基于Hurst指数与盒维数的钻孔应变数据变化特征分析
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摘要
形变观测数据是地震监测预报和地球科学研究的重要数据源,其中环境干扰排除、地震震例等异常数据的检测是形变观测数据推广应用的关键内容。针对形变观测数据中的钻孔应变观测数据,通过计算绘制功率谱图,研究其Hurst指数与盒维数分形特征,实现对观测数据中地震事件等异常数据的检测。实验结果表明钻孔应变观测数据符合1/f分布,其具有长时间记忆的分形特征,Hurst指数与分形盒维数变化都凸显出了地震等异常数据。随着信噪比的下降,钻孔应变观测数据的Hurst指数呈现下降的趋势,其盒维数呈现增加的趋势,进一步证实了Hurst指数与分形盒维数之和为2的关系,而它们的变化较大,表明具有较弱的抗噪能力。此研究结果可为地震研究提供理论基础。
The deformation observation data are crucial in earthquake monitoring and forecasting and earth science. The detection of outlier data,such as environmental interference and earthquake,are very important to apply those data to other fields. The Hurst exponent and the fractal box-dimension of the borehole strain data are studied to detect the outlier data. The experiments indicate that the power spectrum of the borehole strain data resemble the1/f distribution,which means the fractal geometry of the borehole strain data. Its Hurst exponent identifies the characteristics of long-time memory. The outlier data,such as earthquake,can be detected by Hurst exponent and fractal box-dimension. With the decrease of signal-to-noise ratio( SNR),there is an decreasing trend in the Hurst exponent and an increasing trend in the fractal box-dimension,which further confirms the relationship between the Hurst exponent and the fractal box-dimension. However,these indexes change greatly,which indicates that they have poor anti-noise ability. The results can provide the theoretical basis for seismic research.
The deformation observation data are crucial in earthquake monitoring and forecasting and earth science. The detection of outlier data,such as environmental interference and earthquake,are very important to apply those data to other fields. The Hurst exponent and the fractal box-dimension of the borehole strain data are studied to detect the outlier data. The experiments indicate that the power spectrum of the borehole strain data resemble the1/f distribution,which means the fractal geometry of the borehole strain data. Its Hurst exponent identifies the characteristics of long-time memory. The outlier data,such as earthquake,can be detected by Hurst exponent and fractal box-dimension. With the decrease of signal-to-noise ratio( SNR),there is an decreasing trend in the Hurst exponent and an increasing trend in the fractal box-dimension,which further confirms the relationship between the Hurst exponent and the fractal box-dimension. However,these indexes change greatly,which indicates that they have poor anti-noise ability. The results can provide the theoretical basis for seismic research.
引文
1杨学慧,常玉巧,李燕玲,等.用同相叠加方法识别定点形变数据中的降雨影响.大地测量与地球动力学,2016;36(10):936-940Yang Xuehui,Chang Yuqiao,Li Yanling,et al.Distinguishing the rainfall disturbing pattern in crustal deformation recording by in-phase stack of data.Journal of Geodesy and Geodynamics,2016;36(10):936-940
2邢喜民,杨绍富.乌什体应变的气压响应特征分析.大地测量与地球动力学,2016;36(10):930-932Xing Ximin,Yang Shaofu.Exploration of the response characteristics of air pressure to wushi body strain.Journal of Geodesy and Geodynamics,2016;36(10):930-932
3张磊,邵永新,曹井泉,等.蓟县台水管倾斜仪NS向加速北倾异常分析.大地测量与地球动力学,2016;36(4):372-376Zhang Lei,Shao Yongxin,Cao Jingquan,et al.Analysis of acceleration incline to north direction of water tube tilt-meter at Jinxian seismostation.Journal of Geodesy and Geodynamics,2016;36(4):372-376
4徐芳芳,朱威,崔居全,等.黄海M5.1地震前荣成倾斜仪资料异常分析.大地测量与地球动力学,2016;36(1):92-94Xu Fangfang,Zhu Wei,Cui Juquan,et al.Rongcheng inclinometer abnormal data analysis before the Yellow Sea M5.1 earthquake.Journal of Geodesy and Geodynamics,2016;36(1):92-94
5李杰,李希亮,卢双苓,等.濮阳ML4.6地震前泰安台形变异常特征分析.大地测量与地球动力学,2007;27(4):100-104Li Jie,Li Xiliang,Lu Shuangling,et al.On characteristics of deformation anomalies at Taian station before Puyang ML4.6 earthquake.Journal of Geodesy and Geodynamics,2007;27(4):100-104
6高明智,张岑,郝冉,等.江苏省地震前兆台网VP型宽频带垂直摆倾斜仪受气象因素的干扰分析.大地测量与地球动力学,2016;36(特2):44-47Gao Mingzhi,Zhang Cen,Hao Ran,et al.Meteorological interference analysis to vertical pendulum tiltmeter from Jiangsu earthquake precursor observation network.Journal of Geodesy and Geodynamics,2016;36(S2):44-47
7郝冉,高明智,张岑,等.徐州地震台体应变典型干扰识别及异常震例分析.大地测量与地球动力学,2016;36(增刊2):20-23Hao Ran,Gao Mingzhi,Zhang Cen,et al.Typical interference identification and abnormal case analysis of borehole body strain instrument data at Xuzhou seismic station.Journal of Geodesy and Geodynamics,2016;36(S2):20-23
8卢双苓,郝军丽,孟建国,等.分量应变和体应变可靠性检验及特殊事件影响对比分析.大地测量与地球动力学,2016;36(12):1117-1120Lu Shuangling,Hao Junli,Meng Jianguo,et al.Reliability testing of component borehole strain meter and volumetric strain meter and comparative analysis on data impacted by special events.Journal of Geodesy and Geodynamics,2016;36(12):1117-1120
9周志,翟义勇,郑海刚,等.佛子岭地震台VP型与SSQ型倾斜仪观测资料对比分析.地震地磁观测与研究,2016;37(5):95-102Zhou Zhi,Zhai Yiyong,Zheng Haigang,et al.Comparison of the observation data of the SSQ-2I tiltmeter in both Foziling and Huaibei seismic stations.Seismological and Geomagnetic Observation and Research,2016;37(5):95-102
10杨佩琴,林木金,郑建志.龙岩垂直摆倾斜仪在长泰地震前后的异常分析.大地测量与地球动力学,2016;36(增刊2):56-58Yang Peiqin,Lin Mujin,Zheng Jianzhi.Abormal analysis of Longyan vertical pendulum before and after Changtai earthquake.Journal of Geodesy and Geodynamics,2016;36(S2):56-58
11徐进军,郭鑫伟,张洪波,等.汶川台站地倾斜变化特征提取与分析.大地测量与地球动力学,2016;36(3):270-273Xu Jinjun,Guo Xinwei,Zhang Hongbo,et al.Extraction and analysis of variation characteristics of ground tilt at Wenchuan station.Journal of Geodesy and Geodynamics,2016;36(3):270-273
12张凌空,牛安福.不同周期气压波对钻孔体应变仪观测结果的影响.中国地震,2008;24(4):415-421Zhang Lingkong,Niu Anfu.Analysis on the influence of atmospheric pressure wave on the observational curves of borehole volumetric strain instrument at different periods.Earthquake Research in China,2008;24(4):415-421
13张月征,纪洪广,向鹏,等.基于矿山钻孔应变观测数据时程分形特征的冲击地压前兆分析.岩石力学与工程学报,2016;35(增刊1):3222-3231Zhang Yuezheng,Ji Hongguang,Xiang Peng,et al.Analysis of precursor of rock burst based on the fractal characteristics of the mine borehole strain observation data.Chinese Journal of Rock Mechanics and Engineering,2016;35(S1):3222-3231
14邹静,李仲奎.地下洞室变形监测数据的盒维数分形特征分析.岩土力学,2013;34(增刊1):307-312Zou Jing,Li Zhongkui.Research on fractal characteristics of deformation monitoring data’box dimension of underground caverns.Rock and Soil Mechanics,2013;34(S1):307-312
15吴国铭,李熙喆,何宇锋,等.碳酸盐岩储层岩心T2谱分形特征探究---以安岳气田为例.科学技术与工程,2015;15(14):55-59Wu Guoming,Li Xizhe,He Yufeng,et al.The exploration on fractal feature of NMR T2spectra for carbonate reservoir:a case study from Anyue gas field.Science Technology and Engineering,2015;15(14):55-59
16谢道仪,胡明华,丛玮,等.基于分形维数的交通流效率判别技术研究.科学技术与工程,2016;16(24):93-98Xie Daoyi,Hu Minghua,Cong Wei,et al.Identification of traffic flow efficiency based on fractal dimension.Science Technology and Engineering,2016;16(24):93-98
17常旭,刘伊克.Hausdorff分数维识别地震道初至走时.地球物理学报,1998;41(6):826-832Chang Xu,Liu Yike.Distinguishing seismic first break by means of Hausdorff fractal dimension.Chinese Journal of Geophysics,1998;41(6):826-832
18李晋,汤井田,徐志敏,等.基于信噪辨识的矿集区大地电磁噪声压制.地球物理学报,2017;60(2):722-737Li Jin,Tang Jingtian,Xu Zhimin,et al.Magnetotelluric noise suppression based on signal-to-noise identification in ore concentration area.Chinese Journal of Geophysics,2017;60(2):722-737
19訾艳阳,胥永刚,何正嘉.离散振动信号分形盒维数的改进算法和应用.机械科学与技术,2001;20(3):373-375Zi Yanyang,Xu Yonggang,He Zhengjia.Fractal box dimension of discrete vibration signals improved algorithm and applications.Mechanical Science and Technology,2001;20(3):373-375
20 Mandelbrot B B,Wallis J R.Noah,Joseph,and operational hydrology.Water Resources Research,1968;4(5):909-918
21王孝礼,胡宝清,夏军.水文时序趋势与变异点的R/S分析法.武汉大学学报(工学版),2002;35(2):10-12Wang Xiaoli,Hu Baoqing,Xia Jun.R/S analysis method of trend and aberrance point on hydrological time series.Engineering Journal of Wuhan University,2002;35(2):10-12
22江田汉,邓莲堂.Hurst指数估计中存在的若干问题---以在气候变化研究中的应用为例.地理科学,2004;24(2):177-182Jiang Tianhan,Deng Liantang.Some problems in estimating a Hurst exponent.Scientia Geographica Sinica,2004;24(2):177-182
23叶中行,曹奕剑.Hurst指数在股票市场有效性分析中的应用.系统工程,2001;19(3):21-24Ye Zhongxing,Cao Yijian.Application of Hurst exponent in analysis of stock market’s efficiency.Systems Engineering,2001;19(3):21-24
24方怡,黄雅虹,吕悦军,等.液化规范判别与实际震害现象的差异对比---以唐山地震震害为例.震灾防御技术,2016;11(1):76-85Fang Yi,Huang Yahong,LüYuejun,et al.The comparison between liquefaction estimated by code and the earthquake damagetake-tangshan earthquake for example.Technology for Earthquake Disaster Prevention,2016;11(1):76-85
25方怡,赵京轶,吕悦军,等.唐山地区剪切波速现场测试和室内测试值差异研究.工程勘察,2016;44(8):7-10Fang Yi,Zhao Jingyi,LüYuejun,et al.Study on the difference of shear wave velocity values between field and laboratory test in Tangshan.Geotechnical Investigation&Surveying,2016;44(8):7-10
26常旭,刘伊克.地震记录的广义分维及其应用.地球物理学报,2002;45(6):839-846Chang Xu,Liu Yike.The generalized fractal dimension of seismic records and its applications.Chinese Journal of Geophysics,2002;45(6):839-846
2邢喜民,杨绍富.乌什体应变的气压响应特征分析.大地测量与地球动力学,2016;36(10):930-932Xing Ximin,Yang Shaofu.Exploration of the response characteristics of air pressure to wushi body strain.Journal of Geodesy and Geodynamics,2016;36(10):930-932
3张磊,邵永新,曹井泉,等.蓟县台水管倾斜仪NS向加速北倾异常分析.大地测量与地球动力学,2016;36(4):372-376Zhang Lei,Shao Yongxin,Cao Jingquan,et al.Analysis of acceleration incline to north direction of water tube tilt-meter at Jinxian seismostation.Journal of Geodesy and Geodynamics,2016;36(4):372-376
4徐芳芳,朱威,崔居全,等.黄海M5.1地震前荣成倾斜仪资料异常分析.大地测量与地球动力学,2016;36(1):92-94Xu Fangfang,Zhu Wei,Cui Juquan,et al.Rongcheng inclinometer abnormal data analysis before the Yellow Sea M5.1 earthquake.Journal of Geodesy and Geodynamics,2016;36(1):92-94
5李杰,李希亮,卢双苓,等.濮阳ML4.6地震前泰安台形变异常特征分析.大地测量与地球动力学,2007;27(4):100-104Li Jie,Li Xiliang,Lu Shuangling,et al.On characteristics of deformation anomalies at Taian station before Puyang ML4.6 earthquake.Journal of Geodesy and Geodynamics,2007;27(4):100-104
6高明智,张岑,郝冉,等.江苏省地震前兆台网VP型宽频带垂直摆倾斜仪受气象因素的干扰分析.大地测量与地球动力学,2016;36(特2):44-47Gao Mingzhi,Zhang Cen,Hao Ran,et al.Meteorological interference analysis to vertical pendulum tiltmeter from Jiangsu earthquake precursor observation network.Journal of Geodesy and Geodynamics,2016;36(S2):44-47
7郝冉,高明智,张岑,等.徐州地震台体应变典型干扰识别及异常震例分析.大地测量与地球动力学,2016;36(增刊2):20-23Hao Ran,Gao Mingzhi,Zhang Cen,et al.Typical interference identification and abnormal case analysis of borehole body strain instrument data at Xuzhou seismic station.Journal of Geodesy and Geodynamics,2016;36(S2):20-23
8卢双苓,郝军丽,孟建国,等.分量应变和体应变可靠性检验及特殊事件影响对比分析.大地测量与地球动力学,2016;36(12):1117-1120Lu Shuangling,Hao Junli,Meng Jianguo,et al.Reliability testing of component borehole strain meter and volumetric strain meter and comparative analysis on data impacted by special events.Journal of Geodesy and Geodynamics,2016;36(12):1117-1120
9周志,翟义勇,郑海刚,等.佛子岭地震台VP型与SSQ型倾斜仪观测资料对比分析.地震地磁观测与研究,2016;37(5):95-102Zhou Zhi,Zhai Yiyong,Zheng Haigang,et al.Comparison of the observation data of the SSQ-2I tiltmeter in both Foziling and Huaibei seismic stations.Seismological and Geomagnetic Observation and Research,2016;37(5):95-102
10杨佩琴,林木金,郑建志.龙岩垂直摆倾斜仪在长泰地震前后的异常分析.大地测量与地球动力学,2016;36(增刊2):56-58Yang Peiqin,Lin Mujin,Zheng Jianzhi.Abormal analysis of Longyan vertical pendulum before and after Changtai earthquake.Journal of Geodesy and Geodynamics,2016;36(S2):56-58
11徐进军,郭鑫伟,张洪波,等.汶川台站地倾斜变化特征提取与分析.大地测量与地球动力学,2016;36(3):270-273Xu Jinjun,Guo Xinwei,Zhang Hongbo,et al.Extraction and analysis of variation characteristics of ground tilt at Wenchuan station.Journal of Geodesy and Geodynamics,2016;36(3):270-273
12张凌空,牛安福.不同周期气压波对钻孔体应变仪观测结果的影响.中国地震,2008;24(4):415-421Zhang Lingkong,Niu Anfu.Analysis on the influence of atmospheric pressure wave on the observational curves of borehole volumetric strain instrument at different periods.Earthquake Research in China,2008;24(4):415-421
13张月征,纪洪广,向鹏,等.基于矿山钻孔应变观测数据时程分形特征的冲击地压前兆分析.岩石力学与工程学报,2016;35(增刊1):3222-3231Zhang Yuezheng,Ji Hongguang,Xiang Peng,et al.Analysis of precursor of rock burst based on the fractal characteristics of the mine borehole strain observation data.Chinese Journal of Rock Mechanics and Engineering,2016;35(S1):3222-3231
14邹静,李仲奎.地下洞室变形监测数据的盒维数分形特征分析.岩土力学,2013;34(增刊1):307-312Zou Jing,Li Zhongkui.Research on fractal characteristics of deformation monitoring data’box dimension of underground caverns.Rock and Soil Mechanics,2013;34(S1):307-312
15吴国铭,李熙喆,何宇锋,等.碳酸盐岩储层岩心T2谱分形特征探究---以安岳气田为例.科学技术与工程,2015;15(14):55-59Wu Guoming,Li Xizhe,He Yufeng,et al.The exploration on fractal feature of NMR T2spectra for carbonate reservoir:a case study from Anyue gas field.Science Technology and Engineering,2015;15(14):55-59
16谢道仪,胡明华,丛玮,等.基于分形维数的交通流效率判别技术研究.科学技术与工程,2016;16(24):93-98Xie Daoyi,Hu Minghua,Cong Wei,et al.Identification of traffic flow efficiency based on fractal dimension.Science Technology and Engineering,2016;16(24):93-98
17常旭,刘伊克.Hausdorff分数维识别地震道初至走时.地球物理学报,1998;41(6):826-832Chang Xu,Liu Yike.Distinguishing seismic first break by means of Hausdorff fractal dimension.Chinese Journal of Geophysics,1998;41(6):826-832
18李晋,汤井田,徐志敏,等.基于信噪辨识的矿集区大地电磁噪声压制.地球物理学报,2017;60(2):722-737Li Jin,Tang Jingtian,Xu Zhimin,et al.Magnetotelluric noise suppression based on signal-to-noise identification in ore concentration area.Chinese Journal of Geophysics,2017;60(2):722-737
19訾艳阳,胥永刚,何正嘉.离散振动信号分形盒维数的改进算法和应用.机械科学与技术,2001;20(3):373-375Zi Yanyang,Xu Yonggang,He Zhengjia.Fractal box dimension of discrete vibration signals improved algorithm and applications.Mechanical Science and Technology,2001;20(3):373-375
20 Mandelbrot B B,Wallis J R.Noah,Joseph,and operational hydrology.Water Resources Research,1968;4(5):909-918
21王孝礼,胡宝清,夏军.水文时序趋势与变异点的R/S分析法.武汉大学学报(工学版),2002;35(2):10-12Wang Xiaoli,Hu Baoqing,Xia Jun.R/S analysis method of trend and aberrance point on hydrological time series.Engineering Journal of Wuhan University,2002;35(2):10-12
22江田汉,邓莲堂.Hurst指数估计中存在的若干问题---以在气候变化研究中的应用为例.地理科学,2004;24(2):177-182Jiang Tianhan,Deng Liantang.Some problems in estimating a Hurst exponent.Scientia Geographica Sinica,2004;24(2):177-182
23叶中行,曹奕剑.Hurst指数在股票市场有效性分析中的应用.系统工程,2001;19(3):21-24Ye Zhongxing,Cao Yijian.Application of Hurst exponent in analysis of stock market’s efficiency.Systems Engineering,2001;19(3):21-24
24方怡,黄雅虹,吕悦军,等.液化规范判别与实际震害现象的差异对比---以唐山地震震害为例.震灾防御技术,2016;11(1):76-85Fang Yi,Huang Yahong,LüYuejun,et al.The comparison between liquefaction estimated by code and the earthquake damagetake-tangshan earthquake for example.Technology for Earthquake Disaster Prevention,2016;11(1):76-85
25方怡,赵京轶,吕悦军,等.唐山地区剪切波速现场测试和室内测试值差异研究.工程勘察,2016;44(8):7-10Fang Yi,Zhao Jingyi,LüYuejun,et al.Study on the difference of shear wave velocity values between field and laboratory test in Tangshan.Geotechnical Investigation&Surveying,2016;44(8):7-10
26常旭,刘伊克.地震记录的广义分维及其应用.地球物理学报,2002;45(6):839-846Chang Xu,Liu Yike.The generalized fractal dimension of seismic records and its applications.Chinese Journal of Geophysics,2002;45(6):839-846