The selection of half-space or reference sites significantly influences site amplification studies. However, there are no well-defined guidelines in the literature. Generally, a layer with a local shear wave velocity (VS) of more than 760 m/s is considered a bedrock/half-space/reference site. This study attempts to formulate a rationale for selecting bedrock stiffness to be used as a half-space/reference site. For this study, VS,30 (average shear wave velocity of top 30-meter soil strata from shear wave velocity measurements) and the site's fundamental frequency (obtained from Horizontal to vertical spectral ratio of ambient vibration records) were used as proxies to study the influence of bedrock/half-space and development of a rationale for their selection. This study uses strong-motion data from India's sixty-two strong motion stations and a few from Japan (Kik-Net). The results suggest that considering a site with a shear wave velocity of 760 m/s may not be suitable as a half-space/bedrock for most geomorphological conditions. The results also recognize a pattern that can help in the development of a mathematical model for determining the bedrock for a site using VS,30 and its fundamental frequency as a proxy.