Probabilistic Assessment of the Seismic Peak Ground Acceleration (PGA) at seven Colombian Cities

Abstract

This paper presents a probabilistic assessment of peak ground acceleration (PGA) observations at seven Colombian cities located in regions with intermediate and high seismic activity. Frequency histograms of the annual exceedance rates were determined using historical data of the annual rate of exceedance for pre-established values of PGA. After determining distribution parameters by means of the method of moments, several probability density functions were examined in order to evaluate the performance of each function. In most sites, the maximum annual PGA appears to be best modeled by a lognormal distribution, which led to its adoption as parent distribution for the entire group of cities. Once the lognormal function is selected as parent distribution, series of PGA values for arbitrary periods of time may be generated through random simulation. Next, series of maximum values in fifty years of observation were simulated for the seven cities, assuming a Lognormal parent distribution. Analytical solutions for extreme values of different sample sizes of lognormal random variables are not known to the authors. However, since extreme values for large samples of lognormal random variables tend asymptotically to a Type I (Gumbel) probability distribution, the latter was adopted as a possible model for the 50 years PGA distributions suggested in the paper for several Colombian cities, as a useful tool for engineering design, whenever the PGA is regarded as an appropriate seismic intensity measure.