lobes on the inversion results by gradually compressing the wavelet side lobes,thus making the inversion results show an obvious "blocking" effect.The proposed direct inversion method is well-posed and stable.
引文
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[13] ALEMIE W,SACCHI M D.High-resolution three-term AVO inversion by means of a Trivariate Cauchy probability distribution[J].Geophysics,2011,76(1):43-55
[14] 张丰麒,金之钧,盛秀杰,等.贝叶斯三参数低频软约束同步反演[J].石油地球物理勘探,2016,51(5):965-975ZHANG F Q,JIN Z J,SHENG X J,et al.Bayesian prestack three-term inversion with soft low-frequency constraint[J].Oil Geophysical Prospecting,2016,51(5):965-975
[2] 刘勇,方伍宝,李振春,等.基于叠前地震的脆性预测方法及应用研究[J].石油物探,2016,55(3):425-432LIU Y,FANG W B,LI Z C,et al.Brittleness prediction and application based on pre-stack seismic inversion[J].Geophysical Prospecting for Petroleum,2016,55(3):425-432
[3] 李大军,杨晓,王小兰,等.四川盆地W地区龙马溪组页岩气压裂效果评估和产能预测研究[J].石油物探,2017,56(5):735-745LI D J,YANG X,WANG X L,et al.Estimating the fracturing effect and production capacity of the Longmaxi Formation of the Lower Silurian in area W,Sichuan Basin[J].Geophysical Prospecting for Petroleum,2017,56(5):735-745
[4] 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):3786-3794ZONG Z Y,YIN X Y,ZHANG F,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
[5] 李录明,罗省贤,王明春,等.各向异性介质三维纵横波联合叠前反演方法及应用[J].石油地球物理勘探,2010,45(1):60-65LI L M,LUO X X,WANG M C,et al.3D PP-PS joint inversion method and application in anisotropic medium[J].Oil Geophysical Prospecting,2010,45(1):60-65
[6] 魏修成,刘韬,陈天胜,等.射线参数域AVO反演方法[J].中国油气论坛-地球物理勘探技术专题研讨会,2012:30-38WEI X C,LIU T,CHEN T S,et al.AVO inversion method of ray parameters domain[J].China Oil and Gas Forum:Geophysical Exploration Technology Symposium,2012:30-38
[7] 张丰麒,魏福吉,王彦春,等.基于精确Zoeppritz方程三变量柯西分布先验约束的广义线性AVO反演[J].地球物理学报,2013,56(6):2098-2115ZHANG F Q,WEI F J,WANG Y C,et al.Generalized linear AVO inversion with the priori constraint of Trivariate Cauchy distribution based on Zoeppritz equation[J].Chinese Journal of Geophysics,2013,56(6):2098-2115
[8] FANG Y,ZHANG F Q,WANG Y C.Generalized linear joint PP-PS inversion based on two constraints[J].Applied Geophysics,2016,13(1):103-115
[9] 张广智,王丹阳,印兴耀,等.基于MCMC的叠前地震反演方法研究[J].地球物理学报,2011,54(11):2926-2932ZHANG G Z,WANG D Y,YIN X Y,et al.Study on prestack seismic inversion using Markov Chain Monte Carlo[J].Chinese Journal of Geophysics,2011,54(11):2926-2932
[10] 张广智,潘新朋,孙昌路,等.纵横波联合叠前自适应MCMC反演方法[J].石油地球物理勘探,2016,51(5):938-946ZHANG G Z,PAN X P,SUN C L,et al.PP-& PS-wave prestack nonlinear inversion based on adaptive MCMC algorithm[J].Oil Geophysical Prospecting,2016,51(5):938-946
[11] ZHOU L,LI J,CHEN X,et al.Prestack amplitude versus angle inversion for Young's modulus and Poisson's ratio based on the exact Zoeppritz equations[J].Geophysical Prospecting,2017,65(6):1462-1476
[12] 宋建国,郭毓,冉然.基于比值均方根的杨氏模量反演方法[J].地球物理学报,2018,61(4):1508-1518SONG J G,GUO Y,RAN R.Prestack inversion method of Young's modulus based on the root mean square ratio[J].Chinese Journal of Geophysics,2018,61(4):1508-1518
[13] ALEMIE W,SACCHI M D.High-resolution three-term AVO inversion by means of a Trivariate Cauchy probability distribution[J].Geophysics,2011,76(1):43-55
[14] 张丰麒,金之钧,盛秀杰,等.贝叶斯三参数低频软约束同步反演[J].石油地球物理勘探,2016,51(5):965-975ZHANG F Q,JIN Z J,SHENG X J,et al.Bayesian prestack three-term inversion with soft low-frequency constraint[J].Oil Geophysical Prospecting,2016,51(5):965-975