The case for mean rupture distance in ground‐motion estimation

This article advocates for the use of mean rupture distances that we contend are more physically representative of the distance to an earthquake and are simpler than minimum distances. Many current ground‐motion models (GMMs) rely on numerous modifications of minimum rupture distances to accurately model near‐source ground motions. These modifications, that include additional distance definitions and saturation terms, result in complicated functional forms and are often not easily understood on a seismological basis, such as the magnitude‐dependent near‐fault saturation term. The use of mean distance represents the location of a station in relation to the entire rupture plane and results in a simpler, more physically meaningful GMM that models near‐source ground motion as accurately as other GMMs that have more inputs and more complex functional forms. We demonstrate the use of mean distance by developing a GMM for shallow‐crustal earthquakes with the Next Generation Attenuation‐West2 (NGA‐West2) project database. Specifically, we use the generalized mean distance, also known as the power mean, in which the power varies with frequency. We show that this new GMM fits the NGA‐West2 database as well as the NGA‐West2 GMMs and exhibits similar near‐source amplitude scaling. An additional benefit of mean distance is that it can provide a mechanism to account for spatially variable slip. We prospectively validate this GMM against the 2016 M">M 7.8 Kaikōura, New Zealand, earthquake, which was not used in model development. To better understand the magnitude dependence of geometrical spreading, we employ a simple conceptual model based on fundamental principles to show that the GMM is consistent with common seismological understanding.