This dissertation includes three major components. First, ratios between median values and the associated standard deviations for different definitions of the horizontal component of ground motions in Central and Eastern North America are developed using a subset of the NGA-East database. While the most recent studies produced similar results using different subsets of the NGA-West2 database, it is possible that such directionality results may differ for other earthquake datasets and be region specific. The computed median ratios are similar to the ratios provided in recent studies for other regions with a shift in some period ranges with noticeable differences between the standard deviations. Second, a comparison of a hybrid approach and a fully probabilistic approach for incorporating site effects into a probabilistic seismic hazard analysis (PSHA) is presented. In the employed hybrid approach the amplification factors are computed by performing equivalent linear site response analysis. The considered fully probabilistic approach is characterized by higher levels of sophistication in which the rock hazard is convolved with the probability density function of the amplification functions to calculate the surface ground motions. The uncertainties associated with the site characterization is addressed via Monte Carlo randomizations. To fulfill the scope of this study, the employed approaches is highlighted focusing on performing a site-specific PSHA for a Liquid Natural Gas tank located in the Gulf Coast region. Finally, a new ground motion prediction model is developed for the response spectral ratio of vertical-to-horizontal (V/H) components of earthquakes for the Gulf Coast region. The proposed V/H ratio model has the advantage of considering the magnitude, source to site distance, and the shear-wave velocity of soil deposits in the upper 30 m of the site (Vs30) for the peak ground acceleration (PGA), and a wide range of spectral periods. The model is based on a comprehensive set of regression analyses of the newly compiled NGA-East database of available recordings with the moment magnitudes M ≥ 3.4 and the rupture distances RRup