A Coulomb Stress Response Model for Time‐Dependent Earthquake Forecasts. Issue 9 (31st August 2022) - Dahm, Torsten; Hainzl, Sebastian
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. Plain Language Summary: One of the most pressing questions in earthquake physics is understanding where and when earthquakes occur and how seismicity is related to stress changes in the Earth's crust. This question is even more important today because humans are increasingly influencing stresses in the Earth by exploiting the subsurface. So far, two classes of physics‐based seismicity models have been used primarily. One assumes instantaneous earthquake occurrence when stress exceeds a threshold, and the other is based on the nucleation of earthquakes according to friction laws determined in the laboratory. Both models are very different in their approaches, have advantages and disadvantages, and are limited in their applicability. In this paper, we introduce a new concept of seismicity models, which is very simple and short to derive and combines the strengths of both previous models, as shown in various applications to human‐related seismicity. The forecasts of both traditional models turn out to be special cases of the new model. Key Points: We introduce a modified Coulomb Failure seismicity model in which a mean time‐to‐failure replaces instantaneous triggering The model explains the main features of time‐dependent seismicity, including aftershock activity and stress shadow effects As a special case, it includes the rate‐state model solutions but can also handle subcritical stresses and other fracture types