断层分形与多重分形特征及其对突出分布的控制作用
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摘要
为了定量化研究断层构造分布及演化特征,揭示断层构造分形特征对煤与瓦斯突出的控制作用,以焦作矿区断层体系为研究对象,利用单分形理论分析了焦作矿区断层体系的分形特征,利用多重分形理论分别对不同区域进行了多重分形研究,将单分形与多重分形特征进行了对比分析,绘制了多重分形谱,提取了多重分形特征参数,根据焦作矿区实际发生的突出事故的统计规律,将特征参数与突出分布规律进行对比研究,结果表明:焦作矿区断层体系具有明显的分形特征,分维值较好地反映了断层的复杂程度,分维值呈现分区特征,由凤凰山断层和峪河口分为3个区域,各区分形维数与断层的实际展布形态相吻合;单分形分析仅能反映断层复杂程度,未能反映煤与瓦斯突出分布的不均衡性,焦作矿区断层分布具有多重分形特征,且不同区域的多重分形谱形状具有明显差异性;多重分形谱对称性Δf及谱宽Δα等特征参数综合反映了构造背景、断层组合和运动方式的差异,对称性Δf代表了大概率子集和小概率子集的数目,表征了大、小断层的发育程度,谱宽Δα代表了分形结构概率分布不均匀的程度,表征了断层分布的均匀程度;不同区域断层的多重分形显现存在着必然的瓦斯地质原因,谱宽Δα与各区域瓦斯突出严重程度呈现了很好的对应关系;断层多重分形特点与构造演化过程密切相关,通过对比分析不同区域断层多重分形特征,可挖掘断层构造的演化信息,深入认识断层对突出的控制作用,从而对矿区煤与瓦斯突出危险性进行区域性划分。
In order to quantitatively study the distribution and evolution characteristics of fault structure,and to reveal the control effect of fault structure on coal and gas outburst,the fracture system of Jiaozuo mining area was taken as the research object. The fractal characteristics of fault system in Jiaozuo mining area were analyzed by using single fractal theory. The fractal theory has carried out multi-fractal research on different regions. The single fractal and multi-fractal features were compared and analyzed. The multi-fractal spectrum was drawn and the multi-fractal characteristic parameters were extracted. According to the statistical law of the prominent accidents actually occurred in Jiaozuo mining area,the characteristic parameters and the prominent distribution law were compared. The results show that the fault system in Jiaozuo mining area has obvious fractal characteristics,and the fractal dimension reflects the complexity of the fault. The fractal dimension presents the zonal features,from the Fenghuangshan fault and the Yuhekou fault. It can be divided into three regions,and the fractal dimension of each fractal is consistent with the actual distribution pattern of the fault; the single fractal analysis can only reflect the complexity of faults,and fails to reflect the imbalance of coal and gas outburst distribution. The fault distribution in the Jiaozuo mining area has multiple fractal features,and the multifractal spectrum shapes of different regions have significant differences; the multifractal spectrum symmetry Δf and the spectral width Δα and other characteristic parameters comprehensively reflect the difference of tectonic setting,fault combination and motion mode. Symmetry Δf represents the number of large probability subsets and small probability subsets. It also characterizes the development degree of large and small faults. The spectral width Δα represents the degree of uneven distribution of the probability distribution of the fractal structure,and the degree of uniformity of the fault distribution is characterized. The multi-fractal representation of faults in different regions has inevitable gas geological reasons and spectral width. Δα has a good correspondence with the severity of gas outburst in each region; the multifractal characteristics of faults are closely related to the tectonic evolution process. By comparing and analyzing the multifractal features of faults in different regions,the evolution information of fault structures can be excavated,and the control effect of faults on the outburst can be further understood,so as to divide the risk of coal and gas outburst in mining area.
In order to quantitatively study the distribution and evolution characteristics of fault structure,and to reveal the control effect of fault structure on coal and gas outburst,the fracture system of Jiaozuo mining area was taken as the research object. The fractal characteristics of fault system in Jiaozuo mining area were analyzed by using single fractal theory. The fractal theory has carried out multi-fractal research on different regions. The single fractal and multi-fractal features were compared and analyzed. The multi-fractal spectrum was drawn and the multi-fractal characteristic parameters were extracted. According to the statistical law of the prominent accidents actually occurred in Jiaozuo mining area,the characteristic parameters and the prominent distribution law were compared. The results show that the fault system in Jiaozuo mining area has obvious fractal characteristics,and the fractal dimension reflects the complexity of the fault. The fractal dimension presents the zonal features,from the Fenghuangshan fault and the Yuhekou fault. It can be divided into three regions,and the fractal dimension of each fractal is consistent with the actual distribution pattern of the fault; the single fractal analysis can only reflect the complexity of faults,and fails to reflect the imbalance of coal and gas outburst distribution. The fault distribution in the Jiaozuo mining area has multiple fractal features,and the multifractal spectrum shapes of different regions have significant differences; the multifractal spectrum symmetry Δf and the spectral width Δα and other characteristic parameters comprehensively reflect the difference of tectonic setting,fault combination and motion mode. Symmetry Δf represents the number of large probability subsets and small probability subsets. It also characterizes the development degree of large and small faults. The spectral width Δα represents the degree of uneven distribution of the probability distribution of the fractal structure,and the degree of uniformity of the fault distribution is characterized. The multi-fractal representation of faults in different regions has inevitable gas geological reasons and spectral width. Δα has a good correspondence with the severity of gas outburst in each region; the multifractal characteristics of faults are closely related to the tectonic evolution process. By comparing and analyzing the multifractal features of faults in different regions,the evolution information of fault structures can be excavated,and the control effect of faults on the outburst can be further understood,so as to divide the risk of coal and gas outburst in mining area.
引文
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[2]徐志斌,王继尧,张大顺,等.煤矿断层网络复杂程度的分维描述[J].煤炭学报,1996,21(4):358-363.XU Zhibin,WANG Jiyao,ZHANG Dashun,et al.Fractal dimension description of complexity of fault network in coal mines[J].Journal of China Coal Society,1996,21(4):358-363.
[3] SHEPHERD J,RIXON L K,GRIFFITH L.Outbursts and geological structures in coal mines:a review[J].Int J Rock Mech Sci,1981,18:267-283.
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[5]何俊,刘明举,颜爱华.煤田地质构造与瓦斯突出关系分形研究[J].煤炭学报,2002,27(6):623-626.HE Jun,LIU Mingju,YAN Aihua. Fractal research of relation between geological tectonic coalfields and gas outburst[J].Journal of China Coal Society,2002,27(6):623-626.
[6] HIRATA T,SATOH T,ITO K.Fractal structure of spatial distribution of micro fracturing in rock[J]. Geophys J Roy Astron Soc,1987,90,369-374.
[7] YAO Y B,LIU D M,TANG D Z,et al.Fractal characterization of adsorption-pores of coals from North China:An investigation on CH4adsorption capacity of coals[J]. International Journal of Coal Geology,2008,73:27-42.
[8] LI T,CAI M F,CAI M.Earthquake-induced unusual gas emission in coalmines-A km-scale in-situ experimental investigation at Laohutai mine[J].International Journal of Coal Geology,2007,71:209-224.
[9]余恩晓,马立涛,周福双,等.煤岩孔隙结构分形特征表征方法研究[J].煤炭科学技术,2018,46(11):8-12.YU Enxiao,MA Litao,ZHOU Fushuang,et al. Study on method to characterize fractal features of pore structures in coal and rock mass[J].Coal Science and Technology,2018,46(11):8-12.
[10]高尚,王亮,高杰,等.基于分形理论的不同变质程度硬煤孔隙结构试验研究[J].煤炭科学技术,2018,46(8):93-100.GAO Shang,WANG Liang,GAO Jie,et al.Experimental study on pore structures of hard coal with different metamorphic grade based on fractal theory[J].Coal Science and Technology,2018,46(8):93-100.
[11]汤政,姜波,宋昱,等.宿县矿区构造煤压缩特性及孔隙结构分形特征研究[J].煤炭科学技术,2017,45(12):174-181.TANG Zheng,JIANG Bo,SONG Yu,et al. Study on compression characteristics and pore structural fractalfeature of structure coal in Suxian Mining Area[J]. Coal Science and Technology,2017,45(12):174-181.
[12]刘晓冬,徐景祯,王新峰.断裂体系多重分形谱特征及其应用.石油地球物理勘探[J].1999,34(3):285-289,301.LIU Xiaodong,XU Jingzhen,WANG Xinfeng.Multi-fractals spectrumbehavior of fault system and its application[J]. Oil Geophysical Prospecting,1999,34(3):285-289,301.
[13]胡修权,施泽进,田亚铭,等.川东南地区茅口组断裂多重分形特征及意义[J].成都理工大学学报:自然科学版,2014,41(4):476-482.HU Xiuquan, SHI Zejin, TIAN Yaming,et al. Muitifractal feature and significance of Maokou formation faults in the southeast of Sichuan[J]. Journal of Chengdu University of Technology:Science&Technology Edition,2014,41(4):476-482.
[14] PANAHI A,CHENG Q M.Multifractality as a measure of spatial distribution of geochemical patterns[J]. Mathematical Geology,36,827-846.
[15] ZHAO J N,CHEN S Y,ZUO R G,et al.Mapping complexity of spatial distribution of faults using fractal and multifractal models:vectoring towards exploration targets[J]. Computers&Geosciences,2011,37:1958-1966.
[16] XIE S Y,CHENG Q M,CHEN G.Application of local singularity in prospecting potential oil/gas targets[J].Nonlinear Processes in Geophysics,2007,14:285-292.
[17] HIRABAYASHI T,ITO K,YOSHII T. Multifractal analysis of earthquakes[J].Pure and Applied Geophysics,1992,138:591-610.
[18] KIYASHCHENKO D,SMIMOVA N,TROYAN V,et al. Seismic hazard precursory evolution:fractal and multifractal aspects[J].Physics and Chemistry of The Earth,2004,29:4-9.
[19]谢和平,王金安.岩石节理(断裂)表面的多重分形性质[J].力学学报,1998,30(3):314-320.XIE Heping,WANG Jinan. Multifractal behaviors of fracture surfaces in rocks[J]. Acta Mechanica Sinica,1998,30(3):314-320.
[20] SHIVAKUMAR K,RAO M V M S,SRINIVASAN C K,et al.Multifractal Analysis of the Spatial Distribution of Area Rockbursts at Kolar Gold Mines[J]. International Journal of Rock Mechanics and Mining Sciences,1996,33:167-172.
[21]陈雪梅,张晞,徐莉莉,等.煤与矸石分形维数的差异研究[J].煤炭科学技术,2017,45(7):196-199.CHEN Xuemei,ZHANG Xi,XU Lili,et al.Study on fractal dimension differences of coal and rock[J]. Coal Science and Technology,2017,45(7):196-199.
[22]焦作工学院瓦斯地质研究所.瓦斯地质概论[M].北京:煤炭工业出版社,1990.
[23]孙霞,吴自勤,黄畇.分形原理及其应用[M].合肥:中国科技大学出版社,2003.
[24]李彤,商朋见.多重分形在掌纹识别中的研究[J].物理学报,2007,56(8):4393-4400.LI Tong,SHANG Pengjian. A multifractal approach to palmprint recognition[J].Acta Physica Sinica,2007,56(8):4393-4400.
[2]徐志斌,王继尧,张大顺,等.煤矿断层网络复杂程度的分维描述[J].煤炭学报,1996,21(4):358-363.XU Zhibin,WANG Jiyao,ZHANG Dashun,et al.Fractal dimension description of complexity of fault network in coal mines[J].Journal of China Coal Society,1996,21(4):358-363.
[3] SHEPHERD J,RIXON L K,GRIFFITH L.Outbursts and geological structures in coal mines:a review[J].Int J Rock Mech Sci,1981,18:267-283.
[4]刘明举,刘希亮,何俊.煤与瓦斯突出分形预测研究[J].煤炭学报,1998,23(6):616-619.LIU Mingju,LIU Xiliang,HE Jun. Fractal prediction research of coal and gas outburst[J]. Journal of China Coal Society,1998,23(6):616-619.
[5]何俊,刘明举,颜爱华.煤田地质构造与瓦斯突出关系分形研究[J].煤炭学报,2002,27(6):623-626.HE Jun,LIU Mingju,YAN Aihua. Fractal research of relation between geological tectonic coalfields and gas outburst[J].Journal of China Coal Society,2002,27(6):623-626.
[6] HIRATA T,SATOH T,ITO K.Fractal structure of spatial distribution of micro fracturing in rock[J]. Geophys J Roy Astron Soc,1987,90,369-374.
[7] YAO Y B,LIU D M,TANG D Z,et al.Fractal characterization of adsorption-pores of coals from North China:An investigation on CH4adsorption capacity of coals[J]. International Journal of Coal Geology,2008,73:27-42.
[8] LI T,CAI M F,CAI M.Earthquake-induced unusual gas emission in coalmines-A km-scale in-situ experimental investigation at Laohutai mine[J].International Journal of Coal Geology,2007,71:209-224.
[9]余恩晓,马立涛,周福双,等.煤岩孔隙结构分形特征表征方法研究[J].煤炭科学技术,2018,46(11):8-12.YU Enxiao,MA Litao,ZHOU Fushuang,et al. Study on method to characterize fractal features of pore structures in coal and rock mass[J].Coal Science and Technology,2018,46(11):8-12.
[10]高尚,王亮,高杰,等.基于分形理论的不同变质程度硬煤孔隙结构试验研究[J].煤炭科学技术,2018,46(8):93-100.GAO Shang,WANG Liang,GAO Jie,et al.Experimental study on pore structures of hard coal with different metamorphic grade based on fractal theory[J].Coal Science and Technology,2018,46(8):93-100.
[11]汤政,姜波,宋昱,等.宿县矿区构造煤压缩特性及孔隙结构分形特征研究[J].煤炭科学技术,2017,45(12):174-181.TANG Zheng,JIANG Bo,SONG Yu,et al. Study on compression characteristics and pore structural fractalfeature of structure coal in Suxian Mining Area[J]. Coal Science and Technology,2017,45(12):174-181.
[12]刘晓冬,徐景祯,王新峰.断裂体系多重分形谱特征及其应用.石油地球物理勘探[J].1999,34(3):285-289,301.LIU Xiaodong,XU Jingzhen,WANG Xinfeng.Multi-fractals spectrumbehavior of fault system and its application[J]. Oil Geophysical Prospecting,1999,34(3):285-289,301.
[13]胡修权,施泽进,田亚铭,等.川东南地区茅口组断裂多重分形特征及意义[J].成都理工大学学报:自然科学版,2014,41(4):476-482.HU Xiuquan, SHI Zejin, TIAN Yaming,et al. Muitifractal feature and significance of Maokou formation faults in the southeast of Sichuan[J]. Journal of Chengdu University of Technology:Science&Technology Edition,2014,41(4):476-482.
[14] PANAHI A,CHENG Q M.Multifractality as a measure of spatial distribution of geochemical patterns[J]. Mathematical Geology,36,827-846.
[15] ZHAO J N,CHEN S Y,ZUO R G,et al.Mapping complexity of spatial distribution of faults using fractal and multifractal models:vectoring towards exploration targets[J]. Computers&Geosciences,2011,37:1958-1966.
[16] XIE S Y,CHENG Q M,CHEN G.Application of local singularity in prospecting potential oil/gas targets[J].Nonlinear Processes in Geophysics,2007,14:285-292.
[17] HIRABAYASHI T,ITO K,YOSHII T. Multifractal analysis of earthquakes[J].Pure and Applied Geophysics,1992,138:591-610.
[18] KIYASHCHENKO D,SMIMOVA N,TROYAN V,et al. Seismic hazard precursory evolution:fractal and multifractal aspects[J].Physics and Chemistry of The Earth,2004,29:4-9.
[19]谢和平,王金安.岩石节理(断裂)表面的多重分形性质[J].力学学报,1998,30(3):314-320.XIE Heping,WANG Jinan. Multifractal behaviors of fracture surfaces in rocks[J]. Acta Mechanica Sinica,1998,30(3):314-320.
[20] SHIVAKUMAR K,RAO M V M S,SRINIVASAN C K,et al.Multifractal Analysis of the Spatial Distribution of Area Rockbursts at Kolar Gold Mines[J]. International Journal of Rock Mechanics and Mining Sciences,1996,33:167-172.
[21]陈雪梅,张晞,徐莉莉,等.煤与矸石分形维数的差异研究[J].煤炭科学技术,2017,45(7):196-199.CHEN Xuemei,ZHANG Xi,XU Lili,et al.Study on fractal dimension differences of coal and rock[J]. Coal Science and Technology,2017,45(7):196-199.
[22]焦作工学院瓦斯地质研究所.瓦斯地质概论[M].北京:煤炭工业出版社,1990.
[23]孙霞,吴自勤,黄畇.分形原理及其应用[M].合肥:中国科技大学出版社,2003.
[24]李彤,商朋见.多重分形在掌纹识别中的研究[J].物理学报,2007,56(8):4393-4400.LI Tong,SHANG Pengjian. A multifractal approach to palmprint recognition[J].Acta Physica Sinica,2007,56(8):4393-4400.
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