基于L1范数的瞬变电磁非线性反演

孙怀凤, 张诺亚, 柳尚斌, 李敦仁, 陈成栋, 叶琼瑶, 薛翊国, 杨洋. 2019. 基于L1范数的瞬变电磁非线性反演. 地球物理学报, 62(12): 4860-4873, doi: 10.6038/cjg2019M0690
引用本文: 孙怀凤, 张诺亚, 柳尚斌, 李敦仁, 陈成栋, 叶琼瑶, 薛翊国, 杨洋. 2019. 基于L1范数的瞬变电磁非线性反演. 地球物理学报, 62(12): 4860-4873, doi: 10.6038/cjg2019M0690
SUN HuaiFeng, ZHANG NuoYa, LIU ShangBin, LI DunRen, CHEN ChengDong, YE QiongYao, XUE YiGuo, YANG Yang. 2019. L1-norm based nonlinear inversion of transient electromagnetic data. Chinese Journal of Geophysics (in Chinese), 62(12): 4860-4873, doi: 10.6038/cjg2019M0690
Citation: SUN HuaiFeng, ZHANG NuoYa, LIU ShangBin, LI DunRen, CHEN ChengDong, YE QiongYao, XUE YiGuo, YANG Yang. 2019. L1-norm based nonlinear inversion of transient electromagnetic data. Chinese Journal of Geophysics (in Chinese), 62(12): 4860-4873, doi: 10.6038/cjg2019M0690

基于L1范数的瞬变电磁非线性反演

  • 基金项目:

    山东省重点研发计划(2018GSF117020),广西科技基地和人才专项(桂科AD17129047)资助

详细信息
    作者简介:

    孙怀凤, 男, 博士, 副教授, 博士生导师, 主要从事瞬变电磁正反演方面的教学与科研工作.E-mail:sunhuaifeng@gmail.com

    通讯作者: 李敦仁, 男, 教授级高级工程师, 主要从事岩溶地质灾害探测与防治方面的科研与应用研究.E-mail:48388@qq.com
  • 中图分类号: P631

L1-norm based nonlinear inversion of transient electromagnetic data

More Information
  • 瞬变电磁反演存在高度的非线性特征,常用的最小二乘等线性反演方法往往对初始模型高度依赖,并且极易陷入局部最优解.本文基于观测数据与模拟数据的L1范数建立目标函数,采用模拟退火非线性全局最优化方法实现瞬变电磁一维反演.初始模型完全随机产生,通过指数函数退温机制模拟系统能量最小实现迭代,通过接收概率函数评价当前模型,实现局部最优解的跳出,最终实现全局最优化求解.通过数值算例发现,无论给定的反演层数等于还是大于设计模型,都可以获得较好的反演效果,因而可以在反演初始就设计较多的层数,实现反演模型的自动拟合;同时,利用含噪声数据反演进一步验证算法的稳定性.最后,对实测数据进行了反演测试,结果与钻孔编录基本一致,表明提出的基于L1范数的模拟退火反演可用于实测数据处理.

  • 加载中
  • 图 1 

    抽样过程

    Figure 1. 

    Sampling process

    图 2 

    模拟退火算法流程图及伪代码

    Figure 2. 

    Simulated annealing algorithm flow chart and the pseudo code

    图 3 

    D型模型使用2层初始模型反演结果

    Figure 3. 

    2-layer inversion results of D-model

    图 4 

    D型模型使用5层初始模型反演结果

    Figure 4. 

    5-layer inversion results of D-model

    图 5 

    G型模型使用2层初始模型反演结果

    Figure 5. 

    2-layer inversion results of G-model

    图 6 

    G型模型使用5层初始模型反演结果

    Figure 6. 

    5-layer inversion results of G-model

    图 7 

    A型模型使用3层初始模型反演结果

    Figure 7. 

    3-layer inversion results of A-model

    图 8 

    A型模型使用20层初始模型反演结果

    Figure 8. 

    20-layer inversion results of A-model

    图 9 

    Q型模型使用3层初始模型反演结果

    Figure 9. 

    3-layer inversion results of Q-model

    图 10 

    Q型模型使用20层初始模型反演结果

    Figure 10. 

    20-layer inversion results of Q-model

    图 11 

    K型模型使用3层初始模型反演结果

    Figure 11. 

    3-layer inversion results of K-model

    图 12 

    K型模型使用20层初始模型反演结果

    Figure 12. 

    20-layer inversion results of K-model

    图 13 

    H型模型使用3层初始模型反演结果

    Figure 13. 

    3-layer inversion results of H-model

    图 14 

    H型模型使用20层初始模型反演结果

    Figure 14. 

    20-layer inversion results of H-model

    图 15 

    5层模型使用5层初始模型反演结果

    Figure 15. 

    5-layer inversion results of five-layer-model

    图 16 

    5层模型使用20层初始模型反演结果

    Figure 16. 

    20-layer inversion results of five-layer-model

    图 17 

    A型模型含5%高斯噪声反演结果

    Figure 17. 

    A model with 5% Gaussian noise inversion results (Gray curves are noise inversion results)

    图 18 

    工区位置图

    Figure 18. 

    Work location

    图 19 

    点3反演结果图

    Figure 19. 

    Point 3 inversion results

    图 20 

    点10反演结果图

    Figure 20. 

    Point 10 inversion results

    图 21 

    点12反演结果图

    Figure 21. 

    Point 12 inversion results

    图 22 

    反演结果(左)与钻孔结果(右)对比图

    Figure 22. 

    Comparison of inversion results (left) and drilling results (right)

    表 1 

    各类模型反演时间与迭代过程数据对比

    Table 1. 

    Inversion time and iterative process of all models

    正演模型 反演设计层数 迭代次数 迭代误差 反演耗时
    D 2 21 0.002 38 min
    5 24 0.004 12 h
    G 2 24 0.002 53 min
    5 34 0.004 17.5 h
    A 3 40 0.002 8 h
    20 25 0.006 35.3 h
    Q 3 47 0.002 9.5 h
    20 36 0.006 35 h
    K 3 24 0.002 12.5 h
    20 26 0.006 37.5 h
    H 3 22 0.002 7.5 h
    20 32 0.006 31 h
    5层 5 53 0.005 43 h
    20 47 0.006 85.3 h
    下载: 导出CSV

    表 2 

    Line 1测线的发射和接收参数表

    Table 2. 

    Transmission and reception parameters of Line 1

    测线 点数 测线长度 发射参数 接收参数
    回线 电流 基频 关断时间 接收面积
    Line1 25 700 m 1匝×100 m 7 A 25 Hz 10 μs 3400 m2
    下载: 导出CSV

    表 3 

    25 Hz对应的采集道数和中心时间

    Table 3. 

    25 Hz corresponding acquisition channels and center time

    道数 中心时间(μs)
    1 72.5
    2 82.5
    3 92.5
    4 105
    5 117.5
    6 132.5
    7 150
    8 170
    9 192.5
    10 217.5
    11 245
    12 277.5
    13 315
    14 355
    15 402.5
    16 455
    17 512.5
    18 580
    19 655
    20 742.5
    21 837.5
    22 947.5
    23 1072.5
    24 1212.5
    25 1370
    26 1550
    27 1752.5
    28 1980
    29 2240
    30 2532.5
    31 2862.5
    32 3235
    33 3657.5
    34 4137.5
    35 4677.5
    36 5287.5
    37 5977.5
    38 6760
    39 7642.5
    40 8640
    下载: 导出CSV
  •  

    Aarts E H L, VanLaarhoken P J M. 1985. Statistica-cooling:a general approach to combinatorial optimization problems. Philips J. Res., 40(4):193-226. http://cn.bing.com/academic/profile?id=d78b02e989ba2f2e037a48fb887f3aef&encoded=0&v=paper_preview&mkt=zh-cn

     

    Bartels R H, Conn A R. 1982. An approach to nonlinear l1 data fitting.//Hennart J P ed. Numerical Analysis. Berlin, Heidelberg: Springer, 48-58. doi: 10.1007/bfb0092959.

     

    Chen H G, Li J X, Wu J S, et al. 2012. Study on simulated-annealing MT-gravity joint inversion. Chinese Journal of Geophysics (in Chinese), 55(2):663-670, doi:10.6038/j.issn. 0001-5733.2012.02.030.

     

    Cheng J L, Li M X, Xiao Y L, et al. 2014. Study on particle swarm optimization inversion of mine transient electromagnetic method in whole-space. Chinese Journal of Geophysics (in Chinese), 57(10):3478-3484, doi:10.6038/cjg20141033.

     

    Fei Y T. 1995. Error Theory and Data Processing (in Chinese). 3rd edition. Beijing:Mechanical Industry Press.

     

    Feng S C, Wang X B, Ruan S. 2004. Comparison among several inversion algorithms of 1D MT. Oil Geophysical Prospecting (in Chinese), 39(5):594-599, doi:10.3321/j.issn:1000-7210.2004.05.019.

     

    Huang M D, Romeo F, Sangiovanni-Vincentelli A. 1987. An efficient general cooling schedule for simulated annealing.//Proceedings of IEEE International Conference on Computer-Aided Design. Santa Clara: IEEE, 381-384.

     

    Huang Y P, Wang W Z. 1990. Inversion of time domain aeromagnetic data. Acta Geophysica Sinica, 33(1):87-97. http://www.wanfangdata.com.cn/details/detail.do?_type=perio&id=8378b632c23e1114287bdedc3edd3ebd

     

    Jiang E X, Zhao F G, Su Y F. 2008. Numerical Approximation (in Chinese). 2nd ed. Shanghai:Fudan University Press.

     

    Kang L S. 1994. Non-Numerical Parallel Algorithm First Volume:Simulated Annealing Algorithm (in Chinese). Beijing:Science Press.

     

    Kirkpatrick S, Gelatt C D Jr, Vecchi M P. 1983. Optimization by simulated annealing. Science, 220(4598):671-680. doi: 10.1126/science.220.4598.671

     

    Li J H, Zhu Z Q, Liu S C, et al. 2011. Calculation of apparent resistivity in large fixed loop TEM by simulated annealing algorithm. Oil Geophysical Prospecting (in Chinese), 46(1):138-142, doi:10.13810/j.cnki.issn.1000-7210.2011.01.029.

     

    Metropolis N, Rosenbluth A W, Rosenbluth M N, et al. 1953. Equation of state calculations by fast computing machines. The Journal of Chemical Physics, 21(6):1087-1092. doi: 10.1063/1.1699114

     

    Munkholm M S, Auken E. 1996. Electromagnetic noise contamination on transient electromagnetic soundings in culturally disturbed environments. Journal of Environmental and Engineering Geophysics, 1(2):119-127. doi: 10.4133/JEEG1.2.119

     

    Piao H R. 1990. Principle of Electromagnetic Sounding (in Chinese). Beijing:Geological Press.

     

    16.Weidelt, P. Kaikkonen. 1994. Local 1-D interpretation of magnetotelluric B-porlarization impedances. Geophys. J.Int, 117:733-748.

     

    Rothman D H. 1985. Nonlinear inversion, statistical mechanics, and residual statics estimation. Geophysics, 50(12):2784-2796. doi: 10.1190/1.1441899

     

    Rothman D H. 1986. Automatic estimation of large residual statics correction. Geophysics, 51(2):337-346. https://www.researchgate.net/publication/215755464_Automatic_estimation_of_large_residual_statics

     

    Sen M K, Bhattacharya B B, Stoffa P L. 1993. Nonlinear inversion of resistivity sounding data. Geophysics, 58(4):496-507. doi: 10.1190/1.1443432

     

    Shi X M, Wang J Y. 1998. One dimensional magnetotelluric sounding inversion using simulated annealing. Earth Science-Journal of China University of Geosciences (in Chinese), 23(5):542-546. http://d.old.wanfangdata.com.cn/Periodical/dqkx199805020

     

    Stark, P. B., and Parker, R. L. 1995. Bounded-variable least-squares:an algorithm and applications. Computational Statistics, 10:129-41. http://cn.bing.com/academic/profile?id=1cc6de902cd4253b3f65493c0a7563d9&encoded=0&v=paper_preview&mkt=zh-cn

     

    Steven C. Constable, Robert L. Parker, et al. 1987. Occam's inversion; a practical algorithm for generating smooth models from electromagnetic sounding data. Geophysics, 52 (3): 289-300.https://www.researchgate.net/publication/228077488_Occam's_inversion_A_practical_algorithm_for_generating_smooth_models_from_electromagnetic_sounding_data

     

    Vecchi M P, Kirkpatriek S. 1983. Global wiring by simulated annealing. IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems, 2(4):215-222. doi: 10.1109/TCAD.1983.1270039

     

    Wan L, Lin T T, Lin J, et al. 2013. Joint inversion of MRS and TEM data based on adaptive genetic algorithm. Chinese Journal of Geophysics (in Chinese), 56(11):3728-3740, doi:10.6038/cjg20131114.

     

    Wang H J, Luo Y Z. 2003. Algorithm of a 2.5 dimensional finite element method for transient electromagnetic with a central loop. Chinese Journal of Geophysics (in Chinese), 46(6):855-862. http://d.old.wanfangdata.com.cn/OAPaper/oai_doaj-articles_1f803ae0c417b7ced6540e3dd18aa66d

     

    Wang J Y, Oldenburg D, Levy S. 1985. The magnetotelluric interpretation simuIating seismic method. Oil Geophysical Prospecting (in Chinese), 20(1):66-79, doi:10.13810/j.cnki.issn.1000-7210.1985.01.008.

     

    Wang J Y. 2002. Inverse Theory in Geophysics (in Chinese). 2nd ed. Beijing:Higher Education Press.

     

    Wang R, Yin C C, Wang M Y, et al. 2011. Simulated annealing for controlled-source audio-frequency magnetitelluric data inversion. Geophysics, 7(2):E127. http://cn.bing.com/academic/profile?id=80f8e79405a1c065cf6c170b6f9ba1d9&encoded=0&v=paper_preview&mkt=zh-cn

     

    Wilson G A, Raiche A P, Sugeng F. 2006.2.5D inversion of airborne electromagnetic data. Exploration Geophysics, 37(4):363-371. http://d.old.wanfangdata.com.cn/Periodical/gdxxhxxb201708011

     

    Wu Q. 2012. Forward modeling of large loop transient electromagnetic field and wave-field transform theory's study[Master's thesis] (in Chinese). Xi'an:Chang'an University.

     

    Xue G Q, Li X, Di Q Y. 2008. Research progress in TEM forward modeling and inversion calculation. Progress in Geophysics (in Chinese), 23(4):1165-1172. http://www.wanfangdata.com.cn/details/detail.do?_type=perio&id=dqwlxjz200804024

     

    Yin C C, Piao H R. 1991. A study of the dfyinition of apparentresistivity in electromagnetic sounding. Geophysical and Geochemical Exploration (in Chinese), 15(4):290-299. http://en.cnki.com.cn/Article_en/CJFDTOTAL-WTYH199104007.htm

     

    Yin C C, Hodges G. 2007. Simulated annealing for airborne EM inversion. Geophysics, 72(4):F189-F195. doi: 10.1190/1.2736195

     

    Yu P, Wang J L, Wu J S, et al. 2007. Constrained joint inversion of gravity and seismic data using the simulated annealing algorithm. Chinese Journal of Geophysics (in Chinese), 50(2):529-538. http://www.wanfangdata.com.cn/details/detail.do?_type=perio&id=10.1002/cjg2.1056

     

    Zhang Z H. 2007. The system realization of CSAMT data inversion explanation[Master's thesis] (in Chinese). Changchun:Jilin University.

     

    Zhdanov M S. 2010. Electromagnetic geophysics:Notes from the past and the road ahead. Geophysics, 75(5):75A49-75A66. doi: 10.1190/1.3483901

     

    陈华根, 李嘉虓, 吴健生等. 2012. MT-重力模拟退火联合反演研究.地球物理学报, 55(2):663-670, doi:10.6038/j.issn.0001-5733.2012.02.030. http://www.geophy.cn//CN/abstract/abstract8443.shtml

     

    程久龙, 李明星, 肖艳丽等. 2014.全空间条件下矿井瞬变电磁法粒子群优化反演研究.地球物理学报, 2014, 57(10):3478-3484, doi:10.6038/cjg20141033. http://www.geophy.cn//CN/abstract/abstract10897.shtml

     

    费业泰. 1995.误差理论与数据处理.第3版.北京:机械工业出版社.

     

    冯思臣, 王绪本, 阮帅. 2004.一维大地电磁测深几种反演算法的比较研究.石油地球物理勘探, 39(5):594-599, doi:10.3321/j.issn:1000-7210.2004.05.019.

     

    黄皓平, 王维中.1990.时间域航空电磁数据的反演.地球物理学报, 33(1):87-97. doi: 10.3321/j.issn:0001-5733.1990.01.010 http://www.geophy.cn//CN/abstract/abstract4680.shtml

     

    蒋尔雄, 赵风光, 苏仰锋. 2008.数值逼近.第2版.上海:复旦大学出版社.

     

    康立山. 1994.非数值并行算法-第一册:模拟退火算法.北京:科学出版社.

     

    李建慧, 朱自强, 刘树才等. 2011.模拟退火法计算大定源瞬变电磁法的视电阻率.石油地球物理勘探, 46(1):138-142, doi:10.13810/j.cnki.issn.1000-7210.2011.01.029.

     

    朴化荣. 1990.电磁测深法原理.北京:地质出版社.

     

    师学明, 王家映. 1998.一维层状介质大地电磁模拟退火反演法.地球科学-中国地质大学学报, 23(5):542-546. http://d.old.wanfangdata.com.cn/Periodical/dqkx199805020

     

    万玲, 林婷婷, 林君等. 2013.基于自适应遗传算法的MRS-TEM联合反演方法研究.地球物理学报, 56(11):3728-3740, doi:10.6038/cjg20131114. http://www.geophy.cn//CN/abstract/abstract9880.shtml

     

    王华军, 罗延钟. 2003.中心回线瞬变电磁法2.5维有限单元算法.地球物理学报, 46(6):855-862. http://d.old.wanfangdata.com.cn/Periodical/dqwlxb200306020

     

    王家映, Oldenburg D, Levy S. 1985.大地电磁测深的拟地震解释法.石油地球物理勘探, 20(1):66-79, doi:10.13810/j.cnki.issn.1000-7210.1985.01.008.

     

    王家映. 2002.地球物理反演理论.第2版.北京:高等教育出版社.

     

    吴琼. 2012.大回线源电磁场正演与波场变换理论研究[硕士论文].西安:长安大学.

     

    薛国强, 李貅, 底青云. 2008.瞬变电磁法正反演问题研究进展.地球物理学进展, 23(4):1165-1172. http://d.old.wanfangdata.com.cn/Periodical/dqwlxjz200804024

     

    殷长春, 朴化荣. 1991.电磁测深法视电阻率定义问题的研究.物探与化探, 15(4):290-299.

     

    于鹏, 王家林, 吴健生等. 2007.重力与地震资料的模拟退火约束联合反演.地球物理学报, 50(2):529-538. doi: 10.3321/j.issn:0001-5733.2007.02.026 http://www.geophy.cn//CN/abstract/abstract1501.shtml

     

    张志厚. 2007. CSAMT数据处理反演解释系统的实现[硕士论文].长春:吉林大学.

  • 加载中

(22)

(3)

计量
  • 文章访问数:  366
  • PDF下载数:  513
  • 施引文献:  0
出版历程
收稿日期:  2018-12-17
修回日期:  2019-07-08
上线日期:  2019-12-05

目录