利用拟牛顿法和信赖域法联合反演震中分布与一维速度结构
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摘要
本文将拟牛顿法与信赖域法相结合的反演方法用于地震震中和一维速度结构的联合反演.通过数值试验比较发现:用拟牛顿法构造Hessian矩阵,虽然仅利用目标函数的一阶导数信息,但由于保证了正定性和拟牛顿条件,比解析求得Hessian矩阵更加高效稳定,通过与信赖域方法的结合,使得该联合反演方法与经典的联合反演方法相比不仅具有较高的计算效率和较高的反演精度,同时也具有更强的总体收敛性.利用本文方法对台湾集集地震重新定位结果(纬度23.86°N,经度120.80°E,深度10km,发震时刻1999年9月21日17:47:16.0)与前人主流结果一致.此外,该方法对不同初始速度模型以及不同的地震到时数据集均可给出较一致的结果,进一步表明该方法的优越性.本文还利用1998~2001年间华北遥测地震台网40个台站记录到的64次地震的971条P直达波和首波到时资料,采用本文提出的方法吩北京及其邻区的一维地壳P波速度结构进行联合反演,结果表明该地区浅层地壳速度较低,中部地壳速度较高,下部地壳速度逐渐递增.
We propose a hybrid algorithm,which combines the quasi-Newton method and the trust-region method in a least square form,to simultaneously determine hypocenters and velocity structure.Our numerical tests indicate that the Hessian matrix constructed by the quasi-Newton method,with the positive definiteness and the satisfaction of the quasi-Newton condition,is more efficient and stable than the analytical one though only the first-order derivatives of the objective function are used in the quasi-Newton method.Furthermore,combining with the trust-region method,our algorithm of simultaneous determination of hypocenters and velocity structure has been proven to be more accurate and efficient and has better convergent property than the classic method.With our method,we relocate the hypocenter of the Chi-Chi earthquake of Taiwan and obtain the result: latitude 23.86°N,longitude 120.80°E,focal depth 10km,and origin time 17:47:16.0.This result is consistent with the credible previous result,and is robust with different initial values and different data sets.Finally,we apply our method to simultaneously determine hypocenters and 1-D velocity structure of the North China area by using the selected 971 high quality direct and refracted P arrivals of 64 earthquakes from 40 stations of the North China Seismic Network from 1998 to 2001.We find that the upper crust in this studied area has low velocity with a sharp increase at depth of 4km,the middle crust has high velocity (～6km/s),and the lower crust has a positive velocity gradient.
We propose a hybrid algorithm,which combines the quasi-Newton method and the trust-region method in a least square form,to simultaneously determine hypocenters and velocity structure.Our numerical tests indicate that the Hessian matrix constructed by the quasi-Newton method,with the positive definiteness and the satisfaction of the quasi-Newton condition,is more efficient and stable than the analytical one though only the first-order derivatives of the objective function are used in the quasi-Newton method.Furthermore,combining with the trust-region method,our algorithm of simultaneous determination of hypocenters and velocity structure has been proven to be more accurate and efficient and has better convergent property than the classic method.With our method,we relocate the hypocenter of the Chi-Chi earthquake of Taiwan and obtain the result: latitude 23.86°N,longitude 120.80°E,focal depth 10km,and origin time 17:47:16.0.This result is consistent with the credible previous result,and is robust with different initial values and different data sets.Finally,we apply our method to simultaneously determine hypocenters and 1-D velocity structure of the North China area by using the selected 971 high quality direct and refracted P arrivals of 64 earthquakes from 40 stations of the North China Seismic Network from 1998 to 2001.We find that the upper crust in this studied area has low velocity with a sharp increase at depth of 4km,the middle crust has high velocity (～6km/s),and the lower crust has a positive velocity gradient.
引文
[1]Geiger L.Probability method for the determination of earthquakeepicenters from arrival time only.Bull.St.Louis.Univ.,1912,8:60~71
[2]Lee W H K,J C Lahr.HYPO71(revised):a computer program fordetermining hypocenter,magnitude,and first motion pattern of localearthquakes.U.S.G.S.Open-File Rept.,1975.75~311
[3]Crosson R S.Crustal structure modeling of earthquake data,1,Simultaneous least squares estimation of hypocenter and velocityparameters.J.Geophys.Res.,1976,81(17):3036~3046
[4]Aki K,Lee W H K.Determination of three_dimensional velocityanomalies under a seismic array using first P arrival times from localearthquakes,part 1:A homogeneous initial model.J.Geophys.Res.,1976,81(23):4381~4399
[5]Aki K,Christoffersson A,Husebye E S.Determination of the three_dimensional seismic structure of the lithosphere.J.Geophys.Res.,1977,82(2):277~296
[6]Pavlis G,Booker J R.The mixed discrete_continuous inverseproblem:Application of the simultaneous determination of earthquakehypocenters and velocity structure.J.Geophys.Res.,1980,85(B9):4801~4810
[7]Spencer C,Gubbins D.Travel_time inversion for simultaneousearthquake location and velocity structure determination in laterallyvarying media.Geophys.J.Roy.Astr.Soc.,1980,63(2):95~116
[8]刘福田.震源位置和速度结构的联合反演(I)—理论和方法.地球物理学报,1984,27(2):167~175Liu F T.Simultaneous inversion of earthquake hypocenters andvelocity structure(Ⅰ)—Theory and method.Chinese J.Geophys.(in Chinese),1984,27(2):167~175
[9]Husen S,Kissling E,Flueh E,et al.Accurate hypocenterdetermination in the seismogenic zone of the subducting Nazca Plate innorthern Chile using a combined on_/offshore network.Geophys.J.Int.,1999,138(3):687~701
[10]Leitner B,Eberhart_Phillips D,Anderson H,et al.A focused lookat the Alpine fault,New Zealand:Seismicity,focal mechanisms,andstress observations.J.Geophys.Res.,2001,106(B2):2193~2220
[11]Ghose S,Hamburger M W,Virieux J.Three_dimensional velocitystructure and earthquake locations beneath the northern Tien Shan ofKyrgyzstan,central Asia.J.Geophys.Res.,1998,103(B2):2725~2748
[12]Sudo Y,Kong LSL.Three_dimensional seismic velocity structurebeneath Aso Volcano,Kyushu,Japan.B.Volcanol,2001,63(5):326~344
[13]李松林,张先康,W D Mooney,等.伽师地震区地壳细结构及发震断层的初步研究.地球物理学报,2002,45(1):76~82Li S L,Zhang X K,W D Mooney,et al.A preliminary study on finestructures of Jiashi earthquake region and earthquake generating fault.Chinese J.Geophys.(in Chinese),2002,45(1):76~82
[14]袁亚湘,孙文瑜.最优化理论与方法.北京:科学出版社,1997Yuan Y X,Sun W Y.Optimization Theory and Methods(inChinese).Beijing:Science Press,1997
[15]傅承义,陈运泰,祁贵仲.地球物理学基础.北京:科学出版社,1985.307~310Fu C Y,Chen Y T,Qi G Z.Fundamentals of Geophysics(inChinese).Beijing:Science Press,1985.307~310
[16]田,陈晓非.水平层状介质中的快速两点间射线追踪方法.地震学报,2005,27(2):147~154Tian Y,Chen X F.A rapid and accurate two-point ray tracingmethod in horizontally layered velocity model.Acta SeismologicaSinica(in Chinese),2005,27(2):147~154
[17]Kao H,Chen R Y,Chang C H.Exactly where does the 1999 Chi_Chi earthquake in Taiwan nucleate?———Hypocenter relocation usingthe master station method.TAO,2000,11(3):567~580
[18]Chang C H,Wu Y M,Shin T C,et al.Relocation of the 1999 Chi_Chi earthquake in Taiwan.TAO,2000,11(3):581~590
[19]高星,王卫民,姚振兴.用于地震定位的SAMS方法.地球物理学报,2002,45(4):525~532Gao X,Wang W M,Yao Z X.Hypocentral determination usingsimulated annealing method.Chinese J.Geophys.(in Chinese),2002,45(4):525~532
[20]孙若昧,刘福田.京津唐地区地壳结构与强震的发生I.P波速度结构.地球物理学报,1995,38(5):599~607Sun R M,Liu F T.Crust structure and strong earthquake in Beijing,Tianjin,Tangshan area:I.P wave velocity structure.Chinese J.Geophys.(in Chinese),1995,38(5):599~607
[21]国家地震局《深部物探成果》编写组.中国地壳上地幔地球物理探测成果.北京:地震出版社,1986.119~128China Seismological Bureau.Geophysical Exploration of Crust andUpper Mantle in China(in Chinese).Beijing:Seismological Press,1986.119~128
[2]Lee W H K,J C Lahr.HYPO71(revised):a computer program fordetermining hypocenter,magnitude,and first motion pattern of localearthquakes.U.S.G.S.Open-File Rept.,1975.75~311
[3]Crosson R S.Crustal structure modeling of earthquake data,1,Simultaneous least squares estimation of hypocenter and velocityparameters.J.Geophys.Res.,1976,81(17):3036~3046
[4]Aki K,Lee W H K.Determination of three_dimensional velocityanomalies under a seismic array using first P arrival times from localearthquakes,part 1:A homogeneous initial model.J.Geophys.Res.,1976,81(23):4381~4399
[5]Aki K,Christoffersson A,Husebye E S.Determination of the three_dimensional seismic structure of the lithosphere.J.Geophys.Res.,1977,82(2):277~296
[6]Pavlis G,Booker J R.The mixed discrete_continuous inverseproblem:Application of the simultaneous determination of earthquakehypocenters and velocity structure.J.Geophys.Res.,1980,85(B9):4801~4810
[7]Spencer C,Gubbins D.Travel_time inversion for simultaneousearthquake location and velocity structure determination in laterallyvarying media.Geophys.J.Roy.Astr.Soc.,1980,63(2):95~116
[8]刘福田.震源位置和速度结构的联合反演(I)—理论和方法.地球物理学报,1984,27(2):167~175Liu F T.Simultaneous inversion of earthquake hypocenters andvelocity structure(Ⅰ)—Theory and method.Chinese J.Geophys.(in Chinese),1984,27(2):167~175
[9]Husen S,Kissling E,Flueh E,et al.Accurate hypocenterdetermination in the seismogenic zone of the subducting Nazca Plate innorthern Chile using a combined on_/offshore network.Geophys.J.Int.,1999,138(3):687~701
[10]Leitner B,Eberhart_Phillips D,Anderson H,et al.A focused lookat the Alpine fault,New Zealand:Seismicity,focal mechanisms,andstress observations.J.Geophys.Res.,2001,106(B2):2193~2220
[11]Ghose S,Hamburger M W,Virieux J.Three_dimensional velocitystructure and earthquake locations beneath the northern Tien Shan ofKyrgyzstan,central Asia.J.Geophys.Res.,1998,103(B2):2725~2748
[12]Sudo Y,Kong LSL.Three_dimensional seismic velocity structurebeneath Aso Volcano,Kyushu,Japan.B.Volcanol,2001,63(5):326~344
[13]李松林,张先康,W D Mooney,等.伽师地震区地壳细结构及发震断层的初步研究.地球物理学报,2002,45(1):76~82Li S L,Zhang X K,W D Mooney,et al.A preliminary study on finestructures of Jiashi earthquake region and earthquake generating fault.Chinese J.Geophys.(in Chinese),2002,45(1):76~82
[14]袁亚湘,孙文瑜.最优化理论与方法.北京:科学出版社,1997Yuan Y X,Sun W Y.Optimization Theory and Methods(inChinese).Beijing:Science Press,1997
[15]傅承义,陈运泰,祁贵仲.地球物理学基础.北京:科学出版社,1985.307~310Fu C Y,Chen Y T,Qi G Z.Fundamentals of Geophysics(inChinese).Beijing:Science Press,1985.307~310
[16]田,陈晓非.水平层状介质中的快速两点间射线追踪方法.地震学报,2005,27(2):147~154Tian Y,Chen X F.A rapid and accurate two-point ray tracingmethod in horizontally layered velocity model.Acta SeismologicaSinica(in Chinese),2005,27(2):147~154
[17]Kao H,Chen R Y,Chang C H.Exactly where does the 1999 Chi_Chi earthquake in Taiwan nucleate?———Hypocenter relocation usingthe master station method.TAO,2000,11(3):567~580
[18]Chang C H,Wu Y M,Shin T C,et al.Relocation of the 1999 Chi_Chi earthquake in Taiwan.TAO,2000,11(3):581~590
[19]高星,王卫民,姚振兴.用于地震定位的SAMS方法.地球物理学报,2002,45(4):525~532Gao X,Wang W M,Yao Z X.Hypocentral determination usingsimulated annealing method.Chinese J.Geophys.(in Chinese),2002,45(4):525~532
[20]孙若昧,刘福田.京津唐地区地壳结构与强震的发生I.P波速度结构.地球物理学报,1995,38(5):599~607Sun R M,Liu F T.Crust structure and strong earthquake in Beijing,Tianjin,Tangshan area:I.P wave velocity structure.Chinese J.Geophys.(in Chinese),1995,38(5):599~607
[21]国家地震局《深部物探成果》编写组.中国地壳上地幔地球物理探测成果.北京:地震出版社,1986.119~128China Seismological Bureau.Geophysical Exploration of Crust andUpper Mantle in China(in Chinese).Beijing:Seismological Press,1986.119~128
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