A volcanic eruption is usually preceded by seismic precursors, but their interpretation and use for forecasting the eruption onset time remain a challenge. A part of the eruptive processes in open conduits of volcanoes may be similar to those encountered in geysers. Since geysers erupt more often, they are useful sites for testing new forecasting methods. We tested the application of Permutation Entropy (PE) as a robust method to assess the complexity in seismic recordings of the Strokkur geyser, Iceland. Strokkur features several minute-long eruptive cycles, enabling us to verify in 63 recorded cycles whether PE behaves consistently from one eruption to the next one. We performed synthetic tests to understand the effect of different parameter settings in the PE calculation. Our application to Strokkur shows a distinct, repeating PE pattern consistent with previously identified phases in the eruptive cycle. We find a systematic increase in PE within the last 15s before the eruption, indicating that an eruption will occur. We quantified the predictive power of PE, showing that PE performs better than seismic signal strength or quiescence when it comes to forecasting eruptions.

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.