Heterogeneity in Dynamic Rupture Models: Bridging the Gap Between Observed High-Frequency Ground Motion and Rupture Process Complexity

Accurate modeling of earthquake ground motions is critical for understanding rupture dynamics and assessing seismic hazard. However, traditional models that employ simple, smooth dynamic rupture representations often struggle to capture ground motion beyond the corner frequency. This limitation stems from their inability to account for the high-frequency content generated by small-scale complexities in the rupture process, leading to underestimation of the spectral content observed in real earthquake recordings. Here we investigate dynamic rupture models incorporating broadband spatial variability in dynamic rupture parameters. Our study implements a multi-scale heterogeneity approach based on the Von Karman autocorrelation function with power spectral density of k^-2 (Hurst exponent of zero) and correlation lengths that scale with the rupture size. We thereby introduce variations in initial stress, fault strength, and characteristic slip weakening distance across the fault plane. The degree of rupture complexity in our simulations is effectively controlled by the standard deviation of the imposed heterogeneities. We demonstrate the effectiveness of our approach by modeling the apparent source spectra of two Mw~4 events from central Italy up to 25 Hz. The first is a unilateral event showing a strong azimuthal dependence of spectral amplitudes due to directivity effects, while the second is a non-directive bilateral event exhibiting a more homogeneous distribution. By comparing synthetic and observed apparent source spectra, we show how our approach successfully models these two contrasting rupture processes. Furthermore, comparison with the theoretical ω^-2 model provides additional insights into the relationship between source complexity and source spectral characteristics. The dynamic rupture heterogeneities prove crucial for reproducing the high-frequency ground motion components that simple models typically fail to capture. This work represents a significant step forward in bridging the gap between earthquake recordings and numerical modeling, providing a robust framework for understanding and predicting ground motions applicable in earthquake scenario simulations.