Empirical Distance Metrics Relationships and Uncertainties in Seismic Hazard Assessment

Abstract

ABSTRACTThe seismic hazard of an area is determined based on the ground motion observed at that site. The intensity of the ground motion can be predicted using ground -motion models (GMMs). GMMs typically use distance metrics such as the Joyner–Boore distance (RJB) and the rupture distance (RRUP). However, apart from RJB and RRUP, probabilistic seismic hazard analysis (PSHA) also utilizes point-source-based distances like the epicentral distance (REPI) and the hypocentral distance (RHYP). These distance metrics are used for point sources when the fault geometry is unknown or is ignored. To obtain an accurate seismic hazard of an area, we need to determine the relationship between the distance metrics. In this study, we develop empirical relationships between RJB and various other distance metrics. This method avoids conducting computationally intensive tasks such as computing finite-fault-based distances for different fault geometry of a virtual rupture plane for each point source. The empirical equations provide the relation between RJB and target distance metric (Rtarget) based on the magnitude of the earthquake and the dip angle of the fault. In addition, we also require the depth to the top of the rupture to calculate RHYP. We discuss the steps to include the variability due to the conversion of the distance metrics in the PSHA. We have compared the results of this study with other published studies for distance conversion. A simple PSHA study of a circular area of 100 km using Pezeshk et al. (2011) as the GMM determined an increase in hazard using the proposed empirical equations and their uncertainties. The equations developed in this study can be directly applied in PSHA and are independent of the GMMs used for seismic hazard calculations. The equations can also be used for different fault geometries with a range of dip angles varying from 10° to 90°, for magnitudes 5.0–8.0, and distances up to 200 km. We have focused on the central and eastern United States.