With the increasing recognition of the importance of nonergodic components in seismic hazard analysis, it is becoming increasingly important to obtain site‐specific amplification functions (AFs). The most common approach to obtain site‐specific AFs is to perform site response analyses backed by detailed site characterization with measures of uncertainty. An alternative approach would be to utilize ground motions recorded at the site, if any, to constrain site effects. But this approach is only viable if ground‐motion recordings are available, which they generally are not. However, in a seismically active region (such as California), the rate of occurrence of small‐magnitude earthquakes (i.e., M<4.5⁠) is sufficient for weak ground motions to be recorded using a temporarily deployed station, especially for the design of critical structures. This then raises the question: can weak ground motions resulting from small‐magnitude events recorded using temporary seismometers be used to constrain site effects? This study explores the possibility of employing a Bayesian inversion approach for constraining site terms using weak ground motions. Toward this end, ground‐motion recordings associated with two dam sites in northern California were used in a Bayesian inversion scheme to constrain source, path, and site terms with measures of uncertainty. The empirical site transfer functions (TFs) at both sites were compared with analytical site TFs computed using 1D site response analyses. At both sites, the empirical site TFs were observed to be similar to the analytical site TFs. The standard error of the TF estimate suggests that the results are stable when sufficient recordings are available. This work serves to highlight that Bayesian inversions can be used to recover site terms and outlines a procedure for how the results should be interpreted post hoc.

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