A probabilistic framework to model distributions of VS30
The time‐averaged shear‐wave velocity in the upper 30 m depth from the ground surface, or V S 30 "> V S 30 , is often used as a predictor to describe local site effects in ground‐motion models. Although V S 30 "> V S 30 is typically determined from in situ measurements, it is not always feasible to obtain such measurements due to project restrictions or site accessibility. This motivates the development and use of proxy‐based V S 30 "> V S 30 predictions that leverage more readily available secondary information such as surface geology, topographic slope, or geomorphic terrain classes to estimate the mean V S 30 "> V S 30 and associated uncertainty. Traditionally, empirical distributions of V S 30 "> V S 30 have been observed to have long right tails, leading to high levels of associated uncertainty. In this study, we present a physical framework that is grounded in fundamental principles of geostatistics and probability to explain the uncertainty and skewness associated with V S 30 "> V S 30 measurements. Specifically, by invoking Lyapunov’s central limit theorem, we hypothesize that the distribution of V S 30 "> V S 30 can be theoretically approximated by a reciprocal–normal distribution. We show that a non‐normal and skewed distribution of V S 30 "> V S 30 is to be expected and is not a sign of measurement error or sampling bias, although sampling bias can exaggerate such skewness. Our framework also enables us to propose the mode as a characteristic value of V S 30 "> V S 30 measurements, as opposed to the mean or median, which can overestimate the most probable value.