Coulomb failure stress

During the 75 years before the great 1906 earthquake on the San Andreas fault, the San Francisco Bay area suffered at least 14 M_w > 6 shocks on all major faults, including two M_w > 6.8 events; during the succeeding 75 years, there was but one M_w > 6 shock. Evidently, the rate of seismicity is not constant, and the rate –or probability– of earthquakes on one fault is not independent of another. Yet there is nothing in probabilistic seismic hazard assessment, the principal tool of the engineering, insurance, financial, and emergency response communities, that reflects or can reproduce such observations. Earthquake interaction is a fundamental feature of seismicity, leading to earthquake sequences, clustering, and aftershocks. One interaction criterion that promises a deeper understanding of earthquake occurrence, and a better description of probabilistic hazard, is Coulomb stress transfer.

An earthquake reduces the average value of the shear stress on the fault that slipped, but as Chinnery first showed in 1963, shear stress rises at sites in addition to the fault tips. This discovery lay in waiting for 20 years, when lobes of off-fault aftershocks were seen to correspond to small calculated increases in shear or Coulomb stress. In its simplest form, the Coulomb failure stress change, Ds_f (also written DCFS or DCFF) is

(1)

where Dt is the shear stress change on a fault (reckoned positive in the direction of fault slip), Ds_n is the normal stress change (positive if the fault is unclamped), DP is the pore pressure change in the fault zone (positive in compression), and m is the friction coefficient (with range 0-1). Failure is encouraged if Ds_f is positive and discouraged if negative; both increased shear and unclamping of faults promote failure. The tendency of DP to counteract Ds_n is often incorporated into (1) by a reduced ‘effective’ friction coefficient, m’.

The calculated off-fault stress increases are rarely more than a few bars (1 bar = 0.1 MPa ~ atmospheric pressure at sea level), or just a few percent of the mean earthquake stress drop. In addition, the proximity to failure at any site is presumably variable but in any event unknown. So why would aftershocks concentrate at the site of such small stress increases? Studies by our research group and other US and international teams find a surprisingly strong influence of stress change on seismicity, explain seek to explain it in terms of rupture nucleation phenomena observed in the laboratory.