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 (⁠VS) 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 VS profiles. We investigate the performance of the BA23 η for a wide range of realistic gradient VS profiles with VS30 ranging from 180 to 1500 m/s. These gradient VS 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 (⁠Z1.0 and Z2.5⁠) based on western United States sites. Despite observing a VS30 dependence of η⁠, we find that the BA23 η generally works reasonably well for the range of VS 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.

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