Decomposing leftovers: Event, path, and site residuals for a small magnitude ANZA region GMPE

Abstract

Ground‐motion prediction equations (GMPEs) are critical elements of probabilistic seismic hazard analysis (PSHA), as well as for other applications of ground motions. To isolate the path component for the purpose of building nonergodic GMPEs, we compute a regional GMPE using a large dataset of peak ground accelerations (PGAs) from small‐magnitude earthquakes ( ⁠0.5 ≤ M ≤ 4.5 with > 10,000 events, yielding ∼120,000 recordings) that occurred in 2013 centered around the ANZA seismic network (hypocentral distances ≤180 km⁠ ) in southern California. We examine two separate methods of obtaining residuals from the observed and predicted ground motions: a pooled ordinary least‐squares model and a mixed‐effects maximum‐likelihood model. Whereas the former is often used by the broader seismological community, the latter is widely used by the ground‐motion and engineering seismology community. We confirm that mixed‐effects models are the preferred and most statistically robust method to obtain event, path, and site residuals and discuss the reasoning behind this. Our results show that these methods yield different consequences for the uncertainty of the residuals, particularly for the event residuals. Finally, our results show no correlation (correlation coefficient [CC] <0.03⁠ ) between site residuals and the classic site‐characterization term V S30 ⁠ , the time‐averaged shear‐wave velocity in the top 30 m at a site. We propose that this is due to the relative homogeneity of the site response in the region and perhaps due to shortcomings in the formulation of V S30 ⁠ and suggest applying the provided PGA site correction terms to future ground‐motion studies for increased accuracy.