阵列侧向测井反演方法研究与应用
|
摘要
阵列侧向测井是一种新型测井方式,能够同时给出5～6条不同探测深度的测井曲线,因而可给出比较丰富的地层信息。除浅探测深度的响应以外,视电阻率受井眼的影响较小,适用于薄层测井和测量井周围非均匀地层的性质。另外,阵列侧向经过反演可得到较为精确的侵入半径、侵入电阻率和原状地层真电阻率等信息。因此,对阵列侧向测井反演方法的研究,具有一定的理论和现实意义。
阵列侧向测井正演问题是一偏微分方程边值问题,利用变分原理可将偏微分方程边值问题转化为泛函极小问题,因而可使用有限元理论来求解。建立了适合阵列侧向测井响应的泛函表达式,采用网格自动剖分和边界处理技术,从而把求解域离散化。经过单元组装,形成求解域的总矩阵方程,使用多核并行优化的前线解法进行求解,最终实现了阵列侧向测井响应的正演计算。并针对斜井和水平井,对有侵和无侵等条件下的阵列侧向测井响应进行了数值模拟。
阵列侧向测井反演问题一般转化为优化问题进行求解,通过对高斯-牛顿法、Marquardt等传统方法理论上的分析,指出了其在反演计算中所存在的缺点和修订措施,特别给出了Jacobi矩阵计算和阻尼因子定义方式等方面适合阵列侧向测井反演的方案。实现了三参数(原状地层电阻率、侵入带地层电阻率和泥浆侵入半径)和四参数(冲洗带地层电阻率、冲洗带泥浆侵入半径、过渡带泥浆侵入半径和原状地层电阻率)反演。通过对薄层的反演计算,在计算过程中,该改进算法收敛速度快,计算结果准确。
传统优化方法不论怎样改进,仍是一种局部优化方法。而差分进化智能算法是一种全局优化算法,但其后期收敛速度较慢,不能适应实际反演计算。通过把传统优化方法和差分进化智能算法相结合,提出了一种差分进化混合反演算法。计算案例表明,该混合反演算法有全局搜索能力强、局部搜索速度快以及抗噪能力强等特点。
煤层气作为一种新型能源,其勘探开发已经引起广泛重视。而裂隙评价是煤层评价的关键,对煤层气勘探开发及后期管理均有十分重要的作用。使用阵列侧向测井研究了煤层的裂隙参数,从计算结果可以看出,阵列侧向测井响应与裂缝孔隙度、裂缝倾角之间存在良好的相关性。并用Marquardt反演方法对其进行反演处理,可确定相应的裂缝孔隙度及裂缝倾角。
The Array Lateral logging is a new logging mode which can provide five-six logging curves with different investigation depth simultaneously so as to obtain rich formation information. The Array Lateral logging whose apparent resistivity except shallow investigation depth is little affected by borehole is applied to thin layer and inhomogeneous formation around measured well. Some information, such as invasion radius, invasion resistivity, virgin zone resistivity are accurately obtained by inversion. Therefore, the research on inversion of Array Lateral logging has important theoretical and practical significance.
The forward problem of Array Lateral logging is a kind of boundary value problem in partial differential equations which can be solved by finite element method after being transformed into minimum problem of norm function by variational principle. Using the automatic mesh generation and boundary processing method, the solution domain is discretized after building up the norm function suitable for the response of Array Lateral logging. The total matrix equation of solution domain is formed by unit assembly. The frontier solution of multiple cores parallel optimization is applied to achieve the forward calculation finally. Besides, the response of Array Lateral logging with invasion or non-invasion in deviated well and horizontal well is numerically simulated.
In general the inversion problem of Array Lateral logging is solved by being transformed into optimization problem. By analyzing the traditional methods theoretically, such as gauss-newton method, Marquardt method, the existing disadvantages in inversion and corresponding correction measures are pointed out, especially some measures suitable for inversion of Array Lateral logging, like computing the Jacobi matrix and defining damping factor. The three parameters inversion (virgin zone resistivity, invading zone resistivity and invasion radius) and four parameters inversion (flushed zone resistivity, invasion radius of flushed zone, invasion radius of transitional zone and virgin zone resistivity) are carried out. By improving the inversion algorithm for thin layer, the calculation results with fast convergence are accurate.
Whatever we improve the traditional methods, they still belong to local optimization. However, the differential evolution algorithm is a type of global optimization method with slow convergence at later stage and can’t be used for practical inversion. A hybrid inversion method of differential evolution algorithm is proposed in combination with traditional optimization methods and differential evolution algorithm. The calculation results show the hybrid inversion has characteristics of strong global searching ability, fast local searching speed and strong anti-noise ability.
The coal bed methane is a kind of new energy and its exploration and development has attracted extensive attention. As a key to the evaluation of coal bed, the fracture evaluation plays an important role in exploration and development of coal bed methane and later stage management. The Array Lateral logging is applied to study the fracture parameters in coal bed. The results show that the logging response has good correlation with fracture porosity and fracture dip. Using Marquardt inversion for the response, the corresponding fracture porosity and fracture dip can be obtained.
阵列侧向测井正演问题是一偏微分方程边值问题,利用变分原理可将偏微分方程边值问题转化为泛函极小问题,因而可使用有限元理论来求解。建立了适合阵列侧向测井响应的泛函表达式,采用网格自动剖分和边界处理技术,从而把求解域离散化。经过单元组装,形成求解域的总矩阵方程,使用多核并行优化的前线解法进行求解,最终实现了阵列侧向测井响应的正演计算。并针对斜井和水平井,对有侵和无侵等条件下的阵列侧向测井响应进行了数值模拟。
阵列侧向测井反演问题一般转化为优化问题进行求解,通过对高斯-牛顿法、Marquardt等传统方法理论上的分析,指出了其在反演计算中所存在的缺点和修订措施,特别给出了Jacobi矩阵计算和阻尼因子定义方式等方面适合阵列侧向测井反演的方案。实现了三参数(原状地层电阻率、侵入带地层电阻率和泥浆侵入半径)和四参数(冲洗带地层电阻率、冲洗带泥浆侵入半径、过渡带泥浆侵入半径和原状地层电阻率)反演。通过对薄层的反演计算,在计算过程中,该改进算法收敛速度快,计算结果准确。
传统优化方法不论怎样改进,仍是一种局部优化方法。而差分进化智能算法是一种全局优化算法,但其后期收敛速度较慢,不能适应实际反演计算。通过把传统优化方法和差分进化智能算法相结合,提出了一种差分进化混合反演算法。计算案例表明,该混合反演算法有全局搜索能力强、局部搜索速度快以及抗噪能力强等特点。
煤层气作为一种新型能源,其勘探开发已经引起广泛重视。而裂隙评价是煤层评价的关键,对煤层气勘探开发及后期管理均有十分重要的作用。使用阵列侧向测井研究了煤层的裂隙参数,从计算结果可以看出,阵列侧向测井响应与裂缝孔隙度、裂缝倾角之间存在良好的相关性。并用Marquardt反演方法对其进行反演处理,可确定相应的裂缝孔隙度及裂缝倾角。
The Array Lateral logging is a new logging mode which can provide five-six logging curves with different investigation depth simultaneously so as to obtain rich formation information. The Array Lateral logging whose apparent resistivity except shallow investigation depth is little affected by borehole is applied to thin layer and inhomogeneous formation around measured well. Some information, such as invasion radius, invasion resistivity, virgin zone resistivity are accurately obtained by inversion. Therefore, the research on inversion of Array Lateral logging has important theoretical and practical significance.
The forward problem of Array Lateral logging is a kind of boundary value problem in partial differential equations which can be solved by finite element method after being transformed into minimum problem of norm function by variational principle. Using the automatic mesh generation and boundary processing method, the solution domain is discretized after building up the norm function suitable for the response of Array Lateral logging. The total matrix equation of solution domain is formed by unit assembly. The frontier solution of multiple cores parallel optimization is applied to achieve the forward calculation finally. Besides, the response of Array Lateral logging with invasion or non-invasion in deviated well and horizontal well is numerically simulated.
In general the inversion problem of Array Lateral logging is solved by being transformed into optimization problem. By analyzing the traditional methods theoretically, such as gauss-newton method, Marquardt method, the existing disadvantages in inversion and corresponding correction measures are pointed out, especially some measures suitable for inversion of Array Lateral logging, like computing the Jacobi matrix and defining damping factor. The three parameters inversion (virgin zone resistivity, invading zone resistivity and invasion radius) and four parameters inversion (flushed zone resistivity, invasion radius of flushed zone, invasion radius of transitional zone and virgin zone resistivity) are carried out. By improving the inversion algorithm for thin layer, the calculation results with fast convergence are accurate.
Whatever we improve the traditional methods, they still belong to local optimization. However, the differential evolution algorithm is a type of global optimization method with slow convergence at later stage and can’t be used for practical inversion. A hybrid inversion method of differential evolution algorithm is proposed in combination with traditional optimization methods and differential evolution algorithm. The calculation results show the hybrid inversion has characteristics of strong global searching ability, fast local searching speed and strong anti-noise ability.
The coal bed methane is a kind of new energy and its exploration and development has attracted extensive attention. As a key to the evaluation of coal bed, the fracture evaluation plays an important role in exploration and development of coal bed methane and later stage management. The Array Lateral logging is applied to study the fracture parameters in coal bed. The results show that the logging response has good correlation with fracture porosity and fracture dip. Using Marquardt inversion for the response, the corresponding fracture porosity and fracture dip can be obtained.
引文
[1] Chen Y H , Chew W C, Zhang H J. A novel array laterolog method[J]. The Log A nalyst, 1998,39,22-33
[2]杨韡.阵列侧向测井的正反演.勘探地球物理进展[J],2003,26(4):304-308
[3]杨文采.地球物理反演的理论与方法[M].北京:地质出版社,1997
[4]王家映.地理物理反演理论(第二版)[M].北京:高等教育出版社,2002
[5]姚姚.地理物理反演基本理论与应用方法[M].北京:中国地质大学出版社, 2002
[6]徐果明.反演理论及其应用[M].北京:地震出版社,2003
[7]王才经.现代应用数学[M].东营:石油大学出版社,2004
[8]肖庭延,于慎根,王彦飞.反问题的数值解法[M].北京:科学出版社,2003
[9]刘继军.不适定问题的正则化方法及应用[M].北京:科学出版社,2005
[10]黄卡玛,赵翔.电磁场中的逆问题及应用[M].北京:科学出版社,2005
[11]刘争平.人工神经网络在测井—地震资料联合反演中的应用研究[M].北京:科学出版社,2003
[12]姚姚.蒙特卡洛非线性反演方法及应用[M].北京:冶金工业出版社,1997
[13]石琳珂,孙铭心,王广国,等.地球物理遗传反演方法[M].北京:地震出版社,2000
[14]沈连山,李吉,宋海荣等.混沌反演算法在地震预报中的应用[J].大连大学学报,2001,22(4):104-109
[15]魏培君,章梓茂,韩华.双相介质参数反演的混沌搜索方法[J].计算力学学报,2002,19(4):398-402
[16]陈双全,王尚旭,季敏等.地震波阻抗反演的蚁群算法实现[J].石油物探,2005,44(6) :551-553
[17]田明俊,周晶.基于蚁群算法的土石坝土体参数反演[J].岩石力学与工程学报,2005,24(8):1411-1416
[18]田明俊,周晶.岩土工程参数反演的一种新方法[J].岩石力学与工程学报,2005,24(9) :1493-1496
[19]杨光大,陈湛文.地震资料波阻抗多尺度融合反演[J].地球物理学进展,2005,20(3):718-723
[20]宋维琪,赵万金,冯磊等.地震高分辨率反演和地质模拟联合预测薄储层[J].石油学报,2005,26(1):50-54
[21] HU Zhonghui,LI Yuangui,CAI Yunze. Inverse Learning Control of Nonlinear Systems Using Support Vector Machines[J]. Journal of Shanghai Jiaotong University(Science),2005,2:134-138
[22] Barbara Anderson, Thomas Barber, Vladimir Druskin et al. The response of multiarray induction tools in highly dipping formation with invasion and in arbitrary 3D geometries[J].The log analyst.40(5),1999, 326-344
[23]刘振华,林豪,罗俊.横向电阻率测井反演计算[J].测井技术,1999,23(6):433-437
[24]张美玲,邢光龙,刘曼芬,等.阻尼型高斯牛顿法及其在高频电磁波测井反演中的应用[J].2002,19(2):154-158
[25]丁柱,童茂松,潘涛.岩石复电阻率Dias模型及其反演方法[J].2005,24(5):90-92
[26]杨韡.电法测井的快速整体反演及其应用[J].中国石油大学学报,2003,30(2):25-30
[27]杨韡,刘国强,冯启宁,等.双侧向测井响应求取地层参数的Newton--SVD反演方法[J].地球物理学报,1996,39 :356-363
[28]杨韡,冯启宁,尚作源.非均质地层中直流电测井的正反演[J].石油大学学报,1997,21(6):84-89
[29]杨韡,王守东,刘家琦等.电法测井反演的离散牛顿法[J].测井技术,1996,20(1):53-58
[30]张友生,魏斌,杨慧珠.低阻油层双侧向测井的反演研究[J].地球物理学进展,2003,18(1): 84-89
[31]聂在平.电法测井数值模拟研究进展[J].电子科技大学学报,1995,24(7):58-62
[32]赵延文,聂在平.轴对称二维位场的变形玻恩迭代反演[J].电子学报,1997,25(12):10-14
[33]杨峰,聂在平.轴对称二维非均匀介质结构的非线性反演方法[J].红外与毫米波学报,2000,19(6):419-424
[34]邓小波,聂在平,赵延文,等.遗传算法和多重网格在两步线性反演中的应用[J].电波科学学报,2005,20(4):445-451
[35]杨韡,刘家琦.电法测井反问题求解的Monte Carlo方法[J].哈尔滨工业大学学报,1995,27(6):20-21
[36]谭永基,张建峰,李晶.多电极成像测井反演问题的数学模型和数学方法[J].高校应用数学学报,2000,15(3):316-325
[37]丁柱,杨长春,陶宏根,等.神经网络反演双侧向电阻率测井曲线的物理约束[J].地球物理学进展,2002,17(2):331-336
[38]骆淼,潘和平,樊政军,等.测井解释中岩性成份的最优化变尺度法分析[J].物探化探计算技术,2005,27(1):15-19
[39]谭永基,王金莲.用遗传算法计算几个地球物理反问题[J].工程数学学报.2005,22(3):426-434
[40]杨韡.电法测井的快速迭代反演方法[J] .石油大学学报,1999,23(2):34-36
[41]刘振华,林豪.感应横向组合测井联合反演及多解性研究[J].地球物理学进展,2001,16(1):46-55
[42]赵明,高杰,孙友国.常规电测井联合反演研究与实际应用[J].测井技术,2003,27(1):15-19
[43] J.W.Smits,I.Dubourg.Improved Resistivity Interpretation Utilizing a New Array Laterolog Tool and Associated Inversion Processing[J] . Society of Petroleum Engineers,1998,SPE49328
[44] V.Polyakov,T.Habashy.Interactive Log Simulation and Inversion on the Web[J].2004,SPE90909
[45]刘振华,胡启.阵列侧向测井响应的计算及其特征[J].西安石油学院学报(自然科学版).2002,17(1):53-57
[46]杨韡.阵列侧向测井的正反演[J].勘探地球物理进展.2003,26(4) :304-308
[47]刘振华,张霞.阵列侧向测井响应的多参数反演[J].西安石油大学学报(自然科学版).2005,20(1):30-33
[48] Michael A.Frenkel. Real-Time Interpretation Technology for New Multi-Laterolog Array Logging Tool[J].2006, SPE102772
[49] Michael A.Frenkel.Accurate Real-Time Resistivity Interpretation In Vertical and Deviated Wells[J].2007,SPE107266
[50]仵杰,谢尉尉,解茜草.阵列侧向测井仪器的正演响应分析[J].西安石油大学学报(自然科学版).2008,23(1):73-76,80
[51]张建华,刘振华,仵杰.电法测井原理与应用[M].西安:西北大学出版社,2002
[52] http://www.slb.com/media/services/evaluation/petrophysics/resistivity/hrla.pdf
[53]李大潜,谭永基.有限元素法在电法测井中的应用[M].北京:石油工业出版社,1980
[54]谭永基,蔡志杰.数学模型[M].上海:复旦大学出版社,2005
[55]张庚骥.电法测井(下册)[M].北京:石油工业出版社,1986
[56]于永.水平井和大斜度井的测井数值模拟[D].上海:复旦大学博士学位论文,1997
[57]谷超豪,李大潜,陈恕行,郑宋穆,谭永基.数学物理方程(第二版)[M].北京:高等教育出版社,2002
[58]徐长发,李红.实用偏微分方程数值解法(第二版)[M].武汉:华中科技大学出版社,2003
[59]朱伯芳,有限单元法原理与应用[M].北京:水利电力出版社,1979
[60]王勖成,邵敏.有限单元法基本原理与数值方法[M].北京:清华大学出版社,1988
[61]冯康_互动百科. http://www.hudong.com/wiki/%E5%86%AF%E5%BA%B7
[62] http://openmp.org/wp/
[63] http://zh.wikipedia.org/wiki/OpenMP
[64]陈国良.并行算法实践[M].北京:高等教育出版社,2004
[65] Quinn MJ.Parallel programming in C with MPI and OpenMP[M].北京:清华大学出版社,2005
[66] Chandra R, Menon R, Dagum L, et al. Parallel Programming in OpenMP[M].Morgan Kaufman Publishers,2000
[67] Miachael J Quinn.Parallel programming in C with MPI and OpenMP[M]. McGraw-Hill,2003
[68] Barbara Chapman,Gabriele Jost and Ruud van der Pas.Using OpenMP: Portable Shared Memory Parallel Programming[M].MIT Press,2007
[69]多核系列教材编写组.多核程序设计[M].北京:清华大学出版社,2007.
[70]李晓梅,吴建平.数值并行算法与软件[M].北京:科学出版社,2007
[71]陈国良,安虹,陈崚,等.并行算法实践[M].北京:高等教育出版社,2004
[72]郑锋,李名世,蔡佳佳.基于OpenMP的并行遗传算法探讨[J].心智与计算,2007,1(4):395-402
[73]周伟明.多核编程中的负载平衡难题[ EB/ OL ].http://blog.csdn.net/drzhouweiming/ archive/2007/04/17/1568364.aspx
[74]赖建新,胡长军,赵宇迪.OpenMP任务调度开销及负载均衡分析[J].计算机工程,2006,17(10):58-60
[75] OpenMP Architecture Review. OpenMP Application Program Interface[ EB/ OL ] .Version 2.5.http ://www.openmp.org ,2005.
[76]蔡佳佳,李名世,郑锋.多核微机基于OpenMP的并行计算[J].计算机技术与发展,2007,32(18):86-91
[77]邓少贵.大斜度井非均匀地层电测井响应研究[D].东营:中国石油大学(华东)博士学位论文,2006
[78]谭永基,于永.水平井和大斜度井双侧向测井数值模拟[J].复旦学报(自然科学版),1997,36(6):633-638
[79]朱大伟,邓少贵,范宜仁.大斜度井双侧向测井响应数值模拟研究[J].测井技术,2005,29(3):208-211
[80]汪涵明.三维环境中的双侧向测井响应[J].国外测井技术.2001,16(3):49-54
[81]中国石油天然气集团公司测井重点实验室.测井新技术培训教材[M].北京:石油工业出版社,2004
[82] M.William.地球物理数据分析—离散反演理论[M].北京:地质出版社,1980
[83]王振杰.测量中不适定问题的正则化解法[M].北京:科学出版社,2006
[84]王彦飞.反演问题的计算方法及其应用[M].北京:高等教育出版社,2007
[85]徐士良.常用算法程序集(C语言描述)(第三版)[M].北京:清华大学出版社,2004
[86] A.N.Tikhono,A.V.Goncharsky,V.V. Stepanov. Numerical methods for the solution of ill-posed problems[J]. Kluwer Academic Publishers,1995
[87]谢如彪,姜培庆.非线性数值分析[M].上海:上海交通大学出版社,1984
[88] Ortega J M,Reinboldt W C.多元非线性方程组迭代解法[M].朱季纳译.北京:科学出版社,1983
[89]刘钦圣.最小二乘问题计算方法[M].北京:北京工业大学出版社,1989
[90]李庆扬,关治,白峰衫.数值计算原理[M].北京:清华大学出版社,2000
[91]现代应用数学手册编委会.现代应用数学手册(计算与数值分析卷) [M].北京:清华大学出版社,2005
[92]李耐宾,刘海飞,程志平.二维直流电测深反演中雅克比矩阵算法的改进及应用[J].桂林工学院学报, 2006,26(4):473-475
[93] C.T.Kelley. Solving Nonlinear Equations with Newton’s Method. SIAM, Philadelphia, 2003
[94] C. Ma, L. Jiang, Some research on Levenberg–Marquardt method for the nonlinear equations, Appl. Math. Comput. 184(2007) 1032–1040
[95] Fan , J . Pan . A note on the Levenberg– Marquardt parameter , Appl. Math. Comput. (2008),doi:10.1016/j.amc.2008.10.056
[96] Storn,Price. Differential evolution– a simple and efficient heuristic for global optimization over continuous space.Journal of Global Optimization,1997,114:341-359
[97] KV Price,RM Storn,JA Lampinen. Differential Evolution: A Practical Approach to Global Optimization. Springer Berlin Heidelberg,2005
[98] D.G.Mayera,B.P.Kinghorn,A.A.Archer. DiLogging Symposium, 1994: LLL1-LLL10.
[106] Klein J D, Martin P R, Allen D F. The petrophysics of electrically anisotropic reservoirs[J]. The Log Analyst, 1997,33(3):24-36
[107] Philippe, A. P., Roger, N. A. In situ measurements of electrical resistivity, formation anisotropy and tectonic context[C] . SPWLA 31st Annual Logging Symposium. Lafayette Louisiana.1990:24-27
[108]邓少贵,仝兆岐,范宜仁.异性倾斜地层双侧向测井响应数值模拟[J].石油学报,2006,27(3): 61-64
[109]汪宏年,杨善德,常明澈.水平层状各向异性介质中侧向电阻率测井的快速模拟与应用[J].测井技术,1998,22(1):28-31
[110]杨韡.用梯度和感应测井联合确定地层电阻率各向异性[J].地震地质, 2003,25(2):274-278
[111] Sibbit A.M.,Faivre O.The dual laterolog response in fractured rocks[C]. SPWLA 26th Annual Logging Symposium. Dallas Texas. 1985: 16-20
[112]李善军,肖承文,汪涵明,等.裂缝的双侧向测井响应的数学模型及裂缝孔隙度的定量解释[J].地球物理学报,1996,39(6):844-852
[113] Philippe, A. P., Roger, N. A. In situ measurements of electrical resistivity, formation anisotropy and tectonic context[C] . SPWLA 31st Annual Logging Symposium.Lafayette Louisiana.1990:24-27
[114]欧阳健,李善军.双侧向测井识别与评价渤海湾深层裂缝性砂岩油层的解释方法[J].测井技术,2001,25(4):282- 286
[115]李增学,魏久传,刘莹.煤地质学[M].北京:地质出版社,2005:86-92
[2]杨韡.阵列侧向测井的正反演.勘探地球物理进展[J],2003,26(4):304-308
[3]杨文采.地球物理反演的理论与方法[M].北京:地质出版社,1997
[4]王家映.地理物理反演理论(第二版)[M].北京:高等教育出版社,2002
[5]姚姚.地理物理反演基本理论与应用方法[M].北京:中国地质大学出版社, 2002
[6]徐果明.反演理论及其应用[M].北京:地震出版社,2003
[7]王才经.现代应用数学[M].东营:石油大学出版社,2004
[8]肖庭延,于慎根,王彦飞.反问题的数值解法[M].北京:科学出版社,2003
[9]刘继军.不适定问题的正则化方法及应用[M].北京:科学出版社,2005
[10]黄卡玛,赵翔.电磁场中的逆问题及应用[M].北京:科学出版社,2005
[11]刘争平.人工神经网络在测井—地震资料联合反演中的应用研究[M].北京:科学出版社,2003
[12]姚姚.蒙特卡洛非线性反演方法及应用[M].北京:冶金工业出版社,1997
[13]石琳珂,孙铭心,王广国,等.地球物理遗传反演方法[M].北京:地震出版社,2000
[14]沈连山,李吉,宋海荣等.混沌反演算法在地震预报中的应用[J].大连大学学报,2001,22(4):104-109
[15]魏培君,章梓茂,韩华.双相介质参数反演的混沌搜索方法[J].计算力学学报,2002,19(4):398-402
[16]陈双全,王尚旭,季敏等.地震波阻抗反演的蚁群算法实现[J].石油物探,2005,44(6) :551-553
[17]田明俊,周晶.基于蚁群算法的土石坝土体参数反演[J].岩石力学与工程学报,2005,24(8):1411-1416
[18]田明俊,周晶.岩土工程参数反演的一种新方法[J].岩石力学与工程学报,2005,24(9) :1493-1496
[19]杨光大,陈湛文.地震资料波阻抗多尺度融合反演[J].地球物理学进展,2005,20(3):718-723
[20]宋维琪,赵万金,冯磊等.地震高分辨率反演和地质模拟联合预测薄储层[J].石油学报,2005,26(1):50-54
[21] HU Zhonghui,LI Yuangui,CAI Yunze. Inverse Learning Control of Nonlinear Systems Using Support Vector Machines[J]. Journal of Shanghai Jiaotong University(Science),2005,2:134-138
[22] Barbara Anderson, Thomas Barber, Vladimir Druskin et al. The response of multiarray induction tools in highly dipping formation with invasion and in arbitrary 3D geometries[J].The log analyst.40(5),1999, 326-344
[23]刘振华,林豪,罗俊.横向电阻率测井反演计算[J].测井技术,1999,23(6):433-437
[24]张美玲,邢光龙,刘曼芬,等.阻尼型高斯牛顿法及其在高频电磁波测井反演中的应用[J].2002,19(2):154-158
[25]丁柱,童茂松,潘涛.岩石复电阻率Dias模型及其反演方法[J].2005,24(5):90-92
[26]杨韡.电法测井的快速整体反演及其应用[J].中国石油大学学报,2003,30(2):25-30
[27]杨韡,刘国强,冯启宁,等.双侧向测井响应求取地层参数的Newton--SVD反演方法[J].地球物理学报,1996,39 :356-363
[28]杨韡,冯启宁,尚作源.非均质地层中直流电测井的正反演[J].石油大学学报,1997,21(6):84-89
[29]杨韡,王守东,刘家琦等.电法测井反演的离散牛顿法[J].测井技术,1996,20(1):53-58
[30]张友生,魏斌,杨慧珠.低阻油层双侧向测井的反演研究[J].地球物理学进展,2003,18(1): 84-89
[31]聂在平.电法测井数值模拟研究进展[J].电子科技大学学报,1995,24(7):58-62
[32]赵延文,聂在平.轴对称二维位场的变形玻恩迭代反演[J].电子学报,1997,25(12):10-14
[33]杨峰,聂在平.轴对称二维非均匀介质结构的非线性反演方法[J].红外与毫米波学报,2000,19(6):419-424
[34]邓小波,聂在平,赵延文,等.遗传算法和多重网格在两步线性反演中的应用[J].电波科学学报,2005,20(4):445-451
[35]杨韡,刘家琦.电法测井反问题求解的Monte Carlo方法[J].哈尔滨工业大学学报,1995,27(6):20-21
[36]谭永基,张建峰,李晶.多电极成像测井反演问题的数学模型和数学方法[J].高校应用数学学报,2000,15(3):316-325
[37]丁柱,杨长春,陶宏根,等.神经网络反演双侧向电阻率测井曲线的物理约束[J].地球物理学进展,2002,17(2):331-336
[38]骆淼,潘和平,樊政军,等.测井解释中岩性成份的最优化变尺度法分析[J].物探化探计算技术,2005,27(1):15-19
[39]谭永基,王金莲.用遗传算法计算几个地球物理反问题[J].工程数学学报.2005,22(3):426-434
[40]杨韡.电法测井的快速迭代反演方法[J] .石油大学学报,1999,23(2):34-36
[41]刘振华,林豪.感应横向组合测井联合反演及多解性研究[J].地球物理学进展,2001,16(1):46-55
[42]赵明,高杰,孙友国.常规电测井联合反演研究与实际应用[J].测井技术,2003,27(1):15-19
[43] J.W.Smits,I.Dubourg.Improved Resistivity Interpretation Utilizing a New Array Laterolog Tool and Associated Inversion Processing[J] . Society of Petroleum Engineers,1998,SPE49328
[44] V.Polyakov,T.Habashy.Interactive Log Simulation and Inversion on the Web[J].2004,SPE90909
[45]刘振华,胡启.阵列侧向测井响应的计算及其特征[J].西安石油学院学报(自然科学版).2002,17(1):53-57
[46]杨韡.阵列侧向测井的正反演[J].勘探地球物理进展.2003,26(4) :304-308
[47]刘振华,张霞.阵列侧向测井响应的多参数反演[J].西安石油大学学报(自然科学版).2005,20(1):30-33
[48] Michael A.Frenkel. Real-Time Interpretation Technology for New Multi-Laterolog Array Logging Tool[J].2006, SPE102772
[49] Michael A.Frenkel.Accurate Real-Time Resistivity Interpretation In Vertical and Deviated Wells[J].2007,SPE107266
[50]仵杰,谢尉尉,解茜草.阵列侧向测井仪器的正演响应分析[J].西安石油大学学报(自然科学版).2008,23(1):73-76,80
[51]张建华,刘振华,仵杰.电法测井原理与应用[M].西安:西北大学出版社,2002
[52] http://www.slb.com/media/services/evaluation/petrophysics/resistivity/hrla.pdf
[53]李大潜,谭永基.有限元素法在电法测井中的应用[M].北京:石油工业出版社,1980
[54]谭永基,蔡志杰.数学模型[M].上海:复旦大学出版社,2005
[55]张庚骥.电法测井(下册)[M].北京:石油工业出版社,1986
[56]于永.水平井和大斜度井的测井数值模拟[D].上海:复旦大学博士学位论文,1997
[57]谷超豪,李大潜,陈恕行,郑宋穆,谭永基.数学物理方程(第二版)[M].北京:高等教育出版社,2002
[58]徐长发,李红.实用偏微分方程数值解法(第二版)[M].武汉:华中科技大学出版社,2003
[59]朱伯芳,有限单元法原理与应用[M].北京:水利电力出版社,1979
[60]王勖成,邵敏.有限单元法基本原理与数值方法[M].北京:清华大学出版社,1988
[61]冯康_互动百科. http://www.hudong.com/wiki/%E5%86%AF%E5%BA%B7
[62] http://openmp.org/wp/
[63] http://zh.wikipedia.org/wiki/OpenMP
[64]陈国良.并行算法实践[M].北京:高等教育出版社,2004
[65] Quinn MJ.Parallel programming in C with MPI and OpenMP[M].北京:清华大学出版社,2005
[66] Chandra R, Menon R, Dagum L, et al. Parallel Programming in OpenMP[M].Morgan Kaufman Publishers,2000
[67] Miachael J Quinn.Parallel programming in C with MPI and OpenMP[M]. McGraw-Hill,2003
[68] Barbara Chapman,Gabriele Jost and Ruud van der Pas.Using OpenMP: Portable Shared Memory Parallel Programming[M].MIT Press,2007
[69]多核系列教材编写组.多核程序设计[M].北京:清华大学出版社,2007.
[70]李晓梅,吴建平.数值并行算法与软件[M].北京:科学出版社,2007
[71]陈国良,安虹,陈崚,等.并行算法实践[M].北京:高等教育出版社,2004
[72]郑锋,李名世,蔡佳佳.基于OpenMP的并行遗传算法探讨[J].心智与计算,2007,1(4):395-402
[73]周伟明.多核编程中的负载平衡难题[ EB/ OL ].http://blog.csdn.net/drzhouweiming/ archive/2007/04/17/1568364.aspx
[74]赖建新,胡长军,赵宇迪.OpenMP任务调度开销及负载均衡分析[J].计算机工程,2006,17(10):58-60
[75] OpenMP Architecture Review. OpenMP Application Program Interface[ EB/ OL ] .Version 2.5.http ://www.openmp.org ,2005.
[76]蔡佳佳,李名世,郑锋.多核微机基于OpenMP的并行计算[J].计算机技术与发展,2007,32(18):86-91
[77]邓少贵.大斜度井非均匀地层电测井响应研究[D].东营:中国石油大学(华东)博士学位论文,2006
[78]谭永基,于永.水平井和大斜度井双侧向测井数值模拟[J].复旦学报(自然科学版),1997,36(6):633-638
[79]朱大伟,邓少贵,范宜仁.大斜度井双侧向测井响应数值模拟研究[J].测井技术,2005,29(3):208-211
[80]汪涵明.三维环境中的双侧向测井响应[J].国外测井技术.2001,16(3):49-54
[81]中国石油天然气集团公司测井重点实验室.测井新技术培训教材[M].北京:石油工业出版社,2004
[82] M.William.地球物理数据分析—离散反演理论[M].北京:地质出版社,1980
[83]王振杰.测量中不适定问题的正则化解法[M].北京:科学出版社,2006
[84]王彦飞.反演问题的计算方法及其应用[M].北京:高等教育出版社,2007
[85]徐士良.常用算法程序集(C语言描述)(第三版)[M].北京:清华大学出版社,2004
[86] A.N.Tikhono,A.V.Goncharsky,V.V. Stepanov. Numerical methods for the solution of ill-posed problems[J]. Kluwer Academic Publishers,1995
[87]谢如彪,姜培庆.非线性数值分析[M].上海:上海交通大学出版社,1984
[88] Ortega J M,Reinboldt W C.多元非线性方程组迭代解法[M].朱季纳译.北京:科学出版社,1983
[89]刘钦圣.最小二乘问题计算方法[M].北京:北京工业大学出版社,1989
[90]李庆扬,关治,白峰衫.数值计算原理[M].北京:清华大学出版社,2000
[91]现代应用数学手册编委会.现代应用数学手册(计算与数值分析卷) [M].北京:清华大学出版社,2005
[92]李耐宾,刘海飞,程志平.二维直流电测深反演中雅克比矩阵算法的改进及应用[J].桂林工学院学报, 2006,26(4):473-475
[93] C.T.Kelley. Solving Nonlinear Equations with Newton’s Method. SIAM, Philadelphia, 2003
[94] C. Ma, L. Jiang, Some research on Levenberg–Marquardt method for the nonlinear equations, Appl. Math. Comput. 184(2007) 1032–1040
[95] Fan , J . Pan . A note on the Levenberg– Marquardt parameter , Appl. Math. Comput. (2008),doi:10.1016/j.amc.2008.10.056
[96] Storn,Price. Differential evolution– a simple and efficient heuristic for global optimization over continuous space.Journal of Global Optimization,1997,114:341-359
[97] KV Price,RM Storn,JA Lampinen. Differential Evolution: A Practical Approach to Global Optimization. Springer Berlin Heidelberg,2005
[98] D.G.Mayera,B.P.Kinghorn,A.A.Archer. DiLogging Symposium, 1994: LLL1-LLL10.
[106] Klein J D, Martin P R, Allen D F. The petrophysics of electrically anisotropic reservoirs[J]. The Log Analyst, 1997,33(3):24-36
[107] Philippe, A. P., Roger, N. A. In situ measurements of electrical resistivity, formation anisotropy and tectonic context[C] . SPWLA 31st Annual Logging Symposium. Lafayette Louisiana.1990:24-27
[108]邓少贵,仝兆岐,范宜仁.异性倾斜地层双侧向测井响应数值模拟[J].石油学报,2006,27(3): 61-64
[109]汪宏年,杨善德,常明澈.水平层状各向异性介质中侧向电阻率测井的快速模拟与应用[J].测井技术,1998,22(1):28-31
[110]杨韡.用梯度和感应测井联合确定地层电阻率各向异性[J].地震地质, 2003,25(2):274-278
[111] Sibbit A.M.,Faivre O.The dual laterolog response in fractured rocks[C]. SPWLA 26th Annual Logging Symposium. Dallas Texas. 1985: 16-20
[112]李善军,肖承文,汪涵明,等.裂缝的双侧向测井响应的数学模型及裂缝孔隙度的定量解释[J].地球物理学报,1996,39(6):844-852
[113] Philippe, A. P., Roger, N. A. In situ measurements of electrical resistivity, formation anisotropy and tectonic context[C] . SPWLA 31st Annual Logging Symposium.Lafayette Louisiana.1990:24-27
[114]欧阳健,李善军.双侧向测井识别与评价渤海湾深层裂缝性砂岩油层的解释方法[J].测井技术,2001,25(4):282- 286
[115]李增学,魏久传,刘莹.煤地质学[M].北京:地质出版社,2005:86-92
© 2004-2018 中国地质图书馆版权所有 京ICP备05064691号 京公网安备11010802017129号 地址：北京市海淀区学院路29号 邮编：100083 电话：办公室：(+86 10)66554848；文献借阅、咨询服务、科技查新：66554700 |