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The epidemic-type aftershock sequence (ETAS) model is the state-of-the-art approach for modelling short-term earthquake clustering and is preferable for short-term aftershock forecasting. However, due to the large variability of different earthquake sequences, the model parameters must be adjusted to the local seismicity for accurate forecasting. Such an adjustment based on the first aftershocks is hampered by the incompleteness of earthquake catalogues after a mainshock, which can be explained by a blind period of the seismic networks after each earthquake, during which smaller events with lower magnitudes cannot be detected. Assuming a constant blind time, direct relationships based only on this additional parameter can be established between the actual seismicity rate and magnitude distributions and those that can be detected. The ETAS-incomplete (ETASI) model uses these relationships to estimate the true ETAS parameters and the catalogue incompleteness jointly. In this study, we apply the ETASI model to the SE Türkiye earthquake sequence, consisting of a doublet of M 7.7 and M 7.6 earthquakes that occurred within less than half a day of each other on 6 February 2023. We show that the ETASI model can explain the catalogue incompleteness and fits the observed earthquake numbers and magnitudes well. A pseudo-prospective forecasting experiment shows that the daily number of detectable m ≥ 2 can be well predicted based on minimal and incomplete information from early aftershocks. However, the maximum magnitude (M max ) of the next day's aftershocks would have been overestimated due to the highly variable b value within the sequence. Instead, using the regional b value estimated for 2000–2022 would have well predicted the observed M max  values. [ABSTRACT FROM AUTHOR]

The Gutenberg–Richter (GR) and the Omori–Utsu (OU) law describe the earthquakes' energy release and temporal clustering and are thus of great importance for seismic hazard assessment. Motivated by experimental results, which indicate stress-dependent parameters, we consider a combined global data set of 127 main shock–aftershock sequences and perform a systematic study of the relationship between main shock-induced stress changes and associated seismicity patterns. For this purpose, we calculate space-dependent Coulomb Stress (ΔCFS) and alternative receiver-independent stress metrics in the surrounding of the main shocks. Our results indicate a clear positive correlation between the GR b -value and the induced stress, contrasting expectations from laboratory experiments and suggesting a crucial role of structural heterogeneity and strength variations. Furthermore, we demonstrate that the aftershock productivity increases nonlinearly with stress, while the OU parameters c and p systematically decrease for increasing stress changes. Our partly unexpected findings can have an important impact on future estimations of the aftershock hazard. [ABSTRACT FROM AUTHOR]

Aftershock forecast models are usually provided on a uniform spatial grid, and the receiver operating characteristic (ROC) curve is often employed for evaluation, drawing a binary comparison of earthquake occurrences or non-occurrence for each grid cell. However, synthetic tests show flaws in using the ROC for aftershock forecast ranking. We suggest a twofold improvement in the testing strategy. First, we propose to replace ROC with the Matthews correlation coefficient (MCC) and the F1 curve. We also suggest using a multi-resolution test grid adapted to the earthquake density. We conduct a synthetic experiment where we analyse aftershock distributions stemming from a Coulomb failure (ΔCFS) model, including stress activation and shadow regions. Using these aftershock distributions, we test the true ΔCFS model as well as a simple distance-based forecast (R), only predicting activation. The standard test cannot clearly distinguish between both forecasts, particularly in the case of some outliers. However, using both MCC- F1 instead of ROC curves and a simple radial multi-resolution grid improves the test capabilities significantly. The novel findings of this study suggest that we should have at least 8 % and 5 % cells with observed earthquakes to differentiate between a near-perfect forecast model and an informationless forecast using ROC and MCC- F1 , respectively. While we cannot change the observed data, we can adjust the spatial grid using a data-driven approach to reduce the disparity between the number of earthquakes and the total number of cells. Using the recently introduced Quadtree approach to generate multi-resolution grids, we test real aftershock forecast models for Chi-Chi and Landers aftershocks following the suggested guideline. Despite the improved tests, we find that the simple R model still outperforms the ΔCFS model in both cases, indicating that the latter should not be applied without further model adjustments. [ABSTRACT FROM AUTHOR]

The Collaboratory for the Study of Earthquake Predictability (CSEP) is an international effort to evaluate earthquake forecast models prospectively. In CSEP, one way to express earthquake forecasts is through a grid-based format: the expected number of earthquake occurrences within 0.1° × 0.1° spatial cells. The spatial distribution of seismicity is thereby evaluated using the Spatial test (S-test). The high-resolution grid combined with sparse and inhomogeneous earthquake distributions leads to a huge number of cells causing disparity in the number of cells, and the number of earthquakes to evaluate the forecasts, thereby affecting the statistical power of the S-test. In order to explore this issue, we conducted a global earthquake forecast experiment, in which we computed the power of the S-test to reject a spatially non-informative uniform forecast model. The S-test loses its power to reject the non-informative model when the spatial resolution is so high that every earthquake of the observed catalog tends to get a separate cell. Upon analysing the statistical power of the S-test, we found, as expected, that the statistical power of the S-test depends upon the number of earthquakes available for testing, e.g. with the conventional high-resolution grid for the global region, we would need more than 32 000 earthquakes in the observed catalog for powerful testing, which would require approximately 300 yr to record M ≥ 5.95. The other factor affecting the power is more interesting and new; it is related to the spatial grid representation of the forecast model. Aggregating forecasts on multi-resolution grids can significantly increase the statistical power of the S-test. Using the recently introduced Quadtree to generate data-based multi-resolution grids, we show that the S-test reaches its maximum power in this case already for as few as eight earthquakes in the test period. Thus, we recommend for future CSEP experiments the use of Quadtree-based multi-resolution grids, where available data determine the resolution. [ABSTRACT FROM AUTHOR]

Aftershock forecast models are usually provided on a uniform spatial grid, and the receiver operating characteristic (ROC) curve is often employed for evaluation, drawing a binary comparison of earthquake occurrences or non-occurrence for each grid cell. However, synthetic tests show flaws in using ROC for aftershock forecast ranking. We suggest a twofold improvement in the testing strategy. First, we propose to replace ROC with the Matthews correlation coefficient (MCC) and the F1 curve. We also suggest using a multi-resolution test grid adapted to the earthquake density. We conduct a synthetic experiment where we analyze aftershock distributions stemming from a Coulomb Failure (∆ CFS) model, including stress activation and shadow regions. Using these aftershock distributions, we test the true ∆ CFS model as well as a simple distance-based forecast (R), only predicting activation. The standard test cannot clearly distinguish between both forecasts, particularly in the case of some outliers. However, using both MCC-F1 instead of ROC curves and a simple radial multi-resolution grid improves the test capabilities significantly. Our findings suggest that to conduct meaningful tests, we should have at least 8 % and 5 % cells with observed earthquakes to differentiate between a near-perfect forecast model and an informationless forecast using ROC and MCC-F1, respectively. While we cannot change the observed data, we can adjust the spatial grid using a data-driven approach to reduce the disparity between the number of earthquakes and the total number of cells. Using the recently introduced Quadtree approach to generate multi-resolution grids, we test real aftershock forecast models for Chi-Chi and Landers aftershocks following the suggested guideline. Despite the improved tests, we find that the simple R model still outperforms the ∆ CFS model in both cases, indicating that the latter should not be applied without further model adjustments. [ABSTRACT FROM AUTHOR]

On 12 November 2017, an earthquake with a moment magnitude of 7.3 struck the west of Iran near the Iraq border. This event was followed about 9 and 12 months later by two large aftershocks of magnitude 5.9 and 6.3, which together triggered intensive seismic activity known as the 2017–2019 Kermanshah sequence. In this study, we analyse this sequence regarding the potential to forecast the spatial aftershock distribution based on information about the main shock and its largest aftershocks. Recent studies showed that classical Coulomb failure stress (CFS) maps are outperformed by alternative scalar stress quantities, as well as a distance-slip probabilistic model (R) and deep neural networks (DNN). In particular, the R-model performed best. However, these test results were based on the receiver operating characteristic (ROC) metric, which is not well suited for imbalanced data sets such as aftershock distributions. Furthermore, the previous analyses also ignored the potential impact of large secondary earthquakes. For the complex Kermanshah sequence, we applied the same forecast models but used the more appropriate MCC-F1 metric for testing. Similar to previous studies, we also observe that the receiver independent stress scalars yield better forecasts than the classical CFS values relying on the specification of receiver mechanisms. However, detailed analysis based on the MCC-F1 metric revealed that the performance depends on the grid size, magnitude cut-off and test period. Increasing the magnitude cut-off and decreasing the grid size and period reduce the performance of all methods. Finally, we found that the performance of the best methods improves when the source information of large aftershocks is additionally considered, with stress-based models outperforming the R model. Our results highlight the importance of accounting for secondary stress changes in improving earthquake forecasts. [ABSTRACT FROM AUTHOR]

The epidemic-type aftershock sequence (ETAS) model provides an effective tool for predicting the spatio-temporal evolution of aftershock clustering in short-term. Based on this model, a fully probabilistic procedure was previously proposed by the first two authors for providing spatio-temporal predictions of aftershock occurrence in a prescribed forecasting time interval. This procedure exploited the versatility of the Bayesian inference to adaptively update the forecasts based on the incoming information provided by the ongoing seismic sequence. In this work, this Bayesian procedure is improved: (1) the likelihood function for the sequence has been modified to properly consider the piecewise stationary integration of the seismicity rate; (2) the spatial integral of seismicity rate over the whole aftershock zone is calculated analytically; (3) background seismicity is explicitly considered within the forecasting procedure; (4) an adaptive Markov Chain Monte Carlo simulation procedure is adopted; (5) leveraging the stochastic sequences generated by the procedure in the forecasting interval, the N-test and the S-test are adopted to verify the forecasts. This framework is demonstrated and verified through retrospective early forecasting of seismicity associated with the 2017–2019 Kermanshah seismic sequence activities in western Iran in two distinct phases following the main events with Mw7.3 and Mw6.3, respectively. [ABSTRACT FROM AUTHOR]

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 15 s 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. Plain Language Summary: When a volcano shows the first sign of activity, it is challenging to determine whether and when the actual eruption will occur. Usually, researchers create earthquake lists and locate these events to assess this. However, an alternative and simpler method can be directly applied to continuous seismic data. We tested a method that assesses the complexity of signals. We first created synthetic data to find reasonable parameter settings for this method. While volcanoes do not erupt very often, frequent eruptions at geysers allow us to systematically study and compare several eruptions. We analyzed the continuous record of 63 eruptions of the Strokkur geyser, Iceland. Our results show a distinct pattern that repeats from one eruption to the next one. We also find a clear pattern that indicates about 15 s before the next eruption that an eruption will occur. We show that this method performs better in eruption forecasting than assessing the seismic noise or silence caused by the geyser. Key Points: Permutation Entropy (PE) is a simple tool to assess the complexity of a time seriesWe analyzed the PE evolution for 63 eruptive cycles of Strokkur geyser and found characteristic changes in PE during rechargePE is found to be an useful statistical predictor of the eruption times and highlights the precursor 15 s before eruptions [ABSTRACT FROM AUTHOR]

Strong earthquakes cause aftershock sequences that are clustered in time according to a power decay law, and in space along their extended rupture, shaping a typically elongate pattern of aftershock locations. A widely used approach to model earthquake clustering, the Epidemic Type Aftershock Sequence (ETAS) model, shows three major biases. First, the conventional ETAS approach assumes isotropic spatial triggering, which stands in conflict with observations and geophysical arguments for strong earthquakes. Second, the spatial kernel has unlimited extent, allowing smaller events to exert disproportionate trigger potential over an unrealistically large area. Third, the ETAS model assumes complete event records and neglects inevitable short-term aftershock incompleteness as a consequence of overlapping coda waves. These three aspects can substantially bias the parameter estimation and lead to underestimated cluster sizes. In this article, we combine the approach of Grimm et al. (Bulletin of the Seismological Society of America, 2021), who introduced a generalized anisotropic and locally restricted spatial kernel, with the ETAS-Incomplete (ETASI) time model of Hainzl (Bulletin of the Seismological Society of America, 2021), to define an ETASI space-time model with flexible spatial kernel that solves the abovementioned shortcomings. We apply different model versions to a triad of forecasting experiments of the 2019 Ridgecrest sequence, and evaluate the prediction quality with respect to cluster size, largest aftershock magnitude and spatial distribution. The new model provides the potential of more realistic simulations of on-going aftershock activity, e.g. allowing better predictions of the probability and location of a strong, damaging aftershock, which might be beneficial for short term risk assessment and disaster response. [ABSTRACT FROM AUTHOR]

Based on an analysis of continuous monitoring of farm animal behavior in the region of the 2016 M6.6 Norcia earthquake in Italy, Wikelski et al., 2020; (Ethology, 126(9), 2020, 931) conclude that animal activity can be anticipated with subsequent seismic activity and that this finding might help to design a "short‐term earthquake forecasting method." We show that this result is based on an incomplete analysis and misleading interpretations. Applying state‐of‐the‐art methods of statistics, we demonstrate that the proposed anticipatory patterns cannot be distinguished from random patterns, and consequently, the observed anomalies in animal activity do not have any forecasting power. [ABSTRACT FROM AUTHOR]

The Coulomb failure stress (CFS) criterion is the most commonly used method for predicting spatial distributions of aftershocks following large earthquakes. However, large uncertainties are always associated with the calculation of Coulomb stress change. The uncertainties mainly arise due to nonunique slip inversions and unknown receiver faults; especially for the latter, results are highly dependent on the choice of the assumed receiver mechanism. Based on binary tests (aftershocks yes/no), recent studies suggest that alternative stress quantities, a distance‐slip probabilistic model as well as deep neural network (DNN) approaches, all are superior to CFS with predefined receiver mechanism. To challenge this conclusion, which might have large implications, we use 289 slip inversions from SRCMOD database to calculate more realistic CFS values for a layered half‐space and variable receiver mechanisms. We also analyze the effect of the magnitude cutoff, grid size variation, and aftershock duration to verify the use of receiver operating characteristic (ROC) analysis for the ranking of stress metrics. The observations suggest that introducing a layered half‐space does not improve the stress maps and ROC curves. However, results significantly improve for larger aftershocks and shorter time periods but without changing the ranking. We also go beyond binary testing and apply alternative statistics to test the ability to estimate aftershock numbers, which confirm that simple stress metrics perform better than the classic Coulomb failure stress calculations and are also better than the distance‐slip probabilistic model. Key Points: Our tests for many mainshocks indicate that considering the variability of aftershock mechanisms significantly improves Coulomb forecastsA distance‐slip probabilistic model outperforms all stress‐based metrics concerning the forecast of the aftershock areaThe best forecasting metric for aftershock forecasting is simple shear scalars [ABSTRACT FROM AUTHOR]