Relationship between number of events and Coulomb stress changes

Hybrid models in which Coulomb stress changes are combined with statistical methods such as STEP (Short-Term Earthquake Probability) and ETAS (Epidemic-Type Aftershock Sequence) have recently been proposed as alternatives to Coulomb rate-state or statistical models on their own. However, there exists a question about whether to use the sign only or the actual magnitude of the stress change and both alternatives have been proposed. For example, the rate-and-state model uses the magnitude of the stress in their formulation. Here we investigate whether a correlation exists between the magnitude of the stress and either the number of triggered events or the change in earthquake rate. We study the following events: Denali, Landers, Hector Mine, Joshua Tree, Darfield, and the February and June 2011 events in the Canterbury series (New Zealand). We investigate the correlation between the triggered events and the magnitude of the stress change by calculating the average number of events in each interval of stress. We compare different sizes for the bin sizes for the stress (0.1, 0.2, and 0.5 MPa), and different exclusion distances (from 0 to 5 km from the fault planes). Initial results suggest a that the number of triggered events increases with the magnitude of the stress but the slope of that increase, and the stress range over which it is valid, varies from event to event.