13th International Conference on Fracture June 16–21, 2013, Beijing, China -3- hanging wall and in the footwall may become completely dissimilar for the three cases. Note, in all numerical simulations, we assume crack-like rupture, i.e., once a fault segment is ruptured, the accumulated static shear stress on that segment is released and that section of the fault remains broken without being healed. As shown in Fig. 1, fault slip (displacement discontinuity) is oriented so that the fault behaves as a thrust one, but the results shown below are valid also for normal dip-slip faulting. In the following, snapshots of the isochromatic fringe patterns, i.e., contours of the (dynamic) maximum in-plane shear stress (τmax), are exhibited where the fringe order is proportional to τmax (≥ 0) and all types of elastic waves may be displayed. 3. Numerical case studies 3.1. Finite fault buried at depth Figure 2 shows the dynamic rupture-induced stress field for the case of a finite dip-slip fault located at depth (length L = 0.05, depth h = 2 and L = 0.05 2, h = 2 for the vertical and nonvertical cases, respectively). This problem is rather classical in seismology: The entire (short) fault segment breaks instantaneously at time t = 0 to radiate body waves. At time t = 1.5, we recognize weak shear waves radiated from the hypocenter (identified as S in the figure). In the geometrically symmetrical case (Fig. 2a), at t = 3.9, clear but weak surface reflected SS wave and two Rayleigh surface pulses (R) are visible. We also find weak PS waves, the P waves diffracted by the free surface and converted into S waves, but the P wave front propagating from the hypocenter is invisibly weak. These PS waves interact with the outgoing S waves, but their effects seem, again, negligible. At later stages (t = 6.3 and 8.7), both surface pulses R follow the S waves and propagate into the far-field (without decay in these two-dimensional simulations), but the reflected shear wave SS attenuates upon propagation and its interaction with the seismic source (hypocenter), now showing static stress singularities, is very small. Similar discussion holds in the asymmetrical case (Fig. 2b) except that here Rayleigh pulse (Rh) and shear wave (Sh) in the hanging wall are stronger than those (Rf and Sf) in the footwall. It is important to note that in seismology an approximate (kinematic) approach, stacking the finite fault segments and rupturing these segments sequentially, is usually employed to inversely obtain a progressive fault rupture related to an earthquake (seismograms). However, from dynamics point of view this approach may not be valid because, as we see below, the wave field generated in the finite fault segments approach (Fig. 2) has a characteristic radiation pattern very different from the one associated with the continuously rupturing fault (Figs. 3 and 4). This situation is akin to blasting simulations of a progressively detonating column charge: The characteristic dynamic wave patterns in the approximate approach that is based on stacking spherical charges and detonating these charges sequentially are very dissimilar compared with the radiation patterns of continuously exploding charge [19, 20]. 3.2. Fault rupture starting at depth and arresting well below the free surface In Fig. 3, the fault rupture is initiated at depth (h = 2 and 2 for Figs. 3a and 3b, respectively), propagated upwards but suddenly arrested well below the free surface. At time t = 0, fracture starts moving along the prescribed fault plane with a constant speed c, and after a certain time t = L/V it arrests, leaving a final rupture zone of length L = 1. For this crack-like fault model, we assume the constant rupture speed is in the subsonic range, 0.4 cP (~ 0.7 cS; smaller than the Rayleigh wave speed cR). The noteworthy phenomenon observed here is the strong rupture front wave (t = 1.5). In the vertical case (Fig. 3a), the problem is still geometrically symmetrical and the induced particle motions are symmetrical with respect to the rupturing fault plane: Upon arrest, a relatively strong shear wave (S1) is radiated from the upper tip of the ruptured fault plane (interface) (t = 3.9) and
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