Estimating rupture distances without a rupture

Most ground motion prediction equations (GMPEs) require distances that are defined relative to a rupture model, such as the distance to the surface projection of the rupture (RJB) or the closest distance to the rupture plane (RRUP). There are a number of situations in which GMPEs are used where it is either necessary or advantageous to derive rupture distances from point-source distance metrics, such as hypocentral (RHYP) or epicentral (REPI) distance. For ShakeMap, it is necessary to provide an estimate of the shaking levels for events without rupture models, and before rupture models are available for events that eventually do have rupture models. In probabilistic seismic hazard analysis, it is often convenient to use point-source distances for gridded seismicity sources, particularly if a preferred orientation is unknown. This avoids the computationally cumbersome task of computing rupture-based distances for virtual rupture planes across all strikes and dips for each source. We derive average rupture distances conditioned on REPI, magnitude, and (optionally) back azimuth, for a variety of assumed seismological constraints. Additionally, we derive adjustment factors for GMPE standard deviations that reflect the added uncertainty in the ground motion estimation when point-source distances are used to estimate rupture distances.