Care must be taken to provide reliable antiseismic protection in earthquake-prone areas where the impact of a large earthquake in megacities with industrial facilities as well as in ordinary buildings is liable to cause massive 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 permanent ground failure, and notably surface-faulting hazard, a fact tragically illustrated during the recent events of Turkey and Taiwan. The purpose of this contribution is to conduct a survey of our current state of knowledge concerning theoretical relationships between earthquake source parameters, such as moment magnitude (M, Mw), surface wave magnitude (MS), seismic moment (MO), stress drop (Δσ), rupture length (L), and displacement on the fault (D). A relationship is proposed that links MS to L and Δσ: MS = 2 log L + 1.33 log Δσ + 1.66, using a simple rupture model. Earthquake data from all over the world for which the parameters of rupture length, fault width (W), fault displacement, and surface-wave magnitude are available have enabled stress drop values to be computed for each event using both geological observation (Δσ1) and the previously proposed equation (Δσ2). The results obtained tend to indicate that stress drop values increase versus fault width (depth) up to approximately 15 km (corresponding perhaps to the brittle-ductile boundary). This increase 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 Δσ = kWn 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 (Δσ < 100 bars). These results are in agreement with certain laboratory models of the continental lithosphere. Although more data, particularly in the large-magnitude range, 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, the stress drop, the rupture length, and the fault width. Although statistics show that surface faulting appears in most instances at magnitudes of at least 6.1, data from certain regions indicate that seismicity at superficial depths is under certain conditions accompanied by significant surface faulting even for magnitudes as small as 5.5, suggesting a change in scaling law. The threshold magnitude for surface faulting is accordingly seen to depend on the rheology of materials in the fault area and on the stress environment.