Supershear accelerations and Mach-waves from a rupturing front. Part I. Theoretical model and implications

Abstract

Acceleration fields in 3-D elastic media due to a propagating rupture at constant super-shear velocities are evaluated. The elastodynamic Green's tensor and its gradient are obtained in closed-form for arbitrary compressional and shear Mach-numbers and arbitrary source time-function. It is found that the acceleration field consists of three main phases: a Mach-wave, a starting phase, and a stopping phase. The stationary phase approximation is used to obtain the explicit dependence of the Mach-wave peak amplitude on the source, propagation, and media elements. It is shown that the Mach-wave plays a dominant role in the acceleration signal of the near-field zone.