基于FFT-MA的随机介质建模方法
|
摘要
随机介质是描述地球介质小尺度非均匀性的有效模型,在地震散射波场分析、储层描述等领域具有广泛应用,快速准确的随机介质建模方法是开展相关研究的基础与前提.本文首次将FFT-MA(Fast Fourier Transform Moving Average)算法引入到随机介质建模研究中,分析了该方法与传统随机介质建模方法相比具有的优势,并提出了基于FFT-MA的非平稳随机介质建模方法.建模实验表明,与传统的基于谱分解定理的随机介质建模方法相比,基于FFT-MA的方法在空间域产生随机数序列,使随机数序列与结构参数分离,因此,随机数序列与所建模型存在空间上的对应关系,可以分区域建模和局部修改模型.在非平稳随机介质模型建模时,滑动窗口的大小可以根据自相关长度变化而变化,避免了每个采样点都建立一次完整大小的模型,提高了建模效率.因此,FFT-MA随机介质建模方法能准确构建满足自相关函数要求的平稳及非平稳随机介质模型,具有建模效率高、灵活、实用的优点.
Random medium model is an effective tool to characterize the small-scale heterogeneities of the earth.It has been widely used in analysis of the seismic scatter-wave field,reservoir characterization and so forth.In this aspect,a fast and accurate random medium modeling method is the basis for relevant research.This paper introduces the FFT-MA method into random medium modeling,analyzes its advantages,and presents a non-stationary random medium modeling method based on FFT-MA.The modeling experiments indicate that comparing with the traditional random medium modeling method based on spectral decomposition theorem,the method based on FFT-MA can produce the randomness in the spatial domain,which can uncouple the random numbers from the structural parameters.It constructs the link between random numbers and the model in the spatial domain so that it can be used in sub-regional modeling and local modification.It also benefits the non-stationary random medium modeling for changing size of a modeling window along with the change of autocorrelation length.This avoids constructing the whole model each time at every node,thereby improving the modeling efficiency.In one word,FFT-MA random medium modeling can create both stationary and non-stationary random medium models satisfying the expected autocorrelation functions,and is highly efficient,flexible and practical.
Random medium model is an effective tool to characterize the small-scale heterogeneities of the earth.It has been widely used in analysis of the seismic scatter-wave field,reservoir characterization and so forth.In this aspect,a fast and accurate random medium modeling method is the basis for relevant research.This paper introduces the FFT-MA method into random medium modeling,analyzes its advantages,and presents a non-stationary random medium modeling method based on FFT-MA.The modeling experiments indicate that comparing with the traditional random medium modeling method based on spectral decomposition theorem,the method based on FFT-MA can produce the randomness in the spatial domain,which can uncouple the random numbers from the structural parameters.It constructs the link between random numbers and the model in the spatial domain so that it can be used in sub-regional modeling and local modification.It also benefits the non-stationary random medium modeling for changing size of a modeling window along with the change of autocorrelation length.This avoids constructing the whole model each time at every node,thereby improving the modeling efficiency.In one word,FFT-MA random medium modeling can create both stationary and non-stationary random medium models satisfying the expected autocorrelation functions,and is highly efficient,flexible and practical.
引文
Chen B,Ning H X,Xie X B.2016.Investigating the effect of shallow scatterings from small-scale near-surface heterogeneities on seismic imaging:A resolution analysis based method.Chinese Journal of Geophysics(in Chinese),59(5):1762-1775,doi:10.6038/cjg20160520.
Chen K Y.2009.3-D Random modeling scheme and wavefield simulation analysis.Progress in Exploration Geophysics(in Chinese),32(5):315-320.
Feng D S,Wang X.2016.The GPR simulation of bi-phase random concrete medium using finite element of B-spline wavelet on the interval.Chinese Journal of Geophysics(in Chinese),59(8):3098-3109,doi:10.6038/cjg20160832.
Frankel A,Clayton R W.1984.Finite-difference simulation of wave propagation in two-dimensional random media.Bulletin of the Seismological Society of America,74(6):2167-2186.
Frankel A,Clayton R W.1986.Finite difference simulations of seismic scattering implications for the propagation of shortperiod seismic waves in the crust and models of crustal heterogeneity.Journal of Geophysical Research,91(B6):6465-6489,doi:10.1029/JB091iB06p06465.
Frenje L,Juhlin C.1998.Scattering of seismic waves simulated by finite difference modelling in random media:Application to the Gravberg-1well,Sweden.Tectonophysics,293(1-2):61-68,doi:10.1016/S0040-1951(98)00079-1.
Frenje L,Juhlin C.2000.Scattering attenuation:2-D and 3-D finite difference simulations vs.theory.Journal of Applied Geophysics,44(1):33-46,doi:10.1016/S0926-9851(00)00003-3.
Gu Y.2013.Numerical modeling and parameter estimation for 3DNon-stationary random medium[Ph.D.thesis](in Chinese).Wuhan:China University of Geosciences.
Gu Y,Zhu P M,Li H,et al.2014.Estimation of 2dstationary random medium parameters from post-stack seismic data.Chinese Journal of Geophysics(in Chinese),57(7):450-461,doi:10.6038/cjg20140723.
Guo N C,Wang S X,Dong C H,et al.2012.Description of small scale inhomogeneities in seismic prospecting and long-wavelength theory.Chinese Journal of Geophysics(in Chinese),55(7):2385-2401,doi:10.6038/j.issn.0001-5733.2012.07.023.
Guo S L,Ji M E,Zhu P M,et al.2015.Study on multiphase discrete random medium model and its GPR wave field characteristics.Chinese Journal of Geophysics(in Chinese),58(8):2779-2791,doi:10.6038/cjg20150813.
Han Y Y,Zhang Z J,Liang K,et al.2015.Seismic wave field modeling of wave front healing effect in self-organized media using a heterogeneous multi-scale method.Chinese Journal of Geophysics(in Chinese),58(2):643-655,doi:10.6038/cjg20150225.
Ikelle L T,Yung S K,Daube F.1993.2-D random media with ellipsoidal autocorrelation functions.Geophysics,58(9):1359-1372,doi:10.1190/1.1443518.
Irving J,Knight R,Holliger K.2009.Estimation of the lateral correlation structure of subsurface water content from surfacebased ground-penetrating radar reflection images.Water Resources Research,45(12):W12404,doi:10.1029/2008WR007471.
Jiang Z M,Zeng Z F,Li J,et al.2013.Simulation and analysis of GPR signal based on stochastic media model with an ellipsoidal autocorrelation function.Journal of Applied Geophysics,99:91-97,doi:10.1016/j.jappgeo.2013.08.005.
Le Ravalec M,Noetinger B,Hu L Y.2000.The FFT Moving Average(FFT-MA)generator:an efficient numerical method for generating and conditioning Gaussian simulations.Mathematical Geology,32(6):701-723,doi:10.1023/A:1007542406333.
Le Ravalec-Dupin M,Coureaud B,Nicolas L,et al.2004.Conditioning an underground gas storage site to well pressures.Oil&Gas Science and Technology,59(6):611-624,doi:10.2516/ogst:2004044.
Le Ravalec M,Mouche E.2012.Calibrating transmissivities from piezometric heads with the gradual deformation method:An application to the Culebra Dolomite unit at the Waste Isolation Pilot Plant(WIPP),New Mexico,USA.Journal of Hydrology,472-473:1-13,doi:10.1016/j.jhydrol.2012.08.053.
L′Heureux E,Milkereit B,Vasudevan K.2009.Heterogeneity and seismic scattering in exploration environments.Tectonophysics,472(1-4):264-272,doi:10.1016/j.tecto.2008.04.001.
Li C P,Liu X W.2009.Study on amplitude attributes of seismic wave in random-uniform medium model.Geophysical Prospecting for Petroleum(in Chinese),48(5):465-469,doi:10.3969/j.issn.1000-1441.2009.05.006.
Liu J,Ba J,Ma J W,et al.2010.An analysis of seismic attenuation in random porous media.Science China Physics,Mechanics and Astronomy,53(4):628-637,doi:10.1007/s11433-010-0109-y.
Liu J,Wei X C,Ji Y X,et al.2011.An analysis of seismic scattering attenuation in a random elastic medium.Applied Geophysics,8(4):344-354,doi:10.1007/s11770-011-0296-y.
Nelson C E,Hobbs R W,Rusch R.2015.On the use of fractal surfaces to understand seismic wave propagation in layered basalt sequences.Pure and Applied Geophysics,172(7):1879-1892,doi:10.1007/s00024-014-0986-5.
Nukada A,Matsuoka S.2013.Auto-tuning 3-D FFT library for CUDA GPUs.∥Proceedings of the Conference on High Performance Computing Networking,Storage and Analysis.New York:ACM.
Oliver D S.1995.Moving averages for Gaussian simulation in two and three dimensions.Mathematical Geology,27(8):939-960,doi:10.1007/BF02091660.
Pourpak H,Bourbiaux B,Roggero F,et al.2009.An integrated methodology for calibrating a heterogeneous/fractured reservoir model from wellbore flow measurements:Case study.SPEReservoir Evaluation&Engineer,12(3):433-445,doi:10.2118/113528-PA.
Scholer M,Irving J,Holliger K.2010.Estimation of the correlation structure of crustal velocity heterogeneity from seismic reflection data.Geophysical Journal International,183(3):1408-1428,doi:10.1111/j.1365-246X.2010.04793.x.
Sun Z Q,Sun J G,Yue Y B,et al.2016.Ray tracing using GMM-ULTI method in the random media with complex topography.Chinese Journal of Geophysics(in Chinese),59(7):2615-2627,doi:10.6038/cjg20160725.
Wang B L,Yin X Y,Ding L X,et al.2015.Study of fast stochastic inversion based on FFT-MA spectrum simulation.Chinese Journal of Geophysics(in Chinese),58(2):664-673,doi:10.6038/cjg20150227.
Wu H Z,Fu L Y,Lan X W,et al.2008.Analysis of reservoir heterogeneity based on random media models.Process in Geophysics(in Chinese),23(3):793-799.
Wu J F,Yao Y,Sa L M.2007.Analysis on seismic response of special cavernous structure in carbonate.Oil Geophysical Prospecting(in Chinese),42(2):180-185.
Xi X,Yao Y.2002.Simulations of random medium model and intermixed random medium.Earth Science-Journal of China University of Geosciences(in Chinese),27(1):67-71,doi:10.3321/j.issn:1000-2383.2002.01.014.
Xi X,Yao Y.2004.Characteristics of wavefield in 2-D viscoeiastic random medium.Oil Geophysical Prospecting(in Chinese),39(4):381-387.
Xi X,Yao Y.2005.Non-stationary random medium model.Oil Geophysical Prospecting(in Chinese),40(1):71-75,doi:10.13810/j.cnki.issn.1000-7210.2005.01.020.
Xi X,Yao Y,Gu H M.2005.Random cavity medium model and the wave field simulation.Progress in Geophysics(in Chinese),20(2):365-369.
Yin X X,Liu Y.2011.Random Medium 2-D Modeling and its wavefield analysis.Oil Geophysical Prospecting(in Chinese),46(6):862-872,doi:10.13810/j.cnki.issn.1000-7210.2011.06.012.
Zeng X W,Zhang G Y,Wang X M.2004.Modeling of rocks with spatial distributed fractures by random medium theory.Applied Geophysics,1(1):50-55,doi:10.1007/s11770-004-0030-0.
Zhao Y Y,Gu H M,Wang Y,et al.2013.Research on constructing clastic reservoir seismic geologic model under no well condition.Chinese Journal of Geophysics(in Chinese),56(6):2055-2064,doi:10.6038/cjg20130626.
陈波,宁宏晓,谢小碧.2016.通过地震成像分辨率研究近地表复杂介质散射对成像质量的影响.地球物理学报,59(5):1762-1775,doi:10.6038/cjg20160520.
陈可洋.2009.三维随机建模方法及其波场模拟分析.勘探地球物理进展,32(5):315-320.
冯德山,王珣.2016.区间B样条小波有限元GPR模拟双相随机混凝土介质.地球物理学报,59(8):3098-3109,doi:10.6038/cjg20160832.
顾元.2013.三维非平稳随机介质建模与参数估计[博士论文].武汉:中国地质大学.
顾元,朱培民,李辉等.2014.二维叠后地震数据的平稳随机介质参数估计.地球物理学报,57(7):450-461,doi:10.6038/cjg20140723.
郭乃川,王尚旭,董春晖等.2012.地震勘探中小尺度非均匀性的描述及长波长理论.地球物理学报,55(7):2385-2401,doi:10.6038/j.issn.0001-5733.2012.07.023.
郭士礼,冀孟恩,朱培民等.2015.多相离散随机介质模型及其探地雷达波场特征研究.地球物理学报,58(8):2779-2791,doi:10.6038/cjg20150813.
韩颜颜,张忠杰,梁锴等.2015.基于非均匀化多尺度方法的自组织介质波前愈合效应波场模拟.地球物理学报,58(2):643-655,doi:10.6038/cjg20150225.
李灿苹,刘学伟.2009.随机-均匀介质地震波振幅属性研究.石油物探,48(5):465-469,doi:10.3969/j.issn.1000-1441.2009.05.006.
孙章庆,孙建国,岳玉波等.2016.复杂山地随机介质GMM-ULTI法射线追踪.地球物理学报,59(7):2615-2627,doi:10.6038/cjg20160725.
王保丽,印兴耀,丁龙翔等.2015.基于FFT-MA谱模拟的快速随机反演方法研究.地球物理学报,58(2):664-673,doi:10.6038/cjg20150227.
吴何珍,符力耘,兰晓雯.2008.基于随机介质模型的储层非均质性分析.地球物理学进展,2008,23(3):793-799.
吴俊峰,姚姚,撒利明.2007.碳酸盐岩特殊孔洞型构造地震响应特征分析.石油地球物理勘探,42(2):180-185.
奚先,姚姚.2002.随机介质模型的模拟与混合型随机介质.地球科学-中国地质大学学报,27(1):67-71,doi:10.3321/j.issn:1000-2383.2002.01.014.
奚先,姚姚.2004.二维黏弹性随机介质中的波场特征.石油地球物理勘探,39(4):381-387.
奚先,姚姚.2005.非平稳随机介质模型.石油地球物理勘探,40(1):71-75,doi:10.13810/j.cnki.issn.1000-7210.2005.01.020.
奚先,姚姚,顾汉明.2005.随机溶洞介质模型及其波场模拟.地球物理学进展,20(2):365-369.
殷学鑫,刘洋.2011.二维随机介质模型正演模拟及其波场分析.石油地球物理勘探,46(6):862-872,doi:10.13810/j.cnki.issn.1000-7210.2011.06.012
赵迎月,顾汉明,汪勇等.2013.无井条件下建立碎屑岩储层地震地质模型研究.地球物理学报,56(6):2055-2064,doi:10.6038/cjg20130626.
Chen K Y.2009.3-D Random modeling scheme and wavefield simulation analysis.Progress in Exploration Geophysics(in Chinese),32(5):315-320.
Feng D S,Wang X.2016.The GPR simulation of bi-phase random concrete medium using finite element of B-spline wavelet on the interval.Chinese Journal of Geophysics(in Chinese),59(8):3098-3109,doi:10.6038/cjg20160832.
Frankel A,Clayton R W.1984.Finite-difference simulation of wave propagation in two-dimensional random media.Bulletin of the Seismological Society of America,74(6):2167-2186.
Frankel A,Clayton R W.1986.Finite difference simulations of seismic scattering implications for the propagation of shortperiod seismic waves in the crust and models of crustal heterogeneity.Journal of Geophysical Research,91(B6):6465-6489,doi:10.1029/JB091iB06p06465.
Frenje L,Juhlin C.1998.Scattering of seismic waves simulated by finite difference modelling in random media:Application to the Gravberg-1well,Sweden.Tectonophysics,293(1-2):61-68,doi:10.1016/S0040-1951(98)00079-1.
Frenje L,Juhlin C.2000.Scattering attenuation:2-D and 3-D finite difference simulations vs.theory.Journal of Applied Geophysics,44(1):33-46,doi:10.1016/S0926-9851(00)00003-3.
Gu Y.2013.Numerical modeling and parameter estimation for 3DNon-stationary random medium[Ph.D.thesis](in Chinese).Wuhan:China University of Geosciences.
Gu Y,Zhu P M,Li H,et al.2014.Estimation of 2dstationary random medium parameters from post-stack seismic data.Chinese Journal of Geophysics(in Chinese),57(7):450-461,doi:10.6038/cjg20140723.
Guo N C,Wang S X,Dong C H,et al.2012.Description of small scale inhomogeneities in seismic prospecting and long-wavelength theory.Chinese Journal of Geophysics(in Chinese),55(7):2385-2401,doi:10.6038/j.issn.0001-5733.2012.07.023.
Guo S L,Ji M E,Zhu P M,et al.2015.Study on multiphase discrete random medium model and its GPR wave field characteristics.Chinese Journal of Geophysics(in Chinese),58(8):2779-2791,doi:10.6038/cjg20150813.
Han Y Y,Zhang Z J,Liang K,et al.2015.Seismic wave field modeling of wave front healing effect in self-organized media using a heterogeneous multi-scale method.Chinese Journal of Geophysics(in Chinese),58(2):643-655,doi:10.6038/cjg20150225.
Ikelle L T,Yung S K,Daube F.1993.2-D random media with ellipsoidal autocorrelation functions.Geophysics,58(9):1359-1372,doi:10.1190/1.1443518.
Irving J,Knight R,Holliger K.2009.Estimation of the lateral correlation structure of subsurface water content from surfacebased ground-penetrating radar reflection images.Water Resources Research,45(12):W12404,doi:10.1029/2008WR007471.
Jiang Z M,Zeng Z F,Li J,et al.2013.Simulation and analysis of GPR signal based on stochastic media model with an ellipsoidal autocorrelation function.Journal of Applied Geophysics,99:91-97,doi:10.1016/j.jappgeo.2013.08.005.
Le Ravalec M,Noetinger B,Hu L Y.2000.The FFT Moving Average(FFT-MA)generator:an efficient numerical method for generating and conditioning Gaussian simulations.Mathematical Geology,32(6):701-723,doi:10.1023/A:1007542406333.
Le Ravalec-Dupin M,Coureaud B,Nicolas L,et al.2004.Conditioning an underground gas storage site to well pressures.Oil&Gas Science and Technology,59(6):611-624,doi:10.2516/ogst:2004044.
Le Ravalec M,Mouche E.2012.Calibrating transmissivities from piezometric heads with the gradual deformation method:An application to the Culebra Dolomite unit at the Waste Isolation Pilot Plant(WIPP),New Mexico,USA.Journal of Hydrology,472-473:1-13,doi:10.1016/j.jhydrol.2012.08.053.
L′Heureux E,Milkereit B,Vasudevan K.2009.Heterogeneity and seismic scattering in exploration environments.Tectonophysics,472(1-4):264-272,doi:10.1016/j.tecto.2008.04.001.
Li C P,Liu X W.2009.Study on amplitude attributes of seismic wave in random-uniform medium model.Geophysical Prospecting for Petroleum(in Chinese),48(5):465-469,doi:10.3969/j.issn.1000-1441.2009.05.006.
Liu J,Ba J,Ma J W,et al.2010.An analysis of seismic attenuation in random porous media.Science China Physics,Mechanics and Astronomy,53(4):628-637,doi:10.1007/s11433-010-0109-y.
Liu J,Wei X C,Ji Y X,et al.2011.An analysis of seismic scattering attenuation in a random elastic medium.Applied Geophysics,8(4):344-354,doi:10.1007/s11770-011-0296-y.
Nelson C E,Hobbs R W,Rusch R.2015.On the use of fractal surfaces to understand seismic wave propagation in layered basalt sequences.Pure and Applied Geophysics,172(7):1879-1892,doi:10.1007/s00024-014-0986-5.
Nukada A,Matsuoka S.2013.Auto-tuning 3-D FFT library for CUDA GPUs.∥Proceedings of the Conference on High Performance Computing Networking,Storage and Analysis.New York:ACM.
Oliver D S.1995.Moving averages for Gaussian simulation in two and three dimensions.Mathematical Geology,27(8):939-960,doi:10.1007/BF02091660.
Pourpak H,Bourbiaux B,Roggero F,et al.2009.An integrated methodology for calibrating a heterogeneous/fractured reservoir model from wellbore flow measurements:Case study.SPEReservoir Evaluation&Engineer,12(3):433-445,doi:10.2118/113528-PA.
Scholer M,Irving J,Holliger K.2010.Estimation of the correlation structure of crustal velocity heterogeneity from seismic reflection data.Geophysical Journal International,183(3):1408-1428,doi:10.1111/j.1365-246X.2010.04793.x.
Sun Z Q,Sun J G,Yue Y B,et al.2016.Ray tracing using GMM-ULTI method in the random media with complex topography.Chinese Journal of Geophysics(in Chinese),59(7):2615-2627,doi:10.6038/cjg20160725.
Wang B L,Yin X Y,Ding L X,et al.2015.Study of fast stochastic inversion based on FFT-MA spectrum simulation.Chinese Journal of Geophysics(in Chinese),58(2):664-673,doi:10.6038/cjg20150227.
Wu H Z,Fu L Y,Lan X W,et al.2008.Analysis of reservoir heterogeneity based on random media models.Process in Geophysics(in Chinese),23(3):793-799.
Wu J F,Yao Y,Sa L M.2007.Analysis on seismic response of special cavernous structure in carbonate.Oil Geophysical Prospecting(in Chinese),42(2):180-185.
Xi X,Yao Y.2002.Simulations of random medium model and intermixed random medium.Earth Science-Journal of China University of Geosciences(in Chinese),27(1):67-71,doi:10.3321/j.issn:1000-2383.2002.01.014.
Xi X,Yao Y.2004.Characteristics of wavefield in 2-D viscoeiastic random medium.Oil Geophysical Prospecting(in Chinese),39(4):381-387.
Xi X,Yao Y.2005.Non-stationary random medium model.Oil Geophysical Prospecting(in Chinese),40(1):71-75,doi:10.13810/j.cnki.issn.1000-7210.2005.01.020.
Xi X,Yao Y,Gu H M.2005.Random cavity medium model and the wave field simulation.Progress in Geophysics(in Chinese),20(2):365-369.
Yin X X,Liu Y.2011.Random Medium 2-D Modeling and its wavefield analysis.Oil Geophysical Prospecting(in Chinese),46(6):862-872,doi:10.13810/j.cnki.issn.1000-7210.2011.06.012.
Zeng X W,Zhang G Y,Wang X M.2004.Modeling of rocks with spatial distributed fractures by random medium theory.Applied Geophysics,1(1):50-55,doi:10.1007/s11770-004-0030-0.
Zhao Y Y,Gu H M,Wang Y,et al.2013.Research on constructing clastic reservoir seismic geologic model under no well condition.Chinese Journal of Geophysics(in Chinese),56(6):2055-2064,doi:10.6038/cjg20130626.
陈波,宁宏晓,谢小碧.2016.通过地震成像分辨率研究近地表复杂介质散射对成像质量的影响.地球物理学报,59(5):1762-1775,doi:10.6038/cjg20160520.
陈可洋.2009.三维随机建模方法及其波场模拟分析.勘探地球物理进展,32(5):315-320.
冯德山,王珣.2016.区间B样条小波有限元GPR模拟双相随机混凝土介质.地球物理学报,59(8):3098-3109,doi:10.6038/cjg20160832.
顾元.2013.三维非平稳随机介质建模与参数估计[博士论文].武汉:中国地质大学.
顾元,朱培民,李辉等.2014.二维叠后地震数据的平稳随机介质参数估计.地球物理学报,57(7):450-461,doi:10.6038/cjg20140723.
郭乃川,王尚旭,董春晖等.2012.地震勘探中小尺度非均匀性的描述及长波长理论.地球物理学报,55(7):2385-2401,doi:10.6038/j.issn.0001-5733.2012.07.023.
郭士礼,冀孟恩,朱培民等.2015.多相离散随机介质模型及其探地雷达波场特征研究.地球物理学报,58(8):2779-2791,doi:10.6038/cjg20150813.
韩颜颜,张忠杰,梁锴等.2015.基于非均匀化多尺度方法的自组织介质波前愈合效应波场模拟.地球物理学报,58(2):643-655,doi:10.6038/cjg20150225.
李灿苹,刘学伟.2009.随机-均匀介质地震波振幅属性研究.石油物探,48(5):465-469,doi:10.3969/j.issn.1000-1441.2009.05.006.
孙章庆,孙建国,岳玉波等.2016.复杂山地随机介质GMM-ULTI法射线追踪.地球物理学报,59(7):2615-2627,doi:10.6038/cjg20160725.
王保丽,印兴耀,丁龙翔等.2015.基于FFT-MA谱模拟的快速随机反演方法研究.地球物理学报,58(2):664-673,doi:10.6038/cjg20150227.
吴何珍,符力耘,兰晓雯.2008.基于随机介质模型的储层非均质性分析.地球物理学进展,2008,23(3):793-799.
吴俊峰,姚姚,撒利明.2007.碳酸盐岩特殊孔洞型构造地震响应特征分析.石油地球物理勘探,42(2):180-185.
奚先,姚姚.2002.随机介质模型的模拟与混合型随机介质.地球科学-中国地质大学学报,27(1):67-71,doi:10.3321/j.issn:1000-2383.2002.01.014.
奚先,姚姚.2004.二维黏弹性随机介质中的波场特征.石油地球物理勘探,39(4):381-387.
奚先,姚姚.2005.非平稳随机介质模型.石油地球物理勘探,40(1):71-75,doi:10.13810/j.cnki.issn.1000-7210.2005.01.020.
奚先,姚姚,顾汉明.2005.随机溶洞介质模型及其波场模拟.地球物理学进展,20(2):365-369.
殷学鑫,刘洋.2011.二维随机介质模型正演模拟及其波场分析.石油地球物理勘探,46(6):862-872,doi:10.13810/j.cnki.issn.1000-7210.2011.06.012
赵迎月,顾汉明,汪勇等.2013.无井条件下建立碎屑岩储层地震地质模型研究.地球物理学报,56(6):2055-2064,doi:10.6038/cjg20130626.