New empirical relationships among magnitude, rupture length, rupture width, rupture area, and surface displacement

Abstract

Source parameters for historical earthquakes worldwide are compiled to develop a series of empirical relationships among moment magnitude (M), surface rupture length, subsurface rupture length, downdip rupture width, rupture area, and maximum and average displacement per event. The resulting data base is a significant update of previous compilations and includes the additional source parameters of seismic moment, moment magnitude, subsurface rupture length, downdip rupture width, and average surface displacement. Each source parameter is classified as reliable or unreliable, based on our evaluation of the accuracy of individual values. Only the reliable source parameters are used in the final analyses. In comparing source parameters, we note the following trends: (1) Generally, the length of rupture at the surface is equal to 75% of the subsurface rupture length; however, the ratio of surface rupture length to subsurface rupture length increases with magnitude; (2) the average surface displacement per event is about one-half the maximum surface displacement per event; and (3) the average subsurface displacement on the fault plane is less than the maximum surface displacement but more than the average surface displacement. Thus, for most earthquakes in this data base, slip on the fault plane at seismogenic depths is manifested by similar displacements at the surface. Log-linear regressions between earthquake magnitude and surface rupture length, subsurface rupture length, and rupture area are especially well correlated, showing standard deviations of 0.25 to 0.35 magnitude units. Most relationships are not statistically different (at a 95% significance level) as a function of the style of faulting: thus, we consider the regressions for all slip types to be appropriate for most applications. Regressions between magnitude and displacement, magnitude and rupture width, and between displacement and rupture length are less well correlated and have larger standard deviation than regressions between magnitude and length or area. The large number of data points in most of these regressions and their statistical stability suggest that they are unlikely to change significantly in response to additional data. Separating the data according to extensional and compressional tectonic environments neither provides statistically different results nor improves the statistical significance of the regressions. Regressions for cases in which earthquake magnitude is either the independent or the dependent parameter can be used to estimate maximum earthquake magnitudes both for surface faults and for subsurface seismic sources such as blind faults, and to estimate the expected surface displacement along a fault for a given size earthquake.

The 2021 Mw 7.3 Madoi, China Earthquake: Transient Supershear Ruptures on a Presumed Immature Strike‐Slip Fault

“…(a) Relationship between rupture length and moment magnitude of the well-studied supershear strike-slip earthquakes. Red and blue dashed lines represent the empirical relationships between rupture length and moment magnitude for strike-slip and all types of earthquakes, respectively (Wells & Coppersmith, 1994). Yellow circles and red star represent the past supershear earthquakes and the Madoi earthquake, respectively.…”

Diachronous Quaternary Development of the Jiayuguan Fault and Implications for Strain Compartmentalization and Modern Earthquake Hazards in the NW Hexi Corridor, China

“…Although the northwestern section of the JYGF along the Heishan range front lacks a clear surface scarp, the sharply defined linear mountain front and clear fault trace to the SE suggests an active fault system with an along‐strike length of at least 25 km (Figures 2 and 17, B. Chen et al., 2007). Based on the empirical statistical relationship between earthquake magnitude and surface fault length (Mw = 5.00 + 1.22 log(SRL), Wells & Coppersmith, 1994), we calculate a potential earthquake moment magnitude of 6.3–7.1, without considering the possibility of synchronous rupture on subsidiary faults on the hanging wall or other associated faults.…”

“…Publicly available, open‐source Asia High‐Mountain 8‐m DEMs (Shean et al., 2016) and uncrewed aerial vehicle (UAV) photogrammetry‐derived centimeter‐resolution DEMs were analyzed to document fault displacements, fold geometries, and to support sub‐surface fault projections. We also assess the seismic potential of the JYGF based on an empirical statistical relationship between fault length and earthquake magnitude (Wells & Coppersmith, 1994). Finally, we place our results in the context of previously published slip rates for other Quaternary‐active faults in the western Hexi Corridor, to evaluate the degree of strain partitioning, fault connectivity and structural compartmentalization in the Qilian Shan foreland and eastern ATF deforming belt.…”

Stochastic simulation of earthquake ground motions for the seismic assessment of monumental masonry structures: Source‐based vs site‐based approaches

“…The ruptured fault plane employed in 31 (FL1 in Figure 4) has a length and width of 16.5 and 9.4 km, respectively, estimated according to. 72 The strike and dip angles by that study are provided as 165 • and 85 • , respectively. Later, in 66 potential fault plane solutions that could rupture during the 1998 Faial earthquake were studied.…”

“…A review of the relevant literature in the region demonstrates the prevalence of several seismic sources and attenuation models. The ruptured fault plane employed in 31 (FL1 in Figure 4) has a length and width of 16.5 and 9.4 km, respectively, estimated according to 72 . The strike and dip angles by that study are provided as 165° and 85°, respectively.…”