Earthquake Fault Scaling: Self-Consistent Relating of Rupture Length, Width, Average Displacement, and Moment Release

Abstract

In this paper, I propose the scaling relation W C 1 L β (where β ≈ 2=3)to describe the scaling of rupture width with rupture length. I also propose a new displacement relation, where A is the area (LW). By substituting these equations into the definition of seismic moment (M 0 μ DLW), I have developed a series of self-consistent equations that describe the scaling between seismic moment, rupture area, length, width, and average displacement. In addition to β, the equations have only two variables, C 1 and C 2 , which have been estimated empirically for different tectonic settings. The relations predict linear log-log relationships, the slope of which depends only on β.These new scaling relations, unlike previous relations, are self-consistent, in that they enable moment, rupture length, width, area, and displacement to be estimated from each other and with these estimates all being consistent with the definition of seismic moment. I interpret C 1 as depending on the size at which a rupture transitions from having a constant aspect ratio to following a power law and C 2 as depending on the displacement per unit area of fault rupture and so static stress drop. It is likely that these variables differ between tectonic environments; this might explain much of the scatter in the empirical data.I suggest that these relations apply to all faults. For small earthquakes (M < ∼5) β 1, in which case L 3 fault scaling applies. For larger (M > ∼5) earthquakes β 2=3, so L 2:5 applies. For dip-slip earthquakes this scaling applies up to the largest events. For very large (M > ∼7:2) strike-slip earthquakes, which are fault widthlimited, β 0 and assuming D ∝ A p , then L 1:5 scaling applies. In all cases, M 0 ∝ A 1:5 fault scaling applies.

The 2013 European Seismic Hazard Model: key components and results

“…4d) M max is calculated as the arithmetic mean of the estimates obtained from multiple fault scaling relations (Wells and Coppersmith 1994;Hanks and Bakun 2002;Kagan 2002;Leonard 2010). This additional assessment of M max , with respect to that given by compilers of the EDSF, was necessary to further homogenize the fault source dataset.…”

Methodology for earthquake rupture rate estimates of fault networks: example for the western Corinth rift, Greece

“…Mmax values calculated using the equations for normal faults using the rupture area. WC94 refers to Wells and Coppersmith (1994) and Le10 to Leonard (2010) this paper, we also explore a logic tree branch for an alternative rupture set (see Fig. 3) with higher fault connectivity (B14_hc), where faults can break together if their fault traces are separated by 5 km or less, therefore allowing a wider spectrum of possible FtF rupture scenarios (additional scenarios in bold in Table 2).…”

Control spectra for Quito

“…On the bottom right side of this figure, at the slopes of the hills, the Guápulo shrine is located, and towards the north is the Metropolitan Park, where a seismic refraction study was conducted to determine the velocity of shear wave V s30 on a rocky outcrop (Castillo, 2014). Table 1 shows the segments of the thrust faults that cross the city of Quito; the length of the rupture surface was estimated by Alvarado et al (2014) and the area of rupture and the expected maximum magnitude were estimated using the equations proposal in Leonard (2010). The average dip angle of the thrust faults is 550 westward (Alvarado et al, 2014).…”