Geology topics

Nicholas J. van der Elst

Publications and source records attributed to Nicholas J. van der Elst.

At least 19 recordsLinked to original sources

USGS2026

ETAS-positive: Extracting unbiased epidemic-type aftershock models from incomplete earthquake catalogs

Earthquake catalogs are inherently incomplete, and short-term fluctuations in catalog completeness can strongly bias estimates of seismicity parameters. Here, we extend the positive statistics framework recently introduced for estimating Gutenberg–Richter a and b values to the Epidemic-Type Aftershock Sequence (ETAS) model. The approach focuses on complete magnitude–time intervals defined by pairs of earthquakes in which the second event is larger than the first. Comprehensive synthetic tests demonstrate that the proposed ETAS + method retrieves nearly unbiased parameter estimates even from highly incomplete catalogs, whereas parameters obtained using classical estimation approaches are strongly biased. Application to Southern California reveals a similar trend, with the productivity scaling parameter α approaching the b value, consistent with self-similar earthquake triggering within estimation uncertainties. Owing to its robustness against catalog incompleteness and computational efficiency, the ETAS + method provides a powerful new tool for seismicity analysis and earthquake forecasting.

California↗

USGS2026

Rapid characterization of the 2025 Mw 8.8 Kamchatka, Russia earthquake

The 29 July 2025 M w 8.8 Kamchatka, Russia, earthquake was the sixth largest instrumentally recorded earthquake. This event was seismically well observed at regional and teleseismic distances, but publicly available near‐source data were sparse at the time of the event, presenting unique challenges for rapid source and impact characterization. The U.S. Geological Survey (USGS) National Earthquake Information Center provides global real‐time monitoring for earthquakes, including rapid response information products that estimate source characteristics, shaking, and the resulting impacts. We describe the USGS rapid response earthquake information products following the Kamchatka event and discuss their implications for ongoing hazards in the region. We describe potential improvements to our response workflows motivated by this event, including more rapid constraints on source geometries and the automated selection of fault geometries for finite‐fault inversions. The rapid response products together support the interpretation of a unilateral southwestward rupture with significant slip on the southwestern end of the rupture extent. The M w 8.8–9.0 event in 1952, which ruptured a comparable extent of the Kuril–Kamchatka subduction interface, has many similarities to the 2025 rupture. This illustrates that slip deficits may remain following great earthquakes and highlights the usefulness of comparative studies between historic and modern events.

Kuril-Kamchatka subduction zone↗

USGS2025

Mechanics and statistics of postseismic shaking

Analysis of two weeks of continuous post-seismic shaking after the 2019 M7.1 Ridgecrest, CA earthquake sequence using 4 nearby borehole seismometers reveals that continuous ground motions decay as Omori’s law in time and follow the Gutenberg-Richter distribution in logarithmic amplitude. The measured temporal decay in amplitudes agrees with predictions of the rate-and-state framework and indicates shaking amplitudes are proportional to the velocity of afterslip. Our ground motion-based statistical framework provides a basis to forecast shaking intensity in the minutes to hours after a large earthquake.

California↗

USGS2025

A scientific vision and roadmap for earthquake rupture forecast developments, a USGS perspective

We articulate a scientific vision and roadmap for the development of improved Earthquake Rupture Forecast models, which are one of the two main modeling components used in modern seismic hazard and risk analysis. One primary future objective is to provide fully time-dependent models that include both elastic rebound and spatiotemporal clustering nationwide, which is particularly important for shorter-term hazard and risk considerations (e.g., earthquake insurance products). We also discuss the importance and perennial challenges associated with quantifying epistemic uncertainties, including those associated with deformation-model slip rates, un-quantified sampling errors with respect to off-fault seismicity, and any spatial covariances. The need for more physics-based approaches is also emphasized, as is the benefit of adding model valuation (quantifying usefulness) to our verification and validation protocols. Given the multidisciplinary and system-level nature of this activity, modular design is critical. Future updates will also draw from best-available science by both the United States Geological Survey and the external community. The primary goal of this paper is to highlight plans that guide research and facilitate community engagement with model development, especially with respect to lowering the entry barrier for early career scientists and engineers. The paper is written so readers can focus on the sections that interest them most (see table of contents), with the Introduction and Discussion providing a stand-alone overview and summary.

Bulletin of the Seismological Society of America↗

USGS2025

Meet the people where they are: Assessing user needs for aftershock forecast products in El Salvador, Mexico and the United States

Aftershock forecasts can help communities reduce their seismic risk by conveying how many aftershocks can be expected following a large earthquake, and how the expected number of aftershocks and their corresponding ground shaking evolves over time and space. Prior work finds that graphical forecast products may communicate such information better than only text or numbers. To identify which visual products can serve multiple user groups, we held workshops with members of several professions, including emergency managers, engineers, critical infrastructure operators, public health specialists, science communicators, and more. We conducted these workshops in El Salvador, Mexico and the United States to understand which forecast products may be effective across different countries. In these workshops, users performed small-group activities to elicit the types of aftershock forecast information that would support decisions in their respective roles and how this information would optimally be displayed. Maps of shaking hazards were frequently requested across all professions and countries, even for dissimilar forecast uses. The design of these maps, and other product needs, were differentiated by profession, country and other factors. Other forecast products, including those showing forecasts about the magnitudes and time periods of future aftershocks, also served a variety of users, but for different types of decisions. We found a greater variation in user needs by profession than by country, and that user needs also vary with time, communication channel and other contextual factors. We discuss practical implications for user-centered visual communication of operational aftershock forecasts.

International Journal for Disaster Risk Reduction↗

USGS2025

Bayesian ETAS modeling for the Pacific Northwest: Uncovering effects of tectonic regimes, regional differences, and swarms on aftershock parameters

The Pacific Northwest (PNW) of North America has high seismic hazard due to numerous earthquake sources under populated areas. It hosts several tectonic regimes and subregional seismic zones that are hypothesized to have different patterns of earthquake and aftershock occurrence. It is also predisposed to earthquake swarms, which can complicate the statistical modeling of these patterns. We present the first statistical seismicity model of the PNW catalog using the epidemic‐type aftershock sequence (ETAS) framework. We develop a Bayesian inference procedure that provides a stable estimation of both ETAS parameters and their uncertainties for different sets of PNW earthquakes, even those with very sparse catalogs. The Bayesian approach allows us to investigate how parameter estimates change between the intraslab and crustal tectonic regimes, the northern and southern PNW, and when swarms are included and excluded from the catalog. We also utilize our Bayesian framework to calculate parameter estimates under different prior beliefs about PNW seismicity, as well as to propagate catalog measurement errors into ETAS parameter estimates. We discuss the implications of parameter differences across the region for aftershock forecasting for the PNW.

Pacific Northwest↗

USGS2024

Onset of aftershocks: Constraints on the Rate-and-State model

Aftershock rates typically decay with time t after the mainshock according to the Omori–Utsu law, R (t)=K(c+t) −p ⁠ , with parameters K , c , and p . The rate‐and‐state (RS) model, which is currently the most popular physics‐based seismicity model, also predicts an Omori–Utsu decay with p = 1 and a c ‐value that depends on the size of the coseismic stress change. Because the mainshock‐induced stresses strongly vary in space, the c ‐value should vary accordingly. Short‐time aftershock incompleteness (STAI) in earthquake catalogs has prevented a detailed test of this prediction so far, but the newly developed a ‐positive method for reconstructing the true earthquake rate now allows its testing. Using previously published slip models, we calculate the coseismic stress changes for the six largest mainshocks in Southern California in recent decades and estimate the maximum shear as a scalar proxy of the coseismic stress tensor. Aftershock rates reconstructed for events in different stress ranges show that the rates follow a power law with p = 1 independent of stress with no clear sign of a c ‐value. The onset of the power‐law decay is abrupt and more delayed in areas with smaller stress changes. The observations do not necessarily contradict the RS model, as STAI limits the resolution for early aftershocks, and the RS model can reproduce the observations for specific Aσ values. However, the observations lead to strong constraints, namely Aσ <10 kPa and a power‐law decay of the background rate with distance to the fault, with exponent 2.7.

Seismological Research Letters↗

USGS2024

Testing rate‐and‐state predictions of aftershock decay with distance

We analyze aftershocks of the 2019 M 7.1 Ridgecrest mainshock and isolated M 5–6 mainshocks in southern California to test predictions made by the rate‐and‐state friction model of Dieterich (1994) . Rate‐and‐state friction predicts that the seismicity rate after a stress step follows Omori decay, where the Omori c ‐value, which is the saturation in aftershock rate observed at small times, is larger for smaller stress steps. Put in the context of an aftershock sequence, this predicts that the Omori c ‐value will be systematically larger at greater distances from the mainshock. To our knowledge, this predicted effect has not been observed. In part this may be because the Omori c ‐value is difficult to measure because it often reflects short‐term catalog incompleteness rather than a true saturation in aftershock rate. We explore the dependence of the Omori c ‐value on the distance to the mainshock by applying the “ a ‐positive” method ( van der Elst and Page, 2023 ). This method is insensitive to short‐term aftershock incompleteness and allows resolution of the true aftershock rate deep into the mainshock coda. For aftershocks of the Ridgecrest mainshock and stacked M 5–6 mainshocks, we observe systematic differences in early aftershock rates, relative to mainshock distance, consistent with the predictions of rate‐and‐state friction. Furthermore, for the larger Ridgecrest dataset, we observe that aftershocks nearer to the mainshock start earlier, and we resolve a flattening of the Omori curve consistent with a larger Omori c ‐value for the farthest aftershocks, as predicted by Dieterich (1994) .

Seismological Research Letters↗

USGS2024

Developing, testing, and communicating earthquake forecasts: Current practices and future directions

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.

Reviews of Geophysics↗

USGS2024

Aftershock forecasting

Aftershocks can compound the impacts of a major earthquake, disrupting recovery efforts and potentially further damaging weakened buildings and infrastructure. Forecasts of the probability of aftershocks can therefore aid decision-making during earthquake response and recovery. Several countries issue authoritative aftershock forecasts. Most aftershock forecasts are based on simple statistical models that were first developed in the 1980s and remain the best available models. We review these statistical models, and the wide-ranging research to advance aftershock forecasting through better statistical, physical, and machine learning methods. Physics-based forecasts based on mainshock stress changes can sometimes match the statistical models in testing, but don’t yet outperform them. Physical models are also hampered by unsolved problems such as the mechanics of dynamic triggering and the influence of background conditions. Initial work on machine learning forecasts shows promise, and new machine learning earthquake catalogs provide an opportunity to advance all types of aftershock forecasts.

Annual Review of Earth and Planetary Sciences↗

USGS2023

a-positive: A robust estimator of the earthquake rate in incomplete or saturated catalogs

Detection thresholds in earthquake catalogs frequently change in time due to station coverage improvements and network saturation effects during active periods such as mainshock-aftershock cascades. This presents a challenge to seismicity-rate estimation; there is a tradeoff between using as low a minimum magnitude as possible to maximize data while not undercounting the rate due to catalog incompleteness. Here we present a simple method, “ a -positive,” which makes use of differential statistics to robustly estimate the seismicity rate in catalogs with time-varying detection thresholds. We demonstrate the effectiveness of this method for a centuries-long, hybrid earthquake catalog with both historical and instrumentally-detected earthquakes in the Central and Eastern U.S., as well as for the 2019 Ridgecrest aftershock sequence in California, which has rapid changes in completeness due to network saturation. We find that the a -positive method leads to more precise and less biased estimates of seismicity rate than traditional methods. In addition, with our improved estimate of earthquake rate early in the aftershock cascade, we find no evidence of rate-saturation at short times from the mainshock; that is, the Omori c -value is not distinguishable from zero.

JGR Solid Earth↗

USGS2023

Modern products for a vintage event: An update on the 1933 Long Beach, California, earthquake

When a notable earthquake occurs in the United States, a range of familiar real‐ and near‐real‐time products are produced by the U.S. Geological Survey (USGS) Advanced National Seismic System (ANSS), and made available via the ANSS Comprehensive Earthquake Catalog. For historical and early instrumental earthquakes, similar results and products are developed depending on data availability and event significance, drawing from published later studies. The year 2023 marked the ninetieth anniversary of the 11 March 1933 Long Beach, California, earthquake. This anniversary provided the impetus to update ANSS products, drawing on archived and published data. Here, we describe the updated ShakeMap, shaking recordings and intensities, and retrospective aftershock forecast for the Long Beach, California, earthquake. In effect we have developed standard, modern ANSS products for an earthquake that occurred 90 yr ago. Our results show that the distributions of both the ground motions, anchored by three strong‐motion recordings, and aftershock magnitudes are consistent with expectations for an M 6.4 mainshock in Southern California. We show that, notwithstanding possible limitations, instrumentally recorded accelerations from the closest station are consistent with predicted shaking and directly estimated macroseismic intensities. Updated data products have been added to the USGS event page, where they are available for download. Public‐facing products were also created for the anniversary and are freely available on the USGS website.

California↗

USGS2023

Fault roughness at seismogenic depths and links to earthquake behavior

Fault geometry affects the initiation, propagation, and cessation of earthquake rupture, as well as, potentially, the statistical behavior of earthquake sequences. We analyze 18,250 (−0.27 < M < 4.4) earthquakes of the 2016–2019 Cahuilla, California, swarm and, for the first time, use these high‐resolution earthquake locations to map, in detail, the roughness across an active fault surface at depth. We find that the strike‐slip fault is 50% rougher in the slip‐perpendicular direction than parallel to slip. 3D mapping of fault roughness at seismogenic depths suggests that roughness varies by a factor of 8 for length scales of 1 km. We observe that the largest earthquake ( M 4.4) occurred where there is significant fault complexity and the highest measured roughness. We also find that b ‐values are weakly positively correlated with fault roughness. Following the largest earthquake, we observe a distinct population of earthquakes with comparatively low b ‐values occurring in an area of high roughness within the rupture area of the M 4.4 earthquake. Finally, we measure roughness at multiple scales and find that the fault is self‐affine with a Hurst exponent of 0.52, consistent with a Brownian surface.

California↗

USGS2022

Aftershocks preferentially occur in previously active areas

The clearest statistical signal in aftershock locations is that most aftershocks occur close to their mainshocks. More precisely, aftershocks are triggered at distances following a power‐law decay in distance ( Felzer and Brodsky, 2006 ). This distance decay kernel is used in epidemic‐type aftershock sequence (ETAS) modeling and is typically assumed to be isotropic, even though individual sequences show more clustered aftershock occurrence. The assumption of spatially isotropic triggering kernels can impact the estimation of ETAS parameters themselves, such as biasing the magnitude‐productivity term, alpha, and assigning too much weight to secondary rather than primary (direct) triggering. Here we show that aftershock locations in southern California, at all mainshock–aftershock distances, preferentially occur in the areas of previous seismicity. For a given sequence, the scaling between aftershock rates and the previous seismicity rate is approximately linear. However, the total number of aftershocks observed for a given sequence is independent of background rate. We explain both of these observations within the framework of rate‐and‐state friction ( Dieterich, 1994 ).

California↗

USGS2022

Prospective and retrospective evaluation of the U.S. Geological Survey public aftershock forecast for the 2019-2021 Southwest Puerto Rico Earthquake and aftershocks

The M w "> M w 6.4 Southwest Puerto Rico Earthquake of 7 January 2020 was accompanied by a robust fore‐ and aftershock sequence. The U.S. Geological Survey (USGS) has issued regular aftershock forecasts for more than a year since the mainshock, available on a public webpage. Forecasts were accompanied by interpretive and informational material, published in English and Spanish. Informational products included narrative “scenarios” for how the aftershock sequence could play out, infographics, and a report on the potential duration of the aftershock sequence through the next decade. Forecasts are based on the epidemic‐type aftershock sequence (ETAS) model and generated using the USGS AftershockForecaster software—an interactive graphical user interface built on the OpenSHA platform ( Field et al. , 2003 ). The initial forecast is based on past sequences in similar tectonic environments; subsequent forecasts are tuned to the ongoing sequence via Bayesian model updating. Probabilistic aftershock forecasts for the next day, week, month, and year were publicly released and archived at a daily to monthly tempo, allowing for a truly prospective test of the forecast. Here, we evaluate the forecast over the first year of the recorded aftershocks. The ETAS‐based forecast performed well overall, successfully capturing both the chance of having at least one earthquake of a given magnitude in a forecast interval as well as the non‐Poissonian distribution of the total number of aftershocks within an interval. A retrospective analysis shows that the ETAS model is a substantial improvement over the existing Reasenberg and Jones (1989) forecast model. The exercise also reveals some limitations of the current model, in particular, with respect to nonstationarities in the aftershock magnitude distribution and model parameters throughout the evolving sequence.

Puerto Rico↗

USGS2021

Improvements to the Third Uniform California Earthquake Rupture Forecast ETAS Model (UCERF3‐ETAS)

We describe recent improvements to the Third Uniform California Earthquake Rupture Forecast ETAS Model (UCERF3‐ETAS), which continues to represent our most advanced and complete earthquake forecast in terms of relaxing segmentation assumptions and representing multifault ruptures, elastic‐rebound effects, and spatiotemporal clustering (the latter to represent aftershocks and otherwise triggered events). The two main improvements include adding aleatory variability in aftershock productivity and the option to represent off‐fault events with finite‐rupture surfaces. We also summarize the studies that led to these modifications, and reflect on how past and future uses of the model can improve our understanding of earthquake processes and the hazards and risks they pose.

California↗

USGS2021

B-positive: A robust estimator of aftershock magnitude distribution in transiently incomplete catalogs

The earthquake magnitude-frequency distribution is characterized by the b -value, which describes the relative frequency of large versus small earthquakes. It has been suggested that changes in b -value after an earthquake can be used to discriminate whether that earthquake is part of a foreshock sequence or a more typical mainshock-aftershock sequence, with a decrease in b -value heralding a larger earthquake to come. However, the measurement of b -value during an active aftershock sequence is strongly biased by short-term incompleteness of the earthquake catalog and by data-windowing, and these biases have the same direction as the proposed signal. Here I develop a new estimator of the b- value that is insensitive to transient changes in catalog completeness and that does not require data windowing. The new estimator “ b -positive” is based on the positive-only subset of the differences in magnitude between successive earthquakes, which are described by a double-exponential (Laplace) distribution with the same b -value as the magnitude distribution itself. The b -positive estimator greatly improves the robustness of continuous b -value measurements during active earthquake sequences, as well as in historical catalogs with unknown or variable completeness. The new estimator confirms some of the observations of Gulia and Wiemer (2019), although at a reduced level, showing a decrease and recovery of the b -value during several recent foreshock sequences that cannot be attributed simply to measurement bias. However, the unbiased b -value changes may be too subtle to use in a real-time earthquake alarm system.

Journal of Geophysical Research: Solid Earth↗

USGS2020

Potential duration of aftershocks of the 2020 southwestern Puerto Rico earthquake

Abstract Aftershocks (earthquakes clustered spatially and chronologically near the occurrence of a causative earthquake) are ongoing in southwestern Puerto Rico after a series of earthquakes, which include a magnitude 6.4 earthquake that occurred near Barrio Indios, Guayanilla, on January 7, 2020, and affected the surrounding area. This report estimates the expected duration of these aftershocks by incorporating observations of aftershocks as of January 17, 2020, into a well-established statistical model of how earthquake sequences behave. Aftershocks will persist for years to decades, although with decreasing frequency, and earthquakes will likely be felt on a daily basis for up to several months. These estimates have significant uncertainty owing to different scenarios of how the earthquake sequence may evolve over time and could also change if a new large aftershock occurs. This report also estimates the amount of time remaining until the annual probability of magnitude 5, 6, and 7 or greater aftershocks—which could cause additional damage—decreases to 50, 25, 10, 5, and 1 percent. As of this writing, the chance of having a magnitude 6 or greater earthquake within a given year, going forward, will not fall below 25 percent for another 3 months to 3 years. The chance of having a magnitude 5 or greater earthquake will not fall below 25 percent for a decade or more. The aftershocks discussed in this report would be located in the same general area as the aftershocks that have already occurred. Our results do not imply a change in the risk of earthquakes in other parts of Puerto Rico. Resumen Las réplicas (terremotos agrupados espacial y cronológicamente cerca de la ocurrencia de un terremoto causante) están en curso en el suroeste de Puerto Rico después de una serie de terremotos, que incluyen un terremoto de magnitud 6.4, ocurrido cerca del Barrio Indios, Guayanilla, el 7 de enero de 2020 y que afectaron las áreas circundantes. Este informe estima la duración esperada de las réplicas incorporando observaciones de réplicas a partir del 17 de enero de 2020 en un modelo estadístico bien establecido de cómo se comportan las secuencias de terremotos. Las réplicas persistirán durante años o décadas, aunque con una frecuencia decreciente, y los terremotos probablemente se sentirán a diario durante varios meses. Estos estimados tienen una incertidumbre significativa debido a diferentes escenarios de cómo la secuencia del terremoto puede evolucionar con el tiempo y también podrían cambiar si ocurre una nueva réplica grande. Este informe también estima la cantidad de tiempo restante hasta que la probabilidad anual de réplicas de magnitud 5, 6 y 7 o más - que podría causar daños adicionales- disminuya a un 50, 25, 10, 5 y 1 por ciento. Al momento de escribir este artículo, la posibilidad de tener un terremoto de magnitud 6 en un año determinado, en el futuro, no caerá por debajo del 25 por ciento durante otros 3 meses a 3 años. La probabilidad de tener un terremoto de magnitud 5 o mayor no será inferior al 25 por ciento durante una década o más. Las réplicas discutidas en este informe se ubicarían en la misma área general que las réplicas que ya han ocurrido. Nuestros resultados no implican un cambio en el riesgo de terremotos en otras partes de Puerto Rico.

Puerto Rico↗