观测到的小震与大震之间M_L/M_W标度突然改变的理论基础
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摘要
对完全弹性介质中的一组地震,如果应力降和破裂速度不随震级系统变化,进行仪器响应校正后,在可以确定M_L的整个范围内,M_L∝M_W。然而,实际上我们观察到,M_L和M_W偏离了1:1的标度关系。天然地震序列和诱发地震活动实例的详细分析结果表明:对小地震(通常M_W小于2~3),M_L∝1.5 M_W,这和其他研究结果一致。由独立测定若干Q值确定的因果算子Q和合成地震震源时间函数褶积可以再生这一比例关系。数据分析和模拟试验的一个重要结果是,观察到的低于某一确定震级的小地震的脉冲宽度及其相应的拐角频率实际上是不变的。因此,在衰减介质中,小地震信号本质上构成了由地震矩来量度其尺度的介质的脉冲响应。简单的理论分析结果表明,在这种情况下,观察到的M_L和M_W之间的比例系数1.5是矩率函数振幅和持续时间对地震矩固有标度特征和衰减介质频率响应的自然结果。因为这个结果和伍德—安德森地震仪响应对大地震引入的偏差,基于M_L的古登堡—里克特关系失去了物理上的合理性,相对于M_W导致了大地震和小地震不同的b值。
引文
Aki,K.(1967).Scaling law of seismic spectrum,J.Geophys.Res.72,no.4,1217-1231.
Aki,K.,and P.G.Richards(1980).Quantitative Seismology,2 Volumes,W.H.Freeman,San Francisco,California.
Aki,K.,and P.G.Richards(2002).Quantitative Seismology,Second Ed.,University Science Books,Sausalito,California.
Azimi,S.A.,A.V.Kalinin,V.V.Kalinin,and B.L.Pivo-varov(1968).Impulse and transient characteristics of media with linear and quadratic absorp-tion laws,Izvestiya,Phys.Solid Earth 2,88-93.
Baer,M.,N.Deichmann,J.Braunmiller,J.Clinton,S.Husen,D.Fh,D.Giardini,P.Kstli,U.Kradolfer,and S.Wiemer(2007).Earthquakes in Switzerland and surrounding regions during2006,Swiss J.Geosci.100,no.3,517-528,doi:10.1007/s00015-007-1242-0.
Bakun,W.(1984).Seismic moments,local magnitudes and coda-duration magnitudes for earthquakes in central California,Bull.Seismol.Soc.Am.74,439-458.
Bethmann,F.,N.Deichmann,and P.M.Mai(2011).Scaling relations of local magnitude versus moment magnitude for sequences of similar earthquakes in Switzerland,Bull.Seismol.Soc.Am.101,no.2,515-534,doi:10.1785/0120100179.
Bethmann,F.,N.Deichmann,and P.M.Mai(2012).Seismic wave attenuation from borehole and surface records in the top 2.5km beneath the city of Basel,Switzerland,Geophys.J.Int.190,no.2,1257-1270,doi:10.1111/j.1365-246X.2012.05555.x.
Boatwright,J.(1984).The effect of rupture complexity on estimates of source size,J.Geophys.Res.89,no.B2,1132-1146.
Deichmann,N.(1997).Far-field pulse shapes from circular sources with variable rupture velocities,Bull.Seismol.Soc.Am.87,no.5,1288-1296.
Deichmann,N.(2006).Local magnitude,a moment revisited,Bull.Seismol.Soc.Am.96,1267-1277.
Deichmann,N.,and D.Giardini(2009).Earthquakes induced by the stimulation of an enhanced geothermal system below Basel(Switzerland),Seismol.Res.Lett.80,no.5,784-798,doi:10.1785/gssrl.80.5.784.
Deichmann,N.,J.Clinton,S.Husen,B.Edwards,F.Haslinger,D.Fh,D.Giardini,P.Kstli,U.Kra-dolfer,and S.Wiemer(2012).Earthquakes in Switzerland and surrounding regions during2011,Swiss J.Geosci.105,no.3,463-476,doi:10.1007/s00015-012-0116-2.
Deichmann,N.,T.Kraft,and K.F.Evans(2014).I-dentification of faults activated during the stimulation of the Basel geothermal project from cluster analysis and fault mechanisms for the larger magnitude events,Geothermics 52,84-97,doi:10.1016/j.geothermics.2014.04.001.
Edwards,B.(2015).The influence of earthquake magnitude on hazard related to induced seismicity,in Perspectives on European Earthquake Engineering and Seismology,A.Ansal(Editor),in Geotechnical,Geological and Earthquake Engineering,Vol.39,doi:10.1007/978-3-319-16964-4_18.
Edwards,B.,and J.Douglas(2014).Magnitude scaling of induced earthquakes,Geothermics 52,132-139,doi:10.1016/j.geothermics.2013.09.012.
Edwards,B.,B.Allmann,D.Fh,and J.Clinton(2010).Automatic computation of moment magnitudes for small earthquakes and the scaling of local to moment magnitude,Geophys.J.Int.183,407-420,doi:10.1111/j.1365-246X.2010.04743.x.
Edwards,B.,D.Fh,and D.Giardini(2011).Attenuation of seismic shear wave energy in Switzerland,Geophys.J.Int.185,967-984,doi:10.1111/j.1365-246X.2011.04987.x.
Edwards,B.,T.Kraft,C.Cauzzi,P.Kstli,and S.Wie-mer(2015).Seismic monitoring and analysis of deep geothermal projects in St.Gallen and Basel,Switzerland,Geophys.J.Int.201,1020-1037,doi:10.1093/gji/ggv059.
Fh,D.,D.Giardini,P.Kstli,N.Deichmann,M.Gisler,G.Schwarz-Zanetti,S.Alvarez-Rubio,S.Sellami,B.Edwards,B.Allmann,et al.(2011).ECOS-09earthquake catalogue of Switzerland release 2011report and database,public catalogue,17/04/2011,Report SED/RISK/R/001/20110417,Swiss Seismological Service ETHZurich.
Frankel,A.,and L.Wennerberg(1989).Microearthquake spectra from the Anza,California,seismic network:Site response and source scaling,Bull.Seismol.Soc.Am.79,581-609.
Gladwin,M.T.,and F.D.Stacey(1974).Anelastic degradation of acoustic pulses in rock,Phys.Earth.Planet.In.8,332-336.
Goertz-Allmann,B.,B.Edwards,F.Bethmann,N.Deichmann,J.Clinton,D.Fh,and D.Giardini(2011).A new empirical magnitude scaling relation for Switzerland,Bull.Seismol.Soc.Am.101,3088-3095,doi:10.1785/0120100291.
Grünthal,G.,R.Wahlstr9m,and D.Stromeyer(2009).The unified catalogue of earthquakes in central,northern,and northwestern Europe(CENEC)-Updated and expanded to the last millennium,J.Seismol.13,517-541,doi:10.1007/s10950-008-9144-9.
Guilhem,A.,and F.Walter(2015).Full,constrained and stochastic source inversions support evidence for volumetric changes during the Basel earthquake sequence,Swiss J.Geosci.108,no.3,doi:10.1007/s00015-015-0197-9.
Hanks,T.C.,and D.M.Boore(1984).Momentmagnitude relations in theory and practice,J.Geo-phys.Res.89,no.B7,6229-6235.
Hanks,T.C.,and H.Kanamori(1979).A moment magnitude scale,J.Geophys.Res.84,no.B5,2348-2350.
Hring,M.O.,U.Schanz,F.Ladner,and B.C.Dyer(2008).Characterization of the Basel 1 enhanced geothermal system,Geothermics 37,469-495,doi:10.1016/j.geothermics.2008.06.002.
Kraft,T.,and N.Deichmann(2014).High-precision relocation and focal mechanism of the injection induced seismicity at the Basel EGS,Geothermics 52,59-73,doi:10.1016/j.geothermics.2014.05.014.
Krystek,M.,and M.Anton(2007).A weighted total least-squares algorithm for fitting a straight line,Meas.Sci.Tech.18,3438-3442.
Kwiatek,G.,K.Plenkers,and G.Dresen(2011).Source parameters of picoseismicity recorded at Mponeng deep gold mine,South Africa:Implications for scaling relations,Bull.Seismol.Soc.Am.101,2592-2608,doi:10.1785/0120110094.
Munafò,I.,L.Malagnini,and L.Chiaraluce(2016).On the relationship between MW and ML for small earthquakes,Bull.Seismol.Soc.Am.106,no.5,doi:10.1785/0120160130.
Richter,C.F.(1935).An instrumental magnitude scale,Bull.Seismol.Soc.Am.25,1-32.
Ross,Z.E.,Y.Ben-Zion,M.C.White,and F.L.Vernon(2016).Analysis of earthquake body wave spectra for potency and magnitude values:Implications for magnitude scaling relations,Geophys.J.Int.207,1158-1164,doi:10.1093/gji/ggw327.
Sato,T.(1994).Seismic radiation from circular cracks growing at variable rupture velocity,Bull.Seismol.Soc.Am.84,1199-1215.
Sato,T.,and T.Hirasawa(1973).Body wave spectra from propagating shear cracks,J.Phys.Earth21,415-431.
Aki,K.,and P.G.Richards(1980).Quantitative Seismology,2 Volumes,W.H.Freeman,San Francisco,California.
Aki,K.,and P.G.Richards(2002).Quantitative Seismology,Second Ed.,University Science Books,Sausalito,California.
Azimi,S.A.,A.V.Kalinin,V.V.Kalinin,and B.L.Pivo-varov(1968).Impulse and transient characteristics of media with linear and quadratic absorp-tion laws,Izvestiya,Phys.Solid Earth 2,88-93.
Baer,M.,N.Deichmann,J.Braunmiller,J.Clinton,S.Husen,D.Fh,D.Giardini,P.Kstli,U.Kradolfer,and S.Wiemer(2007).Earthquakes in Switzerland and surrounding regions during2006,Swiss J.Geosci.100,no.3,517-528,doi:10.1007/s00015-007-1242-0.
Bakun,W.(1984).Seismic moments,local magnitudes and coda-duration magnitudes for earthquakes in central California,Bull.Seismol.Soc.Am.74,439-458.
Bethmann,F.,N.Deichmann,and P.M.Mai(2011).Scaling relations of local magnitude versus moment magnitude for sequences of similar earthquakes in Switzerland,Bull.Seismol.Soc.Am.101,no.2,515-534,doi:10.1785/0120100179.
Bethmann,F.,N.Deichmann,and P.M.Mai(2012).Seismic wave attenuation from borehole and surface records in the top 2.5km beneath the city of Basel,Switzerland,Geophys.J.Int.190,no.2,1257-1270,doi:10.1111/j.1365-246X.2012.05555.x.
Boatwright,J.(1984).The effect of rupture complexity on estimates of source size,J.Geophys.Res.89,no.B2,1132-1146.
Deichmann,N.(1997).Far-field pulse shapes from circular sources with variable rupture velocities,Bull.Seismol.Soc.Am.87,no.5,1288-1296.
Deichmann,N.(2006).Local magnitude,a moment revisited,Bull.Seismol.Soc.Am.96,1267-1277.
Deichmann,N.,and D.Giardini(2009).Earthquakes induced by the stimulation of an enhanced geothermal system below Basel(Switzerland),Seismol.Res.Lett.80,no.5,784-798,doi:10.1785/gssrl.80.5.784.
Deichmann,N.,J.Clinton,S.Husen,B.Edwards,F.Haslinger,D.Fh,D.Giardini,P.Kstli,U.Kra-dolfer,and S.Wiemer(2012).Earthquakes in Switzerland and surrounding regions during2011,Swiss J.Geosci.105,no.3,463-476,doi:10.1007/s00015-012-0116-2.
Deichmann,N.,T.Kraft,and K.F.Evans(2014).I-dentification of faults activated during the stimulation of the Basel geothermal project from cluster analysis and fault mechanisms for the larger magnitude events,Geothermics 52,84-97,doi:10.1016/j.geothermics.2014.04.001.
Edwards,B.(2015).The influence of earthquake magnitude on hazard related to induced seismicity,in Perspectives on European Earthquake Engineering and Seismology,A.Ansal(Editor),in Geotechnical,Geological and Earthquake Engineering,Vol.39,doi:10.1007/978-3-319-16964-4_18.
Edwards,B.,and J.Douglas(2014).Magnitude scaling of induced earthquakes,Geothermics 52,132-139,doi:10.1016/j.geothermics.2013.09.012.
Edwards,B.,B.Allmann,D.Fh,and J.Clinton(2010).Automatic computation of moment magnitudes for small earthquakes and the scaling of local to moment magnitude,Geophys.J.Int.183,407-420,doi:10.1111/j.1365-246X.2010.04743.x.
Edwards,B.,D.Fh,and D.Giardini(2011).Attenuation of seismic shear wave energy in Switzerland,Geophys.J.Int.185,967-984,doi:10.1111/j.1365-246X.2011.04987.x.
Edwards,B.,T.Kraft,C.Cauzzi,P.Kstli,and S.Wie-mer(2015).Seismic monitoring and analysis of deep geothermal projects in St.Gallen and Basel,Switzerland,Geophys.J.Int.201,1020-1037,doi:10.1093/gji/ggv059.
Fh,D.,D.Giardini,P.Kstli,N.Deichmann,M.Gisler,G.Schwarz-Zanetti,S.Alvarez-Rubio,S.Sellami,B.Edwards,B.Allmann,et al.(2011).ECOS-09earthquake catalogue of Switzerland release 2011report and database,public catalogue,17/04/2011,Report SED/RISK/R/001/20110417,Swiss Seismological Service ETHZurich.
Frankel,A.,and L.Wennerberg(1989).Microearthquake spectra from the Anza,California,seismic network:Site response and source scaling,Bull.Seismol.Soc.Am.79,581-609.
Gladwin,M.T.,and F.D.Stacey(1974).Anelastic degradation of acoustic pulses in rock,Phys.Earth.Planet.In.8,332-336.
Goertz-Allmann,B.,B.Edwards,F.Bethmann,N.Deichmann,J.Clinton,D.Fh,and D.Giardini(2011).A new empirical magnitude scaling relation for Switzerland,Bull.Seismol.Soc.Am.101,3088-3095,doi:10.1785/0120100291.
Grünthal,G.,R.Wahlstr9m,and D.Stromeyer(2009).The unified catalogue of earthquakes in central,northern,and northwestern Europe(CENEC)-Updated and expanded to the last millennium,J.Seismol.13,517-541,doi:10.1007/s10950-008-9144-9.
Guilhem,A.,and F.Walter(2015).Full,constrained and stochastic source inversions support evidence for volumetric changes during the Basel earthquake sequence,Swiss J.Geosci.108,no.3,doi:10.1007/s00015-015-0197-9.
Hanks,T.C.,and D.M.Boore(1984).Momentmagnitude relations in theory and practice,J.Geo-phys.Res.89,no.B7,6229-6235.
Hanks,T.C.,and H.Kanamori(1979).A moment magnitude scale,J.Geophys.Res.84,no.B5,2348-2350.
Hring,M.O.,U.Schanz,F.Ladner,and B.C.Dyer(2008).Characterization of the Basel 1 enhanced geothermal system,Geothermics 37,469-495,doi:10.1016/j.geothermics.2008.06.002.
Kraft,T.,and N.Deichmann(2014).High-precision relocation and focal mechanism of the injection induced seismicity at the Basel EGS,Geothermics 52,59-73,doi:10.1016/j.geothermics.2014.05.014.
Krystek,M.,and M.Anton(2007).A weighted total least-squares algorithm for fitting a straight line,Meas.Sci.Tech.18,3438-3442.
Kwiatek,G.,K.Plenkers,and G.Dresen(2011).Source parameters of picoseismicity recorded at Mponeng deep gold mine,South Africa:Implications for scaling relations,Bull.Seismol.Soc.Am.101,2592-2608,doi:10.1785/0120110094.
Munafò,I.,L.Malagnini,and L.Chiaraluce(2016).On the relationship between MW and ML for small earthquakes,Bull.Seismol.Soc.Am.106,no.5,doi:10.1785/0120160130.
Richter,C.F.(1935).An instrumental magnitude scale,Bull.Seismol.Soc.Am.25,1-32.
Ross,Z.E.,Y.Ben-Zion,M.C.White,and F.L.Vernon(2016).Analysis of earthquake body wave spectra for potency and magnitude values:Implications for magnitude scaling relations,Geophys.J.Int.207,1158-1164,doi:10.1093/gji/ggw327.
Sato,T.(1994).Seismic radiation from circular cracks growing at variable rupture velocity,Bull.Seismol.Soc.Am.84,1199-1215.
Sato,T.,and T.Hirasawa(1973).Body wave spectra from propagating shear cracks,J.Phys.Earth21,415-431.