Theoretical Basis of Some Empirical Relations in Seismology by Hiroo Kanamori And
Theoretical Basis of Some Empirical Relations in Seismology by Hiroo Kanamori And
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发表时间：
1975-10
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通讯作者：
H. Kanamori;D. L. Anderson
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作者：
H. Kanamori;D. L. Anderson
涉及地震力矩M_O，M_S，能量E_S和故障尺寸L（或区域S）的经验关系是根据广泛的地震数据（M_S≧6）和简单的裂纹和动态脱位模型讨论的。 S和log M_O非常线性（斜率〜2/3），表明恒定的应力下降Δσ= 30、100和60 bar in Inter-plate，Intra板和“平均值”。地震分别为大地震，关系m_s〜（2/3）log m_o〜2 log 〜2 log l是由数据建立的。 . For very large earthquakes M_S ∼ (1/3) log M_o ∼ log L ∼ (1/3) log E_S. For very small earthquakes M_S ∼ log M_o ∼ 3 log L ∼ log E_S. Scaling rules假定和合理。明显的压力η是η的效率用简单的几何论证解释了频率关系log n〜-m_s。
Empirical relations involving seismic moment M_o, magnitude M_S, energy E_S and fault dimension L (or area S) are discussed on the basis of an extensive set of earthquake data (M_S ≧ 6) and simple crack and dynamic dislocation models. The relation between log S and log M_o is remarkably linear (slope ∼ 2/3) indicating a constant stress drop Δσ; Δσ = 30, 100 and 60 bars are obtained for inter-plate, intra-plate and “average” earthquakes, respectively. Except for very large earthquakes, the relation M_S ∼ (2/3) log M_o ∼ 2 log L is established by the data. This is consistent with the dynamic dislocation model for point dislocation rise times and rupture times of most earthquakes. For very large earthquakes M_S ∼ (1/3) log M_o ∼ log L ∼ (1/3) log E_S. For very small earthquakes M_S ∼ log M_o ∼ 3 log L ∼ log E_S. Scaling rules are assumed and justified. This model predicts log E_S ∼ 1.5 M_S ∼ 3 log L which is consistent with the Gutenberg-Richter relation. Since the static energy is proportional to σL^3, where σ is the average stress, this relation suggests a constant apparent stress ησ where η is the efficiency. The earthquake data suggest ησ ~ 1/2 Δσ. These relations lead to log S ∼ M_S consistent with the empirical relation. This relation together with a simple geometrical argument explains the magnitude-frequency relation log N ∼ − M_S.