Keywords: b-value, precursor time, spring-slider model, stiffmess ratio, saturation of water
Observations exhibit the temporal variation in b-values prior to a mainshock. The b-value starts to increase from the normal value at time t1, reaches its peak one at time t2, then begins to decrease from the peak one at t2, and returns to the normal one at time t3. As t>t3, the b-value varies around the normal one or rightly decreases with time until the occurrence of the forthcoming mainshock at time t4. The precursor time, T=t4-t1, of b-value anomalies prior to a forthcoming mainshock is related to the magnitude, M, of the event in a form: log(T)=q+rM (T usually in days) where q and r are two constants. In this study, the mechanism causing b-value anomalies prior to a mainshock is explored. From numerical simulations based on the 1-D dynamical spring-slider mode proposed by Burridge and Knopoff (1967), Wang (1995) found a power-law correlation between b and s, where the parameter s is the ratio of the spring constant (K) between two sliders to that (L) between a slider and the moving plate. The power-law correlation are b~s-2/3 for the cumulative frequency and b~s-1/2 for the discrete frequency. Since L of a source area is almost constant for a long time period, b directly relates to K. Lower K results in a higher b-value. Wang (2012) found K=rAvp2, where rA and vp are, respectively, the areal density and P-wave velocity of a fault zone. Experimental results show that vp is strongly influenced by the water saturation in rocks. The water saturation in the source area varies with time, thus leading to a temporal variation in vp as well as K. This results in the temporal variation in b-values prior to a mainshock. The modeled result is consistent with the observed one.