9:30 AM - 9:45 AM
[SSS04-03] Development of a New Spectral Inversion Method Considering with Rupture Directivity
Keywords:Spectral inversion, Rupture directivity, Source spectrum
The spectral inversion method (e.g., Iwata and Irikura, 1988) has been widely used in separating the source, propagation path, and site amplification factors from the observed ground motion data. An estimated source spectrum for an event is independent of the station in this method. However, the apparent source spectra, which are obtained by removing the propagation path and site effects from the observed spectra, varies from station to station. We have showed the azimuthal dependence of both the corner frequencies and fall-off rate in the apparent displacement source spectra for several events in the 2016 Kumamoto earthquake sequence and have found this azimuthal dependence was caused by the fault rupture directivity. To estimate the stable and reliable source, propagation path, and site factors from the observed records, it is necessary to investigate the effect of rupture directivity on estimates of the three factors by the spectral inversion method. In this study, a new spectral inversion method was developed by incorporating the rupture directivity coefficient, which was determined based on the fall-off rates in the apparent source spectra by Somei et al. (2021), into the observation equation. Then, we applied this new spectral inversion method to the dataset of the 2016 Kumamoto earthquake sequence, and compared the obtained three factors with those by the conventional method.
We formularized the new observation equation by adding the term of the rupture directivity to the conventional ones in the spectral inversion method. The term of the rupture directivity was parameterized as the rupture directivity coefficient C n(f) with frequency-dependent n, in order to explain the frequency-dependent source directivity effects (e.g., Pacor et al. 2016). First, we estimated the rupture directivity coefficient based on the fall-off rates in the apparent source spectra which were obtained from the result of the conventional spectral inversion. Then, the weight n(f) in the rupture directivity coefficient was estimated simultaneously with the source, propagation path, and site factors from the observed Fourier amplitude spectra. Based on the obtained source spectrum, the stress drop was estimated from the seismic moment and the source radius (Eshelby, 1957), which was related to the corner frequency (Brune, 1970, 1971).
From the results of applying this new method to the dataset of the 2016 Kumamoto earthquake sequence (Mw: 3.6-5.3), we found the weight n(f) in the rupture directivity coefficient was larger around the corner frequency and then smaller toward the higher frequencies. The variation in apparent source spectra of the events in the 2016 Kumamoto earthquake sequence was successfully explained by this new spectral inversion method. Between the new and conventional methods, we can see the difference in the estimated source spectra for several events. For example of the event with the unilateral rupture directivity, the estimated stress drop changed from 5.4 MPa by the conventional method to 2.3 MPa by the new method. In this case, the corner frequency is estimated to be high and the stress drop is estimated to be large in the conventional method because most of the stations are distributed in the forward rupture propagation direction. The new spectral inversion method can provide us with the stable source spectrum and stress drop by considering the rupture directivity effect. We also found the effect of rupture directivity on the estimate of propagation path and site factors is small because there was no significant difference in their factors between the new and conventional methods.
We formularized the new observation equation by adding the term of the rupture directivity to the conventional ones in the spectral inversion method. The term of the rupture directivity was parameterized as the rupture directivity coefficient C n(f) with frequency-dependent n, in order to explain the frequency-dependent source directivity effects (e.g., Pacor et al. 2016). First, we estimated the rupture directivity coefficient based on the fall-off rates in the apparent source spectra which were obtained from the result of the conventional spectral inversion. Then, the weight n(f) in the rupture directivity coefficient was estimated simultaneously with the source, propagation path, and site factors from the observed Fourier amplitude spectra. Based on the obtained source spectrum, the stress drop was estimated from the seismic moment and the source radius (Eshelby, 1957), which was related to the corner frequency (Brune, 1970, 1971).
From the results of applying this new method to the dataset of the 2016 Kumamoto earthquake sequence (Mw: 3.6-5.3), we found the weight n(f) in the rupture directivity coefficient was larger around the corner frequency and then smaller toward the higher frequencies. The variation in apparent source spectra of the events in the 2016 Kumamoto earthquake sequence was successfully explained by this new spectral inversion method. Between the new and conventional methods, we can see the difference in the estimated source spectra for several events. For example of the event with the unilateral rupture directivity, the estimated stress drop changed from 5.4 MPa by the conventional method to 2.3 MPa by the new method. In this case, the corner frequency is estimated to be high and the stress drop is estimated to be large in the conventional method because most of the stations are distributed in the forward rupture propagation direction. The new spectral inversion method can provide us with the stable source spectrum and stress drop by considering the rupture directivity effect. We also found the effect of rupture directivity on the estimate of propagation path and site factors is small because there was no significant difference in their factors between the new and conventional methods.