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物探与化探  2019, Vol. 43 Issue (6): 1341-1349    DOI: 10.11720/wtyht.2019.0203
  方法研究·仪器研制 本期目录 | 过刊浏览 | 高级检索 |
煤层厚度控制因素的分形奇异值分解法研究
孙雅楠1, 刘星2(), 赵志根1
1. 安徽理工大学 测绘学院,安徽 淮南 232000
2. 安徽理工大学 地球与环境学院,安徽 淮南 232000
A study of fractal singular value decomposition method for controlling factors of coal seam thickness
Ya-Nan SUN1, Xing LIU2(), Zhi-Gen ZHAO1
1. Survey School, Anhui University of Science and Technology, Huainan 232000, China
2. Earth and Environment School, Anhui University of Science and Technology, Huainan 232000, China
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摘要 

煤层的厚度分布是多种地质因素联合控制的结果,不同地区其控煤因素有所不同,以往的研究偏重定性的对比分析,难以准确查明控制因素及其分布。依据煤层厚度空间分布的多重分形特征和广义自相似性原理,将煤层厚度变换到特征空间,进行奇异值分解,根据能量测度和能谱密度所表现出的分形规律,将奇异值分解图用最小二乘法拟合为多段直线,并确定不同的拐点,利用奇异矩阵选取前三段中的奇异值及特征子空间进行重建,将重建后的异常与各个影响煤层厚度的变量相对比,提取各种隐含的控煤地质因素,实现煤层厚度控制因素的定量分析。文中对淮南潘集煤矿(外围)的8号主采煤层进行了实例分析,得到了该地区煤层厚度的主要控制因素是古地形、同沉积构造以及古地理环境中的水动力条件,并与利用对应分析得到的控煤因素进行对比,表明了该方法在定量分析中的有效性。

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孙雅楠
刘星
赵志根
关键词 控煤因素定量分析奇异值分解空间重建异常图    
Abstract

The thickness distribution of coal seams results from the combined control of various geological factors, and the control factors of coal are different in different regions. Previous studies have focused on qualitative comparative analysis, and hence it is very difficult for them to identify accurately the control factors and their distribution. In this study, according to the multi-fractal characteristics and the generalized self-similarity principle of the coal seam thickness spatial distribution, the authors transformed coal seam thickness into feature space and performed singular value decomposition. Based on the fractal law of energy measure and energy spectral density,the authors used the least squares method to fit singular value decomposition figure into multipul lines, determined different inflection points, selected the singular value and the corresponding feature subspace in the first three sections for reconstruction, compared anomalies after reconstruction with various variables that affect the thickness of coal seams, extracted various implicit geological factors for coal control, and thus realized the quantitative analysis of controlling factors of coal seam thickness. The authors analyzed the No. 8 main coal seam in Panji coal mine (peripheral) of Huainan as a study case, detected the fact that the main control factors for the thickness of coal seam in this area are ancient terrain, same sedimentary structure and hydrodynamic conditions in ancient geography, and compared the results with the control factors obtained by the corresponding analysis. The results show the effectiveness of this method in quantitative analysis.

Key wordscontrol coal factor    quantitative analysis    singular value decomposition    space reconstruction    abnormal figure
收稿日期: 2019-04-09      出版日期: 2019-11-28
:  P611  
基金资助:国家重点研发计划项目“面向井下钻孔机器人施工的瓦斯防治钻孔智能设计技术”(2018YFC0808002);国家自然科学基金面上项目“薄松散层覆盖煤矿采空区高光谱遥感特征研究”(41372368)
通讯作者: 刘星
作者简介: 孙雅楠(1994-),女,从事控煤地质因素的定量分析研究工作。Email: 2738063496@qq.com
引用本文:   
孙雅楠, 刘星, 赵志根. 煤层厚度控制因素的分形奇异值分解法研究[J]. 物探与化探, 2019, 43(6): 1341-1349.
Ya-Nan SUN, Xing LIU, Zhi-Gen ZHAO. A study of fractal singular value decomposition method for controlling factors of coal seam thickness. Geophysical and Geochemical Exploration, 2019, 43(6): 1341-1349.
链接本文:  
https://www.wutanyuhuatan.com/CN/10.11720/wtyht.2019.0203      或      https://www.wutanyuhuatan.com/CN/Y2019/V43/I6/1341
Fig.1  潘集煤矿(外围)地质构造简图
Fig.2  71个钻孔点分布
平均值 最小值 最大值 标准差 变异系数 偏度 峰度 Sig.
2.28 0.55 6.48 0.97 42.54 1.71 4.70 0.056
Table 1  K-S正态检验结果
Fig.3  M8H的等值线
Fig.4  M8H奇异值随能量密度的变化
Fig.5  M8H奇异值的积分能量贡献
Fig.6  M8H分形奇异值分解图解
Fig.7  M8H异常
a—第一段奇异值对应子空间的异常重建;b—第二段奇异值对应子空间的异常重建;c—第三段奇异值对应子空间的异常重建;d—第四段奇异值对应子空间的异常重建;e—第五段奇异值对应子空间的异常重建;f—第六段奇异值对应子空间的异常重建
Fig.8  M8DG等值线
Fig.9  SXH等值线
Fig.10  XSHZH等值线
Fig.11  XSHZYB等值线
SXH XSHZH XSHZYB M8DG M8H
SXH 1.000 0.309 -0.175 0.635 0.206
XSHZH 0.309 1.000 -0.298 0.238 0.233
XSHZYB -0.175 -0.298 1.000 -0.128 0.090
M8DG 0.635 0.238 -0.128 1.000 -0.046
M8H 0.206 0.233 0.090 -0.046 1.000
Table 2  变量间的相关关系
成分1 成分2
SXH 0.867 -0.140
XSHZH 0.240 -0.659
XSHZYB -0.047 0.896
M8DG 0.921 -0.072
M8H 0.020 0.047
Table 3  第一段煤厚的成分矩阵
成分1 成分2
SXH 0.880 0.129
XSHZH 0.332 0.704
XSHZYB -0.194 -0.591
M8DG 0.870 0.064
M8H -0.236 0.712
Table 4  第二段煤厚的成分矩阵
成分1 成分2
SXH 0.871 0.168
XSHZH 0.303 0.724
XSHZYB -0.182 -0.560
M8DG 0.890 0.049
M8H -0.152 0.673
Table 5  第三段煤厚的成分矩阵
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