Decay of aftershock activity for Japanese earthquakes

Abstract

[1] Aftershock decay is often correlated with the modified Omori's law: dN/dt = t À1 (1 + t/c) Àp , where dN/dt is the occurrence rate of aftershocks with magnitudes greater than a lower cutoff m, t is time since a mainshock, t and c are characteristic times, and p is an exponent. Extending this approach, we derive two possibilities: (1) c is a constant independent of m and t scales with m and (2) c scales with m and t is a constant independent of m. These two are tested by using aftershock sequences of four relatively recent and large earthquakes in Japan. We first determine for each sequence the threshold magnitude above which all aftershocks are completely recorded and use only events above this magnitude. Then, visual inspection of the decay curves and statistical analysis shows that the second possibility is the better approximation for our sequences. This means that the power law decay of smaller aftershocks starts after larger times from the mainshock. We find a close association of our second result with a solution obtained for a damage mechanics model of aftershock decay. The time delays associated with aftershocks, according to the second possibility, can be understood as the times needed to nucleate microcracks (aftershocks). Our result supports the idea that the c value is a real consequence of aftershock dynamics associated with damage evolution.

Statistical analysis of the 2010MW7.1 Darfield Earthquake aftershock sequence

“…Figure 3 shows that c(m c ) systematically increases with decreasing m c . This shows that the c(m c ) value is more than merely an artefact of incompleteness in the early part of the catalogue as observed for other aftershock sequences around the world (Shcherbakov et al , 2005(Shcherbakov et al , 2006Nanjo et al 2007). …”

“…Aftershocks are an essential part of any major seismic sequence. They occur due to static and dynamic stress redistribution in the vicinity of major earthquakes (Kisslinger 1996;Shcherbakov et al 2005). They also represent an outcome of complex triggering mechanisms which operate in a highly heterogeneous system of non-linearly interacting faults embedded in a visco-elastic medium (Ben-Zion 2008).…”

Anomalous decrease in relatively large shocks and increase in the p and b values preceding the April 16, 2016, M7.3 earthquake in Kumamoto, Japan

“…According to previous cases (e.g., Helmstetter et al 2006;Nanjo et al 2007), M c depends on time t. In creating Fig. 1, we used a moving window approach, whereby the window covered 200 events (red).…”

Triggering Processes in Rock Fracture

“…2) indicate that triggering is absent. This implies that the suggested mechanisms for triggering and the OU relation in damage mechanics-viscoelastic effects [47][48][49] (Figs. S2, S3 [37]).…”