Stress drop, slip type, earthquake magnitude, and seismic hazard

Care must be taken to provide reliable antiseismic protection in earthquake -prone areas where the impact of a large earthquake in megacities with indu strial facilities as well as in ordinary buildings is liable to cause massi ve loss of human life and to cripple the nation's economy. This protection needs to take into account not only vibratory ground motion but also perman ent ground failure, and notably surface-faulting hazard, a fact tragically illustrated during the recent events of Turkey and Taiwan. The purpose of t his contribution is to conduct a survey of our current state of knowledge c oncerning theoretical relationships between earthquake source parameters, s uch as moment magnitude (M, M-w), surface wave magnitude (Ms), seismic mome nt (MO), stress drop (Delta sigma), rupture length (L), and displacement on the fault (D). A relationship is proposed that links Ms to L and Delta sig ma: M-S = 2 log L + 1.33 log Delta sigma + 1.66, using a simple rupture mod el. Earthquake data from all over the world for which the parameters of rup ture length, fault width (W), fault displacement, and surface-wave magnitud e are available have enabled stress drop values to be computed for each eve nt using both geological observation (Delta sigma (1)) and the previously p roposed equation (Delta sigma (2)). The results obtained tend to indicate t hat stress drop values increase versus fault width (depth) up to approximat ely 15 km (corresponding perhaps to the brittle-ductile boundary). This inc rease is more pronounced in the case of reverse faults than it is for those with strike-slip or normal mechanisms. An equation of the type Delta sigma = kW(n) has been used to fit the data, and preliminary values for k and n have been supplied for the three slip types. For depths in excess of 15 km the data do not display significant variation (Delta sigma < 100 bars). The se results are in agreement with certain laboratory models of the continent al lithosphere. Although more data, particularly in the large-magnitude ran ge, are needed to ascertain whether it is the W or the L model that better describes earthquake scaling laws, stress drop does not appear to be fault- length dependent, thus being supportive of the L model. The risk of surface faulting is dependent on the dynamic environment of the fault, that is, th e stress drop, the rupture length, and the fault width. Although statistics show that surface faulting appears in most instances at magnitudes of at l east 6.1, data from certain regions indicate that seismicity at superficial depths is under certain conditions accompanied by significant surface faul ting even for magnitudes as small as 5.5, suggesting a change in scaling la w. The threshold magnitude for surface faulting is accordingly seen to depe nd on the rheology of materials in the fault area and on the stress environ ment.