D-A-CH TAGUNG 2011 - SGEB

1 INTRODUCTIONA key element of seismic hazard assessment (SHA) is the consideration of uncertainties,which are classified as epistemic and aleatory. The epistemic uncertainty reflects theincomplete knowledge of the nature of all inputs to the assessment, the variability of theinterpretation of available data, and the limitations of the technique applied for the analysis.Epistemic uncertainty can be incorporated into SHA using the logic tree method (as in Ref.[1]). At present, an approach based on copula analysis is under examination [2, 3].Aleatory uncertainty is related to the inevitable unpredictability regarding the nature ofground motion parameters. In other words, the aleatory uncertainty describes the disagreementbetween observations and predictive models that is due to the absence of a physical explanationor due to variables that are not included in the predictive equations. Additional explanatoryvariables need to be added to the model to represent repeatable (as opposed to random)influences on the ground motion. Thus, the aleatory component of uncertainty may also reflectepistemic modelling uncertainty regarding the factors controlling the ground motion componentthat have not been included in ground motion models (as in Ref. [4]). Aleatory uncertainty ismainly quantified in SHA through the use of the standard deviation of the data’s scatter aboutthe ground motion prediction equations. It has become common practice to separate the totalaleatory variability into two independent components [4-8], namely, the earthquake-toearthquake(between-earthquake) variability and the site-to-site (within-earthquake) variability.The between-earthquake variability results from event-specific factors that have not beenincluded in the predictive model. The within-earthquake variability reflects the fact thatearthquake ground motion for a given event at different sites must vary to some extent. Thewithin-earthquake variability is determined mostly by peculiarities in the propagation path andlocal site conditions, and there have been attempts to separate the within-earthquake variabilityinto its path-to-path and site-to-site components [9].The ground motion parameter Y at n locations during m earthquakes is represented bylog Yi, j f ( ei, si,j) i i,ji 1,2,..., m;j 1,2,..., n;(1)where eidenotes variables that are properties of the earthquake source, si , jare theproperties of site location j during earthquake i , and f is a suitable function that describesthe dependence of the median value of ground motion parameterlog on the magnitude,distance, local site conditions, etc. (i.e., log Yi, j f ( ei, si,j)). The error random variables iandi, jrepresent the between-earthquake and within-earthquake components of variability22(independent and normally distributed with variances and ), respectively. The value ofiis common to all sites during a particular earthquake i , and the value ofYi , ji. jdepends on the2site. Assuming the independence of the two random terms, the total aleatory variance Tis2 2 2given by T .The between-earthquake correlation of earthquake ground motion, or the similarity ofground motion variability during different earthquakes at the same site, is determined by therelation between the components of variability (as in Ref. [10]):1562