I am looking for some references relating directly the fault rise time (or earthquake rise time) to the moment magnitude. Suggestions?
In a classical dislocation model of a rectangular fault with the constant rupture velocity, the whole rise time of the fault Tw would be the sum of the process-time L/Vr plus a slip time Ts at a point, where L is the representing length of the fault and Vr is the rupture speed. In the scaling law, L is proportional to the seismic moment M0 and Vr is constant, Tw is considered to be proportional with M0^(1/3). Note that Ts is proportional to the whole slip D if the slip velocity is constant (~1m/s) and D is also proportional to M0^(1/3). It is the case for most of the earthquakes except for the Tsunami earthquakes in the subduction zones where Ts could be comparatively long with L/Vr. Please refer to Kanamori, H. and D. L. Anderson (1975) on Bull. Seism. Soc. Am., 65, 1,073-1,095. Also look at Tanioka, Y & Ruff, L.J. (1997) on Seism. Res. Lett., 68(3), 386–400.
For the real source-time function database from more recently established CMT solutions, you can refer to SCARDEC library as in: Vallée, M. Source time function properties indicate a strain drop independent of earthquake depth and magnitude. Nat Commun 4, 2606 (2013). https://doi.org/10.1038/ncomms3606.
Hiroshi Kawase
Dear Kawase sensei,
manhy thanks for your straightforward but very aclaratory explanation. The references you cite have been also truly helpful,
Regards,
Correction: Originally I wrote, "L is proportional to the seismic moment M0", but it should be "L is proportional to 1/3 power of the seismic moment M0 (M0^1/3)".
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