Fault-displacement models for aggregate and principal displacements

New fault-displacement models (FDMs) are developed for the aggregate and principal net surface displacement using the database developed by the Fault Displacement Hazard Initiative Project. An FDM for the aggregate displacement is developed, which is then partitioned into principal and distributed displacements. The model for the aggregate displacement is first formulated in the wavenumber domain to incorporate seismology-based constraints for the extrapolation of the magnitude scaling of median displacements to large-magnitude events. The results from the wavenumber-domain model are then adjusted to fit the empirical moderate-magnitude scaling (M < 7) and the shape of the displacement profile at the ends of the rupture. Segments are used in the model development to better capture the complexity of the variability of the surface-displacement profile along strike, including regions with zero displacements. For applications in which segments cannot be identified, simplified FDMs without segments are developed that treat the number, lengths, and locations of the segments as aleatory variability. The principal-displacement FDM is then developed as an adjustment to the aggregate-displacement FDM. The segmentation and the magnitude dependence of the taper length of individual segments lead to non-self-similar scaling of the median profile along the entire rupture that can have a significant impact on probabilistic fault-displacement hazard analysis (PFDHA) for sites near the ends of faults. A key feature of the new FDMs is the use of a power-normal (Formula presented) distribution for the aleatory variability, which leads to narrower distributions of the displacement for large-magnitude earthquakes compared to the commonly used lognormal distribution. For large-magnitude earthquakes, the expected maximum displacements computed using the power-normal distribution of the FDM are consistent with the observed maximum displacements along strike, supporting the narrower shape of the upper tail of the power-normal distribution for large-magnitude events.