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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]

Computationally efficient alternatives are proposed to the likelihood-based tests employed by the Collaboratory for the Study of Earthquake Predictability for assessing the performance of earthquake likelihood models in the earthquake forecast testing centers. For the conditional L-test, which tests the consistency of the earthquake catalogue with a model, an exact test using convolutions of distributions is available when the number of earthquakes in the test period is small, and the central limit theorem provides an approximate test when the number of earthquakes is large. Similar methods are available for the R-test, which compares the likelihoods of two competing models. However, the R-test, like the N-test and L-test, is fundamentally a test of consistency of data with a model. We propose an alternative test, based on the classical paired t-test, to more directly compare the likelihoods of two models. Although approximate and predicated on a normality assumption, this new T-test is not computer-intensive, is easier to interpret than the R-test, and becomes increasingly dependable as the number of earthquakes increases. [ABSTRACT FROM AUTHOR]

The earthquake size distribution follows, in most instances, a power law, with the slope of this power law, the ‘b value’, commonly used to describe the relative occurrence of large and small events (a high b value indicates a larger proportion of small earthquakes, and vice versa). Statistically significant variations of b values have been measured in laboratory experiments, mines and various tectonic regimes such as subducting slabs, near magma chambers, along fault zones and in aftershock zones. However, it has remained uncertain whether these differences are due to differing stress regimes, as it was questionable that samples in small volumes (such as in laboratory specimens, mines and the shallow Earth's crust) are representative of earthquakes in general. Given the lack of physical understanding of these differences, the observation that b values approach the constant 1 if large volumes are sampled was interpreted to indicate that b = 1 is a universal constant for earthquakes in general. Here we show that the b value varies systematically for different styles of faulting. We find that normal faulting events have the highest b values, thrust events the lowest and strike-slip events intermediate values. Given that thrust faults tend to be under higher stress than normal faults we infer that the b value acts as a stress meter that depends inversely on differential stress. [ABSTRACT FROM AUTHOR]

While deterministically predicting the time and location of earthquakes remains impossible, earthquake forecasting models can provide estimates of the probabilities of earthquakes occurring within some region over time. To enable informed decision‐making of civil protection, governmental agencies, or the public, Operational Earthquake Forecasting (OEF) systems aim to provide authoritative earthquake forecasts based on current earthquake activity in near‐real time. Establishing OEF systems involves several nontrivial choices. This review captures the current state of OEF worldwide and analyzes expert recommendations on the development, testing, and communication of earthquake forecasts. An introductory summary of OEF‐related research is followed by a description of OEF systems in Italy, New Zealand, and the United States. Combined, these two parts provide an informative and transparent snapshot of today's OEF landscape. In Section 4, we analyze the results of an expert elicitation that was conducted to seek guidance for the establishment of OEF systems. The elicitation identifies consensus and dissent on OEF issues among a non‐representative group of 20 international earthquake forecasting experts. While the experts agree that communication products should be developed in collaboration with the forecast user groups, they disagree on whether forecasting models and testing methods should be user‐dependent. No recommendations of strict model requirements could be elicited, but benchmark comparisons, prospective testing, reproducibility, and transparency are encouraged. Section 5 gives an outlook on the future of OEF. Besides covering recent research on earthquake forecasting model development and testing, upcoming OEF initiatives are described in the context of the expert elicitation findings. Plain Language Summary: The exact location, time, and magnitude of future earthquakes cannot be predicted. However, based on past earthquake sequences, it is possible to assess probabilities for future earthquakes. This is called earthquake forecasting. Operational Earthquake Forecasting (OEF) systems are designed to provide near‐real‐time authoritative earthquake forecasts, based on current earthquake activity, to aid the decision‐making of various societal stakeholders. Setting up these systems is complex, involving decisions about which model to use, how to best test the model, and how to turn earthquake probability estimates into practical information. This review captures the current state of OEF worldwide and analyzes expert recommendations on the development, testing, and communication of earthquake forecasts. Section 2 provides an overview of OEF‐related research and the background knowledge required to understand the other parts. Section 3 describes existing OEF systems of Italy, New Zealand, and the United States in detail. Section 4 discusses an elicitation of expert views on modeling, testing, and communicating earthquake forecasts (Mizrahi, Dallo, & Kuratle, 2023, https://doi.org/10.3929/ethz‐b‐000637239). Data from the elicitation allow to identify consensus and dissent on OEF issues and provide guidance for future earthquake forecasting efforts. Finally, Section 5 gives an outlook on future OEF‐related research and planned OEF efforts at various institutions. Key Points: We capture the state of earthquake forecasting systems in Italy, New Zealand, and the United States, and future plans in these and other countriesExperts encourage benchmark comparison, prospective testing, reproducibility and transparency, but avoid endorsing specific models or testsExperts stress the need to co‐design forecast communication products with end‐users to ensure their societal relevance and usefulness [ABSTRACT FROM AUTHOR]

The Collaboratory for the Study of Earthquake Predictability (CSEP) has expanded over the years to many different testing areas hosted at multiple testing centers. Hundreds of earthquake forecast models have been submitted to CSEP and are being tested. New testing metrics were developed and implemented and a lot of progress was made to establish CSEP as an institution that cannot be ignored when issuing earthquake forecasts. Its rigor and independence became the standard in evaluating earthquake forecasts and in reporting on the results.In the framework of the testing activities of the Global Earthquake Model, one line of expanding the capabilities of CSEP was developed at GFZ Potsdam. The group there applied the mechanisms that CSEP introduced to earthquake forecast models to the area of intensity prediction equations (IPEs) and ground-motion prediction equations (GMPEs). The first truly prospective tests were carried out on IPEs for Italy and also on GMPEs for Japan and New Zealand. This new set of tests helped CSEP move into the hazard domain and increase the relevance of its results to the hazard community. Finally, the group at GFZ Potsdam has also conducted the first prospective test of the US national seismic hazard maps. Although these tests have been successful and well-received, they have also shown the limitations of the CSEP approach. Many aspects of seismic hazard or earthquake forecasting remain inherently untestable if only the model forecasts are tested and not the model ingredients. We propose to continue along the lines of the GFZ Potsdam developments and create new areas of activity for CSEP, namely targeted experiments that cannot be conducted with the current CSEP software system. As part of the eGSIM (European Ground Shaking Intensity Models) service, we will introduce permanent testing of IPEs and GMPEs to the testing center to establish strong performance records to be used in hazard models. Further targeted experiments include the predictive power of b-values, discrimination of foreshocks for short-term forecasting, as well as a deeper look into precursory phenomena applying CSEP-style rigorous testing. We support including testability in future hazard models or their components to move to better testable seismic hazard models. Finally, to expand into the risk domain, we will test exposure models against new and independent data. [ABSTRACT FROM AUTHOR]

Slowly-compressed single crystals, bulk metallic glasses (BMGs), rocks, granular materials, and the earth all deform via intermittent slips or 'quakes'. We find that although these systems span 12 decades in length scale, they all show the same scaling behavior for their slip size distributions and other statistical properties. Remarkably, the size distributions follow the same power law multiplied with the same exponential cutoff. The cutoff grows with applied force for materials spanning length scales from nanometers to kilometers. The tuneability of the cutoff with stress reflects 'tuned critical' behavior, rather than self-organized criticality (SOC), which would imply stress-independence. A simple mean field model for avalanches of slipping weak spots explains the agreement across scales. It predicts the observed slip-size distributions and the observed stress-dependent cutoff function. The results enable extrapolations from one scale to another, and from one force to another, across different materials and structures, from nanocrystals to earthquakes. [ABSTRACT FROM AUTHOR]

The Collaboratory for the Study of Earthquake Predictability was developed to prospectively test earthquake forecasts through reproducible and transparent experiments within a controlled environment. From January 2006 to December 2010, the Regional Earthquake Likelihood Models (RELM) Working Group developed and evaluated thirteen time-invariant prospective earthquake mainshock forecasts. The number, spatial and magnitude components of the forecasts were compared to the observed seismicity distribution using a set of likelihood-based consistency tests. In this RELM experiment update, we assess the long-term forecasting potential of the RELM forecasts. Additionally, we evaluate RELM forecast performance against the Uniform California Earthquake Rupture Forecast (UCERF2) and the National Seismic Hazard Mapping Project (NSHMP) forecasts, which are used for seismic hazard analysis for California. To test each forecast's long-term stability, we also evaluate each forecast from January 2006 to December 2015, which contains both five-year testing periods, and the 40- year period from January 1967 to December 2006. Multiple RELM forecasts, which passed the N-test during the retrospective (January 2006 to December 2010) period, overestimate the number of events from January 2011 to December 2015, although their forecasted spatial distributions are consistent with observed earthquakes. Both the UCERF2 and NSHMP forecasts pass all consistency tests for the two five-year periods; however, they tend to underestimate the number of observed earthquakes over the 40-year testing period. The smoothed seismicity model HELMSTETTER-ET-AL.MAINSHOCK outperforms both United States Geological Survey (USGS) models during the second five-year experiment, and contains higher forecasted seismicity rates than the USGS models at multiple observed earthquake locations. [ABSTRACT FROM AUTHOR]

Natural hazards threaten millions of people all over the world. To address this risk, exposure and vulnerability models with high resolution data are essential. However, in many areas of the world, exposure models are rather coarse and are aggregated over large areas. Although OpenStreetMap (OSM) offers great potential to assess risk at a detailed building-by-building level, the completeness of OSM building footprints is still heterogeneous. We present an approach to close this gap by means of crowd-sourcing based on the mobile app MapSwipe, where volunteers swipe through satellite images of a region collecting user feedback on classification tasks. For our application, MapSwipe was extended by a completeness feature that allows to classify a tile as "no building", "complete" or "incomplete". To assess the quality of the produced data, the completeness feature was applied to four regions. The MapSwipe-based assessment was compared with an intrinsic approach to quantify completeness and with the prediction of an existing model. Our results show that the crowd-sourced approach yields a reasonable classification performance of the completeness of OSM building footprints. Results showed that the MapSwipe-based assessment produced consistent estimates for the case study regions while the other two approaches showed a higher variability. Our study also revealed that volunteers tend to classify nearly completely mapped tiles as "complete", especially in areas with a high OSM building density. Another factor that influenced the classification performance was the level of alignment of the OSM layer with the satellite imagery. [ABSTRACT FROM AUTHOR]

On 28 September 2004 there was an earthquake of magnitude 6.0 at Parkfield, California. Here we show that the size distribution of the micro-earthquakes recorded in the decades before the main shock occurred allowed an accurate forecast of its eventual rupture area. Applying this approach to other well monitored faults should improve earthquake hazard assessment in future. [ABSTRACT FROM AUTHOR]

The creation of building exposure models for seismic risk assessment is frequently challenging due to the lack of availability of detailed information on building structures. Different strategies have been developed in recent years to overcome this, including the use of census data, remote sensing imagery and volunteered graphic information (VGI). This paper presents the development of a building-by-building exposure model based exclusively on openly available datasets, including both VGI and census statistics, which are defined at different levels of spatial resolution and for different moments in time. The initial model stemming purely from building-level data is enriched with statistics aggregated at the neighbourhood and city level by means of a Monte Carlo simulation that enables the generation of full realisations of damage estimates when using the exposure model in the context of an earthquake scenario calculation. Though applicable to any other region of interest where analogous datasets are available, the workflow and approach followed are explained by focusing on the case of the German city of Cologne, for which a scenario earthquake is defined and the potential damage is calculated. The resulting exposure model and damage estimates are presented, and it is shown that the latter are broadly consistent with damage data from the 1978 Albstadt earthquake, notwithstanding the differences in the scenario. Through this real-world application we demonstrate the potential of VGI and open data to be used for exposure modelling for natural risk assessment, when combined with suitable knowledge on building fragility and accounting for the inherent uncertainties. [ABSTRACT FROM AUTHOR]

Seven competing models for forecasting medium-term earthquake rates in California are quantitatively evaluated using the framework of the Collaboratory for the Study of Earthquake Predictability (CSEP). The model class consists of contrasting versions of the Every Earthquake a Precursor According to Size (EEPAS) and Proximity to Past Earthquakes (PPE) modelling approaches. Models are ranked by their performance on likelihood-based tests, which measure the consistency between a model forecast and observed earthquakes. To directly compare one model against another, we run a classical paired t-test and its non-parametric alternative on an information gain score based on the forecasts. These test scores are complemented by several residual-based methods, which offer detailed spatial information. The experiment period covers 2009 June–2012 September, when California experienced 23 earthquakes above the magnitude threshold. Though all models fail to capture seismicity during an earthquake sequence, spatio-temporal differences between models also emerge. The overall best-performing model has strong time- and magnitude-dependence, weights all earthquakes equally as medium-term precursors of larger events and has a full set of fitted parameters. Models with this time- and magnitude-dependence offer a statistically significant advantage over simpler baseline models. In addition, models that down-weight aftershocks when forecasting larger events have a desirable feature in that they do not overpredict following an observed earthquake sequence. This tendency towards overprediction differs between the simpler model, which is based on fewer parameters, and more complex models that include more parameters. [ABSTRACT FROM AUTHOR]

Two of the long-standing relationships of statistical seismology are power laws: the Gutenberg–Richter relation describing the earthquake frequency–magnitude distribution, and the Omori–Utsu law characterizing the temporal decay of aftershock rate following a main shock. Recently, the effect of stress on the slope (the b value) of the earthquake frequency–magnitude distribution was determined by investigations of the faulting-style dependence of the b value. In a similar manner, we study here aftershock sequences according to the faulting style of their main shocks. We show that the time delay before the onset of the power-law aftershock decay rate (the c value) is on average shorter for thrust main shocks than for normal fault earthquakes, taking intermediate values for strike-slip events. These similar dependences on the faulting style indicate that both of the fundamental power laws are governed by the state of stress. Focal mechanisms are known for only 2 per cent of aftershocks. Therefore, c and b values are independent estimates and can be used as new tools to infer the stress field, which remains difficult to measure directly. [ABSTRACT FROM AUTHOR]

The Collaboratory for the Study of Earthquake Predictability (CSEP) supports an international effort to conduct and rigorously evaluate earthquake forecasting experiments. CSEP has concluded its first phase of testing (CSEP1) with recent results published in the June/July 2018 Special Issue of Seismological Research Letters. CSEP1 experiments evaluate forecasts expressed as expected rates in small space-magnitude bins that can be updated at regular intervals (e.g., daily or yearly). This experiment design is simple and allows a wide range of models to participate. However, recently developed forecast models, including candidate models for authoritative Operational Earthquake Forecasting (OEF), can simulate thousands of synthetic seismicity catalogs (stochastic event sets), which express important dependency structures between triggered earthquakes. These forecasts eliminate the assumption that seismicity can be described by independent Poisson processes. As part of CSEP's second phase (CSEP2), we are redesigning CSEP's software system to support the testing of such model classes. Requirements include access to high-performance computing, distributed processing of forecasts and evaluations, and simplifying data management, as well as adhering to CSEP's principles of transparency and reproducibility within a controlled, open-source software environment. To begin CSEP2, we have redesigned core CSEP1 evaluations to be consistent with forecasts that produce stochastic event sets; namely, the N-test, the M-test, and the S-test. We apply these tests as part of a retrospective experiment that initially focuses on evaluating UCERF3-ETAS within the California testing region. Additionally, the CSEP2 evaluations are available as part of an open-source Python package that provides tools to conduct regional forecasting experiments. [ABSTRACT FROM AUTHOR]

Log-linear formulation of number of earthquakes decay with magnitude – commonly expressed by b-value - quantifies the relative proportion between most and less hazardous events. Although considered as a "stand-alone" parameter, differences in b are physically related to different states of stress in the crust in a negative linear way. The stress increases with depth linearly in the brittle upper crust: b decreases monotonically with depth until the brittle-ductile transition surface. On the other side, theory of faulting implies that different stress levels accompany different tectonic regimes around the source volume, higher stress for compressive environments and lower stress extensional environments. Thereby, variations of b with faulting style are expected both on local and global scale, and in particular functionally related to the rake angle of focal mechanisms. We analyze a local high-quality, focal mechanisms dataset for Southern California to statistically model and test different dependences of b-values and then gather them in multivariable dependence models. We therefore develop a brand new, numerical Maximum Likelihood Method approach for the estimation of the optimal parameters maximizing the loglikelihood function: the models that best explain the physical reality are the right compromise between the contemporary dependence of b on tectonic styles and depth and a proper complexity level. [ABSTRACT FROM AUTHOR]