Heterogeneity at Current Rupture-length Scales Governs Multi-fault Earthquake Dynamics

Stress-drop heterogeneity is widely recognized as an important control on rupture dynamics of multi-fault earthquakes, yet the influence of its scale dependence remains poorly understood. This study derives analytical expressions for the stress intensity factor and static energy release rate for ruptures propagating through heterogeneous stress-drop distributions in Mode II and III. This solution can approximate the effects of the non-planar fault geometry in Mode III. For a single-wavelength heterogeneity, the effect on rupture energetics is described by a dimensionless response function, involving the Fresnel integrals, that reaches its maximum when the heterogeneity wavelength is comparable to the current rupture length. The influence of both shorter- and longer-wavelength heterogeneities decays away from this characteristic scale. Extending the analysis to self-similar multi-wavelength heterogeneity demonstrates that the dominant contribution to rupture energetics always arises from wavelength components comparable to the rupture length, while shorter-wavelength effects are progressively averaged out due to the integral nature of the energetics. This scale-specific property is inherited by rupture arrest conditions, rupture velocity, and fault slip rate through the energy balance and stress intensity factor. The slip-pulse solution in the current model implies that the characteristic wavelength controlling rupture behavior is correlated with the seismogenic-layer thickness. These results imply that unresolved short-wavelength heterogeneity contributes only weakly to the dynamics of large earthquakes, providing a physical explanation for the reproducibility of large-scale rupture processes in dynamic rupture simulations. The theory suggests that uncertainty in earthquake rupture dynamics is intrinsically scale-dependent and that observational constraints on mechanical structures at scales comparable to the rupture dimension are most important for improving the forecastability of large-earthquake rupture scenarios.