The rupture of earthquakes has long been recognized as far more complex than a simple planar rupture model. However, the planar rupture model remains widely used in most earthquake source inversions and simulations. Geologists have traditionally focused on surface fault traces, using their mapping to explain earthquake dynamics. In contrast, seismologists recognize a significant gap between the long-term development of regional fault networks and the rapid, localized nature of coseismic rupture—not to mention that earthquakes can rupture faults hidden beneath the surface. The lack of a widely accepted quantitative definition of 'complexity' continues to hinder progress in these investigations.

Our study provides a direct and rigorous measurement of rupture complexity during earthquakes based on the distribution of aftershocks. Through fault system simulations, we demonstrate that our measurement captures the fractal properties of rupture. Additionally, a comparison between the measured rupture complexity of large earthquakes and their high-frequency energy radiation clearly shows that high-frequency radiation scales with rupture complexity. Our results also indicate that spatial variations in complexity across different fault segments during a large earthquake can influence the overall rupture process.