Waveform characteristics of deep low-frequency earthquakes: time-series evolution based on the theory of the KM2O-Langevin equation

Abstract

SUMMARY Since the 1970s, deep low-frequency earthquakes (DLF) with depths ranging 20–40 km have been observed just beneath the Japan Island Arc. Almost all of these earthquakes are recognized up to now have had magnitudes less than 2.5, so that we have little information concerning DLF. Employing the theory of KM2O-Langevin equations, we develop a new method to represent the characteristics of the coda parts of DLF, and propose a new concept of ‘average dissipation spectrum’. The new averaging algorithm for the KM2O-Langevin matrix function was applied in the analysis of DLF (M: 1.0), which occurred in Akita prefecture on 2001 July 11, and we succeeded in separating the characteristics of the source vibration system and the source excitation process into the averaged dissipation term and the fluctuation term, respectively. The gaps between the arrival times of the fluctuation term's peaks at three stations near the epicentre are slightly different than the gaps between the S-wave arrival times. Assuming a homogenous crust structure with an S-wave velocity of 4.3 km s−1 and assuming the depth of the second source to be the same as that of the hypocentre, the second source lies about 1.5 km, N 56°E of the hypocentre. We estimate the common characteristics of this DLF successfully by using the ‘average dissipation spectrum’, which is made up of typical frequencies, θk, attenuation factors, Qk and amplitude factors, Ak. The common elements of (θk∼ 1.5, Qk∼−0.3) and (θk∼ 3.25, Qk∼−0.45) among all stations indicate the characteristics of the source dynamics of the Akita DLF. The major parts of the coda waves of DLF satisfy the stationary property, and the causality values for the linear and odd-degree non-linear transformations are relatively higher than those for the even-degree non-linear transformations. These characteristics are quite different from the characteristics of tectonic earthquakes. This quantitative property is common among all DLF.