Gutenberg-Richter Magnitude-frequency Research Articles

A Bayesian Merging of Earthquake Magnitudes Determined by Multiple Seismic Networks

Abstract We introduce a Bayesian algorithm designed to integrate earthquake magnitudes of the same type reported by various seismic networks, aiming to create unified and standardized catalogs suitable for widespread use. The fundamental concept underpinning this algorithm is the utilization of the inherent consistency within each individual network’s magnitude determination process. Assuming that the magnitudes for an earthquake measured by all networks conform to a Gaussian distribution, with a linear function of the unknown true magnitude serving as its mean, we derive the posterior probability distribution of the true magnitude under four different assumptions for the prior distribution: the uninformative uniform distribution, the unbounded Gutenberg–Richter (GR) magnitude–frequency law, the GR magnitude–frequency relationship restricted by the detection rate, and the truncated GR law as priors. We assess the robustness of the method by a test on several synthetic catalogs and then use it to merge the catalogs compiled by five seismic networks in Italy. The results demonstrate that our proposed magnitude-merging algorithm effectively combines the catalogs, resulting in robust and unified data sets that are suitable for seismic hazard assessment and seismicity analysis.

Earthquake Disaster Fatality Data: Temporally Stable Power Law Behavior and Effects of Underreporting

Abstract We investigate changes in the global reported fatalities from earthquake disasters in the global Emergency Events Database (EM-DAT). Drawing parallels with the Gutenberg–Richter frequency–magnitude analysis, in terms of disaster frequency versus the number of casualties, we see a significant overlap of the curves and improving levels of completeness over six 20-year periods. This implies a decrease in underreporting with time. We find that the apparent strong upward trend in the number of (reported) earthquake disasters in EM-DAT is caused by a gradually improved reporting primarily of events killing fewer than 10 people. Our findings imply that the true (reported and unreported) number of earthquake disasters, according to the EM-DAT definition, has been surprisingly constant over, at least, the last 100 yr. We also show that the average annual number of people killed in earthquake disasters is relatively unaffected by spurious trends in reporting and has remained remarkably constant despite population increase. This implies an impressive reduced mortality risk roughly proportional to population increase since 1900. However, there is no indication in the data that the risk of future mega-disasters is negligible, and further major reductions in vulnerability should be actively pursued.

Statistical Seismic Analysis by b-Value and Occurrence Time of the Latest Earthquakes in Italy

The study reported in this paper concerns the temporal variation in the b-value of the Gutenberg–Richter frequency–magnitude law, applied to the earthquakes that struck Italy from 2009 to 2016 in the geographical areas of L’Aquila, the Emilia Region, and Amatrice–Norcia. Generally, the b-value varies from one region to another dependent on earthquake incidences. Higher values of this parameter are correlated to the occurrence of low-magnitude events spread over a wide geographical area. Conversely, a lower b-value may lead to the prediction of a major earthquake localized along a fault. In addition, it is observed that each seismic event has a different “occurrence time”, which is a key point in the statistical study of earthquakes. In particular, its results are absolutely different for each specific event, and may vary from years to months or even just a few hours. Hence, both short- and long-term precursor phenomena have to be examined. Accordingly, the b-value analysis has to be performed by choosing the best time windows to study the foreshock and aftershock activities.

A New Statistical Perspective on Båth’s Law

Abstract The empirical Båth’s law states that the average magnitude difference (ΔM) between a mainshock and its strongest aftershock is ∼1.2, independent of the size of the mainshock. Although this observation can generally be explained by a scaling of aftershock productivity with mainshock magnitude in combination with a Gutenberg–Richter frequency–magnitude distribution, estimates of ΔM may be preferable because they are directly related to the most interesting information, namely the magnitudes of the main events, without relying on assumptions. However, a major challenge in calculating this value is the bias introduced by missing data points when the strongest aftershock is below the observed cut-off magnitude. Ignoring missing values leads to a systematic error because the data points removed are those with particularly large magnitude differences ΔM. The error can be minimized by restricting the statistics to mainshocks that are at least 2 magnitude units above the cutoff, but then the sample size is strongly reduced. This work provides an innovative approach for modeling ΔM by adapting methods for time-to-event data, which often suffer from incomplete observations (censoring). In doing so, we adequately account for unobserved values and estimate a fully parametric distribution of the magnitude differences ΔM for mainshocks in a global earthquake catalog. Our results suggest that magnitude differences are best modeled by the Gompertz distribution and that larger ΔM are expected at increasing depths and higher heat flows.

Rupture Passing Probabilities at Fault Bends and Steps, with Application to Rupture Length Probabilities for Earthquake Early Warning

ABSTRACTEarthquake early warning (EEW) systems can quickly identify the beginning of a significant earthquake rupture, but the first seconds of seismic data have not been found to predict the final rupture length. We present two approaches for estimating probabilities of rupture length given the rupture initiation from an EEW system. In the first approach, bends and steps on the fault are interpreted as physical mechanisms for rupture arrest. Arrest probability relations are developed from empirical observations and depend on bend angle and step size. Probability of arrest compounds serially with increasing rupture length as bends or steps are encountered. In the second approach, time-independent rates among ruptures from the Uniform California Earthquake Rupture Forecast, Version 3 (UCERF3), are interpreted to apply to the time-dependent condition in which rupture grows from a known starting point. Length probabilities from a Gutenberg–Richter magnitude–frequency relation provide a reference of comparison. We illustrate the new approach using the discretized fault model for California developed for UCERF3. For the case of rupture initiating on the southeast end of the San Andreas fault we find the geometric complexity of the Mill Creek section impedes most ruptures, and only ∼5% are predicted to reach to San Bernardino on the eastern edge of the greater Los Angeles region. Conditional probabilities of length can be precompiled in this manner for any initiation point on the fault system and thus are of potential value in seismic hazard and EEW applications.

Responding to Media Inquiries about Earthquake Triggering Interactions

AbstractIn the aftermath of a significant earthquake, seismologists are frequently asked questions by the media and public regarding possible interactions with recent prior events, including events at great distances away, along with prospects of larger events yet to come, both locally and remotely. For regions with substantial earthquake catalogs that provide information on the regional Gutenberg–Richter magnitude–frequency relationship, Omori temporal aftershock statistical behavior, and aftershock productivity parameters, probabilistic responses can be provided for likelihood of nearby future events of larger magnitude, as well as expected behavior of the overall aftershock sequence. However, such procedures generally involve uncertain extrapolations of parameterized equations to infrequent large events and do not provide answers to inquiries about long-range interactions, either retrospectively for interaction with prior remote large events or prospectively for interaction with future remote large events. Dynamic triggering that may be involved in such long-range interactions occurs, often with significant temporal delay, but is not well understood, making it difficult to respond to related inquiries. One approach to addressing such inquiries is to provide retrospective or prospective occurrence histories for large earthquakes based on global catalogs; while not providing quantitative understanding of any physical interaction, experience-based guidance on the (typically very low) chances of causal interactions can inform public understanding of likelihood of specific scenarios they are commonly very interested in.

Critical zone of the branching crack model for earthquakes: Inherent randomness, earthquake predictability, and precursor modelling

The branching crack model for earthquakes was developed by Vere-Jones and Kagan in the 1970s and the 1980s, respectively. With some simple and rational assumptions, its simulation results explain the Gutenberg-Richter magnitude-frequency relationship and the Omori-Utsu aftershock decay formula. By introducing the concept of the critical zone, this model can be connected with the asperity model, the barrier model, and the nucleation model through a parameter – criticality. Particularly, the size of the critical zone determines the maximum magnitude of potential earthquakes and the source of their anomalies. The key to earthquake forecasting is to determine whether the concerned area is in a critical state and how large the critical zone is. We discuss what kinds of anomalies are meaningful as candidates of earthquake precursors. Finally, we outline modelling strategies for earthquake precursors with low probability gains that are due to the inherent randomness of earthquake source processes.

Shaking is Almost Always a Surprise: The Earthquakes That Produce Significant Ground Motion

AbstractAlthough small earthquakes are expected to produce weak shaking, ground motion is highly variable and there are outlier earthquakes that generate more shaking than expected—sometimes significantly more. We explore datasets of M 0.5–8.3 earthquakes to determine the relative impact of frequent, smaller-magnitude earthquakes that rarely produce strong ground motion, to rare, large earthquakes that always cause strong shaking. We find that the natural variability of ground motion, combined with the Gutenberg–Richter magnitude–frequency relationship, ensures that most occurrences of any ground motion come from earthquakes of smaller magnitude than expected, often >2 magnitude units smaller. This holds even for very strong shaking (>20%g), suggesting that M<7 earthquakes could be a significant source of damage.

Probabilistic assessment of earthquake hazard in the Andaman–Nicobar–Sumatra region

The Andaman–Nicobar–Sumatra (ANS) region is a very hazardous area on the globe, which has witnessed a megathrust earthquake of Mw 9.2 on 26 December 2004 and several dozen large earthquakes in the past. We estimate earthquake hazard parameters (i.e. seismic a- and b-values, maximum expected earthquake magnitudes, mean return periods and probabilities of earthquakes) in 11 shallow and 4 intermediate to deep depth seismogenic zones of the ANS region using a uniform and comprehensive earthquake data for the duration 1906–2018. The earthquake hazard scenarios for all seismogenic zones are calculated using the Gutenberg–Richter frequency–magnitude relation and the Gumbel’s extreme value theory. The low b-values ( 0.90) for the earthquake of Mw 7.0 in the next 50 years and 100 years are observed in shallow zones 4–11 (the Sumatra and Nicobar Islands), while only intermediate to deep zone 4 (Sumatra) shows high probabilities. The low return periods ( 0.90) for the earthquake of Mw 7.0 are observed in shallow zones 5–11 (the Nicobar Islands and Sumatra regions), which suggest high earthquake hazard in these zones. The spatial variations of earthquake hazard parameters from one zone to another suggest a large grade of crustal heterogeneity and seismotectonic complexity present in this area.

AFYONKARAHİSAR İLİ İÇİN POİSSON VE GUMBEL DAĞILIM MODELLERİ İLE DEPREM TEHLİKE ANALİZİ

Bu çalışmada 1900-2019 yılları arasında Afyonkarahisar ve çevresinde meydana gelen depremlere ait veriler dikkate alınarak deprem tehlike analizleri gerçekleştirilmiştir. Bu amaçla Boğaziçi Üniversitesi Kandilli Rasathanesi ve Deprem Araştırma Enstitüsü veri tabanından temin edilen, büyüklüğü Mw ≥ 4.0 olan 404 adet deprem verisi kullanılmıştır. Veriler Afyonkarahisar merkezli (38.75° Kuzey Enlemi ve 30.53° Doğu Boylamı) 130 km yarıçaplı dairesel bir alanı kapsamaktadır. Deprem tehlikesinin ortaya konulması amacıyla sismoloji literatüründe kabul gören Gutenberg-Richter Büyüklük-Frekans bağıntısı kullanılmıştır. Farklı büyüklükteki depremlere ait tekrarlanma periyotları ve her büyüklük değeri için deprem tehlikesi Poisson ve Gumbel Uç Değerler dağılım modelleri ile çözümlenmiştir. Farklı kabullere dayanan iki dağılım modelinden elde edilen sonuçlar karşılaştırılmıştır.

Unified Scaling Law for Earthquakes as Applied to Assessment of Seismic Hazard and Associate Risks

The distribution of the number of seismic events by magnitudes—the Gutenberg–Richter frequency–magnitude relation—is of paramount importance for seismic hazard assessment of a territory. The generalization of the Gutenberg–Richter relation—the Unified Scaling Law for Earthquakes (USLE) proposed in 1988 makes it possible to take into account the pattern of epicentral distribution of seismic events when changing the spatial scale of the analysis. This is extremely important for adequate downscaling of the frequency of occurrence into a smaller area within the territory under study (e.g., in the megalopolis). In 2002, Per Buck suggested a dual formulation of USLE where, instead of the number of earthquakes over a certain period of time, the reciprocal of their frequency of occurrence—the time between seismic events—is used. The same year, the Institute of Earthquake Prediction Theory and Mathematical Geophysics of the Russian Academy of Sciences developed a modified algorithm for robust estimation of USLE parameters referred to as Scaling Coefficients Estimation (SCE) for producing seismic hazard maps of territories prone to seismic effects. This brief review is focused on the use of the USLE approach to the assessment of seismic hazard and associated risk.

Dynamics of Induced Seismicity during the Filling of the Nurek Reservoir

The seismological data in the area of induced seismicity in the region of the Nurek reservoir are analyzed. The analysis is based on the developed database for the earthquakes that occurred from 1955 to 1989 and is aimed at finding the regularities in the variations of the parameters of the transitional seismic regime caused by filling a reservoir. These parameters include the b-value—the slope of the graph of the Gutenberg–Richter frequency–magnitude relationship, the fractal dimension d of the set of the epicenters, and fracture cycle parameter q = αb − d, where coefficient α determines the ratio between the magnitude and source size M = α log l + β. It is shown that during the filling of a reservoir, these parameters undergo statistically reliable variations: at the initial stages, the b-value increases, the fractal dimension of the set of epicenters decreases, and the fracture cycle parameter q grows and becomes positive in the middle of the time interval of reservoir filling. After a reservoir is filled, these parameters recover their background values. The aftershock sequences of the three strongest earthquakes—before, in the beginning, and in the middle of the reservoir filling period—are studied. It is confirmed that the Omori parameter p for the aftershock sequences during filling is smaller than for the earthquake before filling. Based on the dynamics of the studied parameters, it is conjectured that the relaxation time of the transitional seismic regime after the emergence of induced seismicity is about 10 years.

Seismic status in Bangladesh

Seismic status in Bangladesh

Natural Time and Nowcasting Earthquakes: Are Large Global Earthquakes Temporally Clustered?

The objective of this paper is to analyze the temporal clustering of large global earthquakes with respect to natural time, or interevent count, as opposed to regular clock time. To do this, we use two techniques: (1) nowcasting, a new method of statistically classifying seismicity and seismic risk, and (2) time series analysis of interevent counts. We chose the sequences of $$M_{\lambda } \ge 7.0$$ and $$M_{\lambda } \ge 8.0$$ earthquakes from the global centroid moment tensor (CMT) catalog from 2004 to 2016 for analysis. A significant number of these earthquakes will be aftershocks of the largest events, but no satisfactory method of declustering the aftershocks in clock time is available. A major advantage of using natural time is that it eliminates the need for declustering aftershocks. The event count we utilize is the number of small earthquakes that occur between large earthquakes. The small earthquake magnitude is chosen to be as small as possible, such that the catalog is still complete based on the Gutenberg-Richter statistics. For the CMT catalog, starting in 2004, we found the completeness magnitude to be $$M_{\sigma } \ge 5.1$$ . For the nowcasting method, the cumulative probability distribution of these interevent counts is obtained. We quantify the distribution using the exponent, $$\beta$$ , of the best fitting Weibull distribution; $$\beta = 1$$ for a random (exponential) distribution. We considered 197 earthquakes with $$M_{\lambda } \ge 7.0$$ and found $$\beta = 0.83 \pm 0.08$$ . We considered 15 earthquakes with $$M_{\lambda } \ge 8.0,$$ but this number was considered too small to generate a meaningful distribution. For comparison, we generated synthetic catalogs of earthquakes that occur randomly with the Gutenberg–Richter frequency–magnitude statistics. We considered a synthetic catalog of $$1.97 \times 10^5$$ $$M_{\lambda } \ge 7.0$$ earthquakes and found $$\beta = 0.99 \pm 0.01$$ . The random catalog converted to natural time was also random. We then generated $$1.5 \times 10^4$$ synthetic catalogs with 197 $$M_{\lambda } \ge 7.0$$ in each catalog and found the statistical range of $$\beta$$ values. The observed value of $$\beta = 0.83$$ for the CMT catalog corresponds to a p value of $$p=0.004$$ leading us to conclude that the interevent natural times in the CMT catalog are not random. For the time series analysis, we calculated the autocorrelation function for the sequence of natural time intervals between large global earthquakes and again compared with data from $$1.5 \times 10^4$$ synthetic catalogs of random data. In this case, the spread of autocorrelation values was much larger, so we concluded that this approach is insensitive to deviations from random behavior.

Modelling correlation between Gutenberg–Richter parameters a and b in PSHA

It is a common practice to describe the activity of a seismogenic source using Gutenberg–Richter magnitude–frequency relation. The use of this relation includes the statistical determination of three parameters, two of which will be discussed in this paper: the exceedance rate of a threshold magnitude and the rate of decay of the exceedance rate with magnitude. The third parameter, M max , which defines the maximum assumed magnitude, will not be treated here. Due to the methods used to estimate the values of these parameters under certain circumstances, their statistical estimators turn out to be correlated. In this paper we explore: (1) the impact of this correlation on seismic hazard for some simple, canonical cases; and (2) practical ways in which this correlation can be propagated through the seismic hazard calculations. We conclude that the impact of correlation on seismic hazard estimates is moderate and that ignoring correlation is frequently a conservative decision. Also, we propose a way in which correlation can be propagated into seismic hazard calculations within the framework of logic trees.

Seismic behaviour of mountain belts controlled by plate convergence rate

The relative contribution of tectonic and kinematic processes to seismic behaviour of mountain belts is still controversial. To understand the partitioning between these processes we developed a model that simulates both tectonic and seismic processes in a continental collision setting. These 2D seismo-thermo-mechanical (STM) models obtain a Gutenberg–Richter frequency–magnitude distribution due to spontaneous events occurring throughout the orogen. Our simulations suggest that both the corresponding slope (b value) and maximum earthquake magnitude (MWmax) correlate linearly with plate convergence rate. By analyzing 1D rheological profiles and isotherm depths we demonstrate that plate convergence rate controls the brittle strength through a rheological feedback with temperature and strain rate. Faster convergence leads to cooler temperatures and also results in more larger seismogenic domains, thereby increasing both MWmax and the relative number of large earthquakes (decreasing b value). This mechanism also predicts a more seismogenic lower crust, which is confirmed by a transition from uni- to bi-modal hypocentre depth distributions in our models. This transition and a linear relation between convergence rate and b value and MWmax is supported by our comparison of earthquakes recorded across the Alps, Apennines, Zagros and Himalaya. These results imply that deformation in the Alps occurs in a more ductile manner compared to the Himalayas, thereby reducing its seismic hazard. Furthermore, a second set of experiments with higher temperature and different orogenic architecture shows the same linear relation with convergence rate, suggesting that large-scale tectonic structure plays a subordinate role. We thus propose that plate convergence rate, which also controls the average differential stress of the orogen and its linear relation to the b value, is the first-order parameter controlling seismic hazard of mountain belts.

Seismic Parameters of Mining-Induced Aftershock Sequences for Re-entry Protocol Development

A common characteristic of deep mines in hard rock is induced seismicity. This results from stress changes and rock failure around mining excavations. Following large seismic events, there is an increase in the levels of seismicity, which gradually decay with time. Restricting access to areas of a mine for enough time to allow this decay of seismic events is the main approach in re-entry strategies. The statistical properties of aftershock sequences can be studied with three scaling relations: (1) Gutenberg–Richter frequency magnitude, (2) the modified Omori’s law (MOL) for the temporal decay, and (3) Bath’s law for the magnitude of the largest aftershock. In this paper, these three scaling relations, in addition to the stochastic Reasenberg–Jones model are applied to study the characteristic parameters of 11 large magnitude mining-induced aftershock sequences in four mines in Ontario, Canada. To provide guidelines for re-entry protocol development, the dependence of the scaling relation parameters on the magnitude of the main event are studied. Some relations between the parameters and the magnitude of the main event are found. Using these relationships and the scaling relations, a space–time–magnitude re-entry protocol is developed. These findings provide a first approximation to concise and well-justified guidelines for re-entry protocol development applicable to the range of mining conditions found in Ontario, Canada.

Probabilistic seismic hazard analysis using a synthetic earthquake catalog: comparison of the Gyeongju City Hall site with the Seoul City Hall site in Korea

Probabilistic seismic hazard analysis (PSHA) generally requires the identification of line sources (active faults) and area sources where seismicity parameters must be determined. It is not easy to identify seismic sources and to estimate seismicity parameters for sources in the intraplate region. We perform an alternative PSHA with a synthetic earthquake catalog, which does not require the delineation of seismic sources. A synthetic catalog of the Korean Peninsula for 500,000 years is constructed by simulating earthquakes using the Monte Carlo method in such a way that an earthquake is randomly selected from the observed earthquake catalog, its epicenter is perturbed by a normally distributed random number, and a magnitude is assigned to the simulated event with a random value generated based on the Gutenberg-Richter magnitude-frequency relation with specified minimum and maximum magnitudes. The seismicity of the Korean Peninsula is thoroughly investigated for estimation of parameters required for synthesizing the catalog. The SMSIM computer program is used to simulate ground motions at sites instead of estimating the ground motion prediction equation. Two sites are chosen for PSHA; the one is the Seoul City Hall site (Seoul site), a densely populated metropolitan site, and the other is the Gyeongju City Hall site (Gyeongju site) close to the epicenter of the M L 5.8 earthquake on 12 September 2016. Seismic hazard curve, uniform hazard spectra (UHSs), and deaggregation of hazard for two sites are presented. The mean return periods for 0.1, 0.2, and 0.3 g at the Seoul site appears to be 1640, 6170, and 17650 years, respectively while those at the Gyeongju site appears to be 327, 1197, and 3548 years, respectively. The mean return periods for the Seoul site are around five times longer than those for the Gyeongju site, and this fact implies that the seismic hazard level of the Gyeongju site is considerably higher than that of the Seoul site. UHSs for 10% and 2% probabilities of exceedance over 50 years are constructed at both sites. The spectra show peak amplifications around the 0.05-s period.

Features of Earthquake Source Process Simulated by Vere‐Jones’ Branching Crack Model

As opposed to the conventional 2D (circular/elliptical crack) and 1D (linear crack) models for earthquake rupture, which are, respectively, for small‐to‐large earthquakes and mega‐earthquakes, Vere‐Jones’ branching crack model describes the extreme case when the entire rupture process is completely controlled by randomness. This article discusses the similar features between the conventional source models and Vere‐Jones’ branching crack model, which include (a) the magnitude–frequency relation, (b) the source time function, and (c) the rupture duration–seismic moment relation. We proved that the Gutenberg–Richter magnitude–frequency relation holds as an asymptote for more general cases of branching processes. The branching crack model shows that the variance of observed rupture durations is relatively larger for small magnitudes and gives a scaling relation of T ∝ M 1/2 between the rupture duration T and the seismic moment M of an earthquake. Moreover, the stochastic property of the branching process explains why the earthquake magnitude cannot be determined until the entire source process is completed. The results in this article imply that the randomness caused by many unknown factors in the complex environments of earthquake sources cannot be ignored, and it can be effectively described by Vere‐Jones’ branching crack model. We conclude that the earthquake rupture is at least an intermediate process between the conventional deterministic model and the stochastic branching crack model if its mechanism is not completely controlled by randomness, as described by the latter.

Joint Determination of Event Epicenter and Magnitude from Seismic Intensities

Characteristic features of seismicity with long recurrence intervals can be deduced from analysis of historical earthquake records that inherently suffer from uncertainty in the event locations and magnitudes. A novel method to determine the event epicenters and magnitudes jointly from seismic intensities is proposed. The probability for a set of event epicenter and magnitude is assessed by accounting the fitness between the observed and reference seismic intensities, spatial‐occurrence probability based on seismicity density distribution, and temporal‐occurrence probability from the Gutenberg–Richter magnitude–frequency relationship. A set of event epicenter and magnitude yielding the peak probability is chosen. The validity of the method is tested for both synthetic and instrumental seismic‐intensity data, confirming high accuracy. The method is applied effectively to historical events with written seismic damage records. It is found that the errors generally decrease with increasing number and azimuthal coverage of seismic‐intensity data, and increase with epicentral distances. The method appears to be promising for historical earthquakes of which source properties are poorly known. The method is applicable for assessment of the properties of long‐period seismicity, which is crucial for assessment of potential seismic hazards.