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Crustal earthquakes in low-strain-rate regions are rare in the human life span but can generate disastrous consequences when they occur. Such was the case in the Canterbury earthquake sequence that began in 2010 and eventually led to almost 200 fatalities. Our study explores this earthquake sequence’s origins by producing an enhanced earthquake catalog in the Canterbury Plains and Otago, South Island, New Zealand. We investigate seismicity rate changes from 2005 to before the 2010 Mw 7.2 Darfield earthquake. During this time, major subduction-zone earthquakes, such as the 2009 Mw 7.8 Dusky Sound earthquake, created measurable coseismic and postseismic strain in the region. We use template matching to expand the catalog of earthquakes in the region, and use a support vector machine classifier to remove false positives and poor detections. We then compare the newly obtained seismicity rates with the coseismic and postseismic crustal strain fields, and find that seismicity rate and crustal strain are positively correlated in the low-stress, low-seismicity region of the northern Canterbury Plains. In contrast, near fast-moving plate-boundary faults, the seismicity rate changes rise without much change in the strain rate. Our analysis reveals a substantial seismicity rate decrease in the western rupture area of the Darfield earthquake, which we infer to be an effect of coseismic and postseismic deformation caused by the Dusky Sound earthquake. We show in low-strain-rate regions, stress perturbation of a few kPas creates substantial seismicity rate change. However, the implication that such seismic quiescence is responsible for the nucleation of the Darfield earthquake requires further studies.

Macroseismic intensities play a key role in the engineering, seismological, and loss modeling communities. However, at present, there is an increasing demand for instrumental data-based loss estimations that require statistical relationships between intensities and strong-motion data. In New Zealand, there was an urgent need to update the ground motion to intensity conversion equation (GMICE) from 2007, developed prior to a large number of recent earthquakes including the 2010–2011 Canterbury and 2016 Kaikōura earthquake sequences. Two main factors now provide us with the opportunity to update New Zealand’s GMICE: (1) recent publication of New Zealand’s Strong-Motion Database, corresponding to 276 New Zealand earthquakes with magnitudes 3.5–7.8 and 4–185 km depths; and (2) recent generation of a community intensity database from GeoNet’s “Felt Classic” (2004–2016) and “Felt Detailed” (2016–2019) questionnaires, corresponding to around 930,000 individual reports. Ground-motion data types analyzed are peak ground velocity (PGV) and peak ground acceleration (PGA). The intensity database contains 67,572 felt reports from 917 earthquakes, with magnitudes 3.5–8.1, and 1797 recordings from 247 strong-motion stations (SMSs), with hypocentral distances of 5–345 km. Different regression analyses were tested, and the bilinear regression of binned mean strong-motion recordings for 0.5 modified Mercalli intensity bins was selected as the most appropriate. Total least squares regression was chosen for reversibility in the conversions. PGV provided the best-fitting results, with lower standard deviations. The influence of hypocentral distance, earthquake magnitude, and the site effects of local geology, represented by the mean shear-wave velocity in the first 30 m depth, on the residuals was also explored. A regional correction factor for New Zealand, suitable for adjustment of global relationships, has also been estimated.

Operational earthquake forecasts (OEFs) are represented as time-dependent probabilities of future earthquake hazard and risk. These probabilities can be presented in a variety of formats, including tables, maps, and text-based scenarios. In countries such as Aotearoa New Zealand, the U.S., and Japan, OEFs have been released by scientific organizations to agencies and the public, with the intent of providing information about future earthquake hazard and risk, so that people can use this information to inform their decisions and activities. Despite questions being raised about the utility of OEF for decision-making, past earthquake events have shown that agencies and the public have indeed made use of such forecasts. Responses have included making decisions about safe access into buildings, cordoning, demolition safety, timing of infrastructure repair and rebuild, insurance, postearthquake building standards, postevent land-use planning, and public communication about aftershocks. To add to this body of knowledge, we undertook a survey to investigate how agencies and GNS Science staff used OEFs that were communicated following the Mw 7.8 2016 Kaikōura earthquake in Aotearoa New Zealand. We found that agencies utilized OEFs in many of the ways listed previously, and we document individual employee’s actions taken in their home-life context. Challenges remain, however, regarding the interpretation of probabilistic information and applying this to practical decision-making. We suggest that science agencies cannot expect nontechnical users to understand and utilize forecasts without additional support. This might include developing a diversity of audience-relevant OEF information for communication purposes, alongside advice on how such information could be utilized.

The 2018 National Seismic Hazard Assessment of Australia incorporated 19 alternative seismic-source models developed by members of the Australian seismological community. The diversity of these models demonstrates the deep epistemic uncertainty that exists with regards to how best to characterize seismicity in stable continental regions. In the face of similarly high uncertainty, a diverse range of ground-motion models was proposed for use. A complex logic tree was developed to incorporate the alternative component models into a single hazard model. Expert opinion was drawn upon to weight the alternative logic-tree branches through a structured expert elicitation process. Expert elicitation aims to transparently and reproducibly characterize the community distribution of expert estimates for uncertain quantities and thereby quantify the epistemic uncertainty around estimates of seismic hazard in Australia. We achieve a multimodel rational consensus in which each model, and each expert, is, in accordance with the Australian cultural myth of egalitarianism, given a “fair go”—that is, judged on their merits rather than their status. Yet despite this process, we find that the results are not universally accepted. A key issue is a contested boundary between what is scientifically reducible and what remains epistemologically uncertain, with a particular focus on the earthquake catalog. Furthermore, a reduction, on average, of 72% for the 10% in 50 yr probability of exceedance peak ground acceleration levels compared with those underpinning existing building design standards, challenges the choice of metrics upon which design codes are based. Both quantification of the bounds of epistemic uncertainties through expert elicitation and reduction of epistemic uncertainties through scientific advances have changed our understanding of how the hazard behaves. Dialog between scientists, engineers, and policy makers is required to ensure that as our understanding of the hazard evolves, the hazard metrics used to underpin risk management decisions are re-evaluated to ensure societal aims are achieved.

This article presents modified Mercalli intensity (MMI) data for the 22 February 2011 Mw 6.2 Christchurch, New Zealand, earthquake. These data include intensity levels above MMI 8 that have not been assigned previously. Two sources of data have been used in this research: GeoNet’s “Felt Classic” online questionnaires and felt reports gathered during a field study in Christchurch in February 2013. Taken together, these sets of data provided 331 valid (i.e., with all the needed information) felt reports in areas of MMI 8 or above, with 299 (90%) of the reports used to assign MMI levels above 8. This article presents a more detailed picture of the geographical damage distribution of this earthquake than has previously been available. The data differentiate damage in the center of Christchurch, with 8 communities assigned a community MMI (CMMI) of 9, 11 communities a CMMI of 10, and 8 communities a CMMI of 11, which is the maximum possible intensity in the New Zealand MMI scale, and a level of intensity not previously reported in New Zealand (Dowrick et al., 2008). The geographical damage distribution for Christchurch has been updated for intensities below MMI 8. This was done using a recently developed method that groups intensity data and allows intensities to be aggregated for a community and a single value assigned. Comparisons between MMI and peak ground velocity using the CMMI data and two ground-motion intensity correlation equations (GMICEs) indicate an underestimation of MMI when using the GMICEs and the need to review New Zealand’s GMICE.

The 2016 M w 7.8 Kaikōura earthquake continued a notable decade of damaging earthquake impacts in New Zealand. The effects were wide ranging across the upper South Island, and included two fatalities, tsunami, tens of thousands of landslides, the collapse of one residential building, and damage to numerous structures and infrastructure. We present a preliminary overview focused on the seismological aspects of this earthquake and the corresponding seismological response effort. The earthquake rupture was extremely complex, involving at least 13 separate faults extending over ∼150 km, from the epicenter in north Canterbury to near the Cook Strait. We use backprojection and slip inversion methods to derive preliminary insights into the rupture evolution, identifying south‐to‐north rupture, including at least three distinct southwest‐to‐northeast propagating phases. The last phase is associated with a strong second pulse of energy release in the northern half of the rupture zone ∼70 s after rupture initiation, which we associate with the Kekerengu–Needles faults where some of the largest surface displacements (dextral) were observed. The mechanism of the mainshock was oblique thrust and relocated aftershocks show a range of thrust and strike‐slip mechanisms across three dominant spatial clusters. GeoNet datasets collected during the Kaikōura earthquake will be crucial in further unraveling details of the complex earthquake rupture and its implications for seismic hazard. Ground motions during the earthquake exceeded 1 g at both ends of the rupture. Spectral accelerations exceeded 500‐year return period design level spectra in numerous towns in the upper South Island, as well as in parts of the capital city of Wellington at critical periods of 1–2 s, influenced by site/basin and directivity effects. Another important part of the response effort has been the provision of earthquake forecasts, as well as consideration of the implications of slow slip on the Hikurangi subduction interface triggered as a result of the Kaikōura earthquake.

Recent damaging earthquakes in New Zealand ruptured faults that were not known to be active. We analyzed New Zealand historical moderate‐to‐great magnitude earthquakes since 1845 ( M w 6–8.2) to estimate the level of completeness of earthquake fault sources in the National Seismic Hazard Model (NSHM) and the paleoseismic record. Our analysis assumes that the historical earthquakes are representative of the paleoseismic record and, due to the small number of events (45 M w ≥6), is qualitative. We find that about half of all historical earthquakes M w ≥7.0 ruptured faults that, based on today’s state of knowledge of active‐fault locations, would not have been identified as active prior to the event. The majority of historical events on faults previously not identified as active were M w

We developed a hybrid time‐dependent seismic‐hazard model for application to the recovery of Canterbury, New Zealand, following the Canterbury earthquake sequence. We combined earthquake‐clustering models of three timescales (short‐term, medium‐term, and long‐term) to develop a model that accounts for the significant epistemic uncertainty in the earthquake rates. For the probabilistic seismic‐hazard calculations, these models were coupled with two ground‐motion prediction equations. The weights for the construction of the hybrid model and for the logic tree were obtained using a structured expert elicitation process. Forecasts from the model have been used to provide earthquake probabilities to a range of end users on timescales from 1 day to 50 years. Additionally, the 50‐year hazard forecast has been used in the revision of the New Zealand building design guidelines and other aspects of the reconstruction of Christchurch.

Since 2014, research groups from Japan, Taiwan, and New Zealand have been collaborating to share research ideas and expertise about topics relevant to the development of national seismic hazard models (NSHMs) in each region. The trilateral collaboration is centered on a series of workshops designed to bring the researchers together. So far, three such meetings have been held: a kick‐off workshop in Taiwan in May 2014, a second workshop in Japan in August 2015, and a third workshop in New Zealand in November 2015. A fourth workshop is planned for late 2016. In this focus section on the joint Japan–Taiwan–New Zealand NSHM, we have collected eight papers that highlight some of the ongoing research that specifically targets improvements in the respective NSHMs.

Earthquake‐hazard models are one of the major contributions provided by the seismological community to tangibly support disaster risk reduction policies at a national level. Although the societal impact of hazard analyses can be huge, the development of models remains a scientific activity developed within frameworks that have a strong national emphasis and partial international recognition. However, broad acceptability of hazard models is a key aspect for achieving authoritativeness and a prerequisite for warranting that their construction is completed using well‐recognized methodologies. As part of an enduring international collaboration between leading organizations operating in the hazard and risk fields in Japan, New Zealand, Taiwan, and the Global Earthquake Model initiative, we discuss the main characteristic of the earthquake source models—as implemented for the OpenQuake engine—used for the calculation of the most recent national seismic‐hazard maps of these three countries. Particular emphasis is placed on comparing the various modeling options adopted in the different tectonic regions, on emphasizing commonalities, and on discussing the most controversial modeling solutions. Despite the many connections from a seismotectonic point of view between the three countries, the comparison highlights different modeling choices for the various tectonic regions, which constitute a spectrum of possible epistemic uncertainties, as well as modeling issues that could be collectively explored in future phases of this international collaboration.

Potential earthquake sources are revealed by the locations of earthquakes in historical and instrumental catalogs and of geologically mapped faults, including plate boundaries. We derive a set of multiplicative hybrid earthquake likelihood models that combine earthquake and fault data for the New Zealand region. In these models, the cell rates in a spatially uniform baseline model are scaled using selected subsets of five covariates derived from the magnitudes and locations of past earthquakes, the location of the boundary between the Australian and Pacific plates, and the location and slip rate of mapped faults. The hybrid model parameters are optimized for earthquakes of M 5 and greater over the period 1987–2006 and tested on earthquakes from the period 2007–2014. No updating of models is undertaken during the fitting or testing period, but we consider two cases of the earthquake-based covariates in the tests: (1) all data prior to 1987 and (2) all data prior to 2007, respectively. Hybrids containing the earthquake-based covariates perform better in the latter case. The most informative hybrid models in the fitting and testing period are composed of three and four covariates, respectively, including both earthquake- and fault-based variables. Proximity to mapped faults is overall the most informative individual covariate. These results can be used to inform better modeling of long-term earthquake occurrence rates for probabilistic seismic-hazard analysis.

A team of earthquake geologists, seismologists, and engineering seis- mologists has collectively produced an update of the national probabilistic seismic hazard (PSH) model for New Zealand (National Seismic Hazard Model, or NSHM). The new NSHM supersedes the earlier NSHM published in 2002 and used as the hazard basis for the New Zealand Loadings Standard and numerous other end-user applica- tions. The new NSHM incorporates a fault source model that has been updated with over 200 new onshore and offshore fault sources and utilizes new New Zealand-based and international scaling relationships for the parameterization of the faults. The dis- tributed seismicity model has also been updated to include post-1997 seismicity data, a new seismicity regionalization, and improved methodology for calculation of the seismicity parameters. Probabilistic seismic hazard maps produced from the new NSHM show a similar pattern of hazard to the earlier model at the national scale, but there are some significant reductions and increases in hazard at the regional scale. The national-scale differences between the new and earlier NSHM appear less than those seen between much earlier national models, indicating that some degree of consis- tency has been achieved in the national-scale pattern of hazard estimates, at least for return periods of 475 years and greater. Online Material: Table of fault source parameters for the 2010 national seismic- hazard model.

This article presents results from the consideration of epistemic uncertainties in New Zealand (NZ) probabilistic seismic‐hazard analysis. Uncertainties in ground‐motion prediction are accounted for via multiple ground‐motion prediction equations within the logic‐tree framework. Uncertainties in the fault‐based seismicity of the earthquake rupture forecast due to uncertainties in fault geometry, slip parameters, and magnitude‐scaling relationships are considered in a Monte Carlo simulation framework. Because of the present lack of fault‐specific data quantifying uncertainties for many faults in NZ, representative values based on judgement and available data for NZ and foreign faults were utilized. Uncertainties in the modelling of background seismicity were not considered. The implications of the considered epistemic uncertainties in terms of earthquake magnitude–frequency distributions and probabilistic seismic‐hazard analyses for two spectral acceleration ordinates, two soil classes, and two locations (Wellington and Christchurch) are examined. The results illustrate that, for the uncertainties considered, the variation in seismic hazard due to the adopted ground‐motion prediction model is larger than that due to the uncertainties in the earthquake rupture forecast. Of the earthquake rupture forecast uncertainties considered, the magnitude‐geometry scaling relationships was the most significant, followed by fault rupture length. Hence, the obtained results provide useful guidance on which modelling issues are the most critical in the reliability of seismic‐hazard analyses for locations in NZ.

We use a database of approximately 200,000 modified Mercalli intensity (MMI) observations of California earthquakes collected from USGS “Did You Feel It?” (DYFI) reports, along with a comparable number of peak ground‐motion amplitudes from California seismic networks, to develop probabilistic relationships between MMI and peak ground velocity (PGV), peak ground acceleration (PGA), and 0.3‐s, 1‐s, and 3‐s 5% damped pseudospectral acceleration (PSA). After associating each ground‐motion observation with an MMI computed from all the DYFI responses within 2 km of the observation, we derived a joint probability distribution between MMI and ground motion. We then derived reversible relationships between MMI and each ground‐motion parameter by using a total least squares regression to fit a bilinear function to the median of the stacked probability distributions. Among the relationships, the fit to peak ground velocity has the smallest errors, though linear combinations of PGA and PGV give nominally better results. We also find that magnitude and distance terms reduce the overall residuals and are justifiable on an information theoretic basis. For intensities MMI≥5, our results are in close agreement with the relations of Wald, Quitoriano, Heaton, and Kanamori (1999); for lower intensities, our results fall midway between Wald, Quitoriano, Heaton, and Kanamori (1999) and those of Atkinson and Kaka (2007). The earthquakes in the study ranged in magnitude from 3.0 to 7.3, and the distances ranged from less than a kilometer to about 400 km from the source. Online Material: Figures showing the relationship between 0.3 s, 1.0 s, and 3.0 s pseudospectral acceleration and MMI.

We present a preliminary probabilistic seismic hazard analysis (PSHA) of a site in the Otway basin, Victoria, Australia, as part of the CO2CRC Otway Project for CO 2 storage risk. The study involves estimating the likelihood of future strong earthquake shaking at the site and utilizes three datasets: (1) active faults, (2) historical seismicity, and (3) geodetic surface velocities. Our analysis of geodetic data reveals strain rates at the limit of detectability and not significantly different from zero. Consequently, we do not develop a geodetic-based source model for this Otway model. We construct logic trees to capture epistemic uncertainty in both the fault and seismicity source parameters and in the ground-motion prediction. A new feature for seismic hazard modeling in Australia, and rarely dealt with in low-seismicity regions elsewhere, is the treatment of fault episodicity (long-term activity versus inactivity) in our Otway model. Seismic hazard curves for the combined (fault and distributed seismicity) source model show that hazard is generally low, with peak ground acceleration estimates of less than 0.1 g at annual probabilities of 10 -3 -10 -4 /yr. Our preliminary analysis therefore indicates that the site is exposed to a low seismic hazard that is consistent with the intraplate tectonic setting of the region and unlikely to pose a significant hazard for CO 2 containment and infrastructure.

An earthquake of Mw 6.1–6.31 (Beavan et al. 2011, page 789 of this issue) that struck Christchurch, New Zealand, on 22 February (21 February, UTC) produced recorded ground motion acceleration over 2 g. The event caused widespread damage with dense recordings of non-linear site behavior. Globally, dense near-field recordings of shallow intraplate earthquakes are rare. It is possible that extreme ground motions are common with this type of earthquake and that their rarity is merely a function of inadequate seismic sampling in the near field of such low-probability, high-potency events. To better define the nature of these events, we calculate apparent stress ( τa ) of the three largest earthquakes in the Canterbury sequence and compare them to global and regional data. We then place recorded PGA and spectral accelerations into the context of regional and global ground motion prediction equations and discuss the implications of high-stress events for future seismic hazard estimates for the region. For the February event, we also briefly explore the implications of directivity on measured ground motions in central Christchurch. The earthquakes that occurred in the Canterbury region of the South Island, New Zealand, from September 2010 to the present have disproportionately large energy magnitudes ( Me ) to their moment magnitudes ( Mw ). They have produced the largest ground motions ever measured in New Zealand. The sequence began with the Mw 7.1 earthquake that occurred about 40 km west of the city of Christchurch on 4 September 2010. The maximum recorded ground acceleration recorded during the event was over 1.25 g, which was experienced near the intersection of the triggering thrust on which the rupture began and the strike-slip Greendale fault that carried most of the moment in the earthquake (Gledhill et al. 2010). Peak ground accelerations (PGA) in the central business district of Christchurch averaged …

We develop a testing methodology for the New Zealand national probabilistic seismic hazard (PSH) model that builds on the groundwork of previous studies. Our fundamental approach is to test the full model, or in other words, the final output of the model (ground-motion exceedance for a given return period). Our results show that the PSH model is rejected as underpredicting the historical number of exceedances for specific peak ground acceleration (PGA) levels obtained directly from instrumental strong-motion data over the last 1–4 decades. However, when aftershock ground motions are removed from the strong-motion data, the model is not inconsistent with the observations. The implications for the PSH model are that the lack of aftershocks in the model led to initial model rejection and that the model may perform better for short (decadal) time periods if aftershocks are included in the PSH model. The results are different from those of earlier Modified Mercalli Intensity (MMI)-based studies that suggested the PSH model was predicting hazard slightly higher than that of the historical record. Our new test dataset has the advantage of using observed PGA rather than PGA inferred from MMI. Establishment of a protocol for formally testing future versions of the New Zealand PSH model within a testing center such as those using the Collaboratory for the Study of Earthquake Predictability protocol will require consideration of the fact that the tests are limited by the available datasets of strong earthquake shaking.

The five-year experiment of the Regional Earthquake Likelihood Models (RELM) working group was designed to compare several prospective forecasts of earthquake rates in latitude–longitude–magnitude bins in and around California. This forecast format is being used as a blueprint for many other earthquake predictability experiments around the world, and therefore it is important to consider how to evaluate the performance of such forecasts. Two tests that are currently used are based on the likelihood of the observed distribution of earthquakes given a forecast; one test compares the binned space–rate–magnitude observation and forecast, and the other compares only the rate forecast and the number of observed earthquakes. In this article, we discuss a subtle flaw in the current test of rate forecasts, and we propose two new tests that isolate the spatial and magnitude component, respectively, of a space–rate–magnitude forecast. For illustration, we consider the RELM forecasts and the distribution of earthquakes observed during the first half of the ongoing RELM experiment. We show that a space–rate–magnitude forecast may appear to be consistent with the distribution of observed earthquakes despite the spatial forecast being inconsistent with the spatial distribution of observed earthquakes, and we suggest that these new tests should be used to provide increased detail in earthquake forecast evaluation. We also discuss the statistical power of each of the likelihood-based tests and the stability (with respect to earthquake catalog uncertainties) of results from the likelihood-based tests.

The short-term earthquake probability (STEP) forecasting model applies the Omori–Utsu aftershock-decay relation and the Gutenberg–Richter frequency-magnitude relation to clusters of earthquakes. It is mainly intended to forecast aftershock activity and depends on a time-invariant background model to forecast most of the major earthquakes. On the other hand, the long-range earthquake forecasting model EEPAS (every earthquake a precursor according to scale) exploits the precursory scale increase phenomenon and associated predictive scaling relations to forecast the major earthquakes months, years, or decades in advance, depending on magnitude. Both models are shown to be more informative than time-invariant models of seismicity. By forming a mixture of the two, we aim to create an even more informative short-term forecasting model. Using the Advanced National Seismic System catalog of California over the period 1984–2004, the optimal mixture model for forecasting earthquakes with M ≥5.0 is a convex linear combination consisting of 0.42 of the EEPAS forecast and 0.58 of the STEP forecast. This mixture gives an average probability gain of more than 2 compared to each of the individual models. Several different mixture models will be submitted to the CSEP Testing Center at the Southern California Earthquake Center to ascertain whether or not this result is borne out by real-time tests of the models against future earthquakes.

The Regional Earthquake Likelihood Models (RELM) project aims to produce and evaluate alternate models of earthquake potential (probability per unit volume, magnitude, and time) for California. Based on differing assumptions, these models are produced to test the validity of their assumptions and to explore which models should be incorporated in seismic hazard and risk evaluation. Tests based on physical and geological criteria are useful but we focus on statistical methods using future earthquake catalog data only. We envision two evaluations: a test of consistency with observed data and a comparison of all pairs of models for relative consistency. Both tests are based on the likelihood method, and both are fully prospective ( i.e. , the models are not adjusted to fit the test data). To be tested, each model must assign a probability to any possible event within a specified region of space, time, and magnitude. For our tests the models must use a common format: earthquake rates in specified “bins” with location, magnitude, time, and focal mechanism limits. Seismology cannot yet deterministically predict individual earthquakes; however, it should seek the best possible models for forecasting earthquake occurrence. This paper describes the statistical rules of an experiment to examine and test earthquake forecasts. The primary purposes of the tests described below are to evaluate physical models for earthquakes, assure that source models used in seismic hazard and risk studies are consistent with earthquake data, and provide quantitative measures by which models can be assigned weights in a consensus model or be judged as suitable for particular regions. In this paper we develop a statistical method for testing earthquake likelihood models. A companion paper (Schorlemmer and Gerstenberger 2007, this issue) discusses the actual implementation of these tests in the framework of the RELM initiative. Statistical testing of hypotheses is a common …

Motivated by the public's desire to learn as much as possible following the occurrence of damaging events, we have developed a methodology to spatially map the probability of earthquake occurrence in the next 24 hours. We start with the simple aftershock model of Reasenberg and Jones (1989, 1990, 1994): \batchmode \documentclass[fleqn,10pt,legalpaper]{article} \usepackage{amssymb} \usepackage{amsfonts} \usepackage{amsmath} \pagestyle{empty} \begin{document} \[\ {\lambda}(t,M)=\frac{10^{a^{{^\prime}}+b(M\_{m}-M)}}{(t+c)^{P}},{\ }M{\geq}M\_{c}\] \end{document}(1) where λ( t, M ) is the rate of aftershocks larger than a magnitude threshold, Mc , and occurring at time t . The constants a and b are derived from the Gutenberg-Richter relationship (Gutenberg and Richter 1944), and p and c result from the modified Omori law (Ogata 1983). The fundamental approach of our model is to combine successively more detailed aftershock forecast models as additional aftershock information becomes available. We start with a static “background” model that has been derived from the 1996 U.S. Geological Survey long-term hazard maps (Frankel et al. 1997). Next, using the corrected Akaike Information Criterion (AICc) (Burnham and Anderson 2002) we combine three additional elements with the background: (1) a generic element based on the average behavior of California aftershock sequences; (2) an element based on the average behavior of the particular aftershock sequence; and (3) a spatially variable element where the aftershock behavior is mapped on a 5-km-square grid. The AICc is a likelihood-based calculation used to select the optimal among multiple models. The calculation takes into account the number of free parameters as well as the amount of observed data; a model with more free parameters must fit the data better than models with fewer parameters to be preferred in the final scoring. Additionally, we do not wish to force only a single model to be selected; therefore AIC weighting is used where a relative weight is derived for each model based on its AICc score, …

We describe the organizational setup and the set of rules developed to test earthquake likelihood models of the Regional Earthquake Likelihood Models (RELM) initiative. Truly prospective testing for a multitude of forecasts in an unbiased and reproducible way requires a set of rules to be obeyed by each model as well as a cyber-infrastructure: the testing center. These rules encompass free parameters, e.g., the testing area and grid, forecast periods, magnitude ranges, earthquake catalogs provided to the models and used for testing, and declustering. A combination of these free parameters defines a class of models. Within RELM we distinguish between five-year models, one-year models, and one-day models, which issue their forecast for the respective periods. While five-year models provide their forecasts as numbers, one-year and one-day models must be installed in the testing center together with their source code to enable yearly or daily forecast generation. Only with installed models can results be reproduced at any time. The declared RELM goal of testing a multitude of forecast models in a prospective (forward-looking) sense is, to our knowledge, unique in seismology. It is the first time that a group of modelers agree to submit their models to a common, community-agreed test against future seismicity. We believe that this is an important milestone for forecasting- and prediction-related research in seismology because it offers an opportunity to overcome past shortcomings and deadlocks. The primary goal of the common testing is not to find the ultimate winner but to advance our current physical understanding and/or the statistical description of the way earthquakes occur. Ultimately this will lead in small steps (or, possibly, giant leaps) to better forecast models. Prospective testing of models in seismology is rare but a few laudable examples exist (Kagan and Jackson 1995, Evison and Rhoades 1999, Rong et …

We investigate the spatial and temporal seismicity parameters and the related probabilistic aftershock hazard for the aftershock sequence of the 1999 M_w 7.1 Hector Mine mainshock and compare it with the neighboring 1992 M_w 7.3 Landers sequence. Using a catalog of 11,000 earthquakes, we determine the earthquake size distribution (b-value), the aftershock decay rate (p-value), and the seismic activity rate (a-value). The b-values are high (b > 1.2) within the rupture area, significantly lower (b ≈ 0.7) north of the rupture area, and increase with time since the mainshock. Probabilistic aftershock hazard maps, computed automatically as early as 4 days after the mainshock, identified the northernmost part of the sequence as the highest-hazard region. These maps show a good agreement between the forecasts and the recorded large aftershocks. Based on the asymmetrical b-value and hazard patterns for both the Hector Mine and Landers sequences, we hypothesize that the mainshock rupture directivity and slip distribution influence aftershock hazard. Current static or dynamic stress triggering models cannot resolve this spatial and temporal evolution of the hazard. Stress tensor inversions of 1400 relocated first-motion focal mechanisms show predominantly a strike-slip stress state with a SW–NE trend of the greatest principal stress. The heterogeneity of the stress field is unusually high near the Hector Mine and Landers mainshock ruptures, particularly near patches of large slip.