Abstract
Seismicity models are probabilistic forecasts of earthquake rates to
support seismic hazard assessment. Physics-based models allow
extrapolating previously unsampled parameter ranges and enable
conclusions on underlying tectonic or human-induced processes. The
Coulomb Failure (CF) and the rate-and-state (RS) models are two
widely-used physics-based seismicity models both assuming pre-existing
populations of faults responding to Coulomb stress changes. The CF model
depends on the absolute Coulomb stress and assumes instantaneous
triggering if stress exceeds a threshold, while the RS model only
depends on stress changes. Both models can predict background earthquake
rates and time-dependent stress effects, but the RS model with its three
independent parameters can additionally explain delayed aftershock
triggering. This study introduces a modified CF model where the
instantaneous triggering is replaced by a mean time-to-failure depending
on the absolute stress value. For the specific choice of an exponential
dependence on stress and a stationary initial seismicity rate, we show
that the model leads to identical results as the RS model and reproduces
the Omori-Utsu relation for aftershock decays as well stress-shadowing
effects. Thus, both CF and RS models can be seen as special cases of the
new model. However, the new stress response model can also account for
subcritical initial stress conditions and alternative functions of the
mean time-to-failure depending on the problem and fracture mode.