Strong motions of 18 earthquakes (3.4 less than or equal to M-J less than or equal to 7.1, M-J: JMA magnitude) in the eastern Tohoku district, Japan, have been observed at 12 borehole sites within a 20- x 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 approximate to 3000 m/sec) and the engineering bedrock (Vs approximate to 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 omega(-2) model with the seismic moment Mo from the Harvard CMT solution estimated for earthquakes of M-J greater than or equal to 5.3. Initial values of corner frequency f(0) are determined based on a previous empirical M-0 - f(0) relationship in this district. Using six moderate-sized earthquakes (5.3 less than or equal to M-J less than or equal to 6.0), we first estimate frequency-dependent Q to be Q = 110f(0.69) (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 f(0) and cutoff frequencies f(max) for all 18 earthquakes and hi, for seven small-sized earthquakes of M-J < 5.3 by minimizing the difference between the model and observed spectra. The average Brune stress drop obtained from an M-0 - f(0) relationship estimated from 17 earthquakes except for the smallest earthquake with M-0 less than 10(21) dyne.cm is 200 bars. The estimated M-0 - f(0) relationship is identical to the one used to calculate initial values of f(0) 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 f(max) on M-0 is not significant, and the logarithmic average of f(max) is found to be 13.5 Hz. By using these controlling parameters and the M-0 - f(0) relationship obtained from a regression analysis, acceleration spectra on the engineering bedrock in sendai can be predicted statistically from X and M-0 or M-J by considering standard deviations of the site response, f(0), and f(max).