Investigating properties of vertical design spectra in Japan by applying differential evolution to KiK-net data

The vertical design spectrum plays an important role in seismic design whether of critical or ordinary structures. However, many studies focused on the vertical to horizontal response spectral ratio and less researchers investigated the properties of vertical design spectra directly. In this study, differential evolution and simulated annealing are firstly examined to determine an appropriate method to estimate the characteristic parameters of the vertical design spectra. Then, the properties of the vertical design spectra in Japan are investigated by applying differential evolution to about 10000 KiK-net seismic data. Compared with epicentral distance, the influence of earthquake magnitude is more obvious which shows up as the linear correlation between the corner period and earthquake magnitude. Moreover, we propose a loglog exponential formula which relates the corner period of vertical design spectra to that of horizontal design spectra, and the formula may be used in other regions.