震源参数之间的定量关系
QUANTIFICATION RELATIONS BETWEEN THE SOURCE PARAMETERS
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摘要: 本文根据建立在平均二维破裂模式基础上的地震定标律,导出了地震矩 M0与各常用震级之间（1gM0-MS,ML,mb）,各种震级之间（Ms-ML,Ms-mb,ML-mb）,各震源参数之间（断层长度IgL,断层面积 lgS,平均错距 lgD-Ms,拐角频率 1gfc-ML）的各种常用的关系式.利用这些关系式,由一个震级值就可以估算出一系列震源参数.本文还求出了平均破裂速度 Vr=2.65km/s,总破裂时间 T（s）=0.5L（km）,平均位错速度 D（t）=11.4m/s.用矩震级 Mw 度量地震的大小,有四个优点:（1）地震矩反映了形变规模的大小,因此是度量地震大小的最佳物理量.（2）它是一个绝对力学标度,对任何大小地震都有意义,可测量,且不产生饱和问题.（3）它和我们已熟悉的震级标度可衔接.（4）它是一个均匀的震级标度,适用于宽尺度的地震统计.因此,Mw 是一种值得推广的震级标度.Abstract: The various useful source-parameter relations between seismic moment and common use magnitude lg(M0)and Ms, ML, mb; between magnitudes Ms and ML,MS and wb, ML and mb; and between magnitude Ms and lg (L) (fault length), lg (W) (fault width), lg (S) (fault area),lg (D) (average dislocation); ML and Ig (fc) (corner frequency)have been derived from the scaling law which is based on an average two-dimensional faultingmodel of a rectengularfault. A set of source-parameters can be estimated from only one magnitude by using these relations. The average rupturevelocityofthe fault Vr = 2.65 km/s, the total time of rupture T(s) = 0.35 (s/km) L (km) and the average dislocation slip rate D (t) = 114m/s are also obtained.There are four strong points to measure earthquake size with the seismic moment magnitude Mw.(1)The seismic moment magnitude shows the strain and rupture size. It is the best seal for the measurement of earthquake size.(2)It is a quantity of absolute mechanics, and has clear physical meaning. Any size of earthquake can be measured. There is no saturation. It can be used to quantify both shallow and deep earthquakes on the basis of the waves radiated.(3)It can link up the previous magnitude scales.(4)It is a uniform scale of measurement of earthquake size. It is suitable for statistics covering a broad range of magnitudes. So the seismic moment magnitude is a promising magnitude worth popularization.
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[1] Kanamori,H,and Anderson. D. L,1975,Theoretical basic of some empirical relation in seismology,Bull Seism.Soc.Amer,65,1037——1095.
[2] Geller,R.J——1976,Scaling relations for earthquake source parameter and magnitude,Bull.Seism,Soc, Amer., 6,1051——1523.
[3] Sato,R.,1979,Theoretical base on relationship between focal parameters and earthquake magnitude.J. Phys,Eurth,27,353——372.
[4] P urcaru,G.and Berckhemer,H——1982. Quantitative relations of seismic source parameters and a classifica——lion of earthquakes,Tectonophysics,84,57——128
[5] NuttG, U,W., 1983. Aaverage sourcparameter relations for mid——plate earthquakes,Bull,Seism,So Amer.,73,511——535.
[6] NuttG, U,W., 1985,Average source——parameter relations for plate——margin earthquakes,Tectonophysics,118,161——174.
[7] Aki,K——1967,Scaling law of seismic spectrum. J,GeophVS. Res——72,1217——1231
[8] Hanks,T.C.and Boore,D,M——1984,Moment magnitude relations in theory and practice,J Geophy's.Res——89,B7,6229——6235,
[9] Joyner,W. B——1984. A scaling law for the spectra of large earthquakes,Bull,Seism,Soc Amer.. 741 167——1188.
[10] Fletcher, J——Boatwright,J——Haar, L——Hanks, T. and McGarr,A——1984 Source parameters for aftershocks of the Oroville,California、earthquake,Bul!,Seism,Soc,Anr., 74,1101——1123
[11] Console,R.and Rovelli,A,1985,Statistical relations between source parameters for low and interme——diate magnitudes(Friuli,1976),Tectonophysirs,118,329——338,
[12] Gusev,A.A,1983,Descriptive statistical model of earthquake source radiation and its application to anestimation of short——period strong motion,Geophys. J,Rot astr. Sor,74,787——808,
[13] 陈培善、陈海通,1989.由三维破裂模式导出的地震定标律.地震学报,11 337——350.
[14] 陈培善、谷继成、李文香,1977.从断裂力学观点研究地震的破裂过程和地震预报.地球物理学报,20.185——262.
[15] 陈培善、卓奎玉.余严、王志刚、黄伟琼、李文香、胡荣盛,1978.唐山地震前后京津唐张地区的应力场.地球物理学报,21, 34——58.
[16] Gupta,H,K.and Rastogi,B,R——1972,Earthquake vs. relation and source multiplicity. Geoply,s. J. R. astr. Soc.,28,65——89.
[17] Duda,S,J——1978. Physical significance of the earthquake magnitude:the present state ofinterpretation of the concept,Tcctonophysics,49, 3/4, 119——130
[18] Madariaga,R——1983 Earthquake source theory:A review. Proceeding the International School Physi——cs Enrico Femai Course 85,North—— Holland,Amsterdam.1——74.[1] Kanamori,H,and Anderson. D. L,1975,Theoretical basic of some empirical relation in seismology,Bull Seism.Soc.Amer,65,1037——1095.
[2] Geller,R.J——1976,Scaling relations for earthquake source parameter and magnitude,Bull.Seism,Soc, Amer., 6,1051——1523.
[3] Sato,R.,1979,Theoretical base on relationship between focal parameters and earthquake magnitude.J. Phys,Eurth,27,353——372.
[4] P urcaru,G.and Berckhemer,H——1982. Quantitative relations of seismic source parameters and a classifica——lion of earthquakes,Tectonophysics,84,57——128
[5] NuttG, U,W., 1983. Aaverage sourcparameter relations for mid——plate earthquakes,Bull,Seism,So Amer.,73,511——535.
[6] NuttG, U,W., 1985,Average source——parameter relations for plate——margin earthquakes,Tectonophysics,118,161——174.
[7] Aki,K——1967,Scaling law of seismic spectrum. J,GeophVS. Res——72,1217——1231
[8] Hanks,T.C.and Boore,D,M——1984,Moment magnitude relations in theory and practice,J Geophy's.Res——89,B7,6229——6235,
[9] Joyner,W. B——1984. A scaling law for the spectra of large earthquakes,Bull,Seism,Soc Amer.. 741 167——1188.
[10] Fletcher, J——Boatwright,J——Haar, L——Hanks, T. and McGarr,A——1984 Source parameters for aftershocks of the Oroville,California、earthquake,Bul!,Seism,Soc,Anr., 74,1101——1123
[11] Console,R.and Rovelli,A,1985,Statistical relations between source parameters for low and interme——diate magnitudes(Friuli,1976),Tectonophysirs,118,329——338,
[12] Gusev,A.A,1983,Descriptive statistical model of earthquake source radiation and its application to anestimation of short——period strong motion,Geophys. J,Rot astr. Sor,74,787——808,
[13] 陈培善、陈海通,1989.由三维破裂模式导出的地震定标律.地震学报,11 337——350.
[14] 陈培善、谷继成、李文香,1977.从断裂力学观点研究地震的破裂过程和地震预报.地球物理学报,20.185——262.
[15] 陈培善、卓奎玉.余严、王志刚、黄伟琼、李文香、胡荣盛,1978.唐山地震前后京津唐张地区的应力场.地球物理学报,21, 34——58.
[16] Gupta,H,K.and Rastogi,B,R——1972,Earthquake vs. relation and source multiplicity. Geoply,s. J. R. astr. Soc.,28,65——89.
[17] Duda,S,J——1978. Physical significance of the earthquake magnitude:the present state ofinterpretation of the concept,Tcctonophysics,49, 3/4, 119——130
[18] Madariaga,R——1983 Earthquake source theory:A review. Proceeding the International School Physi——cs Enrico Femai Course 85,North—— Holland,Amsterdam.1——74.
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