Effects of supershear rupture speed on the high-frequency content of S waves investigated using spontaneous dynamic rupture models and isochrone theory

In this paper we achieve three goals: (1) We demonstrate that crack tips governed by
friction laws, including slip weakening, rate- and state-dependent laws, and thermal
pressurization of pore fluids, propagating at supershear speed have slip velocity functions
with reduced high-frequency content compared to crack tips traveling at subshear speeds.
This is demonstrated using a fully dynamic, spontaneous, three-dimensional 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 supershear speed in the inplane
direction and subshear speed in the antiplane 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 expression
for the spectral characteristics and geometric spreading of two pulses arising from
supershear rupture, the well-known Mach wave, and a second lesser known pulse caused
by rupture acceleration. (3) We demonstrate that the Mach cone amplification of high
frequencies overwhelms the de-amplification of high-frequency content in the slip velocity
functions in supershear ruptures. Consequently, when earthquake ruptures travel at
supershear 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.