## 1 Introduction  
In Croatia, as in many other countries, vertical design ground motions are calculated based on the horizontal design ground motions and do not depend on the soil conditions. In Eurocode 8 [1], which is in use in Croatia [2], vertical design Peak Ground Acceleration (hereinafter, PGA) values are determined by multiplying the horizontal PGA values spectra defined for the \"rock\" ground type (type A) by a constant. This scaling constant changes according to the predominant magnitudes; it is equal to 0.9 for Eurocode 8 Type 1 spectra (magnitudes larger than 5.5) and 0.45 for Type 2 spectra (magnitudes equal to or smaller than 5.5). In both cases, vertical pseudo-absolute acceleration spectra (hereinafter, \(PSA_{vert}\)) are the same for all ground types that are considered in Eurocode 8 [1]. In other words, the Eurocode 8 approach for vertical PGA assumes that seismic wave amplification happens only horizontally and not vertically. This concept underpins the so-called H/V methodology for calculating the natural period of soil vibrations based on microtemors, as suggested by [PERSON] and [PERSON] [3] and later popularized by [PERSON] [4, 5, 6]. However, many studies have demonstrated that this methodology does not always provide realistic results for local soil vibration periods [7; 8; 9; 10; 11]. The initial purpose of this research is to determine the amplification (or de-amplification) impacts of deep soil atop deep geological sediments on vertical _PSA_ spectra. The term \"deep soil\" will refer to the geotechnical site description on the scale of several tens of meters, in this case to sites with more than 100 m of softer soil layers above the first layer with an average shear wave velocity of more than 800 m/s [12; 13]. The term \"deep geological sediments\" will refer to geological settings on the scale of a few kilometers or at least hundreds of meters [14]. Vertical to horizontal _PSA_ ratios obtained in this study will be compared to the ratios defined in two different sets of empirical Ground Motion Prediction Equations (hereinafter, GMPEs). The first set was created for California [15], and these were the only GMPEs we could find that consider the simultaneous impacts of deep geological sediments and deep local soil on the vertical spectra. The second set [16] was created for the former Yugoslavia and is used to compare the vertical and horizontal spectral ratios in deep geological sediments only, as these GMPEs do not consider the effects of deep soils. In this paper, we first develop regional frequency-dependent empirical attenuation equations that consider deep soil sites, then we generate probabilistic seismic hazard _PSAvert_ estimates and compare them to Eurocode 8 spectra, and finally compare the vertical and the horizontal _PSA_ ratios to the ratios suggested by other authors and Eurocode 8 [1]. In addition, seismic hazard maps for the various vibration periods and exceedance probabilities are created. Figure 1 depicts a research framework diagram for this study. This research builds on our previous work [17; 18] on the severity of surface ground motion in low to medium seismicity regions with deep soils atop deeper geological strata. We chose the city of Osijek, Croatia for the case study region since it is in the low to medium seismicity region of the Pannonian basin (see Figure 2 in our accompanying paper on the horizontal spectra [18]). Osijek is also an example of an area where deep geological deposits are found beneath deep soil sites. In our study in [17], we found that vertical PGA is de-amplified by 10% at deep soil sites compared to rock soil sites and \(\sim\)15% at deep geological sediments compared to geological rocks. This study will now focus on _PSAvert_. Figure 1: Framework diagram for this research study. Furthermore, in Eurocode 8 [1], the maximum spectral amplitudes are equal to the product of the vertical PGA and a constant value of 3.0. Another purpose of this study is to examine if this spectral acceleration factor provides realistic \(PSA_{vert}\) estimates.