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 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.