Event terms in the response spectra prediction equation and their deviation due to stress drop variations

We investigated the characteristics of strong ground motions separated from acceleration Fourier spectra and acceleration response spectra of 5% damping calculated from weak and moderate ground motions observed by K-NET, KiK-net, and the JMA Shindokei Network in Japan using the generalized spectral inversion method. The separation method used the outcrop motions at YMGH01 as reference where we extracted site responses due to shallow weathered layers. We include events with JMA magnitude equal to or larger than 4.5 observed from 1996 to 2011. We find that our frequency-dependent Q values are comparable to those of previous studies. From the corner frequencies of Fourier source spectra, we calculate Brune's stress parameters and found a clear magnitude dependence, in which smaller events tend to spread over a wider range while maintaining the same maximum value. We confirm that this is exactly the case for several mainshock-aftershock sequences. The average stress parameters for crustal earthquakes are much smaller than those of subduction zone, which can be explained by their depth dependence. We then compared the strong motion characteristics based on the acceleration response spectra and found that the separated characteristics of strong ground motions are different, especially in the lower frequency range less than 1Hz. These differences comes from the difference between Fourier spectra and response spectra found in the observed data; that is, predominant components in high frequency range of Fourier spectra contribute to increase the response in lower frequency range with small Fourier amplitude because strong high frequency component acts as an impulse to a Single-Degree-of-Freedom system. After the separation of the source terms for 5% damping response spectra we can obtain regression coefficients with respect to the magnitude, which lead to a new GMPE as shown in Fig.1 on the left. Although stress drops for inland earthquakes are 1/7 of the subduction-zone earthquakes, we can see linear regression works quite well. After this linear regression we correlate residuals as a function of Brune's stress parameters of corresponding events as shown in Fig.1 on the right for the case of 1Hz. We found quite good linear correlation, which makes aleatoric uncertainty 40 to 60 % smaller than the original.