We explore the role of scenario‐dependent site amplification on local magnitude () and possible bias it may introduce. is strongly influenced by local site response, which is conditioned by unique local geological factors. To isolate the effect of the near‐surface amplification on , relative differences between station‐specific at the surface and borehole () are studied for 34 sites from the KiK‐net network, Japan. We find strong moment magnitude () dependent scenario‐specific trends over the range . To model these trends, we employ the stochastic method, initially using empirical surface‐to‐borehole (S/B) Fourier spectral ratios for the site term. Simulated data, , based on the available site‐response information are shown to closely match the empirical trends. Subsequently, the site term is replaced with (a) linear 1D shear‐wave (horizontal) transfer function (1D‐SHTF) amplification, (b) horizontal‐to‐vertical ratios, and (c) quarter wavelength amplification to calculate in the absence of S/B. We find that trends are best estimated with S/B as the site term, but in many cases using a linear 1D‐SHTF model is adequate. Furthermore, we discuss how this phenomenon may be related to the observed inequality between and at low magnitudes and how may be used in the future to compute unbiased with greater confidence.