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Estimation of earthquake hazard parameters for incomplete and uncertain data files
Abstract
The maximum likelihood estimation of earthquake hazard parameters (maximum regional magnitudem
max, activity rate λ, and theb parameter in the Gutenberg-Richter distribution) is extended to the cases of incomplete and uncertain data. The method accepts
mixed data containing only large (extreme) events and a variable quality of complete data with different threshold magnitude
values. Uncertainty of earthquake magnitude is specified by two values, the lower and upper magnitude limits. It is assumed
that such an interval contains the real unknown magnitude. The proposed approach allows the combination of different quality
catalog parts, e.g. those where the assignment of magnitude is questionable and those with magnitudes precisely determined.
As an illustration of the method, the seismic hazard analysis for western Norway and adjacent sea area (4–8°E, 58–64°N) is
presented on the basis of the strongest earthquakes felt during the period 1831–1889 and three complete catalog parts, covering
the period 1890–1987.
Key words.Earthquake hazard-incomplete and uncertain data
... The Gutenberg-Richter (1984) recurrence model is applied to estimate the occurrence of various earthquake magnitudes. The parameters of the GR model are determined using the Kijko and Sellevoll (1989) method, which considers the completeness of the earthquake catalog in the analysis. The b value is assumed to be constant throughout the region at b=0.83, and the annual occurrence rate (7.8) is distributed among the seismic sources based on their length. ...
This paper assesses the risk-targeted map for the Golestan province in Iran using the iterative integration procedure. In this approach, the ground motion values are estimated based on the philosophy of a uniform risk level, which differs from the traditional approach of a uniform hazard spectrum. To do so, first, a classical seismic hazard analysis is performed in the region to derive the hazard curves. Then, a generic fragility curve to cover variabilities in structures is employed. The analysis is performed for peak ground acceleration and critical spectral acceleration (S0.2 and S1.0). The results indicate that PGA values for a risk-targeted 1% probability of collapse in 50 years vary between 0.10g and 0.55g. This value is higher than the values available in national seismic code like Standard-2800. Therefore, the results from this study can be used in the next revision of the national seismic code in Iran.
... The MAXC technique has been proven to be robust even in cases in which a limited number of earthquakes is available within each zone [58,59,72]. The λ(M c ) parameter was obtained following the procedure proposed by Kijko and Sellevoll [73], whereas the maximum expected magnitude was calculated by adding a positive correction factor equivalent to 0.5 magnitude units to the maximum observed magnitude [74,75]. The seismicity parameters estimated for each area source for the two models (crustal and slab) are presented in Table S1 in the Supplementary Material. ...
Probabilistic Seismic Hazard Assessment (PSHA) was carried out for the administrative region of Attica (Greece). Peak Ground Acceleration (PGA) and Peak Ground Velocity (PGV) values were calculated for return periods of 475 and 950 years for five sub-areas covering the entire region. PGA hazard curves and Uniform Hazard Spectra (UHS) in terms of spectral acceleration (Sa) values were generated for Athens, Methana, and the capitals of each island of Attica (Salamina, Aegina, Poros, Hydra, Spetses, Kythira, and Antikythira). Area sources were adopted from the Euro-Mediterranean Seismic Hazard Model 2013 (ESHM13) and its update, ESHM20, taking into account both crustal and slab tectonic environments. Ground Motion Prediction Equations (GMPEs) proposed for the Greek territory were ranked for PGA and PGV. Each GMPE was reconstructed as a weighted model, accounting for normal and non-normal focal mechanisms for each area source. PGA, PGV, and Sa values were computed using a logic tree, integrating the seismotectonic models as major branches and sub-logic trees, comprised of multiple ranked GMPEs for each area source, as minor branches. The results showed higher seismic hazard values in sub-areas near the Gulf of Corinth and the slab interface, which could indicate a need to revise the active building code in Attica.
... Different levels of completion for the used earthquake catalogue do not allow determining the Cornell and Vanmarcke (1969) model coefficients by a direct regression. Thus, a statistical approach suggested by Kijko and Sellevoll (1992) was used to calculate the recurrence relationship coefficients. The method takes various periods of completeness into consideration. ...
The Gulf of Aden is one of the active tectonic elements encompassing the Arabian Plate, representing a potential hazard for the southern parts of Oman and Yemen. This calls for an improved seismic source model for the Gulf, which is crucial for any future seismic hazard assessment regardless of the adopted approach. The developed model is delineated based on a statistical analysis of an updated earthquake catalogue, tectonic setting, and stress regime in the Gulf of Aden. Kernel density estimation (KDE) is applied to obtain an approximation of the probability density function that governs the statistical distribution of earthquakes in the area. The spatial distribution of earthquake and seismic moment kernel densities are calculated to contribute to the modeling of the seismic source. Statistical methods were then applied for estimating the maximum possible earthquake magnitude (Mmax) and the earthquake recurrence parameters [annual rate of earthquakes (λ) and β-value] for each delineated seismic zone. The seismotectonic features and the results of statistical analysis led to the delineation of four seismic sources with their essential parameters to produce a more reliable seismic hazard analysis.
... Kijko and Sellevoll presented approaches that combined the historical seismic catalog data (only severe events) with different completeness intervals Sellevoll, 1989 and1990). This approach is similar to the Weichert method (Weichert, 1980). ...
The Gutenberg–Richter (G–R) relationship plays an important role in the probabilistic seismic hazard analysis (PSHA). The G–R relationship uses a seismic catalog to consider a region seismic history in the PSHA processing. But earthquake catalogs are usually facing the problem of missing earthquakes that are known as catalog incompleteness. The estimation of the b-value of the G–R relationship suffers from the catalog incompleteness. To have a more precise b-value, we utilize axillary information to complete the catalog. In this paper, we use the artificial statistical method (ASM) for the estimation of missing values of the Kope-Dagh, Iran seismic catalog. The ASM uses the total probability theory and the Bayes formula to constitute a more complete catalog known as the stochastic synthetic seismic catalog (SSSC). Then we estimate the b-value based on SSSC using the bootstrap method. Since this method considers the extended time interval and the SSSC, we expect that the obtained b-value is more reliable and subtle. Having a more precise b-value helps seismic engineers and decision makers to design safe buildings and mitigate earthquake crisis consequences.
Uttarakhand state of India, being located in the seismically active Himalayan mountain range, is highly prone to seismic hazards. This study presents assessment of seismic hazard of Uttarakhand through probabilistic approach. For conducting this study, a homogenous earthquake catalogue for moment magnitude during the period 1953-2020 with magnitude range of 2.0-6.9 consisting of 522 events was used. Various geological structures viz. folds, faults and lineament as well as thrust, have been identified in the associated regions. The state was divided into several grid points and the seismic hazard was evaluated for each of the grid points through probabilistic method. Finally, based on the analysis results, bedrock level hazard maps were developed for the state for contingency level earthquake (CLE) and maximum credible earthquake (MCE). The estimated peak ground acceleration (PGA) of the state is in the range of 0.16g-0.52g for CLE and the PGA varies for 0.20g-0.61g for MCE level earthquake. Main Central Thrust (MCT), Sunder Nagar fault and Ropar fault were observed to be more hazardous in the northern region of the state.
هدف این مطالعه بررسی حساسیت نتایج تفکیک خطر لرزهای به متغیرهای ورودی تحلیل خطر احتمالاتی زمینلرزه است. برای این منظور، فرآیند تحلیل و تفکیک خطر لرزهای برای گسل شمال تهران انجام میگیرد. از آنجاییکه تعیین دقیق پارامترهای لرزهخیزی شامل ماکزیمم بزرگای محتمل زمینلرزه Mmax، بزرگای حداقل Mmin، و پارامترهای a و b در رابطه گوتنبرگ-ریشتر برای این گسل امکانپذیر نیست، عدمقطعیت شناختی به این پارامترها اختصاص داده شد. سپس به کمک روش تحلیل حساسیت مبتنی بر تجزیه واریانس، سهم هر یک از این چشمههای عدم قطعیت در ایجاد تغییرپذیری در نتایج تفکیک خطر لرزهای تعیین شد. نتایج نشان داد که پارامتر لرزهخیزی شیب رابطه گوتنبرگ-ریشتر، b-value، بیشترین تاثیر را بر بیشینه بزرگای محتمل زمینلرزه مستخرج از فرآیند تفکیک خطر لرزهای دارد.
This report is a summary of earthquake hazard sensitivity assessments for Finnish nuclear power plant sites. In this research project, the impact of the input data parameters and modelling method choices of probabilistic earthquake risk assessments
on the earthquake risk of Finnish nuclear power plant sites were studied.
Cette thèse est consacrée à l’étude de la sismicité de la région Nord-Est de l’Algérie. Elle est la première du genre pour cette région, après l’installation du nouveau réseau sismologique Algérien.
Cette étude démontre de façon claire et définitive que cette région est la plus active du Nord de l’Algérie puisque près de 1/3 des évènements sismiques s’y produisent. D’autre part, on constate que cette sismicité ne touche pas de la même façon les différentes régions de cette partie de l’Algérie. C’est pour cela qu’à partir des données géologiques, tectoniques et sismologiques 9 zones sismogènes et plusieurs sous-zones ont été considérées. Par ailleurs, pour chaque zone et zones-zone sismogène, les valeur de b et Mmax ont été déterminés et comparés à d’autres études.
Dans les zones et sous zones sismogènes deux types de sismicité ont été mis en relief: une sismicité de type induite tel que l’exemple de la crise sismique de Mila en 2007 et une sismicité de type tectonique telle que la séquence sismique de Béni-Ilmane en 2010. Ces deux exemples de sismicité ont été révélées à partir d’études
approfondies suite à des campagnes d’enregistrements instrumentales d’études approfondies en termes de localisation et relocalisation, mécanismes aux foyers, champs de contraintes, paramètres de la source, CFF et la tomographie sismique.
Dans cette thèse, nous avons également mis en évidence de nouvelles failles actives (failles de Béni-Ilmane et la faille de Djebel Akhal) mais également considérées des failles peu étudiées précédemment (la structure transversale de Kherrata, la faille de Tachaouft, la structure d’El Madher et la structure de Bir-Haddada).
Cette thèse reste un document de référence pour plusieurs études ultérieures d’établir un modèle fiablede l’Aléa sismique dans ces régions.
This paper presents the deaggregation of seismic hazard analysis for the Amaravati region of Andhra Pradesh, characterized by moderate seismicity in Peninsular India. The past few major earthquakes in the Peninsular Indian region have attracted many researchers to conduct a micro-level seismic hazard analysis. After the bifurcation of Telangana state from Andhra Pradesh in 2014, Amaravati and adjoining localities have been proposed as new capital to the residual state of Andhra Pradesh. Because of the significance of capital, the present study i.e., deaggregation of seismic hazard of the Amaravati region has been carried out. In this study, the complete analysis was carried out in three stages. First, an updated earthquake catalog has been prepared from a radial distance of 500 km keeping Velgapudi as the center. The seismic hazard parameters were estimated considering the earthquake data after declustering. In the second stage of the study, the probabilistic seismic hazard analysis of the Amaravati region has been carried out considering four potential seismic source zones and using the attenuation relation proposed by the national disaster authority of India (2010). The seismic hazard curves representing the cumulative seismic hazard and the uniform hazard spectra subjected to bedrock conditions of the Amaravati region have been developed. The peak horizontal acceleration and spectral acceleration were estimated up to a maximum spectral period of 2.0 s. In the final stage of the study, the seismic hazard results are further deaggregated to understand the relative ground motion of the earthquake sources in terms of magnitude and hypocentral distance. The deaggregation of seismic hazard is shown for 10%, 5%, and 2% probabilities of exceedance in 50 years corresponding to bedrock conditions. Finally, the obtained results were compared with the latest version of IS: 1893 part-1: 2016 (Criteria for earthquake-resistant design of structures), and noticed that the selected study region was being overestimated. The outcomes of this study could significantly help to generate or scale the acceleration time histories for site-specific ground response analysis, insurance agencies for policy-making, and builders for designing the new structures and retrofitting existing structures.
The following doubly truncated exponential probability density distribution
f ( M ) = β exp { − β ( M − M 0 ) } / { 1 − exp { − β ( M p − M 0 ) } } for M 0 ≦ M ≦ M p f ( M ) = 0 for M ≧ M p , ( a )
where M0 is the threshold magnitude value, and β is a parameter, is proposed for the earthquake occurrence. The relation (a) has been obtained carrying out a simple model based on a number of assumptions, among which the more characterizing is the existence of a maximum regional finite magnitude value Mp. This assumption, derived by an evidence recognized by most seismologists, allows a simple explanation of the known behavior of the experimental cumulative frequency-magnitude graphs.
In order to estimate β and Mp the moments method is suggested, which also represents a maximum likelihood method for β estimation.
Finally, some results of application of the model to six seismic regions are presented.
The truncated Gutenberg-Richter frequency-magnitude relationship in conjunction with a Poisson distribution is used to develop an asymptotic distribution of extreme values. This model is applied to estimate Mmax and to estimate the probability of occurrence of earthquakes in Finland, for earthquakes occurring throughout the period 1700-1979. The earthquake with the greatest magnitude within a 10yr period was used. The application of maximum likelihood procedure for the parameter estimation provides Mmax = 5.0+ or -0.1.-Authors
The maximum-likelihood estimation of earthquake hazard parameters [maxi-mum-regional magnitude (Mm.x), activity rate (X), and b parameter in the Guten-berg-Richter relation] is applied to extreme magnitude distribution, when the extreme magnitudes are taken from not necessarily equal time intervals. As an example, the derived procedures were applied to a set of the largest earthquakes felt in Egypt. The set contain the largest magnitudes from various time intervals (from a 500-to l-yr duration) for the period from 800 B.C. to 1984 A.D.
The maximum likelihood estimation of theb parameter in the Gutenberg-Richter relation is extended to the case of uncertain magnitude. An interval which contains the real unknown magnitude is used rather than the uncertain magnitude itself. The proposed approach is very flexible, it allows for the combination of the parts of a catalog of different quality into a single minimally biased set of recurrence parameters.
Calculus of Probability Mathematical Expectation and Moments of Random Variables Limit Theorems Family of Probability Measures and Problems of Statistics Appendix 2 A. Stieltjes and Lebesgue Integrals Appendih 2 B. Some Important Theorems in Measure Theory and Integration Appendix 2 C. Invariance Appendix 2 D. Statistics, Subfields, and Sufficiency Appendix 2 E. Non-Negative Definiteness of a Characteristic Function Complements and Problems