Estimating the rupture directivity and source parameters of moderate to small earthquakes using the second seismic moment

Rupture processes of large earthquakes have been studied by seismic waveform analysis and directivity effects have also been observed in moderate and small earthquakes.

 

This effect leads to azimuthal and spectral variations in ground motion that can be used to estimate the fault plane orientation or a predominant rupture propagation direction in a particular region or during a seismic sequence. For moderate-to-strong events, directivity at low frequencies can result in potentially destructive pulses with large ground motions, while at high frequencies and for small-to-moderate events, the most pronounced effect is the shift in corner frequencies that results in high-frequency energy arriving in short time intervals.

 

It is therefore of the utmost importance to estimate the directivity effects in engineering applications and seismological studies of earthquake sources. While some methods appear to work well for high magnitude earthquakes, determining directivity and source parameters for small to moderate magnitude earthquakes remains a challenge.

 

One of the most common methods to estimate the directivity from moderate to small earthquakes relies on measuring the duration of the source pulse (the apparent source time function) at each location and then modeling it using a line source. Some approaches rely on the deconvolution of waveforms by an empirical Green’s function (eGf), to overcome the problems associated with the presence of path and site effects.

A promising approach for estimating the rupture directivity effect and associated source properties is based on the calculation of the second seismic moments. In this study we apply the method based on the calculation of the second seismic moments to estimate the rupture process and source parameters to study a Mw 4.7 earthquake that occurred in central Italy during the 2016 - 2017 seismic sequence recorded by the RAN (Rete Accelerometrica Nazionale) and RSN (Rete Sismica Nazionale) italian networks.

We first used synthetic apparent source time functions calculated from a geometric source model obtained from a real event to test the robustness of the method. Then, we applied the second-seismic moment method and the approach based on high-frequency S wave amplitude variations versus source azimuths analysis with an empirical Green's function deconvolution approach and compare the results.