The severity of vertical seismic ground motions is often factored into design regulations as a component of their horizontal counterparts. Furthermore, most design codes, including Eurocode 8, ignore the impact of local soil on vertical spectra. This paper investigates vertical pseudo-absolute acceleration spectral estimates, as well as the ratios of spectral estimates for strong motion in vertical and horizontal directions, for low to medium seismicity regions with deep local soil and deep geological sediments beneath the local soil. The case study region encompasses the city of Osijek in Croatia. New regional frequency-dependent empirical scaling equations are derived for the vertical spectra. According to these equations, for a 0.3 s spectral amplitude at deep soils atop deep geological sediments compared to the rock sites, the maximum amplification is 1.48 times. The spectra of vertical components of various real strong motions recorded in the surrounding region are compared to the empirical vertical response spectra. The new empirical equations are used to construct a Uniform Hazard Spectra for Osijek. The ratios of vertical to horizontal Uniform Hazard Spectra are generated, examined, and compared to Eurocode 8 recommendations. All the results show that local soil and deep geology conditions have a significant impact on vertical ground motions. The results also show that for deep soils atop deep geological strata, Eurocode 8 can underestimate the vertical to horizontal spectral ratios by a factor of three for Type 2 spectra while overestimating them by a factor of two for Type 1 spectra.
Spectral estimates for finite combinations
of Hermite functions and null-controllability of hypoelliptic quadratic equations
