Aftershock Sequence Research Articles

SB-ETAS: using simulation based inference for scalable, likelihood-free inference for the ETAS model of earthquake occurrences

The rapid growth of earthquake catalogs, driven by machine learning-based phase picking and denser seismic networks, calls for the application of a broader range of models to determine whether the new data enhances earthquake forecasting capabilities. Additionally, this growth demands that existing forecasting models efficiently scale to handle the increased data volume. Approximate inference methods such as inlabru, which is based on the Integrated nested Laplace approximation, offer improved computational efficiencies and the ability to perform inference on more complex point-process models compared to traditional MCMC approaches. We present SB-ETAS: a simulation based inference procedure for the epidemic-type aftershock sequence (ETAS) model. This approximate Bayesian method uses sequential neural posterior estimation (SNPE) to learn posterior distributions from simulations, rather than typical MCMC sampling using the likelihood. On synthetic earthquake catalogs, SB-ETAS provides better coverage of ETAS posterior distributions compared with inlabru. Furthermore, we demonstrate that using a simulation based procedure for inference improves the scalability from O(n2)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\mathcal {O}(n^2)$$\\end{document} to O(nlogn)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\mathcal {O}(n\\log n)$$\\end{document}. This makes it feasible to fit to very large earthquake catalogs, such as one for Southern California dating back to 1981. SB-ETAS can find Bayesian estimates of ETAS parameters for this catalog in less than 10 h on a standard laptop, a task that would have taken over 2 weeks using MCMC. Beyond the standard ETAS model, this simulation based framework allows earthquake modellers to define and infer parameters for much more complex models by removing the need to define a likelihood function.

Co-seismic and post-seismic slip associated with the 2021 Mw5.9 Arkalochori, Central Crete (Greece) earthquake constrained by geodetic data and aftershocks

The co-seismic and post-seismic deformation field associated with the Mw5.9 Arkalochori main shock that occurred in central Crete (Greece) on 27 September 2021 is analyzed using Copernicus Sentinel-1A & 1B images, GNSS measurements and seismological data. The fault geometry is constrained through the joint inversion of multiple datasets and the slip distribution for the co-seismic and post-seismic period is obtained using a homogeneous half-space elastic model and the Steepest Descent Method. The results indicate a blind normal fault striking 215° with a 55° dip to the northwest and the co-seismic slip model suggests a nearly circular main slip patch (8 × 6 km2) with a maximum slip of 0.98 m. Post-seismic displacements started rapidly after the main shock followed by a gradual decay as highlighted by the calculated InSAR time series. The temporal evolution of post-seismic slip is described by a simple logarithmic function, decaying faster at the southwest part of the fault. The cumulative afterslip model suggests that the maximum post-seismic slip of 0.23 m occurred within a similar depth range compared to the co-seismic one, yet with a shift towards the southwest. Post-seismic slip inside the main shock rupture area is sustained, highlighting the slow recovery of locking in the co-seismic slip region. Afterslip (seismic or aseismic) played a dominant role in the early post-seismic period acting complementarily to the main rupture. Indications suggest that the spatiotemporal evolution of the productive aftershock sequence may be driven afterslip, alongside other potential factors.

Estimating spatio-temporal variable parameters of Epidemic Type Aftershock Sequence model in a region with limited seismic network coverage: a case study of the East African Rift System

SUMMARY The Epidemic-Type Aftershock Sequence (ETAS) model is currently the most powerful statistical seismicity model that reproduces the general characteristics of earthquake clustering in space and time. However, its application can be hampered by biased parameter estimations related to earthquake catalogue deficiencies, particularly in regions where the spatial coverage of local recording networks is relatively poor. Here, we systematically investigate the possible influences of the effect introduced by data truncation through the choice of the cut-off magnitude (${{m}_{\rm cut}})$ and missing events due to heterogeneity of the seismic network on ETAS parameter estimates along the East African Rift System (EARS). After dividing the region into six source zones based on rheological and mechanical behaviours, the ETAS model is fitted to the earthquakes within each zone using the Davidon–Fletcher–Powell optimization algorithm. The fits and variations in parameter estimates are compared for each zone to the others and the seismological implications are discussed. We found that some parameters vary as a function of ${{m}_{\rm cut}}$ primarily driven by changes in catalogue size. Additionally, a systematic regional dependency of ETAS parameters is found across source zones. Furthermore, a median heat flow value for each analysed source zone in the EARS is calculated. In contrast to previous findings in other tectonic settings, the results reveal no significant correlations between the crustal heat flows and the ETAS parameters describing earthquake productivity (${{K}_0}$) and the relative efficiency of an earthquake with magnitude M to produce aftershocks ($\alpha $). Our findings have significant implications for understanding the mechanisms of earthquake interaction and, therefore, provide tight constraints on the model's parameters that may serve as a testbed for existing earthquake forecasting models in this region where the vulnerability of local buildings and structures exacerbate seismic risk.

Machine-learning based location of the 2021 MW 7.4 Maduo, Qinghai, China earthquake sequence: Insight into intraplate seismogenesis

On 22 May 2021, an MW 7.4 earthquake occurred in Maduo County, Qinghai Province, China, which is located on the Kunlun Mountain Pass-Jiangcuo fault inside the Bayan Har block, providing a good opportunity to investigate seismogenesis of large intraplate earthquakes. We analyze two years of continuous seismic data from June 2021 to June 2023, which were recorded at 34 portable seismic stations of the MaduoArray deployed in the source zone by our group. The LOC-FLOW workflow of automatic detection and location is applied to construct a complete and high-precision seismic catalog for the region, which includes machine-learning phase picking (PhaseNet), earthquake phase association (REAL), velocity model updating and station correction (VELEST), absolute earthquake location (HypoInverse), and relative location (HypoDD). As a result, 78,832 Maduo aftershocks and other local earthquakes are detected and relocated precisely. Our results show that the length of the Maduo aftershock zone is ∼170 km, which is mainly distributed along the NWW-SEE oriented Kunlun Mountain Pass-Jiangcuo fault, and there is a horsetail bifurcation feature at the eastern end of the aftershock sequence. The seismogenic fault is nearly vertical, and local seismicity occurs on both sides of the fault. Our results also show that there is no seismic gap or aftershock sparse area in the region. Previous studies have revealed a low-velocity and high-conductivity anomaly below the source zone, reflecting fluids ascending from the lower crustal flow. These results provide new insights into the cause of the 2021 Maduo earthquake.

Number of Aftershocks in Epidemic-type Seismicity Models

Summary The Epidemic Type Aftershock Sequence (ETAS) model describes how an earthquake generates its own aftershocks. The regular ETAS model assumes that distribution F of the number of direct aftershocks is Poissonian, however there is evidence suggesting that a geometric distribution might be more adequate. Let ${V}_M({m}_ \bullet )$ be the number of $m > M$ aftershocks generated by ${m}_ \bullet $event. In this study we consider the ${V}_M({m}_ \bullet )$ distribution within Epidemic-type Seismicity models, ETAS(F). These models include the Gutenberg-Richter law for magnitude and Utsu law for average ${m}_ \bullet $- productivity, but differ in the type of F distribution for the number $v({m}_ \bullet )$ of direct aftershocks. The class of F is quite broad and includes both the Poisson distribution, which is the basis for the regular ETAS model, and its possible alternative, the Geometric distribution. We replace the traditional $M = {m}_ \bullet - \Delta $ threshold in $\Delta $-analysis with $M = {m}_a - \Delta $ where ${m}_a$ is the distribution mode of the strongest aftershocks. Under these conditions we find the limit ${V}_M({m}_ \bullet )$ distribution at ${m}_ \bullet > > 1$. In the subcritical case, the limit distribution is extremely simple and identical to the $v({m}_\Delta )$ distribution with a suitable magnitude ${m}_\Delta $. This result allows us to validate both the priority of the geometric distribution of F for direct aftershocks and the very concept of epidemic-type clustering on global seismicity data.

Toward Real-Time Ground-Shaking-Intensity Forecasting Using ETAS and GMM: Insights from the Analysis of the 2022 Taitung Earthquake Sequence

Abstract Earthquake forecasting, combined with precise ground-shaking estimations, plays a pivotal role in safeguarding public safety, fortifying infrastructure, and bolstering the preparedness of emergency services. This study introduces a comprehensive workflow that integrates the epidemic-type aftershock sequence (ETAS) model with a preselected ground-motion model (GMM), facilitating accurate short-term forecasting of ground-shaking intensity (GSI), which is crucial for effective earthquake warning. First, an analysis was conducted on an earthquake catalog spanning from 1994 to 2022 to optimize the ETAS parameters. The dataset used in this analysis allowed for the further calculation of total, background, and clustering seismicity rates, which are crucial for understanding spatiotemporal earthquake occurrence. Subsequently, short-term earthquake activity simulations were performed using these up-to-date seismicity rates to generate synthetic catalogs. The ground-shaking impact on the target sites from each synthetic catalog was assessed by determining the maximum intensity using a selected GMM. This simulation process was repeated to enhance the reliability of the forecasts. Through this process, a probability distribution was created, serving as a robust forecasting for GSI at sites. The performance of the forecasting model was validated through an example of the Taitung earthquake sequence in September 2022, showing its effectiveness in forecasting earthquake activity and site-specific GSI. The proposed forecasting model can quickly deliver short-term seismic hazard curves and warning messages, facilitating timely decision making.

A fractional Hawkes process model for earthquake aftershock sequences

Abstract A new type of Hawkes process, known as the fractional Hawkes Process (FHP), has been recently introduced. This process uses a Mittag-Leffler density as the kernel function which is asymptotically a power law and so similar to the Omori–Utsu law, suggesting the FHP may be an appropriate earthquake model. However, it is currently an unmarked point process meaning it is independent of an earthquake’s magnitude. We extend the existing FHP, by incorporating Utsu’s aftershock productivity law and a time-scaling parameter from the fractional Zener Model to a marked version so that it may better model earthquake aftershock sequences. We call this model the ‘Seismic Fractional Hawkes Process’ (SFHP). We then estimate parameters via maximum likelihood and provide evidence for these estimates being consistent and asymptotically normal via a simulation study. The SFHP is then compared to the epidemic type aftershock sequence and FHP models on four aftershock sequences from Southern California and New Zealand. While it is inconclusive if the seismic fractional Hawkes process performs better in a retrospective predictive performance experiment, it does perform favourably against both models in terms of information criteria and residual diagnostics especially when the aftershock clustering is stronger.

Leveraging the ETAS model to forecast mining microseismicity

SUMMARY Mining operations result in changes of the subsurface stress field that can lead to the occurrence of microseismic events. The development of strategies for forecasting and avoidance of significant events is crucial for safe and efficient operations of mines. One such example, discussed here is the observed induced microseismicity in soft rock potash mines. It is primarily driven by the rock excavations but can also be triggered by preceding events or can result from the delayed effects of plastic creep of soft rocks. Therefore, it is important from seismic hazard assessment and risk mitigation points of view to understand the statistical aspects of microseismicity in potash or other types of mines. In this study, the temporal evolution of the induced microseismicity from a potash mine in Saskatchewan is analysed and modelled. Specifically, the epidemic type aftershock sequence model is used to approximate the occurrence rate of the induced mining microseismicity. The estimated parameters signify that the microseismicity displays swarm-type characteristics with limited inter-event triggering. Moreover, the Bayesian predictive framework is used to compute the probabilities of the occurrences of the largest expected events above a certain magnitude for prescribed forecasting time intervals during the evolution of the sequence. This approach for computing the probabilities allows one to incorporate fully the uncertainties of the model parameters. The Markov Chain Monte Carlo sampling of the posterior distribution are used to generate parameter chains to quantify their variability. Furthermore, several statistical tests are conducted to assess the credibility of the obtained retrospective forecasts compared to the observed microseismicity. The obtained results show that the developed approach can accurately forecast the number of events and intensity of the sequence. It also provides a framework for computing the probabilities for the largest expected events.

Log-Linear Model Analysis of Aftershock Sequences: A Review on the 6 February Earthquakes in Turkey

Researchers have conducted numerous studies on earthquakes and aftershocks, some of which have utilized statistical analysis methods. However, there is no direct research examining the interaction between variables thought to influence aftershocks following major earthquakes. In this study, 2194 aftershocks with a magnitude of 3 or higher that occurred after two major earthquakes in Turkey on February 6, 2023 were analyzed using log-linear models with respect to variables such as depth, magnitude, time, and city. At the end of the study, all four primary variables - city, magnitude, depth, and time - were found to be statistically significant. Based on the parameter estimation values, it was found that the probability of aftershocks occurring in Malatya was 1.17 times greater than in Adıyaman, 2.82 times greater than in Gaziantep, and 1.38 times greater than in Hatay, while the probability of aftershocks occurring in Kahramanmaraş was 3 times greater than in Malatya. Thus, it can be said that the aftershocks are influenced by the center of the major earthquake. Additionally, it was found that the probability of aftershocks with a magnitude between 3 and 3.5 was 1.4 times greater than those with a magnitude of 4 or higher, and the probability of aftershocks with a depth of less than 10 kilometers was 2 times greater. We believe that the results of this study will provide information on aftershocks that occur after major earthquakes and will be helpful for future studies.

Seismic fragility analysis of girder bridges under mainshock‐aftershock sequences based on input‐output hidden Markov model

AbstractCurrent seismic design codes for bridge structures do not account for the influence of aftershock sequences, which, to some extent, overestimate the seismic performance for bridges subjected to mainshock‐aftershock (MS‐AS) scenarios. To address the great need for ground motion sequences tailored to specific research sites for fragility analysis, this study proposes a method for generating artificial MS‐AS ground motion sequences based on the evolutional bimodal Kanai–Tajimi model and the Epidemic–Type Aftershock Sequence model. We establish a framework for MS‐AS fragility analysis using an input–output Hidden Markov Model (IOHMM), where the damage states (DS) of bridge piers are considered unobservable and are inferred statistically through damage indices in an unsupervised manner. Model parameters are trained using intensity measure (IM) sequences and damage index (DI) sequences. Fragility curves for both the mainshock and state‐dependent aftershocks considering multiple aftershocks are formulated based on the initial state probability and state transition probabilities of the proposed IOHMM. The fragility analysis results reveal that as the initial seismic damage level increases, the probability of aftershocks causing higher damage levels in the structure also increases, highlighting the significant impact of aftershocks on structural damage increments. Furthermore, we extend the proposed model to a bivariate seismic intensity measure and develop fragility surfaces. The proposed framework provides a novel approach and insights for tackling seismic fragility under multiple aftershocks.

Distribution Related to All Samples and Extreme Events in the ETAS Cluster

Abstract The probabilistic approach of statistical seismology plays a fundamental role in analyzing the evolution of an earthquake sequence at different scales to deliver reliable forecasts of complex earthquake phenomena. This study contributes to the field by extending previous results relative to the extreme events probability. We derive the explicit formulation of the probability of extreme events in any seismic cluster generated by the epidemic-type aftershock sequence model, as a function of time, space, and magnitude. The results give insights into understanding the distinguishing features between mainshocks and foreshocks, thus helping to shed light on earthquake prediction.

Fluids-Triggered Swarm Sequence Supported by a Nonstationary Epidemic-Like Description of Seismicity

Abstract The variation in Coulomb failure stress (CFS) plays a crucial role in either increasing or decreasing seismic activity. In cases in which the standard epidemic-type aftershock sequence (ETAS) model does not adequately fit seismicity data, the potential deviations from empirical laws are explored. These deviations may arise from stress changes imparted by aseismic transients that lead swarm-like earthquake sequences to occur. The time-dependent background rate of seismicity serves as an indicator for detecting changes in CFS or the presence of transient aseismic forcing. We investigate seismic anomalies in the slow deforming Mt. Pollino, Italy seismogenic area, where a 4-yr-long swarm-like sequence partially filled a previously hypothesized seismic gap. The primary process of this seismic swarm is still under debate. Employing a nonstationary ETAS model on a new template-matching high-resolution catalog, we suggest a slow-slip event and fluid interplay as the main aseismic forces in triggering and developing this swarm-like sequence.

Quantifying the expansion rates of aftershock zones for magnitude-7 class earthquakes around the Japanese archipelago

Earthquakes (mainshocks) trigger sequences of aftershocks, the frequency of which diminishes following a power-law decay, while the spatial domain of these aftershocks extends logarithmically over time. The delineation of the aftershock zone can be modulated by variables beyond the magnitude of the mainshock, encompassing the location of the fault (whether the fault is at a plate boundary), the depth at which the event occurs, and the prevailing local stress conditions. Here, we evaluate the expansion rate of aftershock zones by analyzing earthquakes of magnitude-7 class in the vicinity of the Japanese archipelago. Prior studies have offered approximate assessments of expansion rates; however, our approach involves the utilization of a straightforward algorithm for the automated estimation of this metric, facilitating the compilation of a catalog. Across the dataset, no pronounced correlations were discerned between the expansion rate and other examined parameters. Yet, an inverse relationship is identified between the expansion rate and the b value of aftershocks for mainshocks occurring at plate boundaries. This observation suggests that the expansion rate of aftershock zones predominantly mirrors the stress field following the mainshock. Such a pattern is not detected in mainshocks occurring within the plate's interior. While the expansion rate of aftershock zones is likely influenced by various factors, aftershock zones may expand more rapidly with higher differential stress in areas surrounding hypocenters of major interplate earthquakes of magnitude 8 or 9.

Background and clustering characteristics of recent seismicity in Southwestern China

SUMMARY This study analysed seismicity in southwestern China (1 January 2008 to 30 June 2021) using the earthquake catalogue compiled by the China Earthquake Network Center and four different space–time Epidemic-Type Aftershock Sequence models: the 2-D point-source (PS) model, the 2-D finite-source (FS) model, the 3-D PS model and the 3-D FS model. Our objective was to understand the features of the background seismicity and the patterns of earthquake clusters to better evaluate the regional seismic hazard. We carefully investigated the aftershock sequences that followed 7 of the 10 MS ≥ 6.0 earthquakes that have struck this region since the occurrence of the 2008 Wenchuan MS 8.0 earthquake [i.e. the Panzhihua (31 August 2008; MS 6.0), Yaoan (9 July 2009; MS 6.0), Lushan (20 April 2013; MS 7.0), Ludian (3 August 2014; MS 6.5), Jinggu (7 October 2014; MS 6.6), Kangding (11 November 2014; MS 6.3) and Yangbi (21 May 2021; MS 6.4) earthquakes]. Our results revealed the following. (1) The background seismicity level for natural earthquakes is usually stable but can experience sudden change due to major events, such as the 2014 Ludian MS 6.5, and the 2014 Jinggu MS 6.6 events. Such changes in the background rate can reach 50 per cent. (2) Reservoir-induced earthquakes substantially increase the level of regional seismicity, indicating that they cannot be ignored when analysing natural seismicity and evaluating regional earthquake hazards. (3) Events triggered directly by the main shock occur mostly in regions adjacent to areas with large coseismic slip, showing a pattern complementary to the main shock ruptures.

The 2013 Mw 6.2 Shonbeh (Kaki) earthquake (Zagros-Iran): seismo-tectonic implications for the Kazerun shear transition zone from high-resolution aftershock and InSAR data analysis

SUMMARY The aim of this study is to investigate the aftershock sequence data recorded by a dense temporary seismological network deployed in the epicentral area of the 2013 April 9 Shonbeh (Kaki) earthquake, located in the south of the Simply Folded Belt of the Zagros (Iran). For a comprehensive understanding, coseismic displacements of the Shonbeh earthquake have been investigated using Interferometric Synthetic Aperture Radar (InSAR) data. The epicentral distribution of high-resolution relocated aftershocks shows NW–SE and N–S trending of seismicity. The aftershocks are confined between ∼3 and ∼14 km depth, which implies that the rupture occurred mostly within the sedimentary cover beside the fault parameters retrieved from InSAR modelling. Projection of precisely located aftershocks on NE-oriented section and InSAR ground displacement data are consistent with both NW-trending NE- and SW-dipping fault segments. We observe a NNW–SSE right-lateral strike-slip motions that accommodate oblique convergence and differential motion between the North and Central Zagros. The spatial pattern and focal mechanisms of aftershocks are consistent with a distributed deformation between NW–SE trending reverse and N–S trending right-lateral strike-slip fault segments in the south of the Kazerun transition zone that accommodates a wide shear zone.

Reduced seismic activity after mega earthquakes

Mainshocks are often followed by increased earthquake activity (aftershocks). According to the Omori-Utsu law, the rate of aftershocks decays as a power law over time. While aftershocks typically occur in the vicinity of the mainshock, previous studies have suggested that mainshocks can also trigger earthquakes in remote locations, beyond the range of aftershocks. Here we analyze the rate of earthquakes that occurred after mega-earthquakes (with a magnitude of 7.5 or higher) and show that there is a significantly higher occurrence of mega-earthquakes that are followed by reduced activity beyond a certain distance from the epicenter compared to the expected frequency; the results are based on statistical tests we developed. However, the remote earthquake rate after the strongest earthquakes (magnitude ≥8) can also be significantly higher than the expected rate. Comparing our findings to the global Epidemic-Type Aftershock Sequence model, we find that the model does not capture the above findings, hinting at a potential missing mechanism. We suggest that the reduced earthquake rate is due to the release of global energy/tension after substantial mainshock events. This conjecture holds the potential to enhance our comprehension of the intricacies governing post-seismic activity.

Synthesis of Current Seismicity and Tectonics Along the 1857 Mw7.9 Fort Tejon Earthquake Rupture and the Southernmost San Andreas Fault, California, USA

AbstractWe evaluate seismicity and tectonics along the San Andreas Fault (SAF) in southern California to elucidate ongoing near‐field crustal deformation processes. The principal slip surfaces (PSSs) or the fault core that accommodate major earthquakes, form the boundary between the tectonic plates. We analyze seismicity catalogs extending back to 1857, 1932, and 1981 with progressively improved magnitude of completeness and spatial resolution. The 1857 to present statewide catalog that is complete at M5.5+ documents minimal aftershock activity for the Mw7.9 1857 and 1906 Mw7.8 San Francisco earthquakes. The higher quality 1932 and 1981 catalogs show that the PSSs (the rupture zone) of the 1857 Mw7.9 Fort Tejon earthquake exhibits remarkable seismic quiescence both in the core and in the adjacent extended‐damage zone. Further south, the fault core is still aseismic but the shape of the SAF is more complex, and the rate of adjacent seismicity is much higher. This fault complexity and the seismicity rate are larger the more the strike of the SAF deviates from the Pacific plate velocity‐vector direction. The focal mechanisms of the SAF adjacent earthquakes are also heterogeneous and rarely have strikes and dips that are consistent with slip on the nearby PSSs. We infer that the southern SAF is locked, and a lack of seismicity at the core of the fault may be a standard feature of faults that almost exclusively accommodate high‐slip rates by producing major earthquakes. Correspondingly future aftershock sequences of major earthquakes on the southern SAF will likely have below average aftershock productivity.

Performance of AI-Based Phase Picking and Event Association Methods after the Large 2023 Mw 7.8 and 7.6 Türkiye Doublet

ABSTRACT On 6 February 2023, a devastating earthquake doublet consisting of Mw 7.8 and 7.6 events separated by about 9 hr struck the southeastern part of Türkiye. The developing aftershock sequence contained thousands of events during the first few days and overwhelmed the routine algorithms handling their detection and location. In addition, several stations temporarily lost real-time contact and came online again later. At the same time the Omori decay of the aftershock event rate reduced the event frequency and allowed for inclusion of progressively smaller-magnitude events with time. One possibility to help deal with such a complex situation is the use of machine learning (ML) methods to generate earthquake catalogs with a substantially higher number of events. Here, we present high-resolution earthquake catalogs derived with two ML association methods for the first five days of the aftershock sequence of this doublet. In terms of the number of reliably located events, the event catalog created from PhaseNet picks and the GENIE phase association method outperforms both the routine regional catalog and the second ML-derived catalog obtained from the GaMMA phase association method. Although both GaMMA and GENIE catalogs detect about 6 times more events than the routine catalog, GENIE associates on average about double the phases to a single event than GaMMA, which results in better constrained event locations. The spatiotemporal evolution of the event rates is sensitive to changes in the network geometry due to variable station availability. During the first few days, no decay of the event rate in the enhanced catalog is observed due to the inclusion of progressively smaller-magnitude events with time and increased station availability. This study indicates that ML-derived earthquake catalogs for challenging time periods like the early aftershock sequences of large earthquakes have the potential to significantly improve routine event catalogs.

Bayesian earthquake forecasting approach based on the epidemic type aftershock sequence model

The epidemic type aftershock sequence (ETAS) model is used as a baseline model both for earthquake clustering and earthquake prediction. In most forecast experiments, the ETAS parameters are estimated based on a short and local catalog, therefore the model parameter optimization carried out by means of a maximum likelihood estimation may be not as robust as expected. We use Bayesian forecast techniques to solve this problem, where non-informative flat prior distributions of the parameters is adopted to perform forecast experiments on 3 mainshocks occurred in Southern California. A Metropolis–Hastings algorithm is employed to sample the model parameters and earthquake events. We also show, through forecast experiments, how the Bayesian inference allows to obtain a probabilistic forecast, differently from one obtained via MLE.Graphical

SuiETAS: Developing and Testing ETAS-Based Earthquake Forecasting Models for Switzerland

ABSTRACT We present the development and testing of multiple epidemic-type aftershock sequence (ETAS)-based earthquake forecasting models for Switzerland, aiming to identify suitable candidate models for operational earthquake forecasting (OEF) at the Swiss Seismological Service. We consider seven model variants: four variants use parameters obtained through fitting the ETAS model to the Swiss earthquake catalog, and three use generic parameters that were fit to Californian seismicity or global seismicity from regions tectonically similar to Switzerland. The model variants use different pieces of information from the current state-of-the-art time-independent earthquake rate forecast underlying the Swiss seismic hazard model (SUIhaz2015), and one is calibrated on a larger local data set that includes smaller earthquakes by allowing a time-dependent estimate of the completeness magnitude. We test all variants using pseudoprospective short-term (7-day) forecasting experiments and retrospective long-term (30-year) consistency tests. Our results suggest that all ETAS-based models outperform the time-independent SUIhaz2015 forecast in the short term, but two of the model variants overestimate event numbers in the long term. ETAS parameters are found not to be universally transferrable across tectonic regimes, and region-specific calibration is found to add value over generic parameters. Finally, we rank all model variants based on six criteria, including the results of the pseudoprospective and retrospective tests, as well as other criteria such as model run time or consistency with the existing long-term model, using a multicriteria decision analysis approach. Based on this ranking, we propose the ETAS model calibrated on the Swiss catalog, and with the spatial background seismicity distribution of SUIhaz2015 as the ideal candidate for the first Swiss OEF system. All procedures and choices involved in the development and testing of the Swiss ETAS model follow recently established expert recommendations and can act as a reference in the establishment of time-variant earthquake forecasting models for other regions.