靳锡波,王乐洋

• 1:东华理工大学

摘要(Abstract)：

针对最小二乘(LS)方法、总体最小二乘(TLS)方法在用于火山Mogi模型反演压力源参数时,在线性化的过程中容易产生偏差,导致求得的参数解偏离真值的问题。该文分析了Mogi模型的非线性特点,同时考虑了粒子群算法在非线性问题求解的优势,将两者结合得到了一种适用于Mogi模型参数反演的粒子群算法(PSO)。通过模拟算例与真实火山反演的验证,表明该文方法所得结果在模拟算例上相对其他方法所得结果在精度上提高了1～2个数量级且更接近真值,在真实火山反演中其拟合结果更接近地表观测值,表明该文方法在火山Mogi模型反演中具有适用性与有效性。

关键词(KeyWords)： 压力源参数反演;粒子群算法;火山;Mogi模型

Abstract:

Keywords:

基金项目(Foundation): 国家自然科学基金项目(41664001,41874001);; 江西省杰出青年人才资助计划项目(20162BCB23050);; 国家重点研发计划项目(2016YFB0501405)

作者(Author): 靳锡波,王乐洋

DOI: 10.16251/j.cnki.1009-2307.2020.08.010

参考文献(References)：

• [1] MOGI K.Relations between the eruptions of various volcanoes and the deformations of the ground surfaces around them[J].Bulletin of the Earthquake Research Institute,University of Tokyo,1958,36:99-134.
• [2] 于冬冬,王乐洋.火山形变Mogi模型反演的病态总体最小二乘解算方法[J].测绘工程,2017,26(7):22-25.(YU Dongdong,WANG Leyang.The ill-posed total least squares algorithm in volcano inversion of Mogi model[J].Engineering of Surveying and Mapping,2017,26(7):22-25.)
• [3] 胡亚轩,王庆良,崔笃信,等.三种压力源模型对火山区地面变形的影响[J].东北地震研究,2005,21(3):33-38.(HU Yaxuan,WANG Qingliang,CUI Duxin,et al.Influences on surface deformation by the three different stress source models in volcanic area[J].Seismological Research of Northeast China,2005,21(3):33-38.)
• [4] 李克,刘俊清,盘晓东,等.2000—2007年期间长白山天池火山区地壳变形监测与分析[J].地震地质,2009,31(4):639-646.(LI Ke,LIU Junqing,PAN Xiaodong,et al.Crust deformation monitoring and research in tianchi volcanic area,Changbai mountains from 2000-2007[J].Seismology and Geology,2009,31(4):639-646.)
• [5] 胡亚轩,郝明,王雄,等.L曲线法在反演火山区压力源参数中的应用[J].大地测量与地球动力学,2009,29(2):66-70.(HU Yaxuan,HAO Ming,WANG Xiong,et al.Application of L-curve to the inversion of pressure source parameters in volcanic area[J].Journal of Geodesy and Geodynamics,2009,29(2):66-70.)
• [6] 陈国浒.长白山天池火山形变监测与模拟研究[D].北京:中国地震局地质研究所,2007.(CHEN Guohu.Deformation monitoring and simulation research of the Tianchi volcano in the Changbai Mountains[D].Beijing:Institute of Geology,China Earthquake Administration,2007.)
• [7] 胡亚轩,施行觉,王庆良,等.腾冲火山区地表垂直形变分析[J].大地测量与地球动力学,2003,23(2):37-41.(HU Yaxuan,SHI Xingjue,WANG Qingliang,et al.Analysis of vertical deformation in Tengchong volcanic area[J].Journal of Geodesy and Geodynamics,2003,23(2):37-41.)
• [8] 施行觉,胡亚轩,毛竹,等.以垂直形变资料反演腾冲火山区岩浆活动性的初步研究[J].地震研究,2005,28(3):256-261.(SHI Xingjue,HU Yaxuan,MAO Zhu,et al.Vertical deformation inversion of magma activity in Tengchong volcanic area[J].Journal of Seismological Research,2005,28(3):256-261.)
• [9] JI L,IZBEKOV P,SENYUKOV S,et al.Deformation patterns,magma supply,and magma storage at Karymsky Volcanic Center,Kamchatka,Russia,2000-2010,revealed by InSAR[J].Journal of Volcanology & Geohermal Research,2018,352:106-116.
• [10] HOTTA K,IGUCHI M,OHKURA T,et al.Magma intrusion and effusion at Sinabung volcano,Indonesia,from 2013 to 2016,as revealed by continuous GPS observation[J].Journal of Volcanology and Geothermal Research,2019,382:173-183.
• [11] WANG T,DEGRANDPRE K,LU Z,et al.Complex surface deformation of Akutan volcano,Alaska revealed from InSAR time series[J].International Journal of Applied Earth Observation and Geoinformation,2018,64:171-180.
• [12] 王庆良,王文萍.大同机车厂地裂缝强活动深度段位错模型反演[J].大地测量与地球动力学,1998,18(3):80-84.(WANG Qingliang,WANG Wenping.Inversion of dislocation model for depth segment of strong fracture in datong locomotive works[J].Journal of Geodesy and Geodynamics,1998,18(3):80-84.)
• [13] TIAMPO K F,RUNDLE J B,FERNANDEZ J,et al.Spherical and ellipsoidal volcanic sources at Long Valley caldera,California,using a genetic algorithm inversion technique[J].Journal of Volcanology and Geothermal Research,2000,102(3/4):189-206.
• [14] 姜友谊,巨小文,胡亚轩,等.借助Matlab遗传算法反演火山区压力源参数[J].西安科技大学学报,2008,28(1):91-95.(JIANG Youyi,JU Xiaowen,HU Yaxuan,et al.Inversion of pressure source parameters based on Matlab GA toolbox[J].Journal of Xi’an University of Science and Technology,2008,28(1):91-95.)
• [15] 易远元,王家映.地球物理资料非线性反演方法讲座(十)粒子群反演方法[J].工程地球物理学报,2009,6(4):385-389.(YI Yuanyuan,WANG Jiaying.Lecture on non-linear inverse methods in geophysical data(10)particle swarm optimization inversion method[J].Chinese Journal of Engineering Geophysics,2009,6(4):385-389.)
• [16] 冯万鹏,李振洪.InSAR资料约束下震源参数的PSO混合算法反演策略[J].地球物理学进展,2010,25(4):1189-1196.(FENG Wanpeng,LI Zhenhong.A novel hybrid PSO/simplex algorithm for determining earthquake source parameters using InSAR data[J].Progress in Geophysics,2010,25(4):1189-1196.)
• [17]YAMAKAWA N.On the strain produced in a semiinfinite elastic solid by an interior source of stress[J].Zisin(Journal of the Seismological Society of Japan.2nd ser.),1955,8(2):84-98.
• [18]HE S,PREMPAIN E,WU Q H.An improved particle swarm optimizer for mechanical design optimization problems[J].Engineering Optimization,2004,36(5):585-605.
• [19]SHA D Y,HSU C Y.A new particle swarm optimization for the open shop scheduling problem[J].Computers&Operations Research,2008,35(10):3243-3261.
• [20]GONG M,CAI Q,CHEN X,et al.Complex network clustering by multiobjective discrete particle swarm optimization based on decomposition[J].IEEE Transactions on Evolutionary Computation,2014,18(1):82-97.
• [21]GHAMISI P,COUCEIRO M S,MARTINS F M L,et al.Multilevel image segmentation based on fractionalorder darwinian particle swarm optimization[J].IEEE Transactions on Geoscience&Remote Sensing,2014,52(5):2382-2394.
• [22]FAN H Y.A modification to particle swarm optimization algorithm[J].Engineering Computations,2002,19(8):970-989.
• [23]SHI Y,EBERHART R.A modified particle swarm optimizer[C]//Proceeding of IEEE ICEC Conference.Piscataway:IEEE,1999:69-73.
• [24]RATNAWEERA A,HALGAMUGE S K,WATSON H C.Self-organizing hierarchical particle swarm optimizer with time-varying acceleration coefficients[J].IEEE Trans Evol Comput,2004,8(3):240-255.
• [25]DIETERICH J H,DECKER R W.Finite element modeling of surface deformation associated with volcanism[J].Journal of Geophysical Research,1975,80(29):4094-4102.
• [26]王乐洋,余航.火山Mogi模型反演的总体最小二乘联合平差方法[J].武汉大学学报(信息科学版),2018,43(9):1333-1341.(WANG Leyang, YU Hang.Application of total least squares joint adjustment to volcano inversion of Mogi model[J].Geomatics and Information Science of Wuhan University,2018,43(9):1333-1341.)