Heterogeneous self-arrested ruptures leading to spatial variability of radiated energy and Doppler effect of the observed corner frequency

The study of the strong ground motion is of utmost relevance because the amplitude of seismic waves and their frequency content could severely damage structures. As both the amplitude and the frequency content directly depend on the seismic source, a proper description and simulations of the earthquakes’ rupture process are required. This means that realistic source models should incorporate a heterogeneous distribution of rupture parameters that generates self-arrested ruptures. One of these models is a heterogeneous energy-based (HE-B) method, which can describe the kinematic rupture process based on the distribution of residual energy (\({E}^{res}\)). This parameter defines zones in faults where the accumulated energy is larger than the dissipated energy. In this context, this study presents the spatial variations of radiated energy, corner frequency, and stress drop at far-field distances as a consequence of the heterogeneous distribution of positive residual energy. It is found that the rupture of asperities, determined by large values of \({E}^{res}\), strongly shifts the frequency content and generates a Doppler effect of the frequency content. That is, the location in the far-field in direction where the asperity is being ruptured generates traveling waves characterized by an increase of the observed corner frequency, which corresponds to the corner frequency measured by the observer. This implies that different station measures different frequency content implying different estimations of the source parameters. Besides, the variability of the observed corner frequency could break the scaling between the corner frequency and the magnitude. Nevertheless, it is also found that the average observed corner frequency, when considering all the points or stations, is almost the same as that obtained for the seismic source. A similar property is found for radiated energy and stress drop. These results show that the ground motion at a given location varies depending on the heterogeneities of the section of the fault being ruptured.