A review on scaling of earthquake faults

Abstract

Scaling of earthquake faults is important not only for earthquake physics but also seismic hazard assessment. There have been many studies about this topic. It is significant to compile, review, and discuss those studies. This work reviews the observations and modeling of scaling of fault parameters, including the fault length (L), fault width (W), fault area (A), average displacement (D o), maximum displacement (D max), seismic moment (M o), and static stress drop (Δσ). Major issues for reviewing in this work are: (1) assumptions of constant Δσ, of earthquakes and self-similarity of faults; (2) the Land W-models; (3) the L-D o and L-D max scaling relationships; (4) the M o-D o and M o-D max scaling relationships; (5) the D o-A scaling relationships; (6) the M o-A scaling relationships; (7) the L-W scaling relationship; (8) the M o-L and M o-W scaling relationships; and (9) modeling of the M o-L scaling based on the onedimensional spring-slider model in the presence of velocity-weakening friction.

Acoustic Emission during Initiation of a Shear Band in a Metallic Glass as a Method for Verification of the Existence of Scale Invariance

“…In particular, it is noted in [25] that seismic moment M0 and the scale of an earthquake of length L (of the shear band length, but only in the case of seismodislocation length) are connected by relation 2 0 M L . From the analysis of 1308 seismic events, the following interrelation between the studied seismic energy and the seismic moment was established in [26]:…”

Simulation of seismic triggering and failure time perturbations associated with the 30 October 2020 Samos earthquake (Mw 7.0)

“…Instead, we varied the asperity patch length to test the triggering effect on different magnitude earthquakes. For events with Mw < 5, patch length (L) is calculated using the empirical relation between scalar seismic moment (M o ) and circular rupture area (A) from (Wang, 2018), given by…”

“…For earthquakes with Mw < 3.5, ~ 3.5 and 4, L which is equal to the diameter of circular patch is assigned as ~ 0.5, 0.64 and 1.25 km respectively (Table 1). On the other hand, large crustal earthquakes are limited in rupture width and may display a high level of slip heterogeneity, and thus, L of characteristic large events are not empirical scaled with seismic moment (M 0 ) but kept fixed to 5 km following previous simulations works (Wang, 2018;Sopaci and Özacar, 2020). By considering the present ambiguity associated with triggered fault, the range of slip rates (1-5 mm/yr) are tested on both vertical strike-slip and 60° dipping normal faults.…”

A review on studies of the 1999 Chi-Chi Earthquake for resolving the debatable problems in earthquake physics

“…Figure 7 displays the seismogenic zone and ruptured area of an earthquake. In the figure, L, W, and u(x, y, t) represent the fault length, fault width, and time-and-space-dependent displacement with a final slip of D. A detailed description about the model parameters of a seismogenic zone can be seen in Wang (2018a). The bottom line represents the crustal brittle-ductile transition layer with temperature of 300 -450 °C.…”

“…In fact, numerous factors, including wear process, plasticity, strain rate etc., can change the value of w and thus influence the type of earthquake occurrence (see Wang 2018b). Wang (2018a) studied the effect of wear process in the fault zone on earthquake recurrence. His results show that strong wear process can result in aperiodic behavior of earthquakes and thus neither the time-predictable model nor the slip-predictable one can describe the temporal variation in cumulative slip of earthquakes.…”