Shear Mach wave characterization for kinematic fault rupture models with constant supershear rupture velocity

We present the specific amplitude and waveform characteristics of near-source shear Mach waves generated by a kinematic model of supershear rupture at constant velocity nu. Asymptotic analytical solutions are provided for the Mach wave amplitudes, in relationship to the geometrical singularities carried by the S-wave isochrones on the fault plane. The solution is dominated by waves radiated near a critical point source A defined by cos(theta) = beta/nu, where theta is the angle between the rupture ray and the S-wave ray normal to the rupture front at A, and beta is the S-wave velocity (the Mach angle). The far-field, dominant velocity field of the Mach wave related to the mode II component of the slip is proportional to the slip velocity at A and to cos(2 theta)/sin(theta). Thus, the related wave front carries the motion on the fault plane at large distances, with little attenuation, within a beam of Mach wave rays characterized by their angle theta. Numerical calculation of the complete field has been achieved up to 4 Hz, in a homogeneous elastic half-space, and for a vertical strike-slip fault 50 km long equivalent to a magnitude of 7.1. It confirms these theoretical developments, and shows that the peak acceleration and velocities are at least twice that of a standard sub-Rayleigh rupture at 10 km and up to 5 times its value at 30 km. Although the diffusion and diffraction of S waves in the real crust are expected to reduce the coherence of the Mach wave front and hence its peak amplitude, especially at large distances and for high frequencies, our analytical and numerical developments demonstrate that supershear rupture can produce unusually large levels of ground motion at distances ranging from 10 km to a few tens of kilometres, within the Mach wave beam.