Extension of the Aki-Utsu b-Value Estimator for Incomplete Catalogs

Kijko, Andrzej; Smit, A.B.

doi:10.1785/0120110226

Cited by 100 publications

(84 citation statements)

References 32 publications

Supporting

Mentioning

Contrasting

Unclassified

Order By: Relevance

“…The maximization of (31) provides an estimator of β in the form (Kijko and Smit, 2012) E Q -T A R G E T ; t e m p : i n t r a l i n k -; d f 3 2 ; 5 5 ; 1 6 3β r 1 β…”

Section: Only Complete Earthquake Catalogs Are Availablementioning

confidence: 99%

“…Once theβ value is known, the mean value of the earthquake activity rate λ ≡ λm min is calculated. It can be shown (KS-I; Kijko and Smit, 2012) that if the number of seismic events per time unit is a Poisson random variable, the compound Poisson-gamma distribution (13) s min m min ; t t 1 with t 2 t 3 … 0, and n n 1 with n 2 n 3 … 0, the estimator (34) reduces to the classic maximum likelihood estimator of the Poisson distribution parameter and takes the form n=t.…”

Section: Only Complete Earthquake Catalogs Are Availablementioning

confidence: 99%

“…The assessment of hazard parameters from a catalog with varying levels of completeness is no trivial task, and different solutions to the problem have been proposed (Molchan et al, 1970;Rosenblueth, 1986;Rosenblueth and Ordaz, 1987;Kijko and Smit, 2012). However, the most elegant, straightforward, and the best-known solution is the procedure derived by Weichert (1980).…”

Section: Only Complete Earthquake Catalogs Are Availablementioning

confidence: 99%

See 2 more Smart Citations

Estimation of Earthquake Hazard Parameters from Incomplete Data Files. Part III. Incorporation of Uncertainty of Earthquake‐Occurrence Model

Kijko¹,

Smit²,

Sellevoll³

2016

Bulletin of the Seismological Society of America

103

104

View full text Add to dashboard Cite

Most probabilistic seismic-hazard analysis procedures require that at least three seismic source parameters be known, namely the mean seismic activity rate λ, the Gutenberg-Richter b-value, and the area-characteristic (seismogenic source) maximum possible earthquake magnitude m max . In almost all currently used seismic-hazard assessment procedures that utilize these three parameters, it is explicitly assumed that all three remain constant over time and space. However, closer examination of most earthquake catalogs has indicated that significant spatial and temporal variations existed in the seismic activity rate λ, as well as in the Gutenberg-Richter b-value. In this study, the maximum likelihood estimation of these earthquake hazard parameters considers the incompleteness of the catalogs, the uncertainty in the earthquake magnitude determination, as well as the uncertainty associated with the applied earthquake-occurrence models. The uncertainty in the earthquake-occurrence models is introduced by assuming that both the mean seismic activity rate λ and the Gutenberg-Richter b-value are random variables, each described by the gamma distribution. This approach results in the extension of the classic frequency-magnitude Gutenberg-Richter relation and the

show abstract

“…The maximization of (31) provides an estimator of β in the form (Kijko and Smit, 2012) E Q -T A R G E T ; t e m p : i n t r a l i n k -; d f 3 2 ; 5 5 ; 1 6 3β r 1 β…”

Section: Only Complete Earthquake Catalogs Are Availablementioning

confidence: 99%

Section: Only Complete Earthquake Catalogs Are Availablementioning

confidence: 99%

Section: Only Complete Earthquake Catalogs Are Availablementioning

confidence: 99%

See 1 more Smart Citation

Estimation of Earthquake Hazard Parameters from Incomplete Data Files. Part III. Incorporation of Uncertainty of Earthquake‐Occurrence Model

Kijko¹,

Smit²,

Sellevoll³

2016

Bulletin of the Seismological Society of America

103

104

View full text Add to dashboard Cite

show abstract

“…The same result can also be derived using the maximum likelihood method presented in Kijko and Smit [2012;Appendix A]. In practice, the form of equation (6) necessitates two regularity conditions to stabilize the inversion and to produce physically meaningful results: the denominator in equation (6) must be greater than 0 and f T must be greater than 0.…”

Section: Mixing Modelmentioning

confidence: 88%

The magnitude distribution of dynamically triggered earthquakes

Hernández

Brodsky

Elst

2014

Geochem. Geophys. Geosyst.

View full text Add to dashboard Cite

Large dynamic strains carried by seismic waves are known to trigger seismicity far from their source region. It is unknown, however, whether surface waves trigger only small earthquakes, or whether they can also trigger large earthquakes. To partially address this question, we evaluate whether current data can distinguish between the magnitude distribution of triggered and untriggered small earthquakes. We use a mixing model approach in which total seismicity is decomposed into two classes: ''triggered'' events initiated or advanced by far-field dynamic strains and ''untriggered'' spontaneous events consisting of everything else. The b-value of a mixed data set, b MIX , is decomposed into a weighted sum of b-values of its constituent components, b T and b U . We utilize the previously observed relationship between triggering rate and dynamic strain amplitude to identify the fraction of triggered events in populations of earthquakes and then invert for b T . For Californian seismicity, data are consistent with a single-parameter Gutenberg-Richter hypothesis governing the magnitudes of both triggered and untriggered earthquakes.

show abstract

“…A recent study of the GEM Faulted Earth Project characterized the attribute of the Himalayan Frontal Thrust (MFT) fault in the seismic hazard assessment for the frontal Himalaya (Berryman et al, ). In this study, we use a methodology developed by Kijko and Smith () to compute seismicity parameters (e.g., Gutenberg‐Richter b value, rate of seismicity). In general, PSHA procedures assume that seismicity parameters are constant over time.…”

Section: Introductionmentioning

confidence: 99%

Probabilistic seismic hazard assessment of Nepal using multiple seismic source models

Rahman

Bai

2018

Earth and Planetary Physics

View full text Add to dashboard Cite

The potential for devastating earthquakes in the Himalayan orogeny has long been recognized. The 2015 MW7.8 Gorkha, Nepal earthquake has heightened the likelihood that major earthquakes will occur along this orogenic belt in the future. Reliable seismic hazard assessment is a critical element in development of policy for seismic hazard mitigation and risk reduction. In this study, we conduct probabilistic seismic hazard assessment using three different seismogenic source models (smoothed gridded, linear, and areal sources) based on the complicated tectonics of the study area. Two sets of ground motion prediction equations are combined in a standard logic tree by taking into account the epistemic uncertainties in hazard estimation. Long‐term slip rates and paleoseismic records are also incorporated in the linear source model. Peak ground acceleration and spectral acceleration at 0.2 s and 1.0 s for 2% and 10% probabilities of exceedance in 50 years are estimated. The resulting maps show significant spatial variation in seismic hazard levels. The region of the Lesser Himalaya is found to have high seismic hazard potential. Along the Main Himalayan Thrust from east to west beneath the Main Central Thrust, large earthquakes have occurred regularly in history; hazard values in this region are found to be higher than those shown on existing hazard maps. In essence, the combination of long span earthquake catalogs and multiple seismogenic source models gives improved seismic hazard constraints in Nepal.

show abstract

Extension of the Aki-Utsu b-Value Estimator for Incomplete Catalogs

Cited by 100 publications

References 32 publications

Estimation of Earthquake Hazard Parameters from Incomplete Data Files. Part III. Incorporation of Uncertainty of Earthquake‐Occurrence Model

Estimation of Earthquake Hazard Parameters from Incomplete Data Files. Part III. Incorporation of Uncertainty of Earthquake‐Occurrence Model

The magnitude distribution of dynamically triggered earthquakes

Probabilistic seismic hazard assessment of Nepal using multiple seismic source models

Contact Info

Product

Resources

About