Ground motions characterized by a multi-scale heterogeneous earthquake model

We have carried out numerical simulations of seismic ground motion radiating from a mega-earthquake whose rupture process is governed by a multi-scale heterogeneous distribution of fracture energy. The observed complexity of the Mw 9.0 2011 Tohoku-Oki earthquake can be explained by such heterogeneities with fractal patches (size and number), even without introducing any heterogeneity in the stress state. In our model, scale dependency in fracture energy (i.e., the slip-weakening distance Dc) on patch size is essential. Our results indicate that wave radiation is generally governed by the largest patch at each moment and that the contribution from small patches is minor. We then conducted parametric studies on the frictional parameters of peak (τp) and residual (τr) friction to produce the case where the effect of the small patches is evident during the progress of the main rupture. We found that heterogeneity in τr has a greater influence on the ground motions than does heterogeneity in τp. As such, local heterogeneity in the static stress drop (Δτ) influences the rupture process more than that in the stress excess (Δτexcess). The effect of small patches is particularly evident when these are almost geometrically isolated and not simultaneously involved in the rupture of larger patches. In other cases, the wave radiation from small patches is probably hidden by the major contributions from large patches. Small patches may play a role in strong motion generation areas with low τr (high Δτ), particularly during slow average rupture propagation. This effect can be identified from the differences in the spatial distributions of peak ground velocities for different frequency ranges.