Energy flux of propagating ruptures with cohesive force

Abstract

The energy flux F at the rupture tip has been previously computed only for 2D steady-state singular cracks. In this paper, I compute F for fully dynamic 3D ruptures, propagating both with constant and variable rupture speed (v_r) over finite faults directed by a governing law with a cohesive zone (and thus nonsingular ruptures). The results presented here indicate that F is positive and increasing over the whole range of v_r from zero up to P-wave speed. This is in contrast with 2D steady-state singular cracks, which predict the existence of a forbidden zone in the range of rupture speeds because in that interval F would be negative. Moreover, I found that in 3D ruptures with cohesive force, F is proportional to v_r, again in contrast to 2D steady-state singular cracks, in which F is not a unique function of v_r and also exhibits an inverse dependence on v_r. More specifically, it emerges that fast earthquakes tend to have a higher energy flux at the crack tip compared with slow ruptures. Finally, I show that the magnitude of F is basically due to its component aligned in the direction of the initial shear stress.