The square-root-impedance (SRI) method is commonly used to approximate the seismic site amplifications computed using the full-resonance (FR) method for gradient shear-wave velocity (V_S) profiles that are smoothly varying with depth. The SRI site amplifications have been observed to systematically underpredict the FR site amplifications by a ratio of FR/SRI amplifications around 1.05 to 1.3 across a wide  frequency range (Boore, 2013). Recently, Boore and Abrahamson (2023; hereafter, BA23) related this difference in the SRI and FR methods to differences in the exponent η of the ratio of seismic impedances between the two methods. They proposed the implementation of a modified frequency-dependent η in the SRI method to improve its match to the FR site amplifications. This modified η was derived using only five V_S profiles. We investigate the performance of the BA23 η for a wide range of realistic gradient V_S profiles with V_S30 ranging from 180 to 1500 m/s. These gradient V_S profiles are constructed using two power-law functions of depth and are constrained by the assigned VS30 value, the depth and velocity of the half-space, and depths to shear-wave velocity horizons of 1.0 and 2.5 km/s (Z_1.0 and Z_2.5) based on western United States sites. Despite observing a V_S30 dependence of η, we find that the BA23 η generally works reasonably well for the range of V_S profiles analyzed. Using the VS30-dependent η derived in this study results in improvements in matching the FR site amplification compared to using the BA23 η. These improvements are more pronounced for the soft-site conditions and become modest to negligible for the stiff site conditions