What Is Better Than Coulomb Failure Stress? A Ranking of Scalar Static Stress Triggering Mechanisms from 10⁵ Mainshock‐Aftershock Pairs

Abstract

Aftershocks may be triggered by the stresses generated by preceding mainshocks. The temporal frequency and maximum size of aftershocks are well described by the empirical Omori and Bath laws, but spatial patterns are more difficult to forecast. Coulomb failure stress is perhaps the most common criterion invoked to explain spatial distributions of aftershocks. Here we consider the spatial relationship between patterns of aftershocks and a comprehensive list of 38 static elastic scalar metrics of stress (including stress tensor invariants, maximum shear stress, and Coulomb failure stress) from 213 coseismic slip distributions worldwide. The rates of true‐positive and false‐positive classification of regions with and without aftershocks are assessed with receiver operating characteristic analysis. We infer that the stress metrics that are most consistent with observed aftershock locations are maximum shear stress and the magnitude of the second and third invariants of the stress tensor. These metrics are significantly better than random assignment at a significance level of 0.005 in over 80% of the slip distributions. In contrast, the widely used Coulomb failure stress criterion is distinguishable from random assignment in only 51–64% of the slip distributions. These results suggest that a number of alternative scalar metrics are better predictors of aftershock locations than classic Coulomb failure stress change.

Machine Learning in Seismology: Turning Data into Insights

“…Using Bayesian networks, Hincks et al (2018) modeled the joint conditional dependencies between parameters for the Oklahoma seismicity to understand the induced seismicity. Building on the preliminary analyses of Meade et al (2017), DeVries et al (2018) trained a deep NN to forecast aftershock locations using as input the static stress change tensor computed from finite-fault earthquake rupture models.…”

Is Coulomb Stress the Best Choice for Aftershock Forecasting?

“…The recent studies of Meade et al (2017) and DeVries et al (2018) claimed that simple stress metrics, which do not need any specification of the receiver mechanism, are superior to the Coulomb stress calculations. However, their claim can be challenged because of the unrealistic CFS calculations, which did not account for the known uncertainties in the CFS calculations, as well as the potential artifacts and shortcomings of their ROC analysis.…”

Fault Slip Model of the 2018 Mw 6.6 Hokkaido Eastern Iburi, Japan, Earthquake Estimated from Satellite Radar and GPS Measurements

“…Felzer and Brodsky [51] inferred that aftershocks may be driven by a mix of both dynamic and static stress changes. Furthermore, shear stress changes and the invariants of the stress tensor could better explain the aftershock patterns than could the ∆CSC, as reported by several previous studies [52][53][54]. Thus, further research is also needed to reveal the dominant triggering mechanism of the aftershocks following the 2018 Hokkaido eastern Iburi event.…”