A new wavenumber‐domain methodology to model surface‐slip profiles and generate potential displacement profiles for use in probabilistic fault‐rupture hazard analysis is developed. The benefits of this approach are it captures the correlation of the surface‐slip variability along a strike, and it avoids the surface‐rupture length (SRL) normalization. A regularized Fourier transform (RFT) approach is used to compute the Fourier spectra from uneven and biased sampling, typical of surface‐slip data sets. The wavenumber amplitude spectrum for surface displacements is modeled by a functional form based on the shape of the Butterworth filter. The proposed RFT approach is validated using synthetic data sets with known model parameters, which are downsampled to be consistent with the sampling in empirical surface‐rupture data sets. Preliminary models for the scaling of the amplitude and phase derivative as a function of the SRL are developed using a subset of the earthquakes compiled by Wesnousky (2008). The analyzed events range from magnitude 6.1 to 7.9 and include both single and multisegment ruptures.
Compared with other published models, the wavenumber‐spectrum method leads to narrower tails of the slip distribution, which is important for probabilistic fault displacement analyses at long‐return periods. Near the center of the rupture, the wavenumber‐spectrum method gives slip distributions that are consistent with the distributions from the empirical data, but at the ends of the rupture, the wavenumber‐spectrum method underestimates the range of the slip. This discrepancy may reflect limitations of the current data sets in terms of sampling of the slip near the ends of the ruptures. Improved surface‐rupture data sets are currently being compiled and will provide improved constraints at the ends of the ruptures.