Relationship between fault length and magnitude assuming ellipsoidal fault planes rupture areas

Abstract

The 2000 Tottori-ken Seibu Earthquake posed such questions as (1) why coseismic surface ruptures were not associated with earthquake the magnitude of which was 7.3 in JMA scale, or nearly the same as the 1995 Hyogo-ken Nambu Earthquake that accompanied surface ruptures along the Nojima fault and (2) whether the magnitude was predictable in advance or not using tectonic landform and empirical equation between fault length and magnitude in terms of the seismic hazard assessment. Here, we formulated the ellipsoidal rupture areas in order to resolve the difference between surface rupture length and subsurface rupture length in a fault plane. Rectangular fault plane models do not allow the difference. Using this ellipsoidal rupture area, we can improve the relationship between surface fault length, subsurface fault length and magnitude, especially for the fault with short surface length. We used the least-square method to estimate the best-fit coefficients of the ellipsoid fault model with observed parameters of 55 worldwide earthquakes listed in Stirlinget al. (2002). Using our empirical equation based the ellipsoid fault model, the 6km coseismic surface rupture (Fusejimaet al.,2001) of the 2000 Tottori-ken Seibu Earthquake would be as large as magnitude is 7.1. This estimate is far better than the empirical estimate of only 6.1 by Matsuda's (1975) relationship. We also discussed our new model in tectonic viewpoint by applying it to magnitude-frequency relation in certain seismotectonic provinces. Comparison between the Chubu and the Chugoku regions where the density of active faults are respectively high and low, shows the linear relationship between observed seismicity rate and fault length in both regions while the previous model showed a large gap.