Mechanics of 3–D shear cracks between Rayleigh and shear wave rupture speeds

Though mode II shear fractures (primarily strike–slip earthquakes) can not only exceed the shear wave speed of the medium, but can even reach the compressional wave speed, steady–state calculations showed that speeds between the Rayleigh and shear wave speeds were not possible, thus defining a forbidden zone. For more than 30 years it was believed that this result in which the rupture jumps over the forbidden zone, also holds for 3–D ruptures, in which mode II and mode III (mainly dip–slip faulting) are mixed. Using unprecedentedly fine spatial and temporal grids, we show that even in the simple configuration of homogeneous fault properties and linear slip–weakening friction law, a realistic 3–D rupture which starts from rest and accelerates to some higher velocity, actually does pass smoothly through this forbidden zone, but very fast. The energy flux from the rupture tip is always positive, even within the so-called forbidden zone, contrary to the 2–D case. Finally, our results show that the width of the cohesive zone initially decreases, then increases as the rupture exceeds the shear wave speed and finally again decreases as the rupture accelerates to a speed of ~ 90% of the compressional wave speed.