多层水平或倾斜介质中的震源定位
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摘要
为了充分利用矿区岩土体的三维速度结构,以正反演联用法为雏形,提出专门针对水平或倾斜分层介质的定位方法。推导水平分层介质中的波前曲面方程,并基于该方程,从任意观测系统角度,将发震时刻作为未知量引入非线性方程组求解,建立未知数个数等于非线性方程个数的适定非线性方程组,从而建立了波前正演法。不同于正反演联用法通过规则观测系统和曲线拟合确定发震时刻,波前正演法将发震时刻作为未知量,确定震源时空参数需要四个台站的非线性方程。为了简化波前正演法的非线性系统,采用变量代换法,减少了定位参数,从而减小了确定迭代初值的难度。通过将台站所在的原大地坐标系旋转至与介质分界面平行正交,使得新坐标系中的波前面推进方向与坐标轴z平行,从而将波前正演法推广应用于倾斜层状介质,有效解决了倾斜层状介质中的震源定位问题。对波前正演法的16个未知参数相对于3个速度结构参数的条件数进行计算,多种定位条件下的条件数计算结果表明,波前正演法的条件数均远小于10,波前正演法是良态的。
In order to make full use of 3-D velocity structure of the rock mass in the mining area, based on the combined method of forward and inversion as an embryonic form, a new method for positioning of seismic sources in multilayered horizontal or inclined media is put forward. The wave front surface equation in multilayered horizontal media is derived. From the perspective of any field setup, based on the equation, the original time of earthquake is substituted into the nonlinear equations as an unknown quantity. The nonlinear equation set is established, of which the unknowns are equal to the number of nonlinear equations, thus a method for positioning of seismic sources based on forward of wave front is established. The time when the earthquake happens is obtained through inversion and corrected by curve fitting based on regular field setup in the positioning model combined with forward and inversion. The positioning model, based on forward of wave front, which deals with the time of earthquake as an unknown quantity in the nonlinear equations, is different. It obtains spatiotemporal parameters of seismic sources through nonlinear equations of four stations. The number of source parameters is reduced using the method of variable substitution, so the nonlinear system of the positioning model based on forward of wave front is simplified. The determination of iterative initial value is easier. The original geodetic coordinates of stations are rotated into those which are orthogonal or parallel to the interfaces between different media. The forward direction of wave front in the new coordinate system is parallel to the axis z. Thus the positioning model based on forward of wave front is extended to multilayered inclined media. The positioning model based on forward of wave front is an effective method to solve the problem of source positioning in multilayered inclined media. The calculated results of conditional numbers of 16 unknown parameters corresponding to 3 parameters of velocity structure under different conditions show that the conditional numbers of positioning model based on forward of wave front are all far less than 10, and the positioning model based on forward of wave front is in good state.
In order to make full use of 3-D velocity structure of the rock mass in the mining area, based on the combined method of forward and inversion as an embryonic form, a new method for positioning of seismic sources in multilayered horizontal or inclined media is put forward. The wave front surface equation in multilayered horizontal media is derived. From the perspective of any field setup, based on the equation, the original time of earthquake is substituted into the nonlinear equations as an unknown quantity. The nonlinear equation set is established, of which the unknowns are equal to the number of nonlinear equations, thus a method for positioning of seismic sources based on forward of wave front is established. The time when the earthquake happens is obtained through inversion and corrected by curve fitting based on regular field setup in the positioning model combined with forward and inversion. The positioning model, based on forward of wave front, which deals with the time of earthquake as an unknown quantity in the nonlinear equations, is different. It obtains spatiotemporal parameters of seismic sources through nonlinear equations of four stations. The number of source parameters is reduced using the method of variable substitution, so the nonlinear system of the positioning model based on forward of wave front is simplified. The determination of iterative initial value is easier. The original geodetic coordinates of stations are rotated into those which are orthogonal or parallel to the interfaces between different media. The forward direction of wave front in the new coordinate system is parallel to the axis z. Thus the positioning model based on forward of wave front is extended to multilayered inclined media. The positioning model based on forward of wave front is an effective method to solve the problem of source positioning in multilayered inclined media. The calculated results of conditional numbers of 16 unknown parameters corresponding to 3 parameters of velocity structure under different conditions show that the conditional numbers of positioning model based on forward of wave front are all far less than 10, and the positioning model based on forward of wave front is in good state.
引文
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[2]胡静云,李庶林.矿震P波到时拾取优化与降低震源定位误差应用研究[J].岩土工程学报,2014,36(10):1940–1946.(HU Jing-yun,LI Shu-lin.Optimization of picking mine microseismic P-wave arrival time and its application in reducing error of source locating[J].Chinese Journal of Geotechnical Engineering,2014,36(10):1940–1946.(in Chinese))
[3]赵国彦,邓青林,马举.基于FSWT时频分析的矿山微震信号分析与识别[J].岩土工程学报,2015,37(2):306–312.(ZHAO Guo-yan,DENG Qing-lin,MA Ju.Recognition of mine microseismic signals based on FSWT time-frequency analysis[J].Chinese Journal of Geotechnical Engineering,2015,37(2):306–312.(in Chinese))
[4]程爱平,高永涛,梁兴旺,等.煤矿底板潜在突水危险区微震识别研究[J].岩土工程学报,2014,36(9):1727–1732.(CHENG Ai-ping,GAO Yong-tao,LIANG Xing-wang,et al.Identification of potential water inrush areas in coal floor by using microseismic monitoring technique[J].Chinese Journal of Geotechnical Engineering,2014,36(9):1727–1732.(in Chinese))
[5]彭府华,李庶林,程建勇,等.中尺度复杂岩体应力波传播特性的微震试验研究[J].岩土工程学报,2014,36(2):312–319.(PENG Fu-hua,LI Shu-lin,CHENG Jian-yong,et al.Experimental study on characteristics of stress wave propagation in the mesoscale and complex rock mass by microseismic monitoring[J].Chinese Journal of Geotechnical Engineering,2014,36(2):312–319.(in Chinese))
[6]姜福兴,史先锋,王存文,等.高应力区分层开采冲击地压事故发生机理研究[J].岩土工程学报,2015,37(6):1123–1131.(JIANG Fu-xing,SHI Xian-feng,WANG Cun-wen,et al.Mechanical mechanism of rock burst accidents in slice mining face under high pressure[J].Chinese Journal of Geotechnical Engineering,2015,37(6):1123–1131.(in Chinese))
[7]潘立友,陈理强,张若祥.深部两软煤层沿空巷道冲击地压成因与防治研究[J].岩土工程学报,2015,37(8):1484–1489.(PAN Li-you,CHEN Li-jiang,ZHANG Re-xiang.Causes for rockburst and control of gob side entry in deep two soft coal seams[J].Chinese Journal of Geotechnical Engineering,2015,37(8):1484–1489.(in Chinese))
[8]姜福兴,冯宇,KOUAME K A,等.高地应力特厚煤层“蠕变型”冲击机理研究[J].岩土工程学报,2015,37(10):1762–1768.(JIANG Fu-xing,FENG Yu,KOUAME K A,et al.Mechanism of creep-induced rock burst in extra-thick coal seam under high ground stress[J].Chinese Journal of Geotechnical Engineering,2015,37(10):1762–1768.(in Chinese))
[9]杨伟利,姜福兴,杨鹏,等.特厚煤层冲击地压重复发生的机理研究[J].岩土工程学报,2015,37(11):2045–2050.(YANG Wei-li,JIANG Fu-xing,YANG Peng,et al.Mechanism of repeated rock bursts in extra-thick coal seam[J].Chinese Journal of Geotechnical Engineering,2015,37(11):2045–2050.(in Chinese))
[10]于群,唐春安,李连崇,等.基于微震监测的锦屏二级水电站深埋隧洞岩爆孕育过程分析[J].岩土工程学报,2014,36(12):2315–2322.(YU Qun,TANG Chun-an,LI Lian-chong,et al.Nucleation process of rockbursts based on microseismic monitoring of deep-buried tunnels for JinpingⅡHydropower Station[J].Chinese Journal of Geotechnical Engineering,2014,36(12):2315–2322.(in Chinese))
[11]GEIGER L.Probability method for the determination of earth-quake epicenters from arrival time only[J].Bull St Louis Univ,1912,8:60–71.
[12]陈棋福,张跃勤,周静.数字观测时代的全球三维结构与地震定位研究[J].地震,2001,21(2):29–40.(CHEN Qi-fu,ZHANG Yue-qin,ZHOU Jing.Review of earthquake location with three dimensional earth model for digital seismic observation[J].Eearthquake,2001,21(2):29–40.(in Chinese))
[13]潘一山,赵扬锋,官福海,等.矿震监测定位系统的研究及应用[J].岩石力学与工程学报,2007,26(5):1002–1011.(PAN Yi-shan,ZHAO Yang-feng,GUAN Fu-hai,et al.Study on rockburst monitoring and orientation system and its application[J].Chinese Journal of Rock Mechanics and Engineering,2007,26(5):1002–1011.(in Chinese))
[14]张向东,王帅,赵彪,等.二层水平介质中震源的精确定位[J].岩土工程学报,2014,36(6):1044–1050.(ZHANG Xiang-dong,WANG Shuai,ZHAO Biao,et al.Precise positioning in double-layer horizontal media[J].Chinese Journal of Geotechnical Engineering,2014,36(6):1044–1050.(in Chinese))
[15]张向东,王帅,贾宝新.二层水平介质球面波正反演联用与震源定位[J].岩土工程学报,2015,37(2):225–234.(ZHANG Xiang-dong,WANG Shuai,JIA Bao-xin.Positioning of seismic sources combined with forward and inversion of spherical wave in double-layer horizontal media[J].Chinese Journal of Geotechnical Engineering,2015,37(2):225–234.(in Chinese))
[16]曾繁慧.数值分析[M].徐州:中国矿业大学出版社,2009:6–7.(ZENG Fan-hui.Numerical analysis[M].Xuzhou:China University of Mining and Technology Press,2009:6–7.(in Chinese))
[17]李庆扬,王能超,易大义,等.数值分析[M].5版.北京:清华大学出版社,2008:10–11.(LI Qing-yang,WANG Neng-chao,YI Da-yi,et al.Numerical analysis[M].5nd ed.Beijing:Tsinghua University Press,2008:10–11.(in Chinese))
[18]同济大学应用数学系.高等数学(下)[M].5版.北京:高等教育出版社,2002:34–35.(Department of Applied Mathematics,Tongji University.Higher mathematics(Vol2)[M].5nd ed.Beijing:Higher Education Press,2002:34–35.(in Chinese))