一种确定震源中心的方法:逆时成像技术(一)——原理与数值实验
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摘要
研究地震断层的精细结构需要对地震活动精确定位,然而,盖戈类标准定位方法已经不能胜任.现今计算机技术的发展使我们能够直接面对地震定位这个非线性问题,所以,我们提出一种称为逆时成像技术的确定地震震源中心的非线性方法.首先,从位移表示定理出发,阐述了逆时成像技术的原理;然后,通过多组数值实验,论证了这种技术的可行性.由于直接采用直达波信号构建包络信号,进而采用互相关技术测量观测到时,因此,观测到时的准确性和客观性得到了提升;由于采用波形聚束方法直接建立观测到时和震源位置的非线性关系,因此,绕开了盖戈类方法的线性化过程,从而杜绝了非线性问题线性化过程造成的误差;由于采用波形聚束方法而不是经典的最小二乘法求解,所以,克服了最小二乘解对于少数或者个别"出格数据(outlier)"敏感的缺点;由于采用非均匀网格搜索的方法确定非线性系统的解,所以,可以利用解集的特征半径描述解的分辨率,进而利用观测到时的标准差和分辨率来描述解的不确定性,避免了以观测误差为正态分布的假设为前提的统计方法,克服了这类方法常常给出脱离实际意义的结果的不足.然而,由于采用网格搜索方法求解非线性方程,所以,与盖戈类方法相比,计算效率相对较低.例如:这里的每次定位过程在普通的个人计算机上需要大约30s.不过,用时间换取精度也是惯常的选择.
Accurate location of earthquake activity is essentially necessary for study of the detailed structure of faults,however,the standard location methods,such as various versions of Geiger′s methods,don′t work well any longer.Progress in computing technology at present has enabled us to directly face to the non-linear problem of earthquake location,so a new non-linear technique,which may be called time-reversal imaging technique(TRIT),is proposed for determining earthquake-hypocentroids.At first,the technique principle is illustrated by means of displacement representation law.Then feasibility is tested for using groups of numerical tests.Accuracy and objectivity of observation arrival time picking are promoted because direct P-wave train is used to build enveloped signal which is further employed to measure the observation arrival times by means of cross-correlation technique.Error caused by linearization of a non-linear problem is eliminated because a non-linear relation between earthquake location and observation arrival times is constructed based on beam-forming technique,which avoids the process of linearization in Geiger′s methods.The disadvantage that least-squared solution is sensitive to individual or a few outlier(s) in observation data is conquered because the beam-forming technique is employed for solution instead of the least-squared method.The statistical method used to evaluate uncertainty of the solution based on an assumption that residuals are in normal distribution,which often gives results without practical significance,is abandoned because grid-searching technique is used in finding solution,which provides a solution set,the eigen-radius of which describes resolution,and the resolution and the standard deviations are organized to evaluate the uncertainty.However,computing efficiency of the TRIT is rather lower than that of Geiger′s methods due to the grid-searching process,for example,in this study,about 30s are needed for each process on ordinary desktop computer,but it is a usual solution to change time into accuracy.
Accurate location of earthquake activity is essentially necessary for study of the detailed structure of faults,however,the standard location methods,such as various versions of Geiger′s methods,don′t work well any longer.Progress in computing technology at present has enabled us to directly face to the non-linear problem of earthquake location,so a new non-linear technique,which may be called time-reversal imaging technique(TRIT),is proposed for determining earthquake-hypocentroids.At first,the technique principle is illustrated by means of displacement representation law.Then feasibility is tested for using groups of numerical tests.Accuracy and objectivity of observation arrival time picking are promoted because direct P-wave train is used to build enveloped signal which is further employed to measure the observation arrival times by means of cross-correlation technique.Error caused by linearization of a non-linear problem is eliminated because a non-linear relation between earthquake location and observation arrival times is constructed based on beam-forming technique,which avoids the process of linearization in Geiger′s methods.The disadvantage that least-squared solution is sensitive to individual or a few outlier(s) in observation data is conquered because the beam-forming technique is employed for solution instead of the least-squared method.The statistical method used to evaluate uncertainty of the solution based on an assumption that residuals are in normal distribution,which often gives results without practical significance,is abandoned because grid-searching technique is used in finding solution,which provides a solution set,the eigen-radius of which describes resolution,and the resolution and the standard deviations are organized to evaluate the uncertainty.However,computing efficiency of the TRIT is rather lower than that of Geiger′s methods due to the grid-searching process,for example,in this study,about 30s are needed for each process on ordinary desktop computer,but it is a usual solution to change time into accuracy.
引文
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[12]Thurber C H.Nonlinear earthquake location:theory andexamples.Bull.Seism.Soc.Am.,1985,75(3):779-790.
[13]Pavlis G L.Appraising earthquake hypocenter locationerrors:a complete,practical approach for single-eventlocation.Bull.Seism.Soc.Am.,1986,76(6):1699-1717.
[14]Bolt B A.The revision of earthquake epicentres,focal depthsand origin-times using a high-speed computer.Geophys.J.R.Astron.Soc.,1960,3(4):433-440.
[15]Anderson K R.Epicentral location using arrival time order.Bull.Seism.Soc.Am.,1981,71(2):541-546.
[16]Chave A D,Thomson D J,Ander M E.On the robustestimation of power spectra,coherences,and transferfunctions.J.Geophys.Res.,1987,92(B1):633-648.
[17]Andrews D F.A robust method for multiple linearregression.Technometrics,1974,16(4):523-531.
[18]Lilwall R C,Francis T J G.Hypocentral resolution of smallocean bottom seismic networks.Geophys.J.R.Astron.Soc.,1978,54(3):721-728.
[19]Evernden J F.Precision of epicenters obtained by smallnumbers of world-wide stations.Bull.Seism.Soc.Am.,1969,59(3):1365-1398.
[20]Waldhauser F,Ellsworth W L.A Double-differenceearthquake location algorithm:Method and application to theNorthern Hayward fault,California.Bull.Seism.Soc.Am.,2000,90(6):1353-1368.
[21]Geller R J,Mueller C S.Four similar earthquakes in centralCalifornia.Geophys.Res.Lett.,1980,7(10):821-824.
[22]Deichmann N,Garcia-Fernandez M.Rupture geometry fromhigh-precision relative hypocentre locations of microearthquakeclusters.Geophys.J.Int.,1992,110(3):501-517.
[23]Poupinet G,Ellsworth W L,Fréchet J.Monitoring velocityvariations in the crust using earthquake doublets:anapplication to the Calaveras fault,California.J.Geophys.Res.,1984,89(B7):5719-5731.
[24]Scherbaum F,Wendler J.Cross spectral analysis of SwabianJura(SW Germany)three-component microearthquakerecordings.J.Geophys.,1986,60(2):157-166.
[25]Spudich P,Bostwick T.Studies of the seismic coda using anearthquake cluster as a deeply buried seismograph array.J.Geophys.Res.,1987,92(B10):10526-10546.
[26]Frémont M J,Malone S D.High precision relative locationsof earthquakes at Mount St.Helens,Washington.J.Geophys.Res.,1987,92(B10):10223-10236.
[27]Console R,Di Giovambattista R.Local earthquake relativelocation by digital records.Phys.Earth.Planet.Inter.,1987,47:43-49.
[28]Pechmann J C,Thorbjarnardottir B S.Waveform analysis ofpreshock-mainshock-aftershock sequence in Utah.Bull.Seism.Soc.Am.,1990,80(3):519-550.
[29]Aki K,Richards P G.Quantitative Seismology.San Francisco:W.H.Freeman and Company,1980:38-40.
[30]Krüger F,Ohrnberger M.Tracking the rupture of the MW=9.3 Sumatra earthquake over 1150 km at teleseismicdistance.Nature,2005,435(7044):937-939.
[31]Ishii M,Shearer P,Houston H,et al.Extend,duration andspeed of the 2004Sumatra-Andaman earthquake imaged bythe Hi-Net array.Nature,2005,435(7044):933-936.
[32]Xu Y,Koper K D,Sufri O,Zhu L P.Rupture imaging of theMw7.9 12 May 2008 Wenchuan earthquake from backprojection of teleseismic P waves.Geochem.Geophys.Geosyst.,2009,10(4):Q04006.
[33]杜海林.2004年苏门答腊—安达曼大地震能量辐射源的时间域台阵技术分析[硕士论文].北京:中国地震局地球物理研究所,2007.Du H L.Analysis of the energy radiation sources of the 2004Sumatra-Andaman earthquake using time-domain arraytechniques(in Chinese)[Master′s thesis].Beijing:Instituteof Geophysics,China Earthquake Administration,2007.
[34]Rost S,Thomas C.Array seismology:methods andapplications.Rev.Geophys.,2002,40(3):2-1-2-27.
[35]Larmat C,Montagner J P,Fink M,et al.Time-reversalimaging of seismic sources and application to the greatSumatra earthquake.Geophys.Res.Lett.,2006,33(19):L19312.
[36]Kennett B L N.Seismic Wave Propagation in StratifiedMedia.Cambridge:Cambridge University Press,1983:1-342.
[2]Bratt S R,Bache T C.Locating events with a sparse networkof regional arrays.Bull.Seism.Soc.Am.,1988,78(2):780-798.
[3]Flinn E A.Confidence regions and error determinations forseismic event location.Rev.Geophys.,1965,3(1):157-185.
[4]Buland R.The mechanics of locating earthquakes.Bull.Seism.Soc.Am.,1976,66(1):173-187.
[5]Jordan T H,Sverdrup K A.Teleseismic location techniquesand their application to earthquake clusters in the South-Central Pacific.Bull.Seism.Soc.Am.,1981,71(4):1105-1130.
[6]Rowlett H,Forsyth D W.Recent faulting andmicroearthquakes at the intersection of the Vema FractureZone and the Mid-Atlantic Ridge.J.Geophys.Res.,1984,89(B7):6079-6094.
[7]Ito A.High resolution relative hypocenters of similarearthquakes by cross-spectral analysis method.J.Phys.Earth.,1985,33(4):279-294.
[8]Ito A.Earthquake swarm activity revealed from high-resolution relative hypocenters-clustering of microearthquakes.Tectonophysics,1990,175(1-3):47-66.
[9]Smith E G C.Scaling the equations of condition to improveconditioning.Bull.Seism.Soc.Am.,1976,66(6):2075-2076.
[10]Spence W.Relative epicenter determination using P-wavearrival-time differences.Bull.Seism.Soc.Am.,1980,70(1):171-183.
[11]Anderson K R.Robust earthquake location using M-estimates.Phys.Earth Planet.Interiors,1982,30(2-3):119-130.
[12]Thurber C H.Nonlinear earthquake location:theory andexamples.Bull.Seism.Soc.Am.,1985,75(3):779-790.
[13]Pavlis G L.Appraising earthquake hypocenter locationerrors:a complete,practical approach for single-eventlocation.Bull.Seism.Soc.Am.,1986,76(6):1699-1717.
[14]Bolt B A.The revision of earthquake epicentres,focal depthsand origin-times using a high-speed computer.Geophys.J.R.Astron.Soc.,1960,3(4):433-440.
[15]Anderson K R.Epicentral location using arrival time order.Bull.Seism.Soc.Am.,1981,71(2):541-546.
[16]Chave A D,Thomson D J,Ander M E.On the robustestimation of power spectra,coherences,and transferfunctions.J.Geophys.Res.,1987,92(B1):633-648.
[17]Andrews D F.A robust method for multiple linearregression.Technometrics,1974,16(4):523-531.
[18]Lilwall R C,Francis T J G.Hypocentral resolution of smallocean bottom seismic networks.Geophys.J.R.Astron.Soc.,1978,54(3):721-728.
[19]Evernden J F.Precision of epicenters obtained by smallnumbers of world-wide stations.Bull.Seism.Soc.Am.,1969,59(3):1365-1398.
[20]Waldhauser F,Ellsworth W L.A Double-differenceearthquake location algorithm:Method and application to theNorthern Hayward fault,California.Bull.Seism.Soc.Am.,2000,90(6):1353-1368.
[21]Geller R J,Mueller C S.Four similar earthquakes in centralCalifornia.Geophys.Res.Lett.,1980,7(10):821-824.
[22]Deichmann N,Garcia-Fernandez M.Rupture geometry fromhigh-precision relative hypocentre locations of microearthquakeclusters.Geophys.J.Int.,1992,110(3):501-517.
[23]Poupinet G,Ellsworth W L,Fréchet J.Monitoring velocityvariations in the crust using earthquake doublets:anapplication to the Calaveras fault,California.J.Geophys.Res.,1984,89(B7):5719-5731.
[24]Scherbaum F,Wendler J.Cross spectral analysis of SwabianJura(SW Germany)three-component microearthquakerecordings.J.Geophys.,1986,60(2):157-166.
[25]Spudich P,Bostwick T.Studies of the seismic coda using anearthquake cluster as a deeply buried seismograph array.J.Geophys.Res.,1987,92(B10):10526-10546.
[26]Frémont M J,Malone S D.High precision relative locationsof earthquakes at Mount St.Helens,Washington.J.Geophys.Res.,1987,92(B10):10223-10236.
[27]Console R,Di Giovambattista R.Local earthquake relativelocation by digital records.Phys.Earth.Planet.Inter.,1987,47:43-49.
[28]Pechmann J C,Thorbjarnardottir B S.Waveform analysis ofpreshock-mainshock-aftershock sequence in Utah.Bull.Seism.Soc.Am.,1990,80(3):519-550.
[29]Aki K,Richards P G.Quantitative Seismology.San Francisco:W.H.Freeman and Company,1980:38-40.
[30]Krüger F,Ohrnberger M.Tracking the rupture of the MW=9.3 Sumatra earthquake over 1150 km at teleseismicdistance.Nature,2005,435(7044):937-939.
[31]Ishii M,Shearer P,Houston H,et al.Extend,duration andspeed of the 2004Sumatra-Andaman earthquake imaged bythe Hi-Net array.Nature,2005,435(7044):933-936.
[32]Xu Y,Koper K D,Sufri O,Zhu L P.Rupture imaging of theMw7.9 12 May 2008 Wenchuan earthquake from backprojection of teleseismic P waves.Geochem.Geophys.Geosyst.,2009,10(4):Q04006.
[33]杜海林.2004年苏门答腊—安达曼大地震能量辐射源的时间域台阵技术分析[硕士论文].北京:中国地震局地球物理研究所,2007.Du H L.Analysis of the energy radiation sources of the 2004Sumatra-Andaman earthquake using time-domain arraytechniques(in Chinese)[Master′s thesis].Beijing:Instituteof Geophysics,China Earthquake Administration,2007.
[34]Rost S,Thomas C.Array seismology:methods andapplications.Rev.Geophys.,2002,40(3):2-1-2-27.
[35]Larmat C,Montagner J P,Fink M,et al.Time-reversalimaging of seismic sources and application to the greatSumatra earthquake.Geophys.Res.Lett.,2006,33(19):L19312.
[36]Kennett B L N.Seismic Wave Propagation in StratifiedMedia.Cambridge:Cambridge University Press,1983:1-342.
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