10 research outputs found
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