Statistical spectral model of earthquakes in the eastern Tohoku district, Japan, based on the surface and borehole records observed in Sendai

Abstract

Abstract Strong motions of 18 earthquakes (3.4 ≦ MJ ≦ 7.1, MJ: JMA magnitude) in the eastern Tohoku district, Japan, have been observed at 12 borehole sites within a 20- × 20-km region in Sendai. In our previous study, we defined a Pliocene layer, whose S-wave velocity VS is greater than 500 m/sec and whose N value of the standard penetration test is greater than 50, as engineering bedrock in Sendai and calculated 304 engineering bedrock waves (hypocentral distance X = 15 to 300 km) by removing the site response between the engineering bedrock and the surface. As the second stage of our study toward a quantitative prediction of strong ground motions of horizontal components, we propose here a statistical spectral model of the engineering bedrock waves by introducing the site response between the pre-Tertiary bedrock (VS ≈ 3000 m/sec) and the engineering bedrock (VS ≈ 500 to 700 m/sec) and a frequency-dependent Q into Boore's spectral model. We separate the site response between the pre-Tertiary bedrock and the engineering bedrock, an attenuation function, and source spectra from the engineering bedrock spectra by assuming an ω−2 model with the seismic moment M0 from the Harvard CMT solution estimated for earthquakes of MJ ≧ 5.3. Initial values of corner frequency f0 are determined based on a previous empirical M0 − f0 relationship in this district. Using six moderate-sized earthquakes (5.3 ≦ MJ ≦ 6.0), we first estimate frequency-dependent Q to be Q = 110f0.69 (f: frequency) by minimizing the standard deviation of the site response, which is defined as the ratio of observed engineering bedrock spectra with respect to the estimated attenuation and the assumed source spectra. The averaged site response is simultaneously estimated to be 1 at 0.1 Hz, 5 at 1 Hz, and 3 at 20 Hz. We then invert f0 and cutoff frequencies fmax for all 18 earthquakes and M0 for seven small-sized earthquakes of MJ < 5.3 by minimizing the difference between the model and observed spectra. The average Brune stress drop obtained from an M0 − f0 relationship estimated from 17 earthquakes except for the smallest earthquake with M0 less than 1021 dyne·cm is 200 bars. The estimated M0 − f0 relationship is identical to the one used to calculate initial values of f0 so that we do not need to perform the inversion iteratively. The obtained stress drop for subduction zone earthquakes in the eastern Tohoku district is consistent with other previous studies. The dependence of the inverted fmax on M0 is not significant, and the logarithmic average of fmax is found to be 13.5 Hz. By using these controlling parameters and the M0 − f0 relationship obtained from a regression analysis, acceleration spectra on the engineering bedrock in Sendai can be predicted statistically from X and M0 or MJ by considering standard deviations of the site response, f0, and fmax.