4:45 PM - 5:00 PM
[SSS12-12] Estimate of stress drop through Frequency Index and its potential for understanding the physical processes of seismic activity
Keywords:stress drop, Frequency Index, spectral ratio, earthquakes on the border of Yamagata and Fukushima prefectures, spatiotemporal evolution of earthquake swarms, b-value
Stress drop is one of the fundamental physical parameters of earthquake sources. It is usually estimated by measuring the corner frequency of the earthquake spectrum, which is not an easy task due to the seismic attenuation and the station's site effect, particularly for small earthquakes. Here, we propose an alternative method to estimate the stress drop without measuring the corner frequency. We employed the Frequency Index (FI), defined as the logarithm of the ratio of the average spectral amplitude between the low- and high-frequency ranges. FI has been frequently used to distinguish low-frequency earthquakes from ordinary ones. We introduced theoretical FI, in which the average spectral amplitude is expressed as the numerical integration of the product of the source spectrum and attenuation term. By employing a commonly used source model and the relations between the corner frequency and stress drop, the theoretical FI is a function of S-wave velocity, attenuation factor, and stress drop. We expect a slight spatial variation of S-wave velocity and attenuation factor in a small area. Assuming these parameters, we estimate an optimal stress drop to minimize the difference between the observed and theoretical FI. Since there is a trade-off between stress drop and Q values, the assumption of Q value is important. We estimated the Q value from the frequency dependence of the spectral ratio between the two stations.
We applied the proposed method to the triggered earthquake swarm by the great 2011 Tohoku earthquake on the border of Yamagata and Fukushima prefectures in northeastern Japan. We verified the proposed method in two ways: one is a comparison with the ordinary method by measuring the corner frequency, and the other is a comparison with the previous study by Yoshida et al. (2017) by a spectral fitting method in the same area. For the former comparison, we applied a spectral ratio method to the S-wave spectra to eliminate the path and site effects. Stress drops from the two methods are generally consistent. However, it is inconclusive because of the spectral ratio method's small number of stress drops. On the other hand, our results are consistent with those of Yoshida et al. (2017). The median value of our result, 2.47 MPa, is comparable to 2.67 MPa by them. In addition, spatial distribution and temporal variation are similar in the two methods. Thus, we confirmed that our method gives a reasonable estimate of stress drop.
Our method's advantage is its robustness, even for smaller earthquakes. The spectral ratio method of corner frequency estimation uses event pairs regarding smaller earthquakes as the empirical Green's function (EGF). The number of suitable EGF events is limited, and the corner frequencies of EGF events are often unreliable. Our method avoids selecting event pairs, which is why we can get a large number of stress drops. We obtained the stress drop for more than 7000 earthquakes with magnitudes ranging from 1.5 to 4.0. The increased number of stress drops enables a detailed investigation of the spatiotemporal evolution of earthquake swarms and frequency-magnitude analysis. In the case of the analyzed earthquake sequence, the b-values for events with lower stress drop are larger than those with higher stress drop. Thus, the proposed method is promising to deepen our understanding of the underlying physical processes of seismic activity.
We applied the proposed method to the triggered earthquake swarm by the great 2011 Tohoku earthquake on the border of Yamagata and Fukushima prefectures in northeastern Japan. We verified the proposed method in two ways: one is a comparison with the ordinary method by measuring the corner frequency, and the other is a comparison with the previous study by Yoshida et al. (2017) by a spectral fitting method in the same area. For the former comparison, we applied a spectral ratio method to the S-wave spectra to eliminate the path and site effects. Stress drops from the two methods are generally consistent. However, it is inconclusive because of the spectral ratio method's small number of stress drops. On the other hand, our results are consistent with those of Yoshida et al. (2017). The median value of our result, 2.47 MPa, is comparable to 2.67 MPa by them. In addition, spatial distribution and temporal variation are similar in the two methods. Thus, we confirmed that our method gives a reasonable estimate of stress drop.
Our method's advantage is its robustness, even for smaller earthquakes. The spectral ratio method of corner frequency estimation uses event pairs regarding smaller earthquakes as the empirical Green's function (EGF). The number of suitable EGF events is limited, and the corner frequencies of EGF events are often unreliable. Our method avoids selecting event pairs, which is why we can get a large number of stress drops. We obtained the stress drop for more than 7000 earthquakes with magnitudes ranging from 1.5 to 4.0. The increased number of stress drops enables a detailed investigation of the spatiotemporal evolution of earthquake swarms and frequency-magnitude analysis. In the case of the analyzed earthquake sequence, the b-values for events with lower stress drop are larger than those with higher stress drop. Thus, the proposed method is promising to deepen our understanding of the underlying physical processes of seismic activity.