Nonergodic Probabilistic Fault-Displacement Hazard Analysis

ABSTRACT A nonergodic probabilistic fault-displacement hazard analysis (PFDHA) framework is developed using paleoseismic displacement data sets with multiple events at each site. The current earthquake-based and displacement-based approaches can be fit into a general framework of ergodic, partially nonergodic, and nonergodic approaches. The paleoseismic data sets do not include the metadata (magnitude and location along strike) typically used for developing a nonergodic fault-displacement model (FDM). We present an approach for estimating the nonergodic standard deviation without the metadata. We show example hazard calculations for ergodic and nonergodic PFDHAs for three cases: (1) without displacement data for the fault, (2) with displacement data at the site, and (3) with displacement data observed on the fault but located down strike from the site. With no displacement data at the site, the 5th–95th epistemic fractiles of hazard based on the nonergodic FDMs can lead to a displacement range of a factor of 20 for high slip-rate faults at typical return periods between 1000 and 10,000 yr used for design, whereas the ergodic fractiles span a range of a factor of ≤2. This large difference in the epistemic range shows the strong effects of the nonergodic FDM on the fault-displacement hazard. The very large epistemic uncertainty for nonergodic FDMs without data may motivate using an ergodic approach with much smaller epistemic uncertainty; however, the large uncertainty in nonergodic models more accurately reflects the epistemic range that captures the true hazard at the site. The considerable epistemic uncertainty in nonergodic estimations can be significantly reduced with just a few additional fault-specific displacement observations.