Improved scaling relationships for seismic moment and average slip of strike-slip earthquakes incorporating fault slip rate, fault width and stress drop

Abstract

We develop a self‐consistent scaling model relating magnitude M w to surface rupture length ( ⁠L E ⁠ ), surface displacement D E ⁠ , and rupture width W E ⁠ , for strike‐slip faults. Knowledge of the long‐term fault‐slip rate S F improves magnitude estimates. Data are collected for 55 ground‐rupturing strike‐slip earthquakes that have geological estimates of L E ⁠ , D E ⁠ , and S F⁠ , and geophysical estimates of W E ⁠ . We begin with the model of Anderson et al. (2017) , which uses a closed form equation for the seismic moment of a surface‐rupturing strike‐slip fault of arbitrary aspect ratio and given stress drop, Δτ C ⁠ . Using W E estimates does not improve M w estimates. However, measurements of D E plus the relationship between Δτ C and surface slip provide an alternate approach to study W E ⁠ . A grid of plausible stress drop and width pairs were used to predict displacement and earthquake magnitude. A likelihood function was computed from within the uncertainty ranges of the corresponding observed M w and D E values. After maximizing likelihoods over earthquakes in length bins, we found the most likely values of W E for constant stress drop; these depend on the rupture length. The best‐fitting model has the surprising form W E ∝logL E —a gentle increase in width with rupture length. Residuals from this model are convincingly correlated to the fault‐slip rate and also show a weak correlation with the crustal thickness. The resulting model thus supports a constant stress drop for ruptures of all lengths, consistent with teleseismic observation. The approach can be extended to test other observable factors that might improve the predictability of magnitude from a mapped fault for seismic hazard analyses.