图  1   地震后余震序列空间分布(M≥4.0)(b)图

Figure  1.   Regional seismicity (M≥4.0) around Longmenshan fault zone before (a) and after (b) the 2008 Wenchuan M_W7.9 earthquake

图  2   单自由度的弹簧-滑块模型σ和τ分别为断层上加载的正应力和剪切应力，δ₀(t)为远场加载位移， δ(t)为滑块自身的滑动位移， k为弹簧的有效弹性系数

Figure  2.   A simple spring-slide block modelσ and τ are normal and shear stress loaded applied on the slide block, respectively. δ₀(t) is the remote loading displacement, and δ(t) is the slider’s slip displacement. k is an effective spring stiffness

图  3   由单自由度弹簧-滑块模型得到的断层演化全过程示意图(ａ)地震周期中断层滑移速率的演化过程；(ｂ)地震周期中断层状态变量的演化过程

Figure  3.   Temporal evolution of a typical seismic cycle derived from one dimensional spring-block model. (a) Temporal evoluation of fault slip rate during a full seismic cycle; (b) Temporal evoluation of fault state variation during a full seismic cycle

图  4   断层受应力扰动时时钟提前(推迟)示意图(a) Dieterich模型得到的受应力扰动时断层发震的提前(推迟)时间变化量示意图;(b) 传统库仑位错模型给出的受应力扰动时断层发震的提前(推迟)时间变化量示意图

Figure  4.   Clock advance/delay due to static stress perturbation loaded on the fault(a) Clock advance/delay derive from Dieterich model due to static stress perturbation; (b) Clock advance/delay derive from Coulomb dislocation model due to static stress perturbation

图  5   汶川地震后单位时间(月)内M≥3.5 (a)和M≥4.0 (b)余震发生率随时间衰减关系圆点是实际地震数据统计得到的地震发生率， 实线是用对数线性拟合得到的地震发生率，虚线为背景场地震发生率

Figure  5.   (a) The decay of M≥3.5 aftershock seismicty rate by month; (b) The decay of M≥4.0 aftershock seismicty rate by month. Black dots represent the observed aftershock seismicty rate from the Wenchuan mainshock. Solid line denotes the result of log-log regression. The background seismicity rate is shown as the dashed line

图  6   t_e定义的示意图. 其中点线为公式(14)给出的主震后地震发生率随时间衰减关系，点划线为背景场地震发生率， 虚线为R(Δτ→∞)， 实线为R(t₁)；(b) 汶川主震后100小时内地震发生率随时间衰减变化示意图

Figure  6.   (a) The definition of t_e. Dotted line represents the aftershocks seismicity rate variation with time given by equation (14). Dotted line represents background seismicity rate. The dashed line and solid line represent R(Δτ→∞) and R(t₁) respectively; (b) Seismicity rate variations with time during the first 100 hours after the Wenchuan main shock

图  7   2008年汶川M_W7.9地震主震后余震发生率随时间变化． 图中点为由观测得到的M≥4.0的地震发生率， 虚线、 实线和点划线分别给出了当ΔCFF^G=0.4， 0.2和0.15 MPa时余震发生率随时间衰减的过程. 在计算中，aσ=0.05 MPa， t_a=85 a， r₀=0.75次/a

Figure  7.   The decay of aftershock seismicity rate following Wenchuan M_W7.9 mainshock. The observed seismicity rate of earthquakes (M≥4.0) is plotted as dots. Dashed, solid and dotted lines are plotted from equation (14) with ΔCFF^G=0.4, 0.2 and 0.15 MPa respectively. In the computation, aσ=0.05 MPa, t_a=85 a, r₀=0.75/a

图  8   汶川M_W7.9地震主震后余震M≥4.0(a)和M≥5.0 (b)累积次数N随时间变化．图中实线为背景场地震累积次数， 虚线为观测得到的主震后地震累积次数， 点线为应用公式(15)计算得到的地震累积次数． 在计算中点线取aσ=0.05 MPa， t_a=85 a，ΔCFF^G=0.2 MPa， M≥4.0和M≥5.0背景地震发生率分别取0.75次/a和0.073次/a

Figure  8.   The cumulative number， N， of aftershocks with M≥4.0 (a) and M≥5.0 (b) following Wenchuan M_W7.9 mainshock. The cumulative number of background earthquake is shown as the solid line. The observed data of aftershocks are plotted as the dashed line. Earthquake cumulative number denoted by dotted line is plotted from equation (15) with ΔCFF^G=0.2 MPa, aσ=0.05 MPa, t_a=85 a,r₀=0.75/a for M≥4.0 and r₀=0.073/a for M≥5.0

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图  11   Dieterich应力扰动分段模型0时刻为发震时刻， t₁时刻为剪应力变化率回归到背景场水平

Figure  11.   The modified Dieterich model associated with temporal variation of fault shear stress rate The main shock occurred at 0 moment, and at t₁ the stressing rate come back to the background level