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Authors: Bizzarri, A.* 
Spudich, P.* 
Title: Effects of super−shear rupture speed on the high frequency content of S−waves investigated using spontaneous dynamic rupture models and isochrone theory
Issue Date: 11-Dec-2007
DOI: 10.1029/2007JB005146
Keywords: Numerical models
Subject Classification04. Solid Earth::04.06. Seismology::04.06.03. Earthquake source and dynamics 
Abstract: This paper achieves three goals: 1) It demonstrates that crack tips governed by friction laws including slip–weakening, rate–and state–dependent laws, and thermal pressurization of pore fluids, propagating at super–shear speed have slip velocity functions with reduced high frequency content compared to crack tips traveling at sub–shear speeds. This is demonstrated using a fully dynamic, spontaneous, 3–D earthquake model, in which we calculate fault slip velocity at nine points (locations) distributed along a quarter–circle on the fault where the rupture is traveling at super–shear speed in the in–plane direction and sub–shear speed in the anti–plane direction. This holds for a fault governed by the linear slip–weakening constitutive equation, by slip–weakening with thermal pressurization of pore fluid and by rate– and state–dependent laws with thermal pressurization. The same is also true even assuming a highly heterogeneous initial shear stress field on the fault. 2) Using isochrone theory we derive a general expressions for the spectral characteristics and geometric spreading of two pulses arising from super–shear rupture, the well–known Mach wave, and a second lesser known pulse caused by rupture acceleration. 3) The paper demonstrates that the Mach cone amplification of high frequencies overwhelms the deamplification of high frequency content in the slip velocity functions in super–shear ruptures. Consequently, when earthquake ruptures travel at super–shear speed, a net enhancement of high frequency radiation is expected, and the alleged “low” peak accelerations observed for the 2002 Denali and other large earthquakes are probably not caused by diminished high frequency content in the slip velocity function, as has been speculated.
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