Statistical modeling of ground motion relations for seismic hazard analysis

We introduce a new approach for ground motion relations (GMR) in the probabilistic seismic hazard analysis (PSHA), being influenced by the extreme value theory of mathematical statistics. Therein, we understand a GMR as a random function. We derive mathematically the principle of area-equivalence; wherein two alternative GMRs have an equivalent influence on the hazard if these GMRs have equivalent area functions. This includes local biases. An interpretation of the difference between these GMRs (an actual and a modeled one) as a random component leads to a general overestimation of residual variance and hazard. Beside this, we discuss important aspects of classical approaches and discover discrepancies with the state of the art of stochastics and statistics (model selection and significance, test of distribution assumptions, extreme value statistics). We criticize especially the assumption of logarithmic normally distributed residuals of maxima like the peak ground acceleration (PGA). The natural distribution of its individual random component (equivalent to exp(epsilon_0) of Joyner and Boore 1993) is the generalized extreme value. We show by numerical researches that the actual distribution can be hidden and a wrong distribution assumption can influence the PSHA negatively as the negligence of area equivalence does. Finally, we suggest an estimation concept for GMRs of PSHA with a regression-free variance estimation of the individual random component. We demonstrate the advantages of event-specific GMRs by analyzing data sets from the PEER strong motion database and estimate event-specific GMRs. Therein, the majority of the best models base on an anisotropic point source approach. The residual variance of logarithmized PGA is significantly smaller than in previous models. We validate the estimations for the event with the largest sample by empirical area functions. etc

Investigating strong ground-motion variability using analysis of variance and two-way-fit plots

A statistical method to quantitatively assess the relative importance of unmodelled site and source effects on the observed variability (σ) in ground motions is presented. The method consists of analysis of variance (ANOVA) using the computed residuals with respect to an empirical ground-motion model for strong-motion records of various earthquakes recorded at a common set of stations. ANOVA divides the overall variance (σ 2) into the components due to site and source effects (respectively σ S 2 and σ E 2 ) not modelled by the ground-motion model plus the residual variance not explained by these effects (σ R 2 ). To test this procedure, four sets of observed strong-motion records: two from Italy (Umbria-Marche and Molise), one from the French Antilles and one from Turkey, are used. It is found that for the data from Italy, the vast majority of the observed variance is attributable to unmodelled site effects. In contrast, the variation in ground motions in the French Antilles and Turkey data is largely attributable, especially at short periods, to source effects not modelled by the ground-motion estimation equations used