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Scaling relations for strong ground motion prediction models with M² terms

Izumi Research Institute Shimizu Corporation Fukoku-seimei Bldg., 2-2-2 Uchisaiwai-cho, Chiyoda-ku, 100, Tokyo, Japan

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 ^–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_W² term should be negative. On the contrary, positive coefficients of the M_L², m_bLg², and M_J² (M_J: magnitude of Japan Meteorological Agency) terms have been derived by regression analyses of strong ground motions.

Based on the ^–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 terms 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.

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