A Fault Displacement Model Based on the FDHI Database

Fault displacement models are a key component of probabilistic fault displacement hazard analysis (PFDHA), providing the displacement probability density function. We present a new fault displacement model developed using the comprehensive database compiled for the Fault Displacement Hazard Initiative (FDHI) project. The model predicts the total net displacement across multi-stranded surface ruptures as a function of moment magnitude and position along the rupture length. We provide separate models for strike-slip, reverse, and normal faulting. A bilinear magnitude scaling is used to capture the steeper magnitude scaling for smaller magnitudes observed in the data for strike-slip and normal faulting. The scaling for reverse faulting approaches log-linear but still uses a bilinear form. Our flexible location scaling functional form captures the asymmetric profile shapes common in the data for dip-slip events and more symmetrical elliptical profiles in the strike-slip data. We applied a Box-Cox transformation to the displacement dataset so that the data resemble a normal distribution, which allows the transformed displacement to be conveniently modeled as normally distributed. Between- and within-event aleatory variability are modeled separately. All model parameters are estimated using Bayesian regression, which allows within-model epistemic uncertainty to be quantified. Compared with earlier models, the new model produces less aleatory variability and smaller upper-tail displacements for magnitudes greater than about 6.5 for all styles of faulting and all locations along the rupture. Data dispersion at the rupture end-points in the strike-slip and reverse faulting resulted in large aleatory variability. Large aleatory variability for smaller magnitude strike-slip and normal events is driven by a lack of data at smaller magnitudes. The use of a large, high-quality database and advanced statistical modeling techniques in our new model provides improved predictions of fault displacement compared with earlier models.