Scenario‐Dependent Site Effects for the Determination of Unbiased Local Magnitude

We explore the role of scenario‐dependent site amplification on local magnitude (⁠$ML$⁠) and possible bias it may introduce. $ML$ 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 $ML$⁠, relative differences between station‐specific $ML$ at the surface and borehole (⁠$ΔML,STN$⁠) are studied for 34 sites from the KiK‐net network, Japan. We find strong moment magnitude (⁠$M$⁠) dependent scenario‐specific $ΔML,STN$ trends over the range $3.0<M<6.5$⁠. 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, $ΔML,STN(M)$⁠, based on the available site‐response information are shown to closely match the empirical $ΔML,STN$ 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 $ΔML,STN(M)$ in the absence of S/B. We find that $ΔML,STN(M)$ 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 $M$ and $ML$ at low magnitudes and how $ΔML,STN(M)$ may be used in the future to compute unbiased $ML$ with greater confidence.