基于Pareto分布的磁暴感应地电场极值测度模型
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摘要
磁暴感应地电场为电力系统安全运行带来风险,研究极端磁暴地电场水平能够为量化并防御电力系统磁暴灾害风险提供理论支持.提出了基于极值理论的磁暴感应地电场极值测度模型.首先利用地磁观测数据构造年度最大地电场样本数据,建立地电场广义Pareto分布模型,然后利用剩余寿命图和Q-Q图检验模型,并通过Bayes方法估测模型参数,最后计算模型的分位数,即地电场极值测度.利用中国地磁台观测的52年磁暴数据,结合中国喀什地区大地典型结构,估算出喀什地区五十年一遇的感应地电场可达3.288 V.km~(-1),百年一遇地的感应地电场可达3.332 V·km~(-1).利用相同方法还估测了中国部分地磁台站所在区域的地电场极值.研究结果可为估计极值地磁暴提供新思路,也可为分析电力系统磁暴灾害风险提供数据支撑.
Estimation for the level of extreme geoelectric field can provide a basis to quantify the risk of the grounding technology systems due to magnetic storms. The extreme value model of geoelectric field is presented on the basis of the EVT. Firstly, the years maximum sample data of geoelectric field are constructed by using the geomagnetic data, and the general Pareto distribution model is established. Secondly, the model is examined by the mean residual life plot and the Q-Q plot,and the parameters are estimated by Bayes method. Finally, the return period i.e., geoelectric field extreme value, was calculated. The 52 years' data of geomagnetic storms and the Earth resistivity model of Shache, Xinjiang are used to estimate the geoelectric field. The geoelectric field of 50-year is 3.288 V·km~(-1) and that of once-in-a-century is up to 3.332 V·km~(-1) in mid-and low-latitude area.By contrasting with the existing literature analysis, the credibility of model is validated.
Estimation for the level of extreme geoelectric field can provide a basis to quantify the risk of the grounding technology systems due to magnetic storms. The extreme value model of geoelectric field is presented on the basis of the EVT. Firstly, the years maximum sample data of geoelectric field are constructed by using the geomagnetic data, and the general Pareto distribution model is established. Secondly, the model is examined by the mean residual life plot and the Q-Q plot,and the parameters are estimated by Bayes method. Finally, the return period i.e., geoelectric field extreme value, was calculated. The 52 years' data of geomagnetic storms and the Earth resistivity model of Shache, Xinjiang are used to estimate the geoelectric field. The geoelectric field of 50-year is 3.288 V·km~(-1) and that of once-in-a-century is up to 3.332 V·km~(-1) in mid-and low-latitude area.By contrasting with the existing literature analysis, the credibility of model is validated.
引文
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[2] KAPPENMAN J G. An introduction to power grid impacts and vulnerabilities from space weather[J]. Space Storms Space Weather Hazards, 2001, 38(13):351-361
[3] NERC Disturbance Analysis Working Group. 1989 March 13 Geomagnetic Disturbance[R]. Atlanta:NERC,1989:36-60
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[9] PULKKINEN A, PIRJOLA R, VILJANEN A. Statistics of extreme geomagnetically induced current events[J].Space Weather, 2008, 6(7):07001
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[14] WEI Wenbo, JIN Sheng, YE Gaofeng, et al. Conductivity structure of crust and upper mantle beneath the northernTibetan Plateau:Results of super-wide band magnetotelluric sounding[J]. Chin. J. Geophys., 2006, 49(4):1215-1225(魏文博,金胜,叶高峰,等.藏北高原地壳及上地幔导电性结构-超宽频带大地电磁测深研究结果[J].地球物理学报,2006,49(4):1215-1225)
[15] YAN Yongli, MA Xiaobing, CHEN Yun, et al. The study of magnetotelluric sounding on Coqen-Xainza profile in Tibet[J]. Chin. J.Geophys., 2012, 55(8):2636-2642(闫永利,马晓冰,陈埘,等.西藏错勤-申扎剖面大地电磁测深研究[J].地球物理学报,2012, 55(8):2636-2642)
[16] ZHANG Fan, WEI Wenbo, JIN Sheng, et al. Ocean coast effect on land-side magnetotelluric data in the vicinity of the coast[J]. Chin. J. Geophys., 2012, 55(12):4023-4035(张帆,魏文博,金胜,等.海岸效应对近海地区大地电磁测深数据畸变作用研究[J].地球物理学报,2012, 55(12):4023-4035)
[17] BOTELER D H, PIRJOLA R, TRICHTCHENKO L.On calculating the electric and magnetic fields produced in technological systems at the Earth's surface by a"wide"electrojet[J]. J. Atmos. Solar Terr. Phys., 2000,62(14):1311-1315
[18] XU Wenyao. Physics of Electromagnetic Phenomena of the Earth[M]. Hefei:University of Science and Technology of China Press, 2009(徐文耀.地球电磁现象物理学[M].合肥:中国科学技术大学出版社,2009)
[19] AMM O. Ionospheric elementary current systems in spherical coordinates and their application[J]. J. Geomag.Geoelec., 1997, 49(7):947-955
[20] WU Weili, LIU Lianguang. Calculation Method for geoelectric field in mid-and low-latitude area based on sparse geomagnetic data[J]. Chin. J. Space Sci., 2013, 33(6):617-623(吴伟丽,刘连光.基于稀疏地磁数据的中低纬度磁暴感应地电场的算法研究[J].空间科学学报,2013, 33(6):617-623)
[21] SHI Daoji. Practical Extreme Value Statistical Methods[M]. Tianjin:Tianjin Science and Technology Press,2006(史道济.实用极值统计方法[M].天津:天津科学技术出版社,2006)
[22] TIWARI R C, YANG Y Z, ZALKIKAR J N. Bayes estimation for the Pareto failure-model using Gibbs sampling[J].IEEE Trans. Reliab., 1996, 45(3):471-476
[23] MOHAMMED AHMED A O, IBRAHIM N A. Bayesian survival estimator for Weibull distribution with censored data[J]. J.Appl. Sci., 2011, 11(2):393-396
*http://isgi.cetp.ipsl.fr/presenta.htm
**http://www.geomag.org.cn/WebRelation.aspx/
[2] KAPPENMAN J G. An introduction to power grid impacts and vulnerabilities from space weather[J]. Space Storms Space Weather Hazards, 2001, 38(13):351-361
[3] NERC Disturbance Analysis Working Group. 1989 March 13 Geomagnetic Disturbance[R]. Atlanta:NERC,1989:36-60
[4] LIU Lianguang, LIU Chunming, ZHANG Bing, et al.Strong magnetic storm's influence on China's Guangdong power grid[J]. Chin. J. Geophys., 2008, 51(4):976-981(刘连光,刘春明,张冰,等.中国广东电网的几次强磁暴影响事件[J].地球物理学报,2008, 51(4):976-981)
[5] NGWIRA C M, PULKKINEN A, WILDER F D, et al.Extended study of extreme geoelectric field event scenarios for geomagnetically induced current applications[J].Space Weather, 2013, 11(3):121-131
[6] TSURUTANI B T, GONZALEZ W D, LAKHINA G S,et al. The extreme magnetic storm of 1—2 September1859[J]. J. Geophys. Res., 2003, 108(A7):1268
[7] PULKKINEN A, BERNABEU E, EICHNER J, et al.Generation of 100-year geomagnetically induced current scenarios[J]. Space Weather, 2012, 10(4):S04003
[8] THOMSON A W P, DAWSON E B, REAY S J. Quantifying extreme behavior in geomagnetic activity[J]. Space Weather, 2011, 9(10):S10001
[9] PULKKINEN A, PIRJOLA R, VILJANEN A. Statistics of extreme geomagnetically induced current events[J].Space Weather, 2008, 6(7):07001
[10] PULKKINEN A, PIRJOLA R, VILJANEN A. Determination of ground conductivity and system parameters for optimal modeling of geomagnetically induced current flow in technological systems[J]. Earth Planets Space, 2007,59(9):999-1006
[11] PULKKINEN A, AMM O, VILJANEN A. Ionospheric equivalent current distributions determined with the method of spherical elementary current systems[J]. J.Geophys. Res., 2003, 108(A2):1053
[12] YUAN Xuecheng. The Chinese Geophysical Atlas[M].Beijing:Geological Publishing House, 1996(袁学诚.中国地球物理图集[M].北京:地质出版社,1996)
[13] LU Xinbian, SHI Yan, TIAN Chunlai. Tectonic electrical characteristics and A-model subducting patterns of southwest Tarim basin-West Kunlun Area[J]. Exp. Pet. Geol.,1995, 17(3):238-248(鲁新便,石彦,田春来.塔里木盆地西南部-西昆仑地区构造电性特征与A型俯冲模式[J].石油实验地质,1995, 17(3):238-248)
[14] WEI Wenbo, JIN Sheng, YE Gaofeng, et al. Conductivity structure of crust and upper mantle beneath the northernTibetan Plateau:Results of super-wide band magnetotelluric sounding[J]. Chin. J. Geophys., 2006, 49(4):1215-1225(魏文博,金胜,叶高峰,等.藏北高原地壳及上地幔导电性结构-超宽频带大地电磁测深研究结果[J].地球物理学报,2006,49(4):1215-1225)
[15] YAN Yongli, MA Xiaobing, CHEN Yun, et al. The study of magnetotelluric sounding on Coqen-Xainza profile in Tibet[J]. Chin. J.Geophys., 2012, 55(8):2636-2642(闫永利,马晓冰,陈埘,等.西藏错勤-申扎剖面大地电磁测深研究[J].地球物理学报,2012, 55(8):2636-2642)
[16] ZHANG Fan, WEI Wenbo, JIN Sheng, et al. Ocean coast effect on land-side magnetotelluric data in the vicinity of the coast[J]. Chin. J. Geophys., 2012, 55(12):4023-4035(张帆,魏文博,金胜,等.海岸效应对近海地区大地电磁测深数据畸变作用研究[J].地球物理学报,2012, 55(12):4023-4035)
[17] BOTELER D H, PIRJOLA R, TRICHTCHENKO L.On calculating the electric and magnetic fields produced in technological systems at the Earth's surface by a"wide"electrojet[J]. J. Atmos. Solar Terr. Phys., 2000,62(14):1311-1315
[18] XU Wenyao. Physics of Electromagnetic Phenomena of the Earth[M]. Hefei:University of Science and Technology of China Press, 2009(徐文耀.地球电磁现象物理学[M].合肥:中国科学技术大学出版社,2009)
[19] AMM O. Ionospheric elementary current systems in spherical coordinates and their application[J]. J. Geomag.Geoelec., 1997, 49(7):947-955
[20] WU Weili, LIU Lianguang. Calculation Method for geoelectric field in mid-and low-latitude area based on sparse geomagnetic data[J]. Chin. J. Space Sci., 2013, 33(6):617-623(吴伟丽,刘连光.基于稀疏地磁数据的中低纬度磁暴感应地电场的算法研究[J].空间科学学报,2013, 33(6):617-623)
[21] SHI Daoji. Practical Extreme Value Statistical Methods[M]. Tianjin:Tianjin Science and Technology Press,2006(史道济.实用极值统计方法[M].天津:天津科学技术出版社,2006)
[22] TIWARI R C, YANG Y Z, ZALKIKAR J N. Bayes estimation for the Pareto failure-model using Gibbs sampling[J].IEEE Trans. Reliab., 1996, 45(3):471-476
[23] MOHAMMED AHMED A O, IBRAHIM N A. Bayesian survival estimator for Weibull distribution with censored data[J]. J.Appl. Sci., 2011, 11(2):393-396
*http://isgi.cetp.ipsl.fr/presenta.htm
**http://www.geomag.org.cn/WebRelation.aspx/