Estimate of stress drop through Frequency Index and its application to a triggered earthquake swarm in northeastern Japan

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.

We applied and verified 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 confirmed that our results are consistent with those of Yoshida et al. (2017) in both spatial distribution and temporal variation. Our method's advantage is its robustness, even for smaller earthquakes. The traditional method of stress drop estimation uses spectral inversion for event pairs to measure corner frequencies. The number of suitable pairs is limited to a small number. 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 6600 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-vales for events with lower stress drop are evidently 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.