摘要:针对传统感应测井线性迭代反演受初始模型影响的问题,提出一种全局寻优的差分进化感应测井非线性反演算法。利用该反演算法对不同厚度二维轴对称地层模型进行反演研究,在无噪声情况下,反演结果和模型基本一致;在叠加5%,10%和15%随机噪声后,对厚储层反演结果良好,对薄储层反演结果稍差。数值实验结果表明,该反演算法具有很好的全局寻优和抗噪声能力,能有效解决感应测井传统迭代反演对初始模型依赖的问题。
关键词:差分进化算法;感应测井;非线性反演;抗噪性
中图分类号: TP18
文献标志码:A
Abstract: An induction logging inversion algorithm based on the Differential Evolution (DE) was proposed to avoid the dependency of initial model. This inversion algorithm was applied to induction logging inversion on the 2D axisymmetric models of different thickness layers, and yielded consistent results with the models in the noisefree case. When noises of 5%, 10% and 15% were added, the inversion results of thick reservoir remain fairly good but the results of thin reservoir became slightly inferior. The numerical experimental results demonstrate that the proposed inversion algorithm has the capabilities of global optimization and antinoise. It is more independent of initial model than the traditional ones.
Key words: Differential Evolution (DE) algorithm; induction logging; nonlinear inversion; antinoise performance
0引言
感应测井是为解决裸眼井和油基泥浆井中的电阻率测量而发展起来的一种重要的电阻率测量方法[1]。实际测得的感应测井曲线是井眼周围所有介质(钻井泥浆、侵入带、原状地层等)综合影响的结果,为了从中还原出井眼周围介质真实的电阻率空间分布,有必要开展感应测井反演研究。
作为地球物理反演问题的一个分支,感应测井反演同样具有高度非线性、多解性和病态性等特点。目前,感应测井反演主要采用线性迭代反演[2-3],通过将非线性反演问题转换为线性反演问题迭代求解。线性迭代反演的原理是从某一初始模型出发,利用目标函数的梯度信息进行局部搜索,逐步修改模型,最终得到反演结果。给定不同的初始模型,会得到不同的反演结果,若初始模型取得不合适,则可能得到局部最优解,甚至有时会不收敛[4]。全局搜索的非线性反演方法有望解决高度非线性、多解性和病态的地球物理反演问题[5-8]。
差分进化(Differential Evolution, DE)[9-10]是一类基于种群的启发式全局搜索技术,对于实值参数的优化具有较强的鲁棒性,在化工、电力、机械设计、现代农业、信号处理、生物信息、食品安全等领域得到广泛的应用[11-12],近年来,DE被逐步应用到地球物理反演中[8,13-17],但在感应测井反演领域,尚未见其他学者的文献报道[18]。
本文针对感应测井传统线性迭代反演依赖初始模型的问题,提出一种基于差分进化的感应测井非线性反演算法。利用该算法对二维水平轴对称模型开展感应测井反演研究,并分析其抗噪声性能。
1问题描述
本文研究国产0.8m六线圈系在二维水平轴对称介质模型中的正反演问题,仪器参数见参考文献[18]。
从表2~3可以看出,无噪声时,DEILI算法能很好地反演出原状地层电阻率、侵入带电阻率和侵入半径,反演结果准确性最好;随着噪声水平的增大,反演结果的准确性逐步下降。在相同噪声水平下,厚储层的反演结果最好,随着储层厚度的减小,反演结果的准确性逐步下降。
4结语
本文提出一种基于差分进化的感应测井非线性反演(DEILI)算法,采用该DEILI算法对不同厚度储层不同噪声水平的理论模型数据进行反演试算,并分析反演算法对储层厚度的敏感性和抗噪声性能,得到如下结论:1)本文提出的DEILI反演算法,具有不需要给定初始模型、全局搜索能力强的优点和较强的抗噪声能力;2)DEILI反演算法,能很好地反演出厚储层的原状地层电阻率、侵入带电阻率和侵入半径,随着储层厚度的减小,反演结果准确度有所减低;3)目前只针对简单侵入模型进行反演研究,对于复杂侵入情况的正反演,有待于进一步的研究。
参考文献:
[1]XIONG J, ZOU C, MENG X. Using the BICGSTAB algorithm with the incomplete LU factorization precondictioning to implement 2D FDFD induction logging fast forward modeling [J]. Geoscience, 2012, 26(6): 1283-1288.(熊杰,邹长春,孟小红.不完全LU分解预条件BICGSTAB算法实现感应测井二维FDFD快速正演模拟[J].现代地质,2012,26(6):1283-1288.)
[2]WANG H, TAO H, WANG G, et al. A fast approximate iterative inversion technique of dual induction logging data [J]. Chinese Journal of Geophysics, 2007, 50(05): 1614-1622.(汪宏年,陶宏根,王桂萍,等.双感应测井资料的快速近似迭代反演[J].地球物理学报,2007,50(5):1614-1622.)
[3]CHENG Z, SUN B, LIU Z, et al. Joint inversion of the high resolution dual laterolog data with dual induction logging data and its applications [J]. Well Logging Technology, 2010, 34(6): 542-547.(成志刚,孙宝佃,刘振华,等.高分辨率双侧向测井和双感应测井数据联合反演研究与应用[J].测井技术,2010,34(6):542-547.)
[4]DUN Y, YUAN J. Fast inversion for array lateral electriclogging [J]. Journal of Tsinghua University: Science and Technology, 2009, 49(11): 1871-1875.(顿月芹,袁建生.阵列侧向电法测井的快速反演[J].清华大学学报:自然科学版,2009,49(11):1871-1875.)
[5]SHI X, FAN J, LUO H, et al. Adaptive quantum genetic inversion algorithm for onedimensional magnetotelluric inverse problem [J]. Earth Science—Journal of China University of Geosciences, 2009, 34(4): 691-698.(师学明,范建柯,罗红明,等.层状介质大地电磁的自适应量子遗传反演法[J].地球科学:中国地质大学学报,2009,34(4):691-698.)
[6]XU H, WU X. 2D resistivity inversion using the neural network method [J]. Chinese Journal of Geophysics, 2006, 49(2): 584-589.(徐海浪,吴小平.电阻率二维神经网络反演[J].地球物理学报,2006,49(2):584-589.)
[7]FERNANDEZMARTINEZ J L, GONZALO E G, LVAREZD J P, et al. PSO: a powerful algorithm to solve geophysical inverse problems application to a 1DDC resistivity case [J]. Journal of Applied Geophysics, 2010, 71(1):13-25.
[8]XIONG J, MENG X, LIU C, et al. Magnetotelluric inversion based on differential evolution [J]. Geophysical and Geochemical Exploration, 2012, 36(3): 448-451.(熊杰,孟小红,刘彩云,等.基于差分进化的大地电磁反演[J].物探与化探,2012,36(3):448-451.)
[9]STORN R, PRICE K. Differential evolution-a simple and efficient heuristic for global optimization over continuous spaces [J]. Journal of Global Optimization, 1997, 11(4): 341-359.
[10]YANG Q, CAI L, XUE Y. A survey of differential evolution algorithm[J]. Pattern Recognition and Artificial Intelligence, 2008, 21(4): 506-513.(杨启文,蔡亮,薛云灿.差分进化算法综述[J].模式识别与人工智能,2008,21(4):506-513.)
[11]NERI F, TIRRONEN V. Recent advances in differential evolution: a survey and experimental analysis [J]. Artificial Intelligence Review, 2010, 33(1/2): 61-106.
[12]LIU B, WANG L, JIN Y. Advances in differential evolution [J]. Control and Decision, 2007, 22(7): 721-729.(刘波,王凌,金以慧.差分进化算法研究进展[J].控制与决策,2007,22(7):721-729.)
[13]LI Z, XU Y, HAO T, et al. Inversion of crustal velocity model and earthquake relocation by using differential evolution algorithm [J]. Progress in geophysics, 2006, 21(2): 370-378.(李志伟,胥颐,郝天珧,等.利用DE算法反演地壳速度模型和地震定位[J].地球物理学进展,2006,21(2):370-378.)
[14]MIN T, MOU X. Parameter inversion for twodimensional wave equation using differential evolution algorithm [J]. Progress in Geophysics, 2009, 24(5): 1757-1761.(闵涛,牟行洋.二维波动方程参数反演的微分进化算法[J].地球物理学进展,2009,24(5):1757-1761.)
[15]XUE J, XING G, YANG S. A fast and steady hybrid inversion method for electromagnetic propagation resistivity log data [J]. Well Logging Technology, 2006, 30(2): 132-136.(薛继霜,邢光龙,杨善德.电磁传播电阻率测井快速稳定的混合反演方法[J].测井技术,2006,30(2):132-136.)
[16]PAN K, WANG W, TAN Y, et al. Geophysical linear inversion based on hybrid differential evolution algorithm [J]. Chinese Journal of Geophysics, 2009, 52(12): 3083-3090.(潘克家,王文娟,谭永基,等.基于混合差分进化算法的地球物理线性反演[J].地球物理学报,2009,52(12):3083-3090.)
[17]LI Z, FAN Y, DENG S, et al. Inversion of array laterolog by improved differential evolution [J]. Journal of Jilin University: Earth Science, 2010, 40(5): 1199-1204.(李志强,范宜仁,邓少贵,等.基于改进差分进化算法的阵列侧向测井反演[J].吉林大学学报:地球科学版,2010,40(5):1199-1204.)
[18]XIONG J. Nonlinear forward and inversion of induction well logging with geological constrain [D]. Beijing: China University of Geosciences, 2012.(熊杰.基于地质约束的感应测井非线性正反演研究[D].北京:中国地质大学,2012.)