RANSAC-PSO算法的抗差反演——以芦山地震为例
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摘要
本文利用RANSAC-PSO算法研究在反演断层滑动参数时所用大地测量数据包含粗差的问题。在模拟实验中对理论观测值加入1%、5%、10%粗差,分别采用粒子群算法、选权迭代算法和RANSAC-PSO算法反演断层滑动参数。结果表明,当观测值中包含粗差率达10%时,PSO算法反演的滑动参数与理论值相差23.2cm,选权迭代法反演的滑动参数与理论值相差26.2cm,而RANSAC-PSO反演的滑动参数与理论值相差小于1cm。芦山地震具有以逆冲为主兼具少量左旋走滑性质,采用芦山地震同震GPS位移数据分别以PSO算法和RANSAC-PSO算法反演断层滑动参数,RANSAC-PSO算法反演的走滑量为0.051 8m,倾滑量为0.828 9m,均大于PSO的反演结果;释放能量1.000 9×10~(19) N·m(M_W6.63),与GCMT的1.060 0×10~(19)N·m更加吻合。分别用RANSAC-PSO算法与PSO算法反演的滑动参数计算地表水平位移,并与GPS观测进行对比,发现二者在计算距断层的远场点时,计算的水平位移基本一致;而在计算距断层的近场点时,RANSAC-PSO算法表现更为优秀,尤其体现在LS07点上,其计算值与GPS观测值完全重合。
The RANSAC-PSO algorithm is used to study the problem of gross errors ingeodetic data as a resultof fault slip parameters inversion.In the simulation experiment,1%,5% and 10% of the gross errors are added to the theoretical observations.Particle swarm optimization,selecting weight iteration and RANSAC-PSO algorithm are used to inverse the fault slip parameters.The results show that the difference from the theoretical value is 23.2 cm by the PSO,it is 26.2 cm by the selecting weight iteration,however,it is less than 1 cm by RANSAC-PSO,when the gross error rate is 10%.The characteristics of Lushan earthquake are thrust-dominated with a small amount of left-lateral strike-slip.In this paper,the PSO algorithm and RANSAC-PSO algorithm are used to calculate the fault slip parameters,respectively,with the coseismal GPS displacement data.The strike-slip is0.0518 mand dip-slip is 0.8289 mby RANSAC-PSO algorithm,which are greater than the results of PSO.In addition,the energy released is 1.000 9×10~(19) N·m(M_W6.63),which is consistent with GCMT 1.060 0×10~(19) N·m.The horizontal displacements of the ground surface are recalculated with the sliding parameters that invert by the RANSAC-PSO algorithm and the PSO algorithm,respectively.The results show that the calculated horizontal displacements and GPS observations are basically the same as when the points are far away from the fault,the RANSAC-PSO algorithm performs better than PSO when the calculating points are near the fault.The calculated value of LS07 completely coincides with GPS observations.
The RANSAC-PSO algorithm is used to study the problem of gross errors ingeodetic data as a resultof fault slip parameters inversion.In the simulation experiment,1%,5% and 10% of the gross errors are added to the theoretical observations.Particle swarm optimization,selecting weight iteration and RANSAC-PSO algorithm are used to inverse the fault slip parameters.The results show that the difference from the theoretical value is 23.2 cm by the PSO,it is 26.2 cm by the selecting weight iteration,however,it is less than 1 cm by RANSAC-PSO,when the gross error rate is 10%.The characteristics of Lushan earthquake are thrust-dominated with a small amount of left-lateral strike-slip.In this paper,the PSO algorithm and RANSAC-PSO algorithm are used to calculate the fault slip parameters,respectively,with the coseismal GPS displacement data.The strike-slip is0.0518 mand dip-slip is 0.8289 mby RANSAC-PSO algorithm,which are greater than the results of PSO.In addition,the energy released is 1.000 9×10~(19) N·m(M_W6.63),which is consistent with GCMT 1.060 0×10~(19) N·m.The horizontal displacements of the ground surface are recalculated with the sliding parameters that invert by the RANSAC-PSO algorithm and the PSO algorithm,respectively.The results show that the calculated horizontal displacements and GPS observations are basically the same as when the points are far away from the fault,the RANSAC-PSO algorithm performs better than PSO when the calculating points are near the fault.The calculated value of LS07 completely coincides with GPS observations.
引文
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[16]Okada Y.SurfaceDeformation Due to Shear and Tensile Faults in a Half-Space[J].Bulletin of the Seismological Society of America,1985,92(2):1 018-1 040
[17]许才军,周力璇,尹智.2013年MS7.0级中国芦山地震断层曲面模型的构建及其滑动分布的大地测量反演[J].武汉大学学报:信息科学版,2017,42(11):1 165-1 671(Xu Caijun,Zhou Lixuan,Yin Zhi.Construction and Geodesy Slip Inversion Analysis of 2013 Ms7.0 Lushan in China Earthquake’s Curved Fault Modle[J],Geomatics and Information Science of Wuhan University,2017,42(11):1 165-1 671)
[18]Jiang Z,Wang M,Wang Y,et al.GPS Constrained Coseismic Source and Slip Distribution of the 2013 MW6.6Lushan,China,Earthquake and Its Tectonic Implications[J].Geophysical Research Letters,2014.41(2):407-413
[2]陈华根,李嘉虓,吴健生,等.MT-重力模拟退火联合反演研究[J].地球物理学报,2012,55(2):663-670(Chen Huagen,Li Jiaxiao,Wu Jiansheng,et al.Study on Simulated-Annealing MT-Gravity Joint Inversion[J].Chinese Journal of Geophysics,2012,55(2):663-670)
[3]王帅,张永志,姜永涛,等.维多样性的动态权重粒子群算法反演断层滑动速率[J].地球物理学进展,2014(4):1 766-1 771(Wang Shuai,Zhang Yongzhi,Jiang Yongtao,et al.Slip Velocity of Fault Induced by PSO Algorithm with Dynamical Inertial Weight and Dimension Mutation[J].Progress in Geophysics,2014(4):1 766-1 771)
[4]许才军.地球物理大地测量反演理论与应用[M].武汉:武汉大学出版社,2015(Xu Caijun.Joint Inversion Theory Geophysics and Geodesy and It’s Application[M].Wuhan:Wuhan University Press,2015)
[5]赵烨,蒋建国,洪日昌.基于RANSAC的SIFT匹配优化[J].光电工程,2014(8):58-65(Zhao Ye,Jiang Jianguo,Hong Richang.An Optimized SIFT Matching Based on RANSAC[J].Opto-Electronic Engineering,2014(8):58-65)
[6]陈艺虾,孙权森,徐焕宇,等.SURF算法和RANSAC算法相结合的遥感图像匹配方法[J].计算机科学与探索,2012(9):822-828(Chen Yixia,Sun Quansen,Xu Huanyu,et al.Matching Method of Remote Sensing Images Based on SURF Algorithm and RANSAC Algorithm[J].Journal of Frontiers of Computer Science and Technology,2012(9):822-828)
[7]李德仁,袁修孝.误差处理与可靠性理论[M].武汉:武汉大学出版社,2012(Li Deren,Yuan Xiuxiao.Error Processing and Reliability Theory[M].Wuhan:Wuhan University Press,2015)
[8]黄少荣.粒子群优化算法综述[J].计算机工程与设计,2009(8):1 977-1 980(Huang Shaorong.Survey of Particle Swarm Optimization Algorithm[J].Computer Engineering and Design,2009(8):1 977-1 980)
[9]杨维,李歧强.粒子群优化算法综述[J].中国工程科学,2004(5):87-94(Yang Wei,Li Qiqiang.Survey on Particle Swarm Optimization Algorithm[J].Engineering Science,2004(5):87-94)
[10]Zhang Y,Wang S,Ji G.A Comprehensive Survey on Particle Swarm Optimization Algorithm and Its Applications[J].Mathematical Problems in Engineering,2015(1):1-38
[11]Shen L C,Huo X H,Niu Y F.Survey of Discrete Particle Swarm Optimization Algorithm[J].Systems Engineering&Electronics,2008,30(10):1 986-1 952
[12]Hast A,Nysj9J,Marchetti.A Optimal RANSAC—Towards a Repeatable Algorithm for Finding the Optimal Set[J].Journal of Wscg,2013,21(1):21-30
[13]Choi S,Kim T,Yu W.Performance Evaluation of RANSAC Family[C].DBLP,London,2009
[14]张永志,徐海军,王卫东,等.渭河盆地断裂活动速率的粒子群算法反演[J].西北地震学报,2011(4):322-325(Zhang Yongzhi,Xu Haijun,Wang Weidong et.al.Inversion on Slip Velocity of Main Faults in Weihe Basin by Particle Swarm Optimization Algorithm with GPS Data[J],Northwestern Seismological Journal,2011(4):322-325)
[15]段虎荣,张永志,徐海军.改进的粒子群算法在断层滑动速率反演中的应用[J].大地测量与地球动力学,2010(6):31-36(Duan Hurong,Zhang Yongzhi,Xu Haijun.Improved Particle Swarm Optimization Algorithm and It’s Application in Inversion of Slip Velocity of Fault[J],Journal of Geodesy and Geodynamics,2011(6):31-36)
[16]Okada Y.SurfaceDeformation Due to Shear and Tensile Faults in a Half-Space[J].Bulletin of the Seismological Society of America,1985,92(2):1 018-1 040
[17]许才军,周力璇,尹智.2013年MS7.0级中国芦山地震断层曲面模型的构建及其滑动分布的大地测量反演[J].武汉大学学报:信息科学版,2017,42(11):1 165-1 671(Xu Caijun,Zhou Lixuan,Yin Zhi.Construction and Geodesy Slip Inversion Analysis of 2013 Ms7.0 Lushan in China Earthquake’s Curved Fault Modle[J],Geomatics and Information Science of Wuhan University,2017,42(11):1 165-1 671)
[18]Jiang Z,Wang M,Wang Y,et al.GPS Constrained Coseismic Source and Slip Distribution of the 2013 MW6.6Lushan,China,Earthquake and Its Tectonic Implications[J].Geophysical Research Letters,2014.41(2):407-413