球体位错理论计算程序的总体设计与具体实现
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摘要
本文详细介绍了球体位错理论计算程序的总体设计思想、各类配套文件的具体内涵以及各类输出文件的物理含义,同时介绍了程序的使用方法和注意事项,为读者独立使用该程序提供参考。球体位错理论计算程序主要由三部分组成:①位错格林函数计算程序,基于具体的球对称地球模型提供离散的二维格林函数数值框架;②积分计算程序,对离散的格林函数数值框架进行双二次样条插值运算,并对四类独立位错源对应的格林函数进行适当组合,从而计算出任意位置任意类型震源在地表产生的同震变形(含位移、应变、重力变化和大地水准面变化);③辅助文件,用于提供发震断层模型和计算点位信息。一般情况下,读者不需要理解位错格林函数计算程序和积分计算程序,只需要对辅助文件提供的信息进行针对性改动,就可以计算目标地震在目标观测站引起的同震变形。
We present a detailed introduction of the computing codes for the coseismic deformations on a layered spherical earth,including overall design of the programs,detailed information of the supporting documents and physical meanings of the output files.At the same time,we also introduce the basic usage of the computing codes,as well as the matters needing attention.Overall,our computing programs are made of three parts: ① Codes for dislocation Green′s functions,which present two-dimension discrete numerical frame of Green′s functions based on a specific symmetric earth model;② Codes for integration,which perform bi-quadratic spline interpolation operations with the frame of Green′s functions.A suitable combination of four independent dislocations is given to compute the coseismic deformations including displacements,strain,geoid and gravity changes resulting from an arbitrary seismic source at an arbitrary position;③ Supporting documents,which present the information of earthquake′s fault model and observation points.Even without grasping the theories and codes,the readers can also correctly calculate the coseismic deformations caused by an arbitrary earthquake,by suitable changing the information of the supporting documents.Because of this reason the computing codes are easy to be generalized.
We present a detailed introduction of the computing codes for the coseismic deformations on a layered spherical earth,including overall design of the programs,detailed information of the supporting documents and physical meanings of the output files.At the same time,we also introduce the basic usage of the computing codes,as well as the matters needing attention.Overall,our computing programs are made of three parts: ① Codes for dislocation Green′s functions,which present two-dimension discrete numerical frame of Green′s functions based on a specific symmetric earth model;② Codes for integration,which perform bi-quadratic spline interpolation operations with the frame of Green′s functions.A suitable combination of four independent dislocations is given to compute the coseismic deformations including displacements,strain,geoid and gravity changes resulting from an arbitrary seismic source at an arbitrary position;③ Supporting documents,which present the information of earthquake′s fault model and observation points.Even without grasping the theories and codes,the readers can also correctly calculate the coseismic deformations caused by an arbitrary earthquake,by suitable changing the information of the supporting documents.Because of this reason the computing codes are easy to be generalized.
引文
[1]Steketee J A.On Volterra′s dislocations in a semi-infinite elastic medium[J].Can J Phys,1958,36:192-205.
[2]Chinnery M A.The deformation of ground around surface faults[J].Bull Seism Soc Am,1961,51:355-372.
[3]Chinnery M A.The stress changes that accompany strike-slip faulting[J].Bull Seism Soc Am,1963,53:921-932.
[4]Maruyama T.Statical elastic dislocations in an infinite and semi-infinite medium[J].Bull Earthq ResInst,1964,42:289-368.
[5]Okada Y.Surface deformation due to shear and tensile faults in a half-space[J].Bull Seism Soc Am,1985,75:1 135-1 154.
[6]Okada Y.Internal Deformation due to Shear and Tensile Fault s in a Half-space[J].Bull Seism SocAm,1992,82(2):1 018-1 040.
[7]Okubo S.Potential and gravity changes raised by point dislocations[J].Geophys J Int,1991,105:573-586.
[8]Okubo S.Potential and gravity changes due to shear and tensile faults in a half-space[J].J GeophysRes,1992,97:7 137-7 144.
[9]陈运泰,林邦慧,林中洋,等.根据地表形变的观测研究1966年邢台地震的震源过程[J].地球物理学报,1975,18(3):164-181.
[10]陈运泰,黄立人,林邦慧,等.用大地测量资料反演的1976年唐山地震的位错模式[J].地球物理学报,1979,22(3):201-217.
[11]Matsu′ura M,Iwasaki T.Study on and postseismic crustal movements associated with the 1923Kanto earthquake[J].Tectonohysics,1983,97:201-215.
[12]Fujii Y,Nakane K.Horizontal crustal movements in the Kanto-Tokai district,Japan,as deducedfrom geodetic data[J].Tectonophysics,1983,97:115-140.
[13]Tanaka Y,Okubo S,Machida M,et al.First detection of absolute gravity changes caused by earth-quake[J].Geophys Res Lett,2001,28(15):2 979-2 981.
[14]Sun W.Potential and gravity changes caused by dislocations in spherically symmetric earth models[J].Bull Earthquake Res Inst Univ Tokyo,1992,67:89-238.
[15]Sun W,Okubo S.Surface potential and gravity changes due to internal dislocations in a sphericalearth—Ⅰ.Theory for a point dislocation[J].Geophys J Int,1993,114:569-592.
[16]Sun W,Okubo S.Surface potential and gravity changes due to internal dislocations in a sphericalearth—Ⅱ.Application to a finite fault[J].Geophys J Int,1998,132:79-88.
[17]Sun W,Okubo S,Vanicek P.Global displacement caused by dislocations in a realistic earth model[J].J Geophys Res,1996,101:8 561-8 577.
[18]Sun W,Okubo S,Fu G.Green′s functions of co-seismic strain changes and investigation of effect ofearth′s spherical curvature and radial heterogeneity[J].Geophys J Int,2006,167:1 273-1 291.
[19]Sun W,Okubo S.Effect of earth′s spherical curvature and radial heterogeneity in dislocation studiesfor a point dislocation[J].Geophys Res Lett,2002,29(12):10.1029/2001GL014497.
[20]Sun W,Okubo S,Fu G,et al.General formulations of global co-seismic deformations caused by anarbitrary dislocation in a spherically symmetric earth model-Applicable to deformed earth surface andspace-fixed point[J].Geophys J Int,2009,177:817-833.
[21]Sun W,Zhou X.Co-seismic Deflection Change of the Vertical Caused by the 2011Tohoku-OkiEarthquake(MW9.0)[J].Geophys J Int,accepted.
[22]Imanishi Y,Sato T,Higashi T,et al.A network of superconducting gravimeters detects submicro-gal coseismic gravity changes[J].Science,2004,306:476-478.
[23]Pollitz F F.Coseismic deformation from earthquake faulting in a layered spherical Earth[J].Geo-phys J Int,1996,125:1-14.
[24]Pollitz F F.Gravitational viscoelastic post-seismic relaxation on a layered spherical Earth[J].J Geo-phys Res,1997,102:17 921-17 941.
[25]Tanaka Y,Okuno J,Okubo S.A new method for the computation of global viscoelastic post-seismicdeformation in a realistic earth model(Ⅰ)-vertical displacement and gravity variation[J].Geophys JInt,2006,164:273-289.
[26]Tanaka Y,Okuno J,Okubo S.A new method for the computation of global viscoelastic post-seismicdeformation in a realistic earth model(Ⅱ)-Horizontal displacement[J].Geophys J Int,2007,170:1 031-1 052.
[27]Pollitz F F.Post-seismic relaxation theory on a laterally heterogeneous viscoelastic model[J].Geo-phys J Int,2003,155:57-78.
[28]Fu G,Sun W.Surface coseismic gravity changes caused by dislocations in a 3-D heterogeneous earth[J].Geophys J Int,12008,72:479-503.
[29]Fu G,Sun W,Fukuda Y,et al.Coseismic displacements caused by point dislocations in a three-di-mensional heterogeneous,spherical earth model[J].Geophys J Int,2010,183:706-726.
[30]付广裕,孙文科,王阅兵,等.球体位错理论在2011年日本MW9.0～9.1级地震中的应用研究[J].地球物理学报,2012,待发表.
[31]Fu G,Sun W.Effects of spatial distribution of fault slip on calculating co-seismic displacement:Case studies of the Chi-Chi earthquake(MW7.6)and the Kunlun earthquake(MW7.8)[J].GeophysRes Lett,2004,31,L21601.
[32]Dziewonski A M,Anderson D L.Preliminary reference Earth model[J].Phys Earth Planet Inter,1981,25:297-356.
[33]Gilbert F,Dziewonski A M.An application of normal mode theory to the retrieval of structure pa-rameters and source mechanisms from seismic spectra[J].Phil Trans R Soc London A,1975,278:187-269.
[34]付广裕,孙文科.地球横向不均匀结构对地表以及空间固定点同震重力变化的影响[J].地球物理学报,2012,待发表.
[35]Simons M,Minson S E,Sladen A,et al.The 2011Magnitude 9.0Tohoku-Oki Earthquake:Mosa-icking the Megathrust from Seconds to Centuries[J].Science,2011,332:doi:10.1126/science.1206731.
[35]Fu G,Sun W,Fukuda Y,et al.Effects of Earth′s curvature and radial heterogeneity in dislocationstudies:Case studies of the 2008Wenchuan earthquake and the 2004Sumatra earthquake[J].EarthqSci,2010,23:301-308.
[36]Heki K,Matsuo K.Coseismic gravity changes of the 2010earthquake in central Chile from satellitegravimetry[J].Geophys Res Lett,2010,37,L24306,10.1029/2010GL045335.
[37]周新,孙文科,付广裕.重力卫星GRACE监测出2010年智利MW8.8地震的同震重力变化[J].地球物理学报,2012,54(7):1745-1749.
[38]Zhou X,Sun W,Zhao B,et al.Geodetic observations detected co-seismic displacements and gravitychanges caused by the Tohoku-Oki earthquake(MW=9.0)[J].J Geophys Res,submitted.
[2]Chinnery M A.The deformation of ground around surface faults[J].Bull Seism Soc Am,1961,51:355-372.
[3]Chinnery M A.The stress changes that accompany strike-slip faulting[J].Bull Seism Soc Am,1963,53:921-932.
[4]Maruyama T.Statical elastic dislocations in an infinite and semi-infinite medium[J].Bull Earthq ResInst,1964,42:289-368.
[5]Okada Y.Surface deformation due to shear and tensile faults in a half-space[J].Bull Seism Soc Am,1985,75:1 135-1 154.
[6]Okada Y.Internal Deformation due to Shear and Tensile Fault s in a Half-space[J].Bull Seism SocAm,1992,82(2):1 018-1 040.
[7]Okubo S.Potential and gravity changes raised by point dislocations[J].Geophys J Int,1991,105:573-586.
[8]Okubo S.Potential and gravity changes due to shear and tensile faults in a half-space[J].J GeophysRes,1992,97:7 137-7 144.
[9]陈运泰,林邦慧,林中洋,等.根据地表形变的观测研究1966年邢台地震的震源过程[J].地球物理学报,1975,18(3):164-181.
[10]陈运泰,黄立人,林邦慧,等.用大地测量资料反演的1976年唐山地震的位错模式[J].地球物理学报,1979,22(3):201-217.
[11]Matsu′ura M,Iwasaki T.Study on and postseismic crustal movements associated with the 1923Kanto earthquake[J].Tectonohysics,1983,97:201-215.
[12]Fujii Y,Nakane K.Horizontal crustal movements in the Kanto-Tokai district,Japan,as deducedfrom geodetic data[J].Tectonophysics,1983,97:115-140.
[13]Tanaka Y,Okubo S,Machida M,et al.First detection of absolute gravity changes caused by earth-quake[J].Geophys Res Lett,2001,28(15):2 979-2 981.
[14]Sun W.Potential and gravity changes caused by dislocations in spherically symmetric earth models[J].Bull Earthquake Res Inst Univ Tokyo,1992,67:89-238.
[15]Sun W,Okubo S.Surface potential and gravity changes due to internal dislocations in a sphericalearth—Ⅰ.Theory for a point dislocation[J].Geophys J Int,1993,114:569-592.
[16]Sun W,Okubo S.Surface potential and gravity changes due to internal dislocations in a sphericalearth—Ⅱ.Application to a finite fault[J].Geophys J Int,1998,132:79-88.
[17]Sun W,Okubo S,Vanicek P.Global displacement caused by dislocations in a realistic earth model[J].J Geophys Res,1996,101:8 561-8 577.
[18]Sun W,Okubo S,Fu G.Green′s functions of co-seismic strain changes and investigation of effect ofearth′s spherical curvature and radial heterogeneity[J].Geophys J Int,2006,167:1 273-1 291.
[19]Sun W,Okubo S.Effect of earth′s spherical curvature and radial heterogeneity in dislocation studiesfor a point dislocation[J].Geophys Res Lett,2002,29(12):10.1029/2001GL014497.
[20]Sun W,Okubo S,Fu G,et al.General formulations of global co-seismic deformations caused by anarbitrary dislocation in a spherically symmetric earth model-Applicable to deformed earth surface andspace-fixed point[J].Geophys J Int,2009,177:817-833.
[21]Sun W,Zhou X.Co-seismic Deflection Change of the Vertical Caused by the 2011Tohoku-OkiEarthquake(MW9.0)[J].Geophys J Int,accepted.
[22]Imanishi Y,Sato T,Higashi T,et al.A network of superconducting gravimeters detects submicro-gal coseismic gravity changes[J].Science,2004,306:476-478.
[23]Pollitz F F.Coseismic deformation from earthquake faulting in a layered spherical Earth[J].Geo-phys J Int,1996,125:1-14.
[24]Pollitz F F.Gravitational viscoelastic post-seismic relaxation on a layered spherical Earth[J].J Geo-phys Res,1997,102:17 921-17 941.
[25]Tanaka Y,Okuno J,Okubo S.A new method for the computation of global viscoelastic post-seismicdeformation in a realistic earth model(Ⅰ)-vertical displacement and gravity variation[J].Geophys JInt,2006,164:273-289.
[26]Tanaka Y,Okuno J,Okubo S.A new method for the computation of global viscoelastic post-seismicdeformation in a realistic earth model(Ⅱ)-Horizontal displacement[J].Geophys J Int,2007,170:1 031-1 052.
[27]Pollitz F F.Post-seismic relaxation theory on a laterally heterogeneous viscoelastic model[J].Geo-phys J Int,2003,155:57-78.
[28]Fu G,Sun W.Surface coseismic gravity changes caused by dislocations in a 3-D heterogeneous earth[J].Geophys J Int,12008,72:479-503.
[29]Fu G,Sun W,Fukuda Y,et al.Coseismic displacements caused by point dislocations in a three-di-mensional heterogeneous,spherical earth model[J].Geophys J Int,2010,183:706-726.
[30]付广裕,孙文科,王阅兵,等.球体位错理论在2011年日本MW9.0～9.1级地震中的应用研究[J].地球物理学报,2012,待发表.
[31]Fu G,Sun W.Effects of spatial distribution of fault slip on calculating co-seismic displacement:Case studies of the Chi-Chi earthquake(MW7.6)and the Kunlun earthquake(MW7.8)[J].GeophysRes Lett,2004,31,L21601.
[32]Dziewonski A M,Anderson D L.Preliminary reference Earth model[J].Phys Earth Planet Inter,1981,25:297-356.
[33]Gilbert F,Dziewonski A M.An application of normal mode theory to the retrieval of structure pa-rameters and source mechanisms from seismic spectra[J].Phil Trans R Soc London A,1975,278:187-269.
[34]付广裕,孙文科.地球横向不均匀结构对地表以及空间固定点同震重力变化的影响[J].地球物理学报,2012,待发表.
[35]Simons M,Minson S E,Sladen A,et al.The 2011Magnitude 9.0Tohoku-Oki Earthquake:Mosa-icking the Megathrust from Seconds to Centuries[J].Science,2011,332:doi:10.1126/science.1206731.
[35]Fu G,Sun W,Fukuda Y,et al.Effects of Earth′s curvature and radial heterogeneity in dislocationstudies:Case studies of the 2008Wenchuan earthquake and the 2004Sumatra earthquake[J].EarthqSci,2010,23:301-308.
[36]Heki K,Matsuo K.Coseismic gravity changes of the 2010earthquake in central Chile from satellitegravimetry[J].Geophys Res Lett,2010,37,L24306,10.1029/2010GL045335.
[37]周新,孙文科,付广裕.重力卫星GRACE监测出2010年智利MW8.8地震的同震重力变化[J].地球物理学报,2012,54(7):1745-1749.
[38]Zhou X,Sun W,Zhao B,et al.Geodetic observations detected co-seismic displacements and gravitychanges caused by the Tohoku-Oki earthquake(MW=9.0)[J].J Geophys Res,submitted.
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