Scaling law between corner frequency and seismic moment of microearthquakes: Is the breakdown of the cube law a nature of earthquakes?

Abstract

The corner frequency, fC, and the seismic moment, M0, of microearthquakes (local magnitude from -1.3 to 1.3) are estimated from the records of sensors located at an 1800-m-deep borehole at the Nojima fault, central Japan. The digital waveforms of each event are recorded with two different sampling rates, 10 kHz and 100 Hz. The source parameters estimated from high-sampling data satisfy a relationship of M0 fC-3, corresponding to a constant stress drop law, while those calculated from low-sampling data follow a relationship of M0 fC-4. A lack of high frequency components in the 100 Hz sampling data seem to be obvious, indicating that the value of fC and M0 are incorrectly estimated and the relationship of M0 fC-4 is an artifact caused by the limited frequency band of these data. The scaling relationship of M0 fC-3 is, thus, also valid for microearthquakes, and the breakdown of the constant stress drop law, reported in the literature, is not well founded.