Are triggering rates of labquakes universal? Inferring triggering rates from incomplete information

Abstract

The acoustic emission activity associated with recent rock fracture experiments under different conditions has indicated that some features of event-event triggering are independent of the details of the experiment and the materials used and are often even indistinguishable from tectonic earthquakes. While the event-event triggering rates or aftershock rates behave pretty much identical for all rock fracture experiments at short times, this is not the case for later times. Here, we discuss how these differences can be a consequence of the aftershock identification method used and show that the true aftershock rates might have two distinct regimes. Specifically, tests on a modified Epidemic Type Aftershock Sequence model show that the model rates cannot be correctly inferred at late times based on temporal information only if the activity rates or the branching ratio are high. We also discuss both the effect of the two distinct regimes in the aftershock rates and the effect of the background rate on the inter-event time distribution. Our findings should be applicable for inferring event-event triggering rates for many other types of triggering and branching processes as well.

Aftershock Triggering and Spatial Aftershock Zones in Fluid‐Driven Settings: Discriminating Induced Seismicity From Natural Swarms

“…The Long Valley Caldera data as well as the Fillmore data in Figures 3b and 3c may exhibit two different power-law regimes: an initial power-law with  0.8 p at   2 10 (day) t followed by a more rapid decay with exponent  1.5 p . Such a behavior is reminiscent of what has been observed in rock fracture (Baró & Davidsen, 2017;Davidsen et al, 2017) but it cannot be generalized to the other natural swarm case studies. Figures 3a-3d and Figures S8a and S8b also show that only for the Yuha desert and Mogul there are significant deviations from the master curve for smaller arguments.…”

What Controls the Presence and Characteristics of Aftershocks in Rock Fracture in the Lab?

“…over some range (Baró & Davidsen, 2017;Baró et al, 2013;Shcherbakov, Yakovlev, et al, 2005). This condition typically renders exponent values   2…”

Topological Properties of Epidemic Aftershock Processes

“…A clear example of swarm‐like aftershocks is given by the reconstructed triggering trees from the ultrasonic signals recording during the triaxial compression of sandstones (Davidsen et al, ). In this specific case, an ad‐hoc ETAS model can be fitted with an effective ratio α / b ∼0.5 (Baró & Davidsen, ). Notice that the distribution of tree sizes reported by (Zaliapin & Ben‐Zion, ) in hot areas fits a steep power law, which could match a if the data is above s c , typically low for α ≪ b .…”

“…Different modifications of the ETAS model have been proposed to account for more precise observations such as anisotropic spatial drift of the aftershock production and nonfactorizable magnitude dependencies (Ogata & Zhuang, 2006), generalized scaling forms (Davidsen & Baiesi, 2016;Vere-Jones, 2005) or more complex temporal decay forms (Baró & Davidsen, 2017;Davidsen et al, 2017). Such details are excluded from the following mathematical and numerical developments but will be recovered in the discussion section.…”