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 in‐plane 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.