© 2014, Springer Basel. Faults are often embedded in low-velocity fault zones (LVFZ) caused by material damage. Previous 2D dynamic rupture simulations (Huang and Ampuero, 2011; Huang et al., 2014) showed that if the wave velocity contrast between the LVFZ and the country rock is strong enough, ruptures can behave as pulses, i.e. with local slip duration (rise time) much shorter than whole rupture duration. Local slip arrest (healing) is generated by waves reflected from the LVFZ–country rock interface. This effect is robust against a wide range of fault zone widths, absence of frictional healing, variation of initial stress conditions, attenuation, and off-fault plasticity. These numerical studies covered two-dimensional problems with fault-parallel fault zone structures. Here, we extend previous work to 3D and geometries that are more typical of natural fault zones, including complexities such as flower structures with depth-dependent velocity and thickness, and limited fault zone depth extent. This investigation requires high resolution and flexible mesh generation, which are enabled here by the high-order accurate arbitrary high-order derivatives discontinuous Galerkin method with an unstructured tetrahedral element discretization (Peltieset al., 2012). We show that the healing mechanism induced by waves reflected in the LVFZ also operates efficiently in such three-dimensional fault zone structures and that, in addition, a new healing mechanism is induced by unloading waves generated when the rupture reaches the surface. The first mechanism leads to very short rise time controlled by the LVFZ width to wave speed ratio. The second mechanism leads to generally longer, depth-increasing rise times, is also conditioned by the existence of an LVFZ, and persists at some depth below the bottom of the LVFZ. Our simulations show that the generation of slip pulses by these two mechanisms is robust to the depth extent of the LVFZ and to the position of the hypocenter. The first healing mechanism is dominant for events with hypocenter inside the LVFZ. The second one is dominant if the hypocenter is deeper than a shallow LVFZ. These results suggest that the depth-dependence of rise time might help constrain the depth extent of the LVFZ. We also show that ruptures can spontaneously stop in flower-like LVFZs with uniform velocity reduction, but continue propagating as slip pulses if velocity reduction is depth-dependent.