Source parameter scaling for small earthquakes observed at the western Nagano 800-m-deep borehole, Central Japan

Source parameters of 68 small earthquakes (0.6 < M _w < 3.0) in western Nagano, Japan, are investigated to determine the scaling of static stress drop (Δσ _s) and apparent stress (σ _a) with seismic moment (M _o). Data from the 800-m-deep borehole in the area provides clean recordings containing a wide range of frequencies. Source parameters are determined by manipulation of P and S spectra in the frequency domain using individually determined time window lengths for arrivals on each seismogram. Frequency-independent quality factors, Q, corner frequencies, f _c and the amplitude spectra levels are estimated with the best-fitting Brune (1970) ω ² model. A frequency-dependent attenuation model, Q(f), is calculated by spectra normalization. Static stress dropΔσ _s, is self-similar for 10 ¹⁰ < M _o < 10 ¹³ N m and values range between 0.01 and 10 MPa. An F distribution test shows there is a 10% probability that σ _a calculated from Q has a constant mean value for 10 ¹⁰ < M _o < 10 ¹³ N m. Furthermore, σ _a calculated using Q(f) has a significant probability that there is a change in σ _a values with M _o. Using Q(f), 0.02 < σ _a < 2 MPa for M _o > 10 ¹¹ N m, and 0.002 < σ _a < 0.2 MPa for M _o < 10 ¹¹ N m, a narrower range than Q analysis results. Limits in recorded frequencies, variations in time window length, and source complexity are not found to significantly affect the calculation of σ _a. Therefore, the constant scaling of Δσ _s, with M _o and the nonsimilarity and breakdown in σ _a scaling could be true characteristics of small earthquakes (M _w <1.3).