Three-dimensional analytical comprehensive solutions for acoustic emission/microseismic sources of unknown velocity system
DONG Longjun1，2，LI Xibing1，MA Ju1，TANG Lizhong1
(1. School of Resources and Safety Engineering，Central South University，Changsha，Hunan 410083，China；2. Jiaojia Gold Mine，Shandong Gold Group Co. Ltd.，Laizhou，Shandong 261441，China)
Abstract：The location accuracy of traditional methods based on the time difference is always influenced by the iterative method，the initial value and the pre-measured velocity. Solutions are not unique due to the square root calculations. In order to resolve the above two problems，the nonlinear location equations for the time difference of arrivals were simplified to linear equations and an analytical location method without the square root calculations was developed. A set of analytical solutions for AE / microseismic source location (ASS) were proposed for the unknown velocity systems where N = 6. Only the coordinates of the sensors and P-wave arrival times are required by the ASS method to accurately solve the source location parameters in real-time situations. The log-logistic distribution was used to determine the microseismic source locations. The blasting tests in the Dongguashan mine were used to verify the proposed analytical method for N≥6. Results show that the location accuracy of the proposed analytical solution is higher than the traditional method. The method highlights four outstanding advantages: no iterative solution; no pre-measured velocity; no initially evaluated source coordinates and no square root calculations.
[1] MENDECKI A J. Seismic monitoring in mines[M]. London：Chapman and Hall，1997：220–245.
[2] 陈炳瑞，冯夏庭，曾雄辉，等. 深埋隧洞TBM 掘进微震实时监测与特征分析[J]. 岩石力学与工程学报，2011，30(2)：275–283. (CHEN Bingrui，FENG Xiating，ZENG Xionghui，et al. Real-time microseismic monitoring and its characteristic analysis during TBM tunneling in deep-buried tunnel[J]. Chinese Journal of Rock Mechanics and Engineering，2011，30(2)：275–283.(in Chinese))
[3] 董陇军，孙道元，李夕兵，等. 微震与爆破事件统计识别方法及工程应用[J]. 岩石力学与工程学报，2016，35(7)：1 423–1 433.(DONG Longjun，SUN Daoyuan，LI Xibing，et al. A statistical method to identify blasts and microseismic events and its engineering application[J]. Chinese Journal of Rock Mechanics and Engineering，2016，35(7)： 1 423–1 433.(in Chinese))
[4] ORTLEPP W D，STACEY T R. Rockburst mechanisms in tunnels and shafts[J]. Tunneling and Underground Space Technology，1994，9(1)：59–65.
[5] 徐奴文，唐春安，沙 椿，等. 锦屏一级水电站左岸边坡微震监测系统及其工程应用[J]. 岩石力学与工程学报，2010，29(5)：915–935.(XU Nuwen，TANG Chun?an，SHA Chun，et al. Microseismic monitoring system establishment and its engineering applications to left bank slope of Jinping I hydropower station[J]. Chinese Journal of Rock Mechanics and Engineering，2010，29(5)：915–935.(in Chinese))
[6] 唐礼忠，杨承祥，潘长良. 大规模深井开采微震监测系统站网布置优化[J]. 岩石力学与工程学报，2006，25(10)：2 036–2 042.(TANG Lizhong，YANG Chengxiang，PAN Changliang. Optimization of microseismic monitoring network for large-scale deep well mining[J]. Chinese Journal of Rock Mechanics and Engineering，2006，25(10)：2 036–2 042.(in Chinese))
[7] 董陇军，李夕兵，唐礼忠，等. 无需预先测速的微震震源定位的数学形式及震源参数确定[J]. 岩石力学与工程学报，2011，30(10)： 2 057–2 067.(DONG Longjun，LI Xibing，TANG Lizhong，et al. Mathematical functions and parameters for microseismic source location without pre-measuring speed[J]. Chinese Journal of Rock Mechanics and Engineering，2011，30(10)：2 057–2 067.(in Chinese))
[8] 董陇军. 矿山微震震源的高精度定位与实时辨识方法及应用[博士学位论文][D]. 长沙；中南大学，2013.(DONG Longjun. Methodologies and applications for precise location and realtime identification of microseismic sources in mines[Ph. D. Thesis][D]. Changsha：Central South University，2013.(in Chinese))
[9] SCHMIDT R O. A new approach to geometry of range difference location[J]. Aerospace and Electronic Systems，IEEE Transactions on， 1972，(6)：821–835.
[10] ARROWSMITH S J，ARROWSMITH M D，HEDLIN M A H，et al. Discrimination of delay-fired mine blasts in wyoming using an automatic time-frequency discriminant[J]. Bulletin of the Seismological Society of America，2006，96(6)：2 368–2 382.
[11] CHAN Y，HO K. An efficient closed-form localization solution from time difference of arrival measurements[C]// IEEE International Conference on Acoustics. [S. l.]：[s. n.]，1994，2：393–396.
[12] LIU H，MILIOS E. Acoustic positioning using multiple microphone arrays [J]. The Journal of the Acoustical Society of America，2005，117：2 772.
[13] SMITH J，ABEL J. Closed-form least-squares source location estimation from range-difference measurements[J]. Acoustics，Speech and Signal Processing，IEEE Transactions on，1987，35(12)：1 661–1 669.
[14] LI X，DONG L. Comparison of two methods in acoustic emission source location using four sensors without measuring sonic speed[J]. Sensor Lett，2011，9(5)：2 025–2 029.
[15] DURAISWAMI R，ZOTKIN D，DAVIS L. Exact solutions for the problem of source location from measured time differences of arrival[J]. The Journal of the Acoustical Society of America，1999，106：2 277.
[16] BRANDSTEIN M S，ADCOCK J E，SILVERMAN H F. A closed-form method for finding source locations from microphone- array time-decay estimates[C]// International Conference on Acoustics. [S. l.]：[s. n.]，1995，5：3 019–3 022.
[17] BRANDSTEIN M S，ADCOCK J E，SILVERMAN H F. A closed-form location estimator for use with room environment microphone arrays[J]. Speech and Audio Processing，IEEE Transactions on，1997，5(1)：45–50.
[18] GE M. Analysis of source location algorithms：part i. over-view and non-iterative methods[J]. Journal of Acoustic Emission，2003，21：14–28.
[19] GE M. Analysis of source location algorithms：Part II. Itera-tive methods[J]. Journal of Acoustic Emission，2003，21：29–51．
[20] BORKOWSKI K M. Accurate algorithms to transform geocentric to geodetic coordinates[J]. Bulletin Géodésique，1989，63(1)：50–56.
[21] DONG L J，LI X B，ZHOU Z L，et al. Three-dimensional analytical solution of acoustic emission source location for cuboid monitoring network without pre-measured wave velocity[J]. Transactions of Nonferrous Metals Society of China，2015，25(1)：293–302.
[22] DONG L J，LI X B. Three-dimensional analytical solution of acoustic emission or microseismic source location under cube monitoring network[J]. Transactions of Nonferrous Metals Society of China，2012，22(12)：3 087–3 094.
2017, Vol. 36 
