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We utilized the peak frequencies of site amplification pulses obtained from horizontal to vertical Fourier spectral ratios (HVFSR) of Japanese recordings at 1,657 sites, and found that the lowest peak frequency, which is the fundamental frequency (f₀), correlates well with the thickness of the soil column, and the peak frequency with highest HVFSR amplitude (f_peak) correlates with the stiffness of shallow soils. However, the f₀ and f_peak estimated by the definition frequently overlap and do not correlate to shallow soil stiffness and soil thickness. In this study, we provide two correlation factors and functions of fit: 1) the correlation of a peak frequency to the soil thickness represented by the depth to an isotopic soil layer with shear wave velocity of 1.4 km/s called f_depth; 2) the correlation of a peak frequency to the shallow soil stiffness represented by the time-averaged shear wave velocity in the upper 30 m of the soil …