Empirical method for deriving horizontal site amplification factors considering nonlinear soil behaviors based on K-NET and KiK-net records throughout Japan

Based on the observed strong-motion records of K-NET and KiK-net, we utilized 1,065 earthquake observation stations installed throughout Japan, gathering more than 140,000 recordings for weak motions with a peak ground acceleration (PGA) of less than 100 cm/s(2) and more than 5,300 records for strong motions with a PGA of more than 100 cm/s(2). These 1,065 sites detected at least one recording with a PGA value greater than 100 cm/s(2). These recordings were used to quantify the horizontal-to-vertical spectral ratio (HVSR) difference between weak and strong shakings. Based on the observations, the discrepancy in HVSR between weak and strong shakings can be depicted as a shift both in the frequency and amplitude axes in the logarithmic coordinate system. This kind of shift can be favorably interpreted by an established diffused field theory of the HVSR of earthquakes. Based on the concept of shifts, new empirical functions are proposed to modify the averaged HVSR in linear cases in order to acquire the HVSR in nonlinear regimes. Subsequently, an improved vertical amplification correction function, which considers the time-averaged shear wave velocity down to 30 m, was used to convert the modified HVSR into the horizontal site amplification factor (HSAF) in nonlinear regimes. The new methodology adopted in this study, which does not require detailed soil layer information, is convenient for obtaining the HSAF by considering empirically obtained nonlinear soil behaviors.