Improved Scaling Relationships for Seismic Moment and Average Slip of Strike‐Slip Earthquakes Incorporating Fault‐Slip Rate, Fault Width, and Stress Drop

We develop a self‐consistent scaling model relating magnitude $Mw$ to surface rupture length (⁠$LE$⁠), surface displacement $DE$⁠, and rupture width $WE$⁠, for strike‐slip faults. Knowledge of the long‐term fault‐slip rate $SF$ improves magnitude estimates. Data are collected for 55 ground‐rupturing strike‐slip earthquakes that have geological estimates of $LE$⁠, $DE$⁠, and $SF$⁠, and geophysical estimates of $WE$⁠. 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, $ΔτC$⁠. Using $WE$ estimates does not improve $Mw$ estimates. However, measurements of $DE$ plus the relationship between $ΔτC$ and surface slip provide an alternate approach to study $WE$⁠. 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 $Mw$ and $DE$ values. After maximizing likelihoods over earthquakes in length bins, we found the most likely values of $WE$ for constant stress drop; these depend on the rupture length. The best‐fitting model has the surprising form $WE∝logLE$—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.