Magnitude-Scaling Rate in Ground-Motion Prediction Equations for Response Spectra from Large Subduction Interface Earthquakes in Japan

Magnitude-scaling rates (MSRs; the rates of increase in predicted response spectra with increasing moment magnitude) are evaluated for three ground-motion prediction equations for response spectra from subduction interface earthquakes, including two empirical models developed for data from Japan and a model based on synthetic records generated by using a stochastic finite-fault model. MSRs vary significantly among the three models, and the difference between the two empirical models is unacceptably large. A set of 2100 strong-motion records from subduction interface events with a magnitude of 6.5 or larger from Japan, including the 11 March 2011 magnitude 9 earthquake, were compiled. The earthquakes were grouped according to magnitude, so that the magnitude spread in each group is less than 0.2 magnitude units. Each earthquake group was treated as a single event with magnitude equal to the average magnitude for the group. A simple attenuation model was fitted to the normalized and grouped data. The model has a constant term for each earthquake group to represent the effect of magnitude. Three separate functions of magnitude (a linear model for events with a magnitude greater than 7, a bilinear model, and a curved model) were then fitted to the constants, and MSRs were derived from these functions. At short periods, the derived MSRs are only a fraction of those from two of the three attenuation models. At spectral periods greater than 0.5 s, the derived MSRs are between about 1/3 and 1/2 of those of the two empirical models but are closer to those based on a set of synthetic records.