Evaluating the Minimum Number of Earthquakes in Empirical Site Response Assessment: Input for New Requirements for Microzonation in the Swiss Building Codes

Site-specific hazard analyses and microzonation are important products for densely populated areas and facilities of special risk. The empirical amplification function is classically estimated using the standard spectral ratio (SSR) approach. The SSR simply consists in comparing earthquake recordings on soil sites with the recording of the same earthquake on a close-by rock reference. Recording a statistically significant number of earthquakes to apply the SSR can however be difficult, especially in low seismicity areas and noisy urban environments. On the contrary, computing the SSR from too few earthquakes can lead to an uncertain evaluation of the mean amplification function. Defining the minimum number of earthquake recordings in empirical site response assessment is thus important. We compute empirical amplification functions at 60 KiKnet sites in Japan from several hundred earthquakes and three Swiss sites from several tens of earthquakes. We performed statistical analysis on the amplification functions to estimate the geometric mean and standard deviation and more importantly to determine the distribution law of the amplification factors as a function of the number of recordings. Independent to the site and to the frequency, we find that the log-normal distribution is a very good approximation for the site response. Based on that, we develop a strategy to estimate the minimum number of earthquakes from the confidence interval definition. We find that 10 samples are the best compromise between minimizing the number of recordings and having a good statistical significance of the results. As a general rule, a minimum of 10 uncorrelated earthquakes should be considered, but the higher the number of earthquakes, the lower the uncertainty on the geometric mean of the site amplification function. Moreover, the linear site response is observed to be independent to the intensity of the ground motion level for the analyzed dataset.