Density-sensitivity analysis about prestack multi-parameter inversion based on the exact Zoeppritz equation
Guo Qiang1, Zhang Hongbing1, Cao Chenghao2, Han Feilong1, Shang Zuoping3
1. College of Earth Science and Engineering, Hohai University, Nanjing, Jiangsu 210098, China; 2. Institute of Geology and Geophysics, Chinese Academy of Sciences, Beijing 100029, China; 3. College of Mechanics and Materials, Hohai University, Nanjing, Jiangsu 210098, China
Abstract:Prestack seismic inversion based on the exact Zoeppritz equation and its approximations has been widely adopted but complicated problems remain.Multi-parameter inversion results are unstable,especially for the parameter of density.We develop an inversion method by constructing a new objective function which includes the edge-preserving regularization and soft constraints based on Markov random domain.We apply the fast simulated annealing algorithm to solve the nonlinear optimization problem based on the exact Zoeppritz equation.Numerical results indicate that the density is insensitive to angle variation within small incidence angle range,but it makes more contribution to the reflectivity magnitude variation.Test results on 2-D synthetic data demonstrate that a satisfactory inverted density result can be achieved within small incidence angles with the proposed approach.Field data inverted results provide detailed stratigraphic information well-matched with logging data over most parts.
Virieux J,Operto S.An overview of full-waveform inversion in exploration geophysics.Geophysics,2009,74(6):WCC1-WCC26.
[3]
Tarantola A,Valette B.Generalized nonlinear inverse problems solved using the least squares criterion.Review of Geophysics and Space Physics,1982,20(2):219-232.
[4]
Bae H S,Pyun S,Chung W et al.Frequency-domain acoustic-elastic coupled waveform inversion using the Gauss-Newton conjugate gradient method.Geophysi-cal Prospecting,2012,60(3):413-432.
[5]
姚姚.地球物理非线性反演模拟退火法的改进.地球物理学报,1995,38(5):643-650.Yao Yao.Improvement on nonlinear geophysical inversion simulated annealing.Chinese Journal of Geophysics,1995,38(5):643-650.
[6]
张霖斌,姚振兴,纪晨等.快速模拟退火算法及应用.石油地球物理勘探,1997,32(5):645-660.Zhang Linbin,Yao Zhenxing,Ji Chen et al.Fast simulated annealing algorithm and its application.OGP,1997,32(5):654-660.
Chiappa F,Mazzotti A.Estimation of petrophysical parameters by linearized inversion of angle domain pre-stack data.Geophysical Prospecting,2009,57(3):413-426.
[9]
Down J E.Seismic Paramter Estimation from AVO Inversion[D].University of Calgary,Canada,2005.
[10]
田军,吴国忱,宗兆云.鲁棒性AVO三参数反演方法及不确定性分析.石油地球物理勘探,2013,48(3):443-449.Tian Jun,Wu Guochen,Zong Zhaoyun.Robust three-term AVO inversion and uncertainty analysis.OGP,2013,48(3):443-449.
[11]
Aki K,Richards P G.Quantitative Seismology:Theory and Methods.W.H.Freeman and Co.,1980.
[12]
Shuey R T.A simplification of the Zoeppritz equa-tions.Geophysics,1985,50(4):609-614.
[13]
Fatti J L,Smith G C,Vail P J et al.Detection of gas in sandstone reservoirs using AVO analysis:A 3-D seismic case history using the Geostack technique.Geophysics,1994,59(9):1362-1376.
[14]
邓炜,印兴耀,宗兆云等.基于逆算子估计的高阶AVO非线性反演.石油地球物理勘探,2016,51(5):955-964.Deng Wei,Yin Xingyao,Zong Zhaoyun et al.High-order nonlinear AVO inversion based on estimated inverse operator.OGP,2016,51(5):955-964.
[15]
Zhi L X,Chen S Q,Li X Y.Amplitude variation with angle inversion using the exact Zoeppritz equations-Theory and methodology.Geophysics,2016,81(2):N1-N15.
[16]
黄捍东,王彦超,郭飞等.基于佐普里兹方程的高精度叠前反演方法.石油地球物理勘探,2013,48(5):740-749.Huang Handong,Wang Yanchao,Guo Fei et al.High precision prestack inversion algorithm based on Zoe-ppritz equations.OGP,2013,48(5):740-749.
[17]
Chemingui N,Biondi B.Seismic data reconstruction by inversion to common offset.Geophysics,2002,67(5):1575-1585.
[18]
Ghosh S K.Limitations on impedance inversion of band-limited reflection data.Geophysics,2000,65(3):951-957.
[19]
吉洪诺夫,阿尔先宁著;王秉忱译.不适定问题的解法.北京:地质出版社,1979.
[20]
Sen M K,Roy I G.Computation of differential seismograms and iteration adaptive regularization in pre-stack waveform inversion.Geophysics,2003,68(6):2026-2039.
[21]
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.石油地球物理勘探,2016,51(5):965-975.Zhang Fengqi,Jin Zhijun,Sheng Xiujie et al.Bayesian prestack three-term inversion with soft low-frequency constraint.OGP,2016,51(5):965-975.
[22]
张宏兵,尚作萍,杨长春.波阻抗反演正则参数估计.地球物理学报,2005,48(1):181-188.Zhang Hongbing,Shang Zuoping,Yang Changchun.Estimation of regular parameters for the impedance inversion.Chinese Journal of Geophysics,2005,48(1):181-188.
[23]
Zhang H,Shang Z,Yang C.Adaptive reconstruction method of impedance model with absolute and relative constraints.Journal of Applied Geophysics,2009,67(2):114-124.
[24]
Yan Z,Gu H.Non-linear prestack seismic inversion with global optimization using an edge-preserving smoothing filter.Geophysical Prospecting,2013,61(4):747-760.
[25]
Kabir N,Crider R,Ramkhelawan R et al.Can hydrocarbon saturation be estimated using density contrast parameter?CSEG Recorder,2006,31(6):31-37.
[26]
Zong Z,Yin X,Wu G.AVO inversion and poroelasti-city with P-and S-wave moduli.Geophysics,2012,77(6):N17-N24.
[27]
Zong Z,Yin X,Wu G.Elastic impedance paramete-rization and inversion with Young's modulus and Poisson's ratio.Geophysics,2013,78(6):N35-N42.
[28]
Liang Lifeng,Zhang Hongbing,Dan Zhiwei et al.Prestack density inversion using the Fatti equation constrained by the P-and S-wave impedance and density.Applied Geophysics,2017,14(1):133-141.
[29]
Charbonnier P,Blanc-Féraud L,Aubert G.Determini-stic edge-preserving regularization in computed imaging.IEEE Transactions on Image Processing,1997,6(2):298-311.
[30]
Geman D,Yang C.Nonlinear image recovery with half-quadratic regularization.IEEE Transactions on Image Processing,1995,4(7):932-946.
[31]
Huang Handong,Zhang Ruwei,Shen Guoqiang et al.Study of prestack elastic parameter consistency inversion methods.Applied Geophysics,2011,8(4):311-318.