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# [SSS31-08] Re-examination of scaling relations for crustal earthquakes.

Keywords:scaling relation, crustal earthquake, earthquake source model, earthquake hazard assessment

1) Matsuda (1975) : log L=0.6M

_{j}-2.9

2) Takemura (1998) : log L=0.75M

_{w}-3.77 (6.8≤M

_{w})

3) Irikura and Miyake (2001) : M

_{0}=(S/4.24×10

^{5})

^{2}×10

^{-7}(6.5≤M

_{W}<7.4)

4) Tajima et al. (2013) : M

_{0}=0.877×S×10

^{11}(7.5≤M

_{w})

5) Murotani et al. (2015) : M

_{0}=1.0×S×10

^{11}(7.4≤M

_{w})

These scaling formulas indicate relation between one variable parameter (i.e. fault length L or fault area S) and the seismic moment or magnitude. When we calculate seismic moment with these scaling formulas and slip amount using the formulas, Mo=μDS and S=LW, the resulting slip amounts vary from formula to formula. When we assume a fault with L=50km and W=20km, we obtain Mw=7.10 and average slip D=1.64 by Irikura and Miyake (2001) and Mw=7.29 and average slip D=3.21 by Takemura (1998). Such differnces would significantly affect the results of seismic hazard assessments.

In this study we proposed a scaling relation of seismic moment with two variables parameters, fault area S and average slip D. We used the same earthquake data used in Irikura and Miyake (2001) and Takemura (1998). We obtained regression line with principal component analysis. The relation between the residual of slip Δ D and the residual of area Δ S could be expressed by logΔ D = -logΔS (Δ D * ΔS = 1), which indicates that fault area S and the average slip D are not independent parameters on earthquake data used in this study.