Length‐Scale‐Dependent Relationships between VS30 and Topographic Slopes in Southern California

In engineering seismology, the time‐averaged shear‐wave velocity (⁠$VS$⁠) of the upper 30 m of the crust (⁠$VS30$⁠) is the primary parameter used in ground‐motion models to predict seismic site effects. $VS30$ is typically derived from in situ recordings of $VS$⁠, although proxy‐based approaches (using geologic and/or geomorphometric classifications) are provisionally adopted when measurement‐based $VS30$ are sparse or not readily available. Despite the acceptance of proxy approaches, there are limited studies that examine the empirical relationships between $VS30$ and topographic attributes measured from various length scales and different resolutions of the digital elevation model. In this study, we examine the relationships between compiled $VS30$ measurements from 218 sites in southern California and topographic metrics of slope and relief measured over various length scales. We find that the correlations between topographic metrics and $VS30$ are weak but statistically significant. The correlations are improved when topographic slopes and relief are measured over length scales longer than typical hillslopes and $VS30$ sites are separated by different geologic groups. This is likely because $VS30$⁠, especially on the rock sites, is better reflected in topographic metrics that capture large‐scale topographic relief, as well as landscape positions such as hilltops and valley bottoms.