Constraining the roughness degree of slip heterogeneity

This article investigates different approaches for assessing the degree of roughness of the slip distribution of future earthquakes. First, we analyze a database of slip images extracted from a suite of 152 finite-source rupture models from 80 events (M-w = 4.1-8.9). This results in an empirical model defining the distribution of the slip spectrum corner wave numbers (k(c)) as a function of moment magnitude. To reduce the "epistemic" uncertainty, we select a single slip model per event and screen out poorly resolved models. The number of remaining models (30) is thus rather small. In addition, the robustness of the empirical model rests on a reliable estimation of k(c) by kinematic inversion methods. We address this issue by performing tests on synthetic data with a frequency domain inversion method. These tests reveal that due to smoothing constraints used to stabilize the inversion process, k(c) tends to be underestimated. We then develop an alternative approach: (1) we establish a proportionality relationship between k(c) and the peak ground acceleration (PGA), using a k(2) kinematic source model, and (2) we analyze the PGA distribution, which is believed to be better constrained than slip images. These two methods reveal that k(c) follows a lognormal distribution, with similar standard deviations for both methods.