基于三维快速扫描算法与到时差数据库技术的层状介质震源定位方法研究
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摘要
定位算法是微震监测的核心,而速度模型是影响微震定位算法精度的主要因素。快速扫描法(fast sweeping method,FSM)是一种基于复杂速度模型利用求解程函方程(eikonal equation)计算地震波初至到时的算法,已广泛应用于地震定位及地球物理勘探等领域。将该方法引入岩土工程稳定性监测与评价领域,提出一种针对层状速度模型的震源快速定位方法。建立笛卡尔坐标系下三维FSM算法,分别在单一速度模型和水平分层速度模型中采用FSM算法计算点震源初至波走时,与理论解对比分析算法精度及其误差分布特征;进而针对层状速度模型,提出一种基于FSM算法的到时差数据库微地震震源快速定位方法;与基于简化地质模型的传统定位算法进行对比,研究该方法定位精度和计算效率。结果表明,相比较于传统定位方法,提出的基于FSM算法建立的到时差数据库震源定位方法对于层状地质模型微地震事件位置精度具有显著提升,且大大缩减了定位耗时。该算法可为层状地层震源定位、微震监测及室内声发射监测等提供重要的理论和技术支撑。
The velocity model is the major factor affecting the seismic source localization algorithm which is the core of microseismic monitoring technique. Based on the complex velocity model, the fast sweeping method(FSM) is an algorithm to calculate the first arrival time of the seismic wave by using the eikonal equation. This method has been widely applied in the fields of earthquake localization and geophysical exploration. In this study, this method was introduced in the field of microseismic monitoring in geotechnical engineering. Especially for layered velocity models, a fast localization technique was established based on the fast sweeping method(FSM). Firstly, the fast sweeping method(FSM) in a 3 D Cartesian coordinate system was proposed to calculate the initial travel time of the point source in the single velocity model and horizontal layered velocity model. Compared with the theoretical solution, the accuracy of the algorithm and its error distribution characteristics were analyzed. The travel time results calculated by the fast sweeping method(FSM) and theoretical solutions were compared to analyze the algorithm precision and error distribution characteristics. Secondly, a rapid seismic source localization technique was put forward for the layered velocity model based on the database of the arrival time differences which were calculated by fast sweeping method(FSM). Finally, the positioning accuracy and computational efficiency between the new localization technique and traditional method based on the isotropy velocity model were compared and analyzed. This study showed that the proposed technique for the layered velocity model presented a favorable accuracy and computational efficiency, and also reduced the location time significantly compared with traditional location methods. The technique can provide significant theoretical and technical support for the microseismic source localization in complex layer and acoustic emission monitoring in the laboratory.
The velocity model is the major factor affecting the seismic source localization algorithm which is the core of microseismic monitoring technique. Based on the complex velocity model, the fast sweeping method(FSM) is an algorithm to calculate the first arrival time of the seismic wave by using the eikonal equation. This method has been widely applied in the fields of earthquake localization and geophysical exploration. In this study, this method was introduced in the field of microseismic monitoring in geotechnical engineering. Especially for layered velocity models, a fast localization technique was established based on the fast sweeping method(FSM). Firstly, the fast sweeping method(FSM) in a 3 D Cartesian coordinate system was proposed to calculate the initial travel time of the point source in the single velocity model and horizontal layered velocity model. Compared with the theoretical solution, the accuracy of the algorithm and its error distribution characteristics were analyzed. The travel time results calculated by the fast sweeping method(FSM) and theoretical solutions were compared to analyze the algorithm precision and error distribution characteristics. Secondly, a rapid seismic source localization technique was put forward for the layered velocity model based on the database of the arrival time differences which were calculated by fast sweeping method(FSM). Finally, the positioning accuracy and computational efficiency between the new localization technique and traditional method based on the isotropy velocity model were compared and analyzed. This study showed that the proposed technique for the layered velocity model presented a favorable accuracy and computational efficiency, and also reduced the location time significantly compared with traditional location methods. The technique can provide significant theoretical and technical support for the microseismic source localization in complex layer and acoustic emission monitoring in the laboratory.
引文
[1]GEIGER L.Probability method for the determination of earthquake epicenters from the arrival time only(translated from Geiger’s 1910 German article)[J].Bulletin of St.Louis University,1912,8(1):56-71.
[2]黄晓红,孙国庆,张凯月.基于全相位多次互相关的Geiger声发射源定位方法[J].岩土力学,2018(4):1362-1368.HUANG Xiao-hong,SUN Guo-qing,ZHANG Kai-yue.Localization of Geiger acoustic emission source based on all-phase analysis and several times cross-correlation[J].Rock and Soil Mechanics,2018(4):1362-1368.
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[5]YOUNG R P,COLLINS D S,REYES-MONTES J M,et al.Quantification and interpretation of seismicity[J].International Journal of Rock Mechanics and Mining Sciences,2004,41(8):1317-1327.
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[11]吴顺川,陈子健,张诗淮,等.缓倾地层微震定位算法探讨及其数值验证[J].岩土力学,2018(1):297-307.WU Shun-chuan,CHEN Zi-jian,ZHANG Shi-huai,et al.Microseismic location algorithm for gently inclined strata and its numerical verification[J].Rock and Soil Mechanics,2018(1):297-307.
[12]VINJE V,IVERSEN E,GJ YSTDAL H.Travel time and amplitude estimation using wavefront construction[J].Geophysics,1993,58(8):1157-1166.
[13]VIDALE J.Finite-difference calculation of travel time in three dimensions[J].Geophysics,1990,55:521-526.
[14]赵烽帆,马婷,徐涛.地震波初至走时的计算方法综述[J].地球物理学进展,2014,29(3):1102-1113.ZHAO Feng-fan,MA Ting,XU Tao.A review of the travel-time calculation methods of seismic first break[J].Process in Geophysics,2014,29(3):1102-1113.
[15]刘斌.地震学原理与应用[M].北京:中国科学技术大学出版社,2009.LIU Bin.Principles and applications of seismology[M].Beijing:Press of University of Science and Technology of China,2009.
[16]TSAI Y H R,GIGA Y,OSHER S.A level set approach for computing discontinuous solutions of a class of Hamilton-Jacobi equations[J].Mathematics of Computation,2001,72(241):159-181.
[17]SETHIAN J A,POPOVICI A M.3-D traveltime computation using the fast marching method[J].Geophysics,1999,64(2):516-523.
[18]HASSOUNA S M,FARAG A A.Multi Stencils fast marching methods:a highly accurate solution to the Eikonal equation on Cartesian domains[J].Pattern Analysis&Machine Intelligence IEEE Transactions,2007,29(9):1563-1574.
[19]郭亮,戴峰,徐奴文,等.基于MSFM的复杂速度岩体微震定位研究[J].岩石力学与工程学报,2017,36(2):394-406.GUO Liang,DAI Feng,XU Nu-wen,et al.Reasearch on MSFM-based microseismic source location of rock mass with complex velocities[J].Chinese Journal of Rock Mechanics and Engineering,2017,36(2):394-406.
[20]ZHAO H.A fast sweeping method for Eikonal equations[J].Mathematics of Computation,2005,74(250):603-627.
[21]CHEN W,CHOU C S,KAO C Y.Lax-Friedrichs multigrid fast sweeping methods for steady state problems for hyperbolic conservation laws[J].Journal of Scientific Computing,2015,64(3):591-618.
[22]LUO S,QIAN J.Factored singularities and high-order Lax-Friedrichs sweeping schemes for point-source traveltimes and amplitudes[J].Journal of Computational Physics,2011,230(12):4742-4755.
[23]LAN H.Comparative study of the free-surface boundary condition in two-dimensional finite-difference elastic wave field simulation[J].Journal of Geophysics&Engineering,2011,8(8):275.
[24]HUANG J,REYES-MONTES J M,MAXWELL S,et al.A new finite difference Eikonal equation solver for anisotropic medium[C]//77th EAGE Conference and Exhibition 2015.Madrid:[s.n.],2015.
[25]冯康.数值计算方法[M].北京:国防工业出版社,1978.FENG Kang.Numerical computation method[M].Beijing:National Defense Industry Press,1978.
[26]江海宇.油田压裂微地震地面监测速度模型校正及定位研究[D].长春:吉林大学,2016.JANG Hai-yu.The research on microseismic location and velocity optimization for microseismic monitoring on surface[D].Changchun:Jilin University,2016.
[2]黄晓红,孙国庆,张凯月.基于全相位多次互相关的Geiger声发射源定位方法[J].岩土力学,2018(4):1362-1368.HUANG Xiao-hong,SUN Guo-qing,ZHANG Kai-yue.Localization of Geiger acoustic emission source based on all-phase analysis and several times cross-correlation[J].Rock and Soil Mechanics,2018(4):1362-1368.
[3]RABINOWITZ N.Microearthquake location by means of nonlinear simplex procedure[J].Bulletin of the Seismological Society of America,1988,78(1):380-384.
[4]JONES R H,STEWART R C.A method for determining significant structures in a cloud of earthquakes[J].Journal of Geophysical Research Atmospheres,1997,102(B4):8245-8254.
[5]YOUNG R P,COLLINS D S,REYES-MONTES J M,et al.Quantification and interpretation of seismicity[J].International Journal of Rock Mechanics and Mining Sciences,2004,41(8):1317-1327.
[6]SAMBRIDGE M S.Non-linear arrival time inversion:constraining velocity anomalies by seeking smooth models in 3-D[J].Geophysical Journal International,1990,102(3):653-677.
[7]BULANT P.Two-point ray tracing in 3-D[J].Pure and Applied Geophysics,1996,148(3):421-447.
[8]JULIAN B R,GUBBINS D.Three dimensional seismic ray tracing[J].Journal of Geophysical Research,1977,43:95-113.
[9]UM J,THURBER C.A fast algorithm for two-point seismic ray tracing[J].Bulletin of the Seismological Society of America,1987,77(3):972-986.
[10]TIAN Y,CHEN X F.A rapid and accurate two-point ray tracing method in horizontally layered velocity model[J].Acta Seismologica Sinica,2005,18(2):154-161.
[11]吴顺川,陈子健,张诗淮,等.缓倾地层微震定位算法探讨及其数值验证[J].岩土力学,2018(1):297-307.WU Shun-chuan,CHEN Zi-jian,ZHANG Shi-huai,et al.Microseismic location algorithm for gently inclined strata and its numerical verification[J].Rock and Soil Mechanics,2018(1):297-307.
[12]VINJE V,IVERSEN E,GJ YSTDAL H.Travel time and amplitude estimation using wavefront construction[J].Geophysics,1993,58(8):1157-1166.
[13]VIDALE J.Finite-difference calculation of travel time in three dimensions[J].Geophysics,1990,55:521-526.
[14]赵烽帆,马婷,徐涛.地震波初至走时的计算方法综述[J].地球物理学进展,2014,29(3):1102-1113.ZHAO Feng-fan,MA Ting,XU Tao.A review of the travel-time calculation methods of seismic first break[J].Process in Geophysics,2014,29(3):1102-1113.
[15]刘斌.地震学原理与应用[M].北京:中国科学技术大学出版社,2009.LIU Bin.Principles and applications of seismology[M].Beijing:Press of University of Science and Technology of China,2009.
[16]TSAI Y H R,GIGA Y,OSHER S.A level set approach for computing discontinuous solutions of a class of Hamilton-Jacobi equations[J].Mathematics of Computation,2001,72(241):159-181.
[17]SETHIAN J A,POPOVICI A M.3-D traveltime computation using the fast marching method[J].Geophysics,1999,64(2):516-523.
[18]HASSOUNA S M,FARAG A A.Multi Stencils fast marching methods:a highly accurate solution to the Eikonal equation on Cartesian domains[J].Pattern Analysis&Machine Intelligence IEEE Transactions,2007,29(9):1563-1574.
[19]郭亮,戴峰,徐奴文,等.基于MSFM的复杂速度岩体微震定位研究[J].岩石力学与工程学报,2017,36(2):394-406.GUO Liang,DAI Feng,XU Nu-wen,et al.Reasearch on MSFM-based microseismic source location of rock mass with complex velocities[J].Chinese Journal of Rock Mechanics and Engineering,2017,36(2):394-406.
[20]ZHAO H.A fast sweeping method for Eikonal equations[J].Mathematics of Computation,2005,74(250):603-627.
[21]CHEN W,CHOU C S,KAO C Y.Lax-Friedrichs multigrid fast sweeping methods for steady state problems for hyperbolic conservation laws[J].Journal of Scientific Computing,2015,64(3):591-618.
[22]LUO S,QIAN J.Factored singularities and high-order Lax-Friedrichs sweeping schemes for point-source traveltimes and amplitudes[J].Journal of Computational Physics,2011,230(12):4742-4755.
[23]LAN H.Comparative study of the free-surface boundary condition in two-dimensional finite-difference elastic wave field simulation[J].Journal of Geophysics&Engineering,2011,8(8):275.
[24]HUANG J,REYES-MONTES J M,MAXWELL S,et al.A new finite difference Eikonal equation solver for anisotropic medium[C]//77th EAGE Conference and Exhibition 2015.Madrid:[s.n.],2015.
[25]冯康.数值计算方法[M].北京:国防工业出版社,1978.FENG Kang.Numerical computation method[M].Beijing:National Defense Industry Press,1978.
[26]江海宇.油田压裂微地震地面监测速度模型校正及定位研究[D].长春:吉林大学,2016.JANG Hai-yu.The research on microseismic location and velocity optimization for microseismic monitoring on surface[D].Changchun:Jilin University,2016.