Magnitude Distribution Of Earthquakes Research Articles

Seismotectonics-Driven Estimation of b-Value: Implications for Seismic Hazard Assessment

Abstract Taking full advantage of good-quality historical earthquake and seismogenic source data available for Italy (Catalogo Parametrico dei Terremoti Italiani [CPTI15] and Database of Individual Seismogenic Sources [DISS] databases), we tested the regional variability of the b-value of the Gutenberg–Richter law, focusing on the dominantly extensional, nearly 1200-km-long seismogenic corridor straddling the Apennines chain; an 18,200 km2 area generating about 45% of the seismic moment released countrywide. We carefully chose and tested the most appropriate completeness interval and completeness magnitude (Mc), and used the Lilliefors method, the Utsu test, and a bootstrap technique to verify the quality of our results and inferences. The 0.65 b-value we obtained is substantially lower than b-values used in Italian seismic hazard models, often close to 1.0; yet it predicts more accurately the observed Apennines earthquake record, suggesting that most currently adopted magnitude-frequency distributions underpredict events in the Mw range 6.0–7.1 and overpredict those in the range 5.2–5.5. We also highlight that the time, space, and magnitude distribution of the largest Italian earthquakes hardly follows the Gutenberg–Richter law: it rather favors a characteristic behavior. We contend that the b-value is too critical of a parameter for being calculated using statistically weak data sets, such as those resulting from overly detailed area-source models: one may end up characterizing low-hazard areas more accurately than high-hazard areas. Conversely, we advocate the use of fewer, larger area sources that fully exploit the current understanding of regional seismotectonics, as a way of obtaining more realistic regional hazard models.

The estimation of b-value of the frequency–magnitude distribution and of its 1σ intervals from binned magnitude data

SUMMARY The estimation of the slope (b-value) of the frequency–magnitude distribution of earthquakes is based on a formula derived by Aki decades ago, assuming a continuous exponential distribution. However, as the magnitude is usually provided with a limited resolution, its distribution is not continuous but discrete. In the literature, this problem was initially solved by an empirical correction (due to Utsu) to the minimum magnitude, and later by providing an exact formula such as that by Tinti and Mulargia, based on the geometric distribution theory. A recent paper by van der Elst showed that the b-value can be estimated also by considering the magnitude differences (which are proven to follow an exponential discrete Laplace distribution) and that in this case the estimator is more resilient to the incompleteness of the magnitude data set. In this work, we provide the complete theoretical formulation including (i) the derivation of the means and standard deviations of the discrete exponential and Laplace distributions; (ii) the estimators of the decay parameter of the discrete exponential and trimmed Laplace distributions and (iii) the corresponding formulas for the parameter b. We deduce (iv) the standard 1σ intervals for the estimated b. Moreover, we are able (v) to quantify the error associated with the Utsu minimum-magnitude correction. Furthermore, we have discussed the formulas to produce statistically independent magnitude differences. We tested extensively the b-value estimators on simulated synthetic data sets including complete catalogues as well as catalogues affected by a strong incompleteness degree such as aftershock sequences where the incompleteness is made to vary from one event to the next. We have also analysed the real aftershock sequence of the 30/10/2016 Norcia (central Italy) to integrate the finding of the simulations. To judge the performance of the various estimators we have introduced an index p that can be seen as a non-parametric extension of the Student's t index. The main outcomes of this paper are that (1) the b-value estimators devised for continuous magnitude data are not adequate for binned magnitudes, (2) for complete data sets, estimators based on magnitudes and on magnitude differences provide substantially equivalent results, (3) for incomplete magnitude data sets, estimators based on magnitude differences provide better results and (4) for incomplete aftershock sequences there is no evidence that methods based on positive magnitude differences are superior than other methods using differences. This conclusion is further confirmed by our analysis of the above-mentioned Norcia seismic sequence. This last finding contrasts with the van der Elst's claim that the so called ${{b}_ + }$ method is the most adequate to treat real aftershock sequences.

Stress spatial distributions, the Gutenberg–Richter and Omori–Utsu laws

We investigate several earthquake models in one and two dimensions of space and analyze in these models the stress spatial distribution. We show that the statistical properties of stress distribution are responsible for the distribution of earthquake magnitudes, as described by the Gutenberg–Richter (GR) law. A series of predictions is made based on the analogies between the stress profile and one-dimensional random curves or two-dimensional random surfaces. These predictions include the b-value, which determines the ratio of small to large seismic events and, in two-dimensional models, we predict the existence of aftershocks and their temporal distribution, known as the Omori–Utsu law. Both the GR and Omori–Utsu law are properties which have been extensively validated by earthquake observations in nature.

A statistical framework for detection of b-value anomalies in Italy

SUMMARY This study presents a new robust statistical framework, in which to measure relative differences, or deviations from a hypothetical reference value, of Gutenberg–Richter b-value. Moreover, it applies this method to recent seismicity in Italy, to find possible changes of earthquake magnitude distribution in time and space. The method uses bootstrap techniques, which have no prior assumptions about the distribution of data, keeping their basic features. Excluding Central Italy, no significative b-value variation is found, revealing that the frequency–magnitude distribution exponent is substantially stable or that data are not able to reveal hidden variations. Considering the small size of examined magnitude samples, we cannot definitively decide if the higher b-values in Central Italy, consistently founded by all applied tests, have a physical origin or result from a statistical bias. In any case, they indicate short-lived excursions which have a temporary nature and, therefore, cannot be associated solely to spatial variations in tectonic framework. Both the methodological issues and the results of the application to seismicity in Italy show that a correct assessing of b-value changes requests appropriate statistics, that accurately quantify the low accuracy and precision of b-value estimation for small magnitude samples.

Testing the Predictive Power of b Value for Italian Seismicity

A very efficient method for estimating the completeness magnitude mc and the scaling parameter b of earthquake magnitude distribution has been thoroughly tested using synthetic seismic catalogues. Subsequently, the method was employed to assess the capability of the b-value in differentiating between foreshocks and aftershocks, confirming previous findings regarding the Amatrice-Norcia earthquake sequence. However, a blind algorithm reveals that the discriminative ability of the b-value necessitates a meticulous selection of the catalogue, thereby reducing the predictability of large events occurring subsequent to a prior major earthquake.

On the b-value dependency of injection-induced seismicity on geomechanical parameters

Variability in the b-value, which describes the frequency distribution of earthquake magnitudes, is usually attributed to variations in differential stress in the setting of natural and laboratory earthquakes. However, differential stress is unlikely to explain b-value variations on the reservoir scale of injection-induced seismicity cases where significant differential stress variability can hardly be expected. We investigate the responsible geomechanical parameters for the b-value reduction observed in injection-induced seismicity at the Basel EGS field in Switzerland, for which a measured in-situ stress model and fault orientations of numerous microseismic events are available. We estimate the shear and normal stresses along faults, differential stress, pore pressure increase at failure, and the Coulomb failure stress, for each event. Event magnitude and shear stress display the most systematic and clear correlation between each other, while other parameters do not show a clear correlation with event magnitude. We further examine the relationship between the b-value and these geomechanical parameters. We discover that the b-value systematically decreases with increasing shear stress. Again, other geomechanical parameters do not show a clear correlation with the b-value. We conclude that b-value variability is explained by variations in shear stress in the injection-induced seismicity setting, where near constant differential stress conditions are expected. Furthermore, we observe that b-value reduction with time also correlates with an increasing number of events along faults having high shear stress, which strongly supports our conclusions. Thus, we discovered a profound physical mechanism behind b-value variation in injection-induced seismicity beyond general understanding of b-value variation.

Earthquake magnitude distribution and aftershocks: A statistical geometry explanation.

The emergence of a power-law distribution for the energy released during an earthquake is investigated in several models. Generic features are identified which are based on the self-affine behavior of the stress field prior to an event. This field behaves at large scale as a random trajectory in one dimension of space and a random surface in two dimensions. Using concepts of statistical mechanics and results on the properties of these random objects, several predictions are obtained and verified, in particular the value of the power-law exponent of the earthquake energy distribution (the Gutenberg-Richter law) as well as a mechanism for the existence of aftershocks after a large earthquake (the Omori law).

Estimating the recurrence of earthquakes with statistical methods in the city of Bingöl, Eastern Turkey: a district-based approach

This study discusses the temporal distribution of earthquake magnitudes in the city of Bingöl, near Karlıova Triple Junction. We determine the probability distributions and return periods of earthquakes for all districts of Bingöl. Bingöl has eight districts; namely Adaklı, Central, Genç, Karlıova, Kiğı, Solhan, Yayladere, and Yedisu. In six of them, active faults were mapped previously (Adaklı, Central, Genç, Karlıova, Solhan, and Yedisu). We consider 5 time-dependent probability distributions for analysis. Using the annual maximum earthquake magnitudes, the best fit arises from the Gumbel distribution for Central, Karlıova, and Adaklı Districts. For the Genç District, where the least maximum earthquake magnitude is reported, the Weibull distribution gives the best fit. The return period and maximum annual earthquake magnitude relations suggest the following results. For the Central and Karlıova Districts along which maximum earthquake magnitudes are reported, every 250 years a 6.7 M, and 7.2 M occurs respectively. These results are compatible with the results of paleo-seismological data reported along the NAFZ and the EAFZ. For a 10-year return period, earthquake magnitudes reach 3.9 and 5.1 in all districts. It is important to note that in the Yedisu District, the maximum earthquake magnitudes seem as 5.1 M for the 1000-year return period, incompatible with previously published findings probably because low quality seismic data in this region.

Spatio-temporal analysis of b-value prior to 28 April 2021 Assam Earthquake and implications thereof

Here, we report a Spatio-temporal analysis of the frequency magnitude distribution of earthquakes (b-value) before the 28th April 2021 (Mw 6.4) earthquake event observed in northeast India. To esti- mate the average b-value for the study region, a data set of 750 earthquake events with magnitude Mw ≥ 3.9 is extracted from the homogenous part of the earthquake catalog (1950-2021) documented by the United States Geological Survey (USGS) and International seismological center (ISC) in the region. For spatial analysis of the disparities in b-value, the whole study region is subdivided into 16 square grids of dimension 1o×1o and the b-value is calculated for each subsection. In congruence with other studies, this work yields b-values ranging from 0.66 to 1.25. After the calculation of the b-value for each grid, it is observed that the grid with the epicentral location of the 28th April 2021 (6.4) earthquake has a low b-value. Accordingly, the spatial correlation and aberrant pattern between b-value and focal depth have been comprehensively explored. It is observed that the b-value sig- nificantly dips within a depth range of ~15-35 km which implicates high-stress accumulation and crustal homogeneity. The depth-wise variation in b-value infers the antithetical relationship between b-value and crustal stress. Mostly interplate earthquakes are observed in the study region; thereby hinting at intense seismicity at the upper crust.

Revisiting b-value for extended Kopili region of Northeast India and probabilistic estimation of seismic hazard attributes thereof

Kopili fault and its' surroundings of northeast India have remained witness to some devastating earthquakes. The complex tectonic feature of this region incurs a high seismicity rate relative to other regions. Very recently, an earthquake of magnitude 6.4 (MW) has jolted this region. Considering the persistently rising seismicity pattern of this region, the present study intends to integrate the frequency magnitude distribution of earthquakes with other pertinent seismic hazard parameters. This work presents the estimation of the return period and probability of non-exceedance of medium to large earthquakes for the Kopili fault and its' surroundings via the extreme value method. Two statistical methods, namely the Gutenberg-Richter(G-R) power law and Gumbel extreme value method (GEVM), are applied for the correct estimation of the b-value for the Kopili fault and its' surrounding region. The uniform and homogenous magnitude scale dataset consisting of 550 events observed within a limit of 350 km from the Kopili fault (1964 to 2022) are used in the study. The b-value computed using GR relation was found to be unsatisfactory (0.73) due to an inadequate dataset—thus Gumbel's extreme value method is used for the estimation of the b-value (0.97). Gumbel's extreme value method is used for the calculation of the probability of occurrence of earthquakes, return period, and the most probable earthquake magnitude for the study region. The most probable annual earthquake is found to be ∼ MW 4.99. The return period and probability of occurrence of design-based earthquakes are also calculated. The correlation between b-value, seismic moment, and fractal dimension for seismic hazard analysis is also investigated. The antithetical relationship between seismic moment and b-value is observed for the region while the deep-root character of the Kopili fault and the strong, unfractured character of the Shillong plateau is highlighted with the spatial distribution of fractal dimension in the study region.

Linking Earthquake Magnitude‐Frequency Statistics and Stress in Visco‐Frictional Fault Zone Models

AbstractThe ability to estimate the likelihood of given earthquake magnitudes is critical for seismic hazard assessment. Earthquake magnitude‐recurrence statistics are empirically linked to stress, yet which fault‐zone processes explain this link remains debated. We use numerical models to reproduce the interplay between viscous creep and frictional sliding of a fault‐zone, for which inter‐seismic locking becomes linked to stress. The models reproduce the empirical stress‐dependent earthquake magnitude distribution observed in nature. Stress is related to the likelihood a fault section is near frictional failure, influencing likely rupture lengths. An analytical model is derived of a fault consisting of identical patches, each with a probability of inter‐seismic locking. It reproduces a similar magnitude‐recurrence relationship, which may therefore be caused by probabilistic clustering of locked fault patches. Contrasts in earthquake statistics between regions could therefore be explained by stress variation, which has future potential to further constrain statistical models of regional seismicity.

Frequency magnitude distribution and spatial correlation dimension of earthquakes in north-east Himalaya and adjacent regions

Abstract The north-east sector of the Himalaya is one of the most active tectonic belts, with complex geological and tectonic features. The b-value and spatial correlation dimension (Dc) of earthquake distribution in the north-east Himalaya and its adjacent regions (20–32°N and 88–98°E) are estimated in the present study. Based on seismicity and faulting pattern, the region is divided into five active regions, namely the (i) South-Tibet, (ii) Eastern-Syntaxis, (iii) Himalayan-Frontal Arc, (iv) Arakan-Yoma belt and (v) Shillong-Plateau. A homogeneous catalogue of 1,416 earthquakes (mb ≥ 4.5) has been prepared from a revised catalogue of the ISC (International Seismological Centre). The b-value has been appraised by the maximum likelihood estimation method, while Dc values have been calculated by the correlation integral method; b-values of 1.08 ± 0.09, 1.13 ± 0.05, 0.92 ± 0.05, 1.00 ± 0.03 and 0.98 ± 0.08 have been computed for the South-Tibet, Eastern-Syntaxis, Himalayan-Frontal Arc, Arakan-Yoma belt and Shillong-Plateau region, respectively. The Dc values computed for the respective regions are 1.36 ± 0.02, 1.74 ± 0.04, 1.57 ± 0.01, 1.8 ± 0.01, and 1.83 ± 0.02. These values are > 1.5, except for the South-Tibet (1.36 ± 0.02). The b-values around the global average value (1.0) reflect the stress level and seismic activity of the regions, while high Dc values refer to the heterogeneity of the seismogenic sources.

A Note on the Estimation of the Maximum Possible Earthquake Magnitude Based on Extreme Value Theory for the Groningen Gas Field

ABSTRACT Extreme value statistics is a popular and frequently used tool to model the occurrence of large earthquakes. The problem of poor statistics arising from rare events is addressed by taking advantage of the validity of general statistical properties in asymptotic regimes. In this note, I argue that the use of extreme value statistics for the purpose of practically modeling the tail of the frequency–magnitude distribution of earthquakes can produce biased and thus misleading results because it is unknown to what degree the tail of the true distribution is sampled by data. Using synthetic data allows to quantify this bias in detail. The implicit assumption that the true Mmax is close to the maximum observed magnitude Mmax,observed restricts the class of the potential models a priori to those with Mmax=Mmax,observed+ΔM with an increment ΔM≈0.5…1.2. This corresponds to the simple heuristic method suggested by Wheeler (2009) and labeled “Mmax equals Mobs plus an increment.” The incomplete consideration of the entire model family for the frequency–magnitude distribution neglects, however, the scenario of a large so far unobserved earthquake.

3D-ИССЛЕДОВАНИЕ СЕЙСМИЧНОСТИ: ОЦЕНКИ, ТОЧНОСТЬ И ПРЕДСТАВИТЕЛЬНОСТЬ МОДЕЛЕЙ, СТАБИЛЬНОСТИ СЕЙСМОТЕКТОНИЧЕСКИХ НАПРЯЖЕНИЙ И РЕОЛОГИЧЕСКИХ ВОЗМОЖНОСТЕЙ ИНТЕРПРЕТАЦИИ ПРОСТРАНСТВЕННЫХ РАСПРЕДЕЛЕНИЙ ЗЕМЛЕТРЯСЕНИЙ

With an increase in the number of seismic stations and their throughput in the Amur region, the representativeness of the catalog grows. The author has analyzed the earthquake magnitudes distribution in four time ranges and revealed their static regularity. Earthquake magnitude distributions mark large tectonic structures. It allows the study of three-dimensional geological structure of the Amur region in continuous space, and over a wide time range.

Earthquake Magnitude Distributions on Northern Caribbean Faults From Combinatorial Optimization Models

AbstractOn‐fault earthquake magnitude distributions are calculated for northern Caribbean faults using estimates of fault slip and regional seismicity parameters. Integer programming, a combinatorial optimization method, is used to determine the optimal spatial arrangement of earthquakes sampled from a truncated Gutenberg‐Richter distribution that minimizes the global misfit in slip rates on a complex fault system. Slip rates and their uncertainty on major faults are derived from a previously published GPS block model for the region, with fault traces determined from offshore geophysical mapping and previously published onshore studies. The optimal spatial arrangement of the sampled earthquakes is compared with the 500‐year history of earthquake observations. Rupture segmentation of the subduction interface along the Hispaniola‐Puerto Rico Trench (PRT) fault and seismic coupling on the PRT fault appear to exert the primary control over this spatial arrangement. Introducing a rupture barrier for the Hispaniola‐PRT fault northwest of Mona Passage, based on geophysical and seismicity observations, and assigning a low slip rate of 2 mm/yr on the PRT fault are most consistent with historical earthquakes in the region. The addition of low slip‐rate secondary faults as well as segmentation of the Hispaniola and Septentrional strike‐slip fault improves the consistency with historical seismicity. An important observation from the modeling is that varying the slip rate on the PRT fault and different segmentation scenarios result in significant changes to the optimal magnitude distribution on faults farther away. In general, optimal on‐fault magnitude distributions are more complex and inter‐dependent than is typically assumed in probabilistic seismic hazard analysis and probabilistic tsunami hazard analysis.

Seismicbvalue within the Montney play of northeastern British Columbia, Canada

Critical analysis of induced earthquake occurrences requires comprehensive data sets obtained by dense seismographic networks. In this study, using such data sets, I take a detailed investigation into induced seismicity that occurred in the Montney play of northeastern British Columbia, mostly caused by hydraulic fracturing. The frequency–magnitude distribution (FMD) of earthquakes in several temporal and spatial clusters show fundamental discrepancies between seismicity in the southern Montney play (2014–2018) and the northern area (2014–2016). In both regions, FMDs follow the linear Gutenberg–Richter (G–R) relationship for magnitudes up to 3.0. While in southern Montney, within the Fort St. John graben complex, the number of earthquakes at larger magnitudes falls off rapidly below the G–R line, within the northern area with a dominant compressional regime, the number of events increases above the G–R line. This systematic difference may have important implications with regard to seismic hazard assessments from induced seismicity in the two regions, although caution in the interpretation is warranted due to local variabilities. While for most clusters within the southern Montney area, the linear or truncated G–R relationship provide reliable seismicity rates for events below magnitude 4.0, the G–R relationship underestimates the seismicity rate for magnitudes above 3.0 in northern Montney. Using a well-located data set of earthquakes in southern Montney, one can observe generally that (1) seismic productivity correlates well with the injected volume during hydraulic fracturing and (2) there is a clear depth dependence for the G–R b value; clusters with deeper median depths show lower b values than those with shallower depths.

Physics-based simulation of sequences with multiple main shocks in Central Italy

SUMMARYThe application of a physics-based earthquake simulator to Central Italy allowed the compilation of a synthetic seismic catalogue spanning 100 000 yr, containing more than 300 000 M ≥ 4.0 simulated earthquakes, without the limitations that real catalogues suffer in terms of completeness, homogeneity and time duration. The seismogenic model upon which we applied the simulator code was derived from version 3.2.1 of the Database of Individual Seismogenic Sources (DISS; http://diss.rm.ingv.it/diss/), selecting, and modifying where appropriate, all the fault systems that are recognized in the portion of Central Italy considered in this study, with a total of 54 faults. Besides tectonic stress loading and static stress transfer as in the previous versions, the physical model on which the latest version of our simulation algorithm is based also includes the Rate and State constitutive law that helps to reproduce Omori's law. One further improvement in our code was also the introduction of trapezoidal-shaped faults that perform better than known faults. The resulting synthetic seismic catalogue exhibits typical magnitude, space and time features which are comparable to those in real observations. These features include the total seismic moment rate, the earthquake magnitude distribution, and the short- and medium-term earthquake clustering. A typical aspect of the observed seismicity in Central Italy, as well as across the whole Italian landmass and elsewhere, is the occurrence of earthquake sequences characterized by multiple main shocks of similar magnitude. These sequences are different from the usual earthquake clusters and aftershock sequences, since they have at least two main shocks of similar magnitude. Therefore, special attention was devoted to verifying whether the simulated catalogue includes this notable aspect. For this purpose, we developed a computer code especially for this work to count the number of multiple events contained in a seismic catalogue under a quantitative definition. We found that the last version of the simulator code produces a slightly larger number of multiple events than the previous versions, but not as large as in the real catalogue. A possible reason for this drawback is the lack of components such as pore-pressure changes due to fluid-diffusion in the adopted physical model.

Magnitude distribution complexity and variation at The Geysers geothermal field

SUMMARYEarthquake magnitude (size) distribution is a major component required for seismic hazard assessment and therefore, the accurate determination of its functional shape and variation is a task of utmost importance. Although often considered as stationary, the magnitude distribution at particular sites may significantly vary over time and space. In this study, the well-known Gutenberg–Richter (GR) law, which is widely assumed to describe earthquake magnitude distribution, is tested for a case study of seismicity induced by fluid injection at The Geysers (CA, USA) geothermal field. Statistical tests are developed and applied in order to characterize the magnitude distribution of a high quality catalogue comprising seismicity directly associated with two injection wells, at the north western part of The Geysers. The events size distribution variation is investigated with respect to spatial, temporal, fluid injection and magnitude cut-off criteria. A thorough spatio-temporal analysis is performed for defining seismicity Clusters demonstrating characteristic magnitude distributions which significantly differ from the ones of the nearby Clusters. The magnitude distributions of the entire seismic population as well as of the individual Clusters are tested for their complexity in terms of exponentiality, multimodal and multibump structure. Then, the Clusters identified are further processed and their characteristics are determined in connection to injection rate fluctuations. The results of the analysis clearly indicate that the entire magnitude distribution is definitely complex and non-exponential, whereas subsequent periods demonstrating significantly diverse magnitude distributions are identified. The regional seismicity population is divided into three major families, for one of which exponentiality of magnitude distribution is clearly rejected, whereas for the other two the GR law b-value is directly proportional to fluid injection. In addition, the b-values of these Families seem to be significantly magnitude dependent, a fact that is of major importance for seismic hazard assessment implementations. To conclude, it is strongly suggested that magnitude exponentiality must be tested before proceeding to any b-value calculations, particularly in anthropogenic seismicity cases where complex and time changeable processes take place.

Risk from Oklahoma’s Induced Earthquakes: The Cost of Declustering

ABSTRACTThe U.S. Geological Survey (USGS) has for each year 2016–2018 released a one-year seismic hazard map for the central and eastern United States (CEUS) to address the problem of induced and triggered seismicity (ITS) in the region. ITS in areas with historically low rates of earthquakes provides both challenges and opportunities to learn about crustal conditions, but few scientific studies have considered the financial risk implications of damage caused by ITS. We directly address this issue by modeling earthquake risk in the CEUS using the 1 yr hazard model from the USGS and the RiskLink software package developed by Risk Management Solutions, Inc. We explore the sensitivity of risk to declustering and b-value, and consider whether declustering methods developed for tectonic earthquakes are suitable for ITS. In particular, the Gardner and Knopoff (1974) declustering algorithm has been used in every USGS hazard forecast, including the recent 1 yr forecasts, but leads to the counterintuitive result that earthquake risk in Oklahoma is at its highest level in 2018, even though there were one-fifth as many earthquakes as occurred in 2016. Our analysis shows that this is a result of (1) the peculiar characteristics of the declustering algorithm with space-varying and time-varying seismicity rates, (2) the fact that the frequency–magnitude distribution of earthquakes in Oklahoma is not well described by a single b-value, and (3) at later times, seismicity is more spatially diffuse and seismicity rate increases are closer to more populated areas. ITS in Oklahoma may include a combination of swarm-like events with tectonic-style events, which have different frequency–magnitude and aftershock distributions. New algorithms for hazard estimation need to be developed to account for these unique characteristics of ITS.

The Effects of Aleatory Variabilities of Seismicity on Probabilistic Seismic Hazard Assessment

ABSTRACTAleatory variability is the natural randomness in a process and can affect probabilistic seismic hazard assessment (PSHA). In this study, considering a simple case of a square areal source zone, I employ Monte Carlo methods to estimate aleatory uncertainties due to random variations in temporal, spatial, and magnitude distribution of seismicity within the zone for PSHA. The results show that (1) uncertainty from aleatory variability in PSHA is significant for areas with low-seismic activity, (2) the ratio of the 85th to 15th percentiles of peak ground acceleration (PGA) decreases as the occurrence rate increases, and (3) accounting for random variations in seismic parameters changes the estimated PGA by more than 10%. My analysis applies to the case in which there are fewer than 10 earthquakes over 50 yr, the site is located outside of the areal source, and b≥1.0. This situation should be considered in PSHA due to the cutoff effect of the magnitude lower limit. In addition, the sensitivity analysis shows that random variations in earthquake magnitude distribution are the largest contributor to aleatory uncertainty in most cases.