矿井富水区陷落柱成像研究
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摘要
针对目前矿井富水区超前探测瞬变电磁法常用的时域有限差分(FDTD)方法时间步长选取受限于Courant-Friedrich-Lewy稳定性条件的问题,同时为进一步提高电磁计算效率和富水区成像分辨率,提出将逆时偏移成像算法和Crank-Nicolson时域有限差分(CN-FDTD)方法应用于矿井富水区陷落柱成像研究。首先介绍了逆时偏移成像算法和CN-FDTD方法基本原理;然后建立了矿井富水区陷落柱三维空间模型,研究了激励源线圈频率和角度对成像分辨率的影响,并得出了矿井富水区陷落柱成像结果;最后分析了CN-FDTD方法的计算效率。试验结果表明:当激励源线圈峰值频率为65 MHz且激励源线圈平行于xoz平面时,富水区陷落柱成像分辨率较高;基于CN-FDTD逆时偏移成像算法的矿井富水区陷落柱成像与实际模型相符;CN-FDTD方法较传统FDTD方法计算效率高,内存占比小。
In order to solve the problem that selection of time step was limited by Courant-FriedrichLewy stability condition in current finite-difference time-domain(FDTD)method commonly used in advanced detection transient electromagnetic method of water-rich area in coal mine,and further improve electromagnetic calculation efficiency and imaging resolution of water-rich area,reverse time migration imaging algorithm and Crank-Nicolson finite-difference time-domain(CN-FDTD)method were applied to research of karst collapse pillar(KCP)imaging of water-rich area in coal mine.Firstly,basic principles of reverse time migration imaging algorithm and CN-FDTD method were introduced.Then a threedimensional KCP model of water-rich area in coal mine was established.Influence of frequency and angle of excitation source coil on imaging resolution was researched,and imaging results of the KCP were obtained.Finally,computational efficiency of CN-FDTD method was analyzed.The experimental results show that when peak frequency of excitation source coil is 65 MHz and the excitation source coil is parallel to xoz plane,imaging resolution of the KCP is high.The KCP imaging of water-rich area in coal mine based on CN-FDTD reverse time migration imaging method is consistent with the actual model.Compared with traditional FDTD method,CN-FDTD method has higher computational efficiency and smaller memory proportion.
In order to solve the problem that selection of time step was limited by Courant-FriedrichLewy stability condition in current finite-difference time-domain(FDTD)method commonly used in advanced detection transient electromagnetic method of water-rich area in coal mine,and further improve electromagnetic calculation efficiency and imaging resolution of water-rich area,reverse time migration imaging algorithm and Crank-Nicolson finite-difference time-domain(CN-FDTD)method were applied to research of karst collapse pillar(KCP)imaging of water-rich area in coal mine.Firstly,basic principles of reverse time migration imaging algorithm and CN-FDTD method were introduced.Then a threedimensional KCP model of water-rich area in coal mine was established.Influence of frequency and angle of excitation source coil on imaging resolution was researched,and imaging results of the KCP were obtained.Finally,computational efficiency of CN-FDTD method was analyzed.The experimental results show that when peak frequency of excitation source coil is 65 MHz and the excitation source coil is parallel to xoz plane,imaging resolution of the KCP is high.The KCP imaging of water-rich area in coal mine based on CN-FDTD reverse time migration imaging method is consistent with the actual model.Compared with traditional FDTD method,CN-FDTD method has higher computational efficiency and smaller memory proportion.
引文
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[16]LU Xinglin,SONG Ao,QIAN Rongyi,et al.Anisotropic reverse-time migration of groundpenetrating radar data collected on the sand dunes in the Badain Jaran Desert[J].IEEE Journal of Selected Topics in Applied Earth Observations and Remote Sensing,2018,11(2):647-654.
[17]程飞.多井井间三维波场数值模拟与逆时偏移成像研究[D].武汉:中国地质大学,2015.
[18]王京.隧道空间有限元地震波场模拟与逆时偏移成像[D].武汉:中国地质大学,2017.
[19]YANG Y.The three-dimensional unconditionally stable FDTD algorithm based on Crank-Nicolson method[C]//IEEE Antennas and Propagation Society International Symposium,Albuquerque,2006:81-84.
[20]WANG Zhiyong,DING Hao,LU Guijin,et al.Reverse-time migration based optical imaging[J].IEEE Transactions om Medical Imaging,2016,35(1):273-281.
[2]周金,程久龙,温来福.矿井瞬变电磁法反演方法研究进展与展望[J].煤矿安全,2017,48(4):180-183.ZHOU Jin,CHENG Jiulong,WEN Laifu.Research progress and prospect on inversion methods of mine transient electromagnetic method[J].Safety in Coal Mines,2017,48(4):180-183.
[3]孟强华,窦文武.瞬变电磁探测在煤矿采空区积水边界探测中的应用[J].煤炭技术,2018,37(2):123-125.MENG Qianghua,DOU Wenwu.Application of transient electromagnetic detection in goaf water boundary detection in coal mine[J].Coal Technology,2018,37(2):123-125.
[4]王鹏.厚煤层露天矿地下水瞬变电磁法探测[J].煤矿安全,2019,50(1):153-156.WANG Peng.Detection of groundwater in thick coal seam open pit by TEM[J].Safety in Coal Mines,2019,50(1):153-156.
[5]ROY K K,VERMA S K,MALLICK K.Deep electromagnetic exploration[M].Berlin:Springer,1999.
[6]KRIVOCHIEVA S,CHOUTEAU M.Whole-space modeling of a layered earth in time-domain electromagnetic measurements[J].Journal of Applied Geophysics,2002,50(4):375-391.
[7]常江浩.煤矿富水区矿井瞬变电磁响应三维数值模拟及应用[D].徐州:中国矿业大学,2017.
[8]张广博.掘进工作面富水区瞬变电磁法多分量探测物理模拟及应用[D].徐州:中国矿业大学,2016.
[9]许新刚.矿井含水构造瞬变电磁场响应及透视技术研究[D].徐州:中国矿业大学,2017.
[10]于景邨,常江浩,苏本玉,等.老空水全空间瞬变电磁法探测三维数值模拟研究[J].煤炭科学技术,2015,43(1):95-99.YU Jingcun,CHANG Jianghao,SU Benyu,et al.Study on whole space transient electromagnetic method prospect three dimensional numerical modeling of gob water[J].Coal Science and Technology,2015,43(1):95-99.
[11]刘尧.基于有限差分的瞬变电磁三维数值模拟[D].北京:中国地质大学(北京),2015.
[12]徐兴荣,王西文,王宇超,等.基于波场分离理论的逆时偏移成像条件研究及应用[J].地球物理学进展,2012,27(5):2084-2090.XU Xingrong,WANG Xiwen,WANG Yuchao,et al.Study and application of imaging condition for reverse-time migration based on wave-fields separation[J].Progress in Geophysics,2012,27(5):2084-2090.
[13]朱尉强,黄清华.探地雷达衰减补偿逆时偏移成像方法[J].地球物理学报,2016,59(10):3909-3916.ZHU Weiqiang,HUANG Qinghua.Attenuation compensated reverse time migration method of ground penetrating radar signals[J].Chinese Journal of Geophysics,2016,59(10):3909-3916.
[14]刘学建,刘伊克.表面多次波最小二乘逆时偏移成像[J].地球物理学报,2016,59(9):3354-3365.LIU Xuejian,LIU Yike.Least-squares reverse-time migration of surface-related multiples[J].Chinese Journal of Geophysics,2016,59(9):3354-3365.
[15]鲁兴林,钱荣毅.地质雷达有限差分逆时偏移方法研究[J].地球物理学进展,2017,32(2):885-890.LU Xinglin,QIAN Rongyi.Ground-penetrating radar finite-difference reverse time migration[J].Progress in Geophysics,2017,32(2):885-890.
[16]LU Xinglin,SONG Ao,QIAN Rongyi,et al.Anisotropic reverse-time migration of groundpenetrating radar data collected on the sand dunes in the Badain Jaran Desert[J].IEEE Journal of Selected Topics in Applied Earth Observations and Remote Sensing,2018,11(2):647-654.
[17]程飞.多井井间三维波场数值模拟与逆时偏移成像研究[D].武汉:中国地质大学,2015.
[18]王京.隧道空间有限元地震波场模拟与逆时偏移成像[D].武汉:中国地质大学,2017.
[19]YANG Y.The three-dimensional unconditionally stable FDTD algorithm based on Crank-Nicolson method[C]//IEEE Antennas and Propagation Society International Symposium,Albuquerque,2006:81-84.
[20]WANG Zhiyong,DING Hao,LU Guijin,et al.Reverse-time migration based optical imaging[J].IEEE Transactions om Medical Imaging,2016,35(1):273-281.