Yoshimitsu Fukushima
Scaling relations for strong ground motion prediction models with M ² terms
Bulletin of the Seismological Society of America (April 1996), 86(2):329-336

Abstract:
In most previous studies on the attenuation relation of strong ground motion, the increase in amplitude with earthquake magnitude was expressed by a linear relation. However, if the omega (super -2) source model is assumed, the corner period of the spectrum varies with the magnitude, and the scaling law of the source spectrum amplitude becomes a complicated function of magnitude. The scaling relation of the spectrum amplitude with M _w can be simply approximated as a quadratic function, and the coefficient of the M ² _w term should be negative. On the contrary, positive coefficients of the M ² _L , m ² _bLg , and M ² _J (M _J : magnitude of Japan Meteorological Agency) terms have been derived by regression analyses of strong ground motions. Based on the omega (super -2) model, semi-empirical relations between Mo and the magnitudes were derived. Further, the seismological scaling law of the source spectrum obtained from the relation between Mo and the magnitudes was approximated as a quadratic function of the magnitude, and positive coefficients of the squared magnitude tens were obtained. These results stem from the definitions of magnitude derived from amplitudes of seismograms around a specific period of 1.0 sec for M _L and m _bLg and of 5.0 sec for M _j .