13th International Conference on Fracture June 16–21, 2013, Beijing, China -5- interacts with the free surface. The reflected shear wave (SS) and another shear (S2) wave generated by the stopping phase of the rupture process interact with the ruptured interface but their influence on the interface seems relatively small. Rayleigh pulses propagating along the free surface are much stronger than those in Fig. 2a. When the fault plane is nonvertical (Fig. 3b), the geometrical symmetry is totally broken: The induced stress is much larger in the footwall than in the hanging wall, with a much stronger shear Sf wave recognizable in the footwall. It is contrary to the previous and the following observations (Figs. 2b and 4b) where the dynamic disturbances are stronger in the hanging wall than in the footwall, and it may be due to the strong rupture front wave that is diffracted at the upper tip of the ruptured interface and flows into the footwall across the unbroken (extended) section of the fault plane. 3.3. Fault rupture approaching the free surface from bottom The wave field where the fault breaks the free surface is shown in Fig. 4. As in the previous case (Fig. 3), the crack-like rupture, starting at t = 0, propagates along the fault plane with a constant speed c = 0.4 cP for a length L = 2 until it surfaces. In both vertical and nonvertical cases, when the rupture front approaches the free surface, four Rayleigh-type pulses are generated: two propagating along the free surface into the opposite directions to the far-field (labeled as R or Rh, Rf), the other two moving back along the ruptured interface downwards into depth (I). This downward surface-type pulse can be observed also in the numerical simulations of borehole blasting in a rock mass where the explosive charge is detonated at the bottom and a detonation front moves along an explosive column toward the free surface (bottom-to-top blasting); Rayleigh pulses are generated when the detonation front reaches the surface and they may move downwards along the explosive column [19, 20]. If the fault is vertical and geometrically symmetrical (Fig. 4a), the downward interface pulses may largely control the stopping phase of the dynamic rupture on the fault. If the fault is nonvertical and asymmetrical (Fig. 4b), the downward interface pulse and the outward-moving surface pulse (Rh) interact with each other to induce a specific shear wave, corner wave (C), in the hanging wall. This corner wave carries concentrated wave energy and generates strong particle motions in the hanging wall. In the footwall, on the contrary, the weaker surface pulse (Rf) dominates the ground (free surface) motion and the interaction of this surface pulse with the interface pulse moving in the opposite direction (I) is also small. Thus, the asymmetric ground motion, abovementioned and often observed in shallow dip-slip earthquakes, may be caused. The P and S waves generated in the footwall upon fault surfacing (Pf, Sf) is also relatively strong, but they are much weaker than the corner wave in the hanging wall. The generation of the interface pulse and the corner wave has not been well recognized so far, partly because these waves may not be expected for a fault fracturing only at depth (Figs. 2 and 3), but we should note that similar rupture pattern (downwards rupture after initial upward one) has been reported for the rupture development related to the 2011 off the Pacific coast of Tohoku, Japan, earthquake [21]. In the simulation of the surfacing nonvertical fault, the shallowest part (length 0.15, i.e., three times the grid spacing; see Fig. 1b) is assumed vertical so that we can numerically treat the corner effect appropriately in the framework of the finite difference method: This geometry is selected so as to avoid the problems related to analytical singularities. However, further computations may indicate that qualitatively same phenomena can be observed without this short vertical section, i.e., even when the nonvertical fault rupture stops just below the free surface (at a very shallow depth of 0.15). However, the amplitudes of the induced surface, interface pulses and the corner waves become smaller. Figure 2 (continued). Snapshots of the dynamic stress field (isochromatic fringe patterns) associated with the rupture of the (a) vertical and (b) nonvertical finite dip-slip seismic sources at depth. The fringe order is proportional to the magnitude of the maximum in-plane shear stress (τmax). Rupture is initiated at time t = 0. Weak Rayleigh surface pulses as well as the waves reflected at the free surface can be recognized.
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