峰值速度和加速度对环境剪应力的依赖性

DEPENDENCE OF PEAK ACCELERATION AND PEAK VELOCITY ON THE ENVIRONMENT SHEAR STRESS

从导出的地震定标律和地震破裂过程的断裂力学模式出发,得到了震源平均位移、速度和加速度谱的表达式,进而又推导出震源的峰值位移d_m,速度v_m和加速度a_m的表达式:d_m=k_dM_0~2/~3τ_0^(2/3),v=k_vM_0^(1/3)τ_0^(4/3),a_m=k_aτ_0~2式中M_0是地震矩,τ_0是环境剪应力值,k_d,k_v,k_a为适当的常数.我们选用了66个地震的观测资料,这些地震的矩震级范围包括了从1级左右的极微震,3—5级的小震,直到6—7级的大震;地震矩从10~9—10^(20)Nm,跨越了10个数量级,并用这些地震检验了上述公式. 令所有地震的平均应力为5MPa,定出常数k_d,k_v,k_a,进而由速度和加速度观测资料求得66个地震的环境剪应力τ_0值,这些数值相当稳定.多数极微震的τ_0值在2—4MPa之间;小震的τ_0值多数在4—8MPa左右;大震的τ_0值为10MPa左右。τ_0值对震源深度和断层类型有明显的依赖性.一般深度很浅的小震和极微震,τ_0值很低;正断层地震的τ_0值相对较低;逆断层地震的τ_0值较高;走滑断层地震的τ_0值则居中.

Starting from the scaling law derived by authors and earthquake rupture model according to fracture mechanics, the average source spectra of displacement, velocity and acceleration have been obtained, then the expressions of peak displacement, velocity and acceleration have been derived, they areThe observed data of 66 earthquakes are selected, their range of seismic moment magnitude Mw, is very large, from tremors (Mw,1.0) to small earthquakes(Mw= 3-5), to large earthquakes (Mw = 6-7); the seismic moment is from 109 to 1020 Nm, amount to 10 order magnitude. Above expressions are examinated by these data, and the results are encouraging.Setting average environment shear stress equal to 5MPa for all earthquakes, the constants kd,kv,ka can be determined, then the values of environment shear stress for 66 earthquakes are obtained from data of peak acceleration and velocity, these stress values r0 are quite stable. Most of r0 for tremors are from 2 to 4MPa; 4-8MPa for small earthquakes; about 10MPa for large earthquakes. There are obvious dependence of earthquake depth and fault type on environment shear stress. The values of environment shear stress are usually very low for tremors and small earthquakes with shallow depth; they are relatively low for normal fault earthquakes; they are relatively high for thrust fault earthquakes; they are intermediate for strike slip earthquakes.