Effect of fault heterogeneity on rupture dynamics: An experimental approach using ultrafast ultrasonic imaging

Transcription

1 JOURNAL OF GEOPHYSICAL RESEARCH: SOLID EARTH, VOL. 118, , doi: /2013jb010231, 2013 Effect of fault heterogeneity on rupture dynamics: An experimental approach using ultrafast ultrasonic imaging S. Latour, 1,2 C. Voisin, 2,3 F. Renard, 2,3,4 E. Larose, 2,3 S. Catheline, 2,5 and M. Campillo 2,3 Received 27 March 2013; revised 30 October 2013; accepted 3 November 2013; published 21 November [1] This study is devoted to the experimental investigation of the interaction of a propagating rupture with one or several mechanical heterogeneities. We developed a friction laboratory experiment where a soft elastic solid slides past a rigid flat plate. The system is coupled to an original medical imaging technique, ultrasound speckle interferometry, that allows observing the rupture dynamics as well as the emitted elastic shear wavefield into the solid body. We compare the dynamics of propagating rupture for a homogeneous flat interface and for three cases of heterogeneous sliding surfaces: (1) an interface with a single point-like barrier made of a small rock pebble, (2) an interface with a single linear barrier that joins the edges of the faults in a direction perpendicular to slip, and (3) an interface with multiple barriers disposed on half of its surface area, creating a heterogeneous zone. We obtain experimental observations of dynamic effects that have been predicted by numerical dynamic rupture simulations and provide experimental observations of the following phenomena: a barrier can stop or delay the rupture propagation; a linear single barrier can change the rupture velocity, increasing or decreasing it; we observe transition from subshear to supershear propagation due to the linear barrier; a large heterogeneous area slows down the rupture propagation. We observe a strong variability of the rupture dynamics occurring for identical frictional conditions, which we impute to heterogeneity of the stress field due to both the loading conditions and memory of the stress field due to previous rupture events. Citation: Latour, S., C. Voisin, F. Renard, E. Larose, S. Catheline, and M. Campillo (2013), Effect of fault heterogeneity on rupture dynamics: An experimental approach using ultrafast ultrasonic imaging, J. Geophys. Res. Solid Earth, 118, , doi: /2013jb Introduction [2] Strong motions records show that the rupture process occurring on faults during an earthquake is generally complex. Kinematic and/or dynamic inversions of seismic motions reveal complex slip patterns as well as relatively complex slip history for most large earthquakes. This complexity may stem from the intrinsic friction law (either slip-dependent or rate-and-state dependent) that develops different rupture propagation modes (either crack-like or pulse-like) or rupture velocity (subshear or supershear). This complexity may stem also from the variations of stress and/or strength along the fault, and earthquakes can be Additional supporting information may be found in the online version of this article. 1 Laboratoire de Géologie, École Normale Supérieure, UMR 8538 CNRS, Paris, France. 2 ISTerre, Université Grenoble Alpes, Grenoble, France. 3 ISTerre, CNRS, Grenoble, France. 4 Physics of Geological Processes, University of Oslo, Oslo, Norway. 5 LabTAU INSERM U1032, University of Lyon, Lyon, France. Corresponding author: S. Latour, Laboratoire de Géologie, École Normale Supérieure, UMR 8538 CNRS, 24 Rue Lhomond, Paris CEDEX , France. (soumaya.latour@ens.fr) American Geophysical Union. All Rights Reserved /13/ /2013JB understood as complex slipping processes with variable resistance on the barriers [Beroza and Mikumo, 1996; Voisin et al., 2002], inducing a generally nonuniform coseismic slip (see, for example, Scholz [2002], Aki and Richards [2002], Mai and Beroza [2002], Lavallée et al. [2006], and the finite-source rupture model database srcmod/). [3] Faults and subduction zones are generally segmented, with barriers that can stop or delay the rupture propagation. Those barriers have been related to the fault complexity itself. We note here that the term barrier has been used with different meanings depending on the authors. In this study, it is used to refer to a zone with a higher frictional resistance than the surrounding. This definition does not imply anything on the loading stress of this zone, which depends both on the loading and slipping history. Aki [1979] proposed that barriers can be linked either to geometrical irregularities of the fault, like bending or segmentation, or to the heterogeneity of rock physical properties along the fault. Indeed, rupture dynamics is controlled by the absolute value of stress on the fault at the beginning of slip and by the frictional properties along the fault surface. Nonuniformity of the elastic properties and of the lithology, and geometrical irregularities of faults at all scales (i.e., segmentation and roughness of the fault plane) [e.g., Power et al.,

2 1987; Wesnousky, 2006; Candela et al., 2011] can result in heterogeneous distribution of the stress accumulated during tectonic loading. Moreover, strength heterogeneities can prevent or limit the slip in some places. By creating heterogeneity of slip during the rupture process, they also result in a complexity of the distribution of stress that remains present after a seismic event, as observed along the Nojima fault [Bouchon et al., 1998]. [4] Numerical simulations have investigated the role of a barrier by introducing either a prestress heterogeneity and/or a frictional heterogeneity along the fault. Such simulations have demonstrated that, depending on the loading stress and properties of the barrier, a rupture can keep propagating through the barrier or stop completely [Das and Aki, 1977; Voisin et al., 2002]. The barrier itself may slip along with the rupture front, or with a time delay. Interestingly, when the barrier happens to fail, it may initiate a transition from subshear to supershear propagation [Dunham et al., 2003;Page et al., 2005;Liu and Lapusta, 2008]. Supershear ruptures have raised a strong interest because of the possible associated Mach waves that bear the potential for great destructions, increasing seismic hazard in the vicinity of the faults prone to produce such supershear ruptures. Supershear ruptures have been observed for several earthquakes. The first observation was performed for the 1979 Imperial Valley earthquake [Archuleta, 1984]. It was later observed over longer distances for the 1999 Izmit earthquake [Bouchon et al., 2001], the 2001 Kunlun rupture [Bouchon and Vallee, 2003], and the 2002 Denali earthquake [Dunham and Archuleta, 2004]. The geological conditions necessary to maintain a sustained supershear propagation are not completely understood yet, but the seldom observations of such ruptures suggest a simple planar fault free from geometrical or stress heterogeneities [Bouchon et al., 2010]. Indeed, the rupture velocity depends on the distribution and strength of these heterogeneities. In favorable conditions, they can prevent supershear propagation or slow down the rupture [Mikumo and Miyatake, 1978; Fukuyama and Madariaga, 2000; Schmedes et al., 2010; Latour et al., 2011a]. [5] Several experiments have allowed to study some aspects of rupture dynamics. Rosakis et al. [1999] showed the physical existence of supershear rupture propagation. Initiation [Ohnaka and Shen, 1999; Rubinstein et al., 2004], bending of the fault [Rousseau and Rosakis, 2003], and pulse-like rupture mode [Lykotrafitis et al., 2006] were also investigated. The dynamic effects of stress heterogeneity were studied by Ben-David et al. [2010] and Rubinstein et al. [2011], who observed that rupture velocity is highly controlled by the distribution of tangential and normal stresses, and that high complexity in the rupture process and in the sequence of rupture occurrences arises from stress heterogeneity. The dynamic effects of strength heterogeneity were studied by Nielsen et al. [2010] on a 1-D fault. These authors measured experimentally how a viscous patch may stop rupture propagation by introducing a mechanical complexity along the interface that breaks. [6] In a previous study [Latour et al., 2011b], we developed a new experimental method for investigating rupture dynamics. To that end, we built a dynamic friction laboratory experiment in which a soft elastic solid is sliding over a rigid flat plate. We associated to this experiment a medical imaging device that uses acoustic speckle interferometry [Sandrin 5889 et al., 2002]. This imaging technique was first developed for medical applications [Bercoff et al., 2004; Gallot et al., 2011]. We used it for the first time to obtain 3-D observations of the propagation of ruptures along bimaterial interfaces, as well as the shear waves radiated into the volume by the slipping events. The friction interface can be prepared with uniform friction properties so that it produces dynamic propagating rupture during slip events [Latour et al., 2011b]. An interesting feature of this experiment is that it allows imaging ruptures occurring on the 2-D interface, thus illuminating the geometric effect of the rupture propagation. [7] In the present study, we use this imaging technique to study the effect of barriers on rupture propagation and bring experimental information that helps understanding their role during coseismic slip. We address the questions of the repeatability of the dynamic effect of a barrier, the effect of the barrier on rupture velocity, and the role of the barrier geometry. We test three different geometries for the barrier. In the first case, we study a single point-like barrier located at a central position on the otherwise homogeneous rupture area. In the second case, we investigate the effect of a linear barrier that joins the edges of the friction interface in the direction perpendicular to rupture propagation. In the third and final case, we study the effect of a wide heterogeneous zone in which barriers are disposed according to a regular pattern (distributed barrier). We report the experimental observations and then discuss them with respect to existing numerical studies and examples of earthquake source dynamics. 2. Materials and Methods 2.1. Slider Preparation and Properties [8] The experiments involve sliding a linear elastic solid along a rigid interface and imaging the rupture dynamics by acoustic means. We use a soft hydrogel solid slider made of a tangle of polymeric chains of PolyVynilAlcohol (PVA), holding water [Fromageau et al., 2007]. The slider is prepared by dissolving 10% weight of PVA powder into boiling water and adding 1% of powdered cellulose, as these particles diffract ultrasounds and are needed to record the acoustic data. The obtained solution is poured into a convenient mold, cooled to ambient temperature, and then frozen to 20 ı C. It is submitted to three cycles of freezingdefreezing between 20 ı C and ambient temperature. The effect of these cycles is to increase the shear modulus of the gel and therefore its shear wave speed. The shear wave (S wave) speed of the slider has been measured equal to c s = m/s, while the compressional ultrasonic wave (P wave) speed was c p = 1480 m/s, similar to that in water. The slider 61018cm 3 in size and incompressible. It does obey the classical linear elastodynamic theory in the range of explored deformation and frequencies. Indeed, hydrogels used in the experiments are known to be highly linear media. In Catheline et al. [2003], nonlinear effects are observed for deformation up to 40%. In the present experiments, the measured deformations barely reach 4%. In addition, harmonics which are the signature of nonlinear wave propagation, were undetected. As far as acoustoelasticity effects in gels are concerned, changes in the S wave speed due to the loading stress are estimated to 5% [Gennisson et al., 2007], which is in the range of the uncertainty for the measurement of c s.

3 Figure 1. (a) Experimental setup of a soft elastic solid sliding past a rigid glass plate. The positions of the two planes P1 and P2 of observation of the shear waves are indicated in the insets on the right. Schematic arrangement of frictional heterogeneities (small rock pebbles) along the interface to create: (b) a single point-like barrier, (c) a single linear barrier, and (d) a large heterogeneous zone (distributed barrier). (e and f) Photographs of the elastic slider made of hydrogel coated with sand and the disposition of the pebbles on the glass plate, corresponding to the geometries of Figures 1c and 1d, respectively. The sanded face of the gel is afterward placed over the glass plate and the pebbles Preparation of the Sliding Interface [9] The hydrogel slider lies on a glass plate and is maintained by a holder to which an acoustic probe can be attached (Figure 1a). The glass plate can be moved horizontally at a controlled velocity. The holder consists of an upper plate on which we can add dead weights to increase the normal stress at the sliding interface and a vertical part that prevents the gel moving with the glass plate. The vertical part of the holder locks the slider along one of its vertical edge, the opposite edge being let free. The slider is therefore fixed in the laboratory referential, while the plate is moving underneath. [10] In Latour et al. [2011b], we previously observed that a stick-slip behavior can be induced by sand coating the frictional interface. The sand coating is homogeneous on the interface at the observational scale and allows to obtain a friction that is higher than the gel-glass interface, thus allowing a stick-slip behavior. Because the sand remains attached to the gel by capillarity, the frictional behavior of the slider is controlled by the friction properties 5890

4 placing only one pebble at the center of the frictional interface (Figure 1b). In the second series of experiments, we construct a linear barrier by lining up pebbles across the whole width of the interface, to create a continuous obstacle to the propagation of the rupture (Figures 1c and 1e). In the third set of experiments, we dispose regularly a network of pebbles over half of the sliding interface (Figures 1d and 1f), creating a so-called distributed barrier. In this network the pebbles are approximately distant of 1 cm of their nearest neighbors. The stick-slip behavior occurs for the three sets of experiments as it is for the homogeneous case, a situation that allows us to compare the rupture propagation along a homogeneous and a heterogeneous interface and to investigate the dynamic interaction of a propagating rupture with different barriers. Figure 2. Example of an acoustic speckle recorded by the transducer, in echo of two successive acoustic emissions. The acoustic signal received in the time window around t is determined by a group of scatterers at a distance d = c p t/2. The same signal is received with a time advance of dt after the next acoustic emission. This delay is due to the motion of the group of scatterers toward the transducer. Their displacement ı is related to the time delay by ı = c p dt/2. between the sand and the glass and by the elastic properties of the gel. [11] In the present study, we focus on the interaction of a propagating rupture with a barrier. We create heterogeneities along the interface with rock pebbles. The pebbles are irregular and vary between 5 to 8 mm in size. They are disposed on the glass plate and covered with the sand-coated gel slider (Figures 1e and 1f). Due to the deformation of the hydrogel slider around the pebbles, they remain fixed with respect to the slider. This can be checked by comparing the pebbles position after and before the experiment. The sliding thus occurs between the glass and the pebbles. We assume that the frictional force of the pebbles on the glass is stronger than the friction of the sand, because the deformed gel over them applies a locally stronger normal stress. The pebbles therefore act as strength barriers. We use the following experimental protocol: we prepare and place the glass plate, gel, sand, and pebble(s), and then move the bottom glass plate at constant velocity (2.7 mm s 1 ). We wait for the stickslip regime before beginning the observations. Although this loading rate does not reproduce the ratio of loading velocity over the S wave speed of natural faults (around in natural faults, in our experiments), it is a good compromise. It allow us to measure 10 to 20 successive events, and the delays between successive events are sufficiently large to discard some possible direct dynamic interaction due to waves between the events. We test the effects of three different geometries of heterogeneity (Figure 1). In the first set of experiments, we create a point-like barrier by 2.3. Acoustic Speckle Interferometry [12] The imaging method, acoustic speckle interferometry, takes advantage of the very specific elastic properties of the hydrogel [Gallot et al., 2011]. It allows imaging shear wave propagation, as well as the ruptures propagating along the gel-glass interface. The method consists in sending acoustic pulsed plane P waves in the solid and analyzing the echoes recorded between each pulse. A set of 64 directional acoustic transducers, arranged in a line 4.8 cm long, emit simultaneous acoustic pulses. The acoustic pulses have a central frequency of 5.5 MHz and are emitted at a rate of 2 khz. The emitted P wavefronts therefore propagate along a plane in front of the acoustic probe. The P waves are scattered by the cellulose grains inside the gel fabric. The same acoustic probe records the echoes due to the scatterers, between two emissions. [13] The echo emitted by one scatterer interferes constructively or destructively with its neighbor s scatterer. Due to the randomness of the scatterers distribution in the volume of the gel, the recorded signal, called acoustic speckle, has a noisy aspect (see Figure 2). However, the signal recorded at time t after the emission of the pulse is completely determined by the distribution of the scatterers located at a distance d = tc p /2, corresponding to a forth and back propagation of the P wave. If between two successive acquisitions the gel is submitted to some motion, bringing this same group of scatterers slightly further or closer to the acoustic probe, the reception time of its specific signal shows a measured delay, either positive or negative. The particle displacement, and therefore its velocity, can be calculated from this delay. The delay is measured by cross-correlating the successive signals. To get a complete image of the particle displacement in the plane in front of the acoustic probe, the signal received by each transducer is divided into time windows. The signal in each window is then correlated to the following record, in order to calculate the reception delay for every distance in front of the transducer (Figure 2). Thanks to a parabolic interpolation of the correlation peak, a precision of 1 m is reached for the displacement measured between two acoustic pulses. Motions in directions perpendicular to the acoustic wave propagation are ignored because, at first order, they do not change the distance between the scatterers and the acoustic transducers. Finally, we obtain a movie of the particle velocity component in the direction of the acoustic emission, at a rate of 2 khz, and with a precision of 2 mm s

5 line (corresponding to the bottom line), and the shear wavefield in the gel is well imaged. The records are up to 2.25 s long, which allows comparing successive slipping events that occur in quite comparable conditions (same interface and same loading conditions). Figure 3. Propagation of a rupture along a homogeneous interface: time-lapse views of the horizontal component of particle velocity in the horizontal plane P1 (see Figure 1a), located 8 mm above the frictional interface. A rupture front propagates in the +x direction. Its average velocity is measured equal to ms 1, which corresponds to a supershear rupture. Time t = 0 is arbitrarily attributed to the first frame. (The corresponding movie is available in the supporting information.) [14] We can set the acoustic probe in two positions to observe the horizontal v x component of the particle velocity in two planes of interest (Figure 1). The plane P1 is horizontal, parallel to the sliding interface and located 8 mm above it. Observations along this plane gives information about the rupture dynamics at the interface. The plane P2 is vertical. In this plane the rupture can be seen only along one 3. Spontaneous Rupture Propagation Along a Homogeneous Interface 3.1. Observation of the Rupture Propagation [15] Latour et al. [2011b] showed that with a homogeneous interface (coated with sand), ultrasound speckle interferometry allows to follow the propagation of ruptures along the interface. We tested the effect of normal stress on the coherent propagation of a rupture front along the sandcoated interface. At low normal stress, the rupture fronts are often poorly spatially coherent, and the rupture appears like disordered patches sliding one after the other without a clear propagation pattern. Increasing the normal stress reduces the occurrence of this disordered sliding behavior and promotes the occurrence of coherent propagating rupture fronts. Therefore, we performed all the experiments presented in the following with the maximum available normal stress (14.5 kpa). [16] An example of these coherent rupture fronts is displayed in Figure 3. The observation, performed in the horizontal plane P1, is a representative image of the rupture process occurring at the interface 8 mm below. The slipping zone, shown in red color, corresponds to a coherent motion in the +x direction, opposite to the plate motion: The rupture is releasing the stress loading due to the plate motion. The rupture propagates in the +x direction, which is from the locked edge of the slider to the free edge. Most of the ruptures propagate in this direction, which we interpret to be an effect of the asymmetric loading apparatus, which concentrates the stress on the locked edge of the slider. Most of the rupture fronts propagate across the whole observed area (10 cm long, 4.8 cm large). However, some weak ruptures spontaneously stop after 3 to 4 cm of distance of propagation. In order to focus on the interaction of a rupture front with a barrier, we place the heterogeneities beyond these 4 cm of distance. This way, we eliminate the weak ruptures and we make sure that a vivid rupture front is interacting with the barrier. The rupture fronts propagate in a direction roughly parallel to slip, albeit the proportion of rupture front with oblique directionality is not negligible. For this reason, it is important to measure the rupture velocity in the plane P1, and to be cautious with rupture velocity measured on the vertical plane P2, which can provide only apparent velocities Rupture Velocity, Supershear Rupture, and Mach Fronts [17] The rupture propagation velocity is measured with the acoustic speckle interferometry. It ranges between 5 and 13 m/s, depending on the event. Given that the shear wave speed in the material is c s = m/s, this range of velocities covers subshear rupture propagation as well as supershear rupture propagation. For example, the event displayed in Figure 3 is a supershear event, whose velocity has been measured equal to v r = m/s (Figure 9), which 5892

6 is 150% of the shear wave velocity of the gel. A supershear rupture like this one emits a Mach front that is propagating inside the medium without geometrical attenuation. Details about the Mach wavefront are given in a previous study [Latour et al., 2011b]. Concerning the rupture mode, it is also interesting to remark that during the rupture propagation, the apparently slipping zone keeps a width of a few centimeters. The rupture is thus probably a pulse-like rupture. However, given that the observation is done in a plane located 8 mm above the interface, the possibility that slow slip velocity occurs on the surface after the passage of the peak slip velocity, and would be too small to create a measurable signal 8 mm above the surface, cannot be completely discarded. [18] We can note here that there is a large difference of the elastic properties on both side of the interface, between the gel and the glass plate. It has been shown [Anooshehpoor and Brune, 1999; Baumberger et al., 2002; Xia et al., 2005] that such an asymmetry of mechanical properties across the interface can play an important role on the rupture mode, favoring, for example, the supershear rupture mode in one direction of propagation, or the pulse-like rupture instead of crack-like rupture. In the following, we focus on the interaction of the propagating ruptures with barriers. The homogeneous case serves here as a reference framework that includes the effect of asymmetry, allowing to discuss independently the effects of the barriers. 4. Interaction of a Propagating Rupture With an Isolated Point-Like Barrier [19] We performed a series of experiments with a single point-like barrier located in the middle of the observational area (Figure 1b) and observed its interaction with the propagating coherent rupture fronts. When an effect of the point-like barrier is observed, the dynamic behavior falls in one of the following general classes: [20] 1. The rupture is stopped at the barrier. The barrier may eventually break (Figure 4a), although it is not always the case; [21] 2. The rupture propagates around the barrier, with the slip velocity locally attenuated by the barrier. The barrier may sometimes break, but only significantly later (Figure 4b). [22] 3. The rupture front propagates through the barrier, with the slip velocity strongly reinforced by the simultaneous slip of the barrier (Figure 4c). [23] The various plots displayed in Figure 4 present one typical event for each of the classes described above. The measurements are made in the horizontal plane P1 parallel to the interface. Breaking of the barrier is observed for the cases a and c. For each event, t =0is arbitrarily attributed to the first snapshot. [24] In Figure 4a, at t = 0, the rupture front is propagating from the left side; at t =1ms, the rupture front is arriving at the barrier, and a peak of particle velocity at the barrier position shows that it is breaking. In the two following snapshots, the S wave radiated by the breaking of the barrier can be seen and the rupture propagation is stopped. In Figure 4b (middle snapshots), at t =0, the rupture front is propagating from the left side; at t =1.5ms, the rupture front is observed to propagate around the barrier, but not 5893 over it. In the following snapshot, the rupture front continues to propagate, with a local attenuation due to the interaction with the barrier. The absence of S wave propagating from the pebble position indicates that the barrier did not break. In Figure 4c, at t = 0, a rupture front propagates from the left side and starts interacting with the barrier. At t =2.5ms, the barrier slips suddenly, creating a peak of particle velocity. The emitted circular shear wave can easily be distinguished to initiate and then propagate from t =2.5to t =4.5ms. At t =4.5ms, the shear wave initiated a rupture in the right part of the image, which can be distinguished from the shear wave because of its higher amplitude (the S wave attenuates while the rupture is self-sustained and does not attenuate). [25] In Figures 4a and 4c, the breaking of the barrier radiates a wavefield characterized by a local peak of velocity, followed by the propagation of a circular S wave centered on the barrier position and that attenuates while propagating. This local peak is generally preceded and accompanied by a very peculiar radiation in the form of two earlobes (Figure 4a second snapshot and Figure 4c first two snapshots). This radiation is the signature of the near-field terms of the wavefield, as demonstrated in Latour et al. [2011b]. The wavefield due to the barrier breaking has a very specific signature that can be distinguished from the general wavefield radiated by the rupture front. Therefore, it is possible to confirm that in Figure 4b, the barrier does not break when the rupture front reaches it. In this case the rupture front propagates around the barrier and reforms behind it. The amplitude of the slip velocity is locally attenuated where the rupture front interacted with the barrier. There, the barrier prevents the release and successive propagation of the elastic energy and does not contribute to the overall rupture propagation. [26] The behavior of the barrier is not easy to predict. Successive events with very similar loading conditions and interface properties have differences in their propagation. As discussed in section 7.1, we propose that this variability is due to the inheritance of the stress field from one event to the following one. [27] This first series of experiments confirms that an isolated barrier can play an important role in the rupture dynamics and the radiated wavefield. Concerning the rupture dynamics, we observe that the barrier can stop the rupture front or delay it, introducing an irregular propagation history. Concerning the radiated wavefield, the barrier can act as a secondary source of radiation when it breaks, or conversely attenuate the amplitude of the S wave emitted by the rupture front when it does not break. 5. Interaction of a Propagating Rupture With a Linear Barrier [28] In a second series of experiments, we constructed a single linear barrier (Figure 1c) made of aligned pebbles. This geometry, invariant in the y direction, presents three differences with respect to the previous point-like barrier. First, with this geometry, the rupture front cannot propagate around the barrier. Second, one ensures to get a part of the barrier in the vertical observation plane P2, allowing observation in this plane. Third, the barrier clearly divides

7 Figure 4. Example of the three classes of interactions of a rupture with a point-like barrier: time-lapse views of the horizontal component of particle velocity in the horizontal plane P1 (see Figure 1a), located 8 mm above the frictional interface for three events (see text). The gray circle shows the approximate position of the pebble acting as a point-like barrier. (a) The rupture front is stopped by the barrier, which breaks immediately. (b) The rupture front bypasses the barrier and continues to propagate. (c) The rupture front passes across the barrier, and the sudden break of it enhances the rupture. Time t = 0 is arbitrarily attributed to the first frame for each event. (The corresponding movies are available in the supporting information.) the interface into two homogeneous areas, as would, for example, do a jog on a real fault in a first-order approximation. This geometry allows measuring rupture velocities unequivocally before and after the interaction with the barrier. [29] Here again we focus on the interaction of a coherent rupture front with the barrier. We observe that the rupture fronts usually pause when arriving at the barrier. In some cases the propagation completely stops and does not continue beyond the barrier. In other cases the rupture front, after a delay at the barrier, propagates ahead of the barrier. In the majority of these cases, the second part of the rupture is triggered by the sudden slip of the barrier, which emits S waves in the gel. Finally, for some rare events, after a delay at the barrier, the rupture front continues coherently at the other side, but without triggering the slip of the barrier. The variability of the propagation behavior is demonstrated in Figure 5, where the displacement of two points located one in front of the barrier, and one ahead of it are displayed during a 2.25 s time interval. Given the relatively fast rupture propagation velocity, an event that propagates through the barrier is characterized by a quasi-simultaneous slip of both points at this time scale. If the rupture propagation stops at the barrier, only the point in front of the barrier slips. We can thus reconstruct the extent of propagation for each event. Figure 5 shows that 16 events occurred in the 2.25 s time window. The lateral extent of these 16 events is different from one event to another. Seven rupture events spread 5894

8 Figure 5. (a) Displacement measured in two locations along the sliding interface: before the barrier (blue) and after the barrier (red). On each curve, the regularly decreasing parts correspond to loading phases and steps correspond to sudden slip events. The events that rupture only the area before the barrier are highlighted by the vertical light blue lines, and events that rupture areas both before and after the barrier are highlighted by the vertical purple lines. Yellow and green diamonds show the times at which the barrier slips. (b) Representation of the successive events. Black lines show the length of the interface ruptured for each event. Dashed lines show that the event exits the observed area (10 cm long), and probably ruptured the whole interface (18 cm long). Yellow diamonds correspond to a slip of the barrier simultaneous to a rupture event, while green diamond corresponds to an isolated slip of the barrier. The absence of a regular scheme is characteristic of the highly variable behavior. over all the area of observation, i.e., they propagated through the barrier. There is no clear pattern of organization in their occurrence. The barrier itself presents a nondeterministic behavior; in a sense that, it is not possible to prejudge of the breaking or not of the barrier by knowing the total displacement. Its breaking occurrence is not periodic either. Sometimes it breaks during a small event, without triggering further rupture propagation. Sometimes it breaks separately from the occurrence of a slipping event (green diamonds). This is interpreted as the combined action of the stress concentration created by the previous slip event and the constant background loading. [30] In the following, we focus on the ruptures that crossed the barrier. An observation in the vertical plane P2 of one event is displayed in Figure 6a. The rupture radiates S waves that propagate in the gel and are observed in the plane P2. If the rupture is supershear, the S waves form an elastic Mach front that appears as a planar S wavefront. When a rupture is subshear, an S wavefront is also visible, but should appear as curved. In the first snapshot of Figure 6a, the wavefront radiated by the rupture front can be clearly observed, just after the rupture paused at the barrier. There is a delay of 7 ms before the barrier slips (third snapshot). In the last snapshot, a new rupture front propagates in the second part of the slipping area. The spherical S wave due to the sudden motion of the barrier can be distinguished. Its amplitude is much smaller than that of the wavefront radiated by the rupture, and attenuates when propagating away from the barrier location. At 3.5 ms, far away from the fault, the radiation of the barrier is not easily detected as it is attenuated due to geometrical bulk spreading. This particular event is marked by a second rupture front that propagates ahead of the shear wave, suggesting that it is supershear. The angle between the interface and the radiated S wavefront is also smaller than for the first S wavefront (see the first snapshot). It is thus probable that the second rupture front is 5895

9 Figure 6. Two ruptures that propagate across the linear barrier and through the whole interface. (a) View of the horizontal component of particle velocity in the vertical plane P2. The frictional interface is located at the bottom line (z =0). The blue circle shows the position of the linear barrier. (b) View of the horizontal component of particle velocity in the plane P1, 8 mm above the frictional interface. The circles show the positions of the barrier. After passing the barrier, the front propagates with a higher velocity than before. In both cases, S waves emitted by the barrier breaking can be distinguished (purple arrows). Note that in Figure 6b, the time intervals between each frame are irregular. Time t =0is arbitrarily attributed to the first frame for each event. (The corresponding movies are available in the supporting information.) faster than the first one. However, because it can be ambiguous to distinguish between an actual planar wavefront and a slightly curved S wavefront, and because of the projection effects due to the observation of a 3-D phenomenon in a plane, assertions about the changes in the rupture velocity cannot be said for certain from the observation in the plane P2. [31] Conversely, the rupture velocities can be unequivocally measured in the plane P1 parallel to the interface. The slipping event presented in Figure 6b first propagates with an oblique direction across the first part of the slipping area up to the barrier. Its velocity can be measured in the direction 5896 of propagation and gives ms 1, which is a subshear value, very close to the S waves velocity (Figure 9). After a time delay of a few milliseconds, the barrier suddenly slips, emitting an S wave (third snapshot). In the last snapshot, this S wave triggers a second rupture front ahead of the barrier, which propagates in the direction parallel to slip. Its velocity is measured to be 10 1 ms 1, which is a supershear velocity. We observe here a transition from subshear to supershear rupture velocity triggered by the presence of a barrier. [32] Extending this observation to the seven recorded events for which it was possible to measure with good

10 Figure 7. Two ruptures interacting with a distributed barrier observed in the vertical plane P2. The bottom line is the frictional interface. (a) The rupture stops at the limit of the heterogeneous zone. (b) The rupture continues with a possibly smaller velocity, and the S wave emitted by the heterogeneities is distinguished. The gray rectangle under each frame shows schematically the zone in which heterogeneities were located. In the dark zone in Figure 7b, acoustic data were unusable due to the reflections of the elastic waves on a pebble that covered the signal. Note the irregular time intervals between each frame. Time t =0is arbitrarily attributed to the first frame for each event. (The corresponding movies are available in the supporting information.) confidence a rupture velocity before and after the interaction with the barrier, we find that for five out of the seven events, the rupture velocity is higher after passing the barrier than before. These five events also correspond to the events for which the barrier breaks. In the remaining two events, the barrier did not break and the rupture velocity was lower after crossing the barrier. Thus, a barrier can also diminish the rupture velocity, and this may be related to the fact that when the barrier does not break, it reduces the energy available to break the interface ahead of it. The number of occurrences is too small to be definitive on this aspect of the rupture process. The only solid conclusion for now is that the presence of a barrier can either increase or decrease the rupture velocity. [33] We can summarize the observations for the case of a linear barrier as follows. The dynamics of the rupture is clearly influenced by the barrier, as the barrier either stops or delays the rupture propagation. The barrier can 5897 change the direction of rupture propagation, and the rupture velocity is modified after its interaction with the barrier. Concerning the radiated wavefield, the barrier acts as a secondary source of S waves when it breaks. However, due to geometrical diffraction, the amplitude of these waves decays more rapidly than the amplitude of the wavefront that is radiated by the rupture propagation, and they can become poorly distinguishable at some distance away from the fault. 6. Rupture Propagation Along a Heterogeneous Interface [34] In this third series of experiments, we investigate the behavior of a coherent rupture front propagating along a homogeneous interface and entering a highly heterogeneous interface. A wide heterogeneous zone is created by disposing multiple pebbles on the right part of the slid-

11 Figure 8. A rupture propagates in the heterogeneous area (distributed barrier). View of the horizontal component of particle velocity in the horizontal plane P1, 8 mm above the frictional interface. The dashed line shows the approximate limit between the homogeneous zone on the left side and the heterogeneous zone covered with pebbles on the right side. The rupture propagated in the heterogeneous zone with a velocity smaller than in the homogeneous zone. The direction of propagation was also modified. The shear wave emitted by the heterogeneities can be distinguished. Time t = 0 is arbitrarily attributed to the first frame. (The corresponding movie is available in the supporting information.) ing area, covering 60 % of its surface area (Figures 1d and 1f ). In this configuration, we again observe a large variability of rupture propagation patterns. Some of the ruptures stop propagating when entering the heterogeneous zone. When the rupture propagates through the heterogeneous area, its front is generally less coherent than in the homogeneous zone and the rupture process is complicated by the simultaneous or delayed rupture of some of the barriers. [35] Figure 7 presents two examples of ruptures propagating at the interface and the subsequently radiated S wave in the gel. Observations are made in the vertical plane P2. In Figure 7a, the rupture has stopped at the boundary of the heterogeneous zone, whereas in Figure 7b, it has propagated into the heterogeneous zone. [36] The dynamic effect of the heterogeneities is clearly seen in this Figure 7b: at t = 2 ms, the slip velocity is attenuated as if the rupture would stop. However, in the following snapshot, one of the barrier is slipping, which keeps the rupture front going. In the last snapshot, the rupture front reaches the end of the observation area. The effects of the heterogeneous zone are also observed in the radiated wavefield: A clear change of the angle between the interface and the S wavefront shows that the rupture front was either deviated or slowed down because of the heterogeneous zone. Moreover, the S wave radiated by one of the heterogeneities can be distinguished as a semicircle centered at the interface, at the location of the heterogeneity. [37] Figure 8 displays a rupture observed in the plane P1, parallel to the interface and 8 mm above it. This event propagates through the heterogeneous zone. When entering the heterogeneous zone, the direction of rupture propagation changes and the front becomes less coherent due to the effect of the multiple rupture of heterogeneities, whose radiated waves can be distinguished. A measurement of the rupture velocity perpendicularly to the front gives an estimate of m s 1 in the homogeneous zone and m s 1 in the heterogeneous zone. [38] To measure the rupture velocities, we report the position of the rupture front for every 0.5 ms time step (Figures 9a 9c). Figure 9a displays the propagation of the front along a homogeneous interface (see Figure 3), whereas Figure 9b shows the propagation of a front interacting with a linear barrier (see Figure 6b), and Figure 9c shows the propagation of the front interacting with a distributed barrier (see Figure 8). We then draw lines roughly perpendicular to each rupture front and measure the position of the intersection of the fronts and these lines. We report these position as a function of time (Figures 9d and 9e). In these plots, the black curves correspond to the S waves velocity into the slider, which can be compared to rupture velocity. Finally, to obtain a numerical value of the rupture velocity for each event, we compute the rupture velocity for each couple of points and represent these data in histograms (Figures 9g 9i). The mean value and standard deviation give robust estimate of the rupture velocity and uncertainty. This analysis shows that the rupture displayed in Figure 8 propagated at velocity almost equal to the S wave speed and was slowed down by the heterogeneous zone (Figure 9). The other observations in which the rupture front in the heterogeneous zone was coherent enough to measure a rupture velocity all showed a decrease of the rupture velocity. [39] In summary, the observations performed with acoustic speckle interferometry show the strong influence of the distributed barrier both in the rupture dynamics and in the radiated wavefield. The rupture direction often changes when entering the heterogeneous zone. The rupture velocity is decreased by the presence of the heterogeneities. The radiated wavefield becomes more complex when the rupture enters the heterogeneous zone, due to the barriers acting as secondary sources of energy when they break. 5898

12 Figure 9. (a c) Positions of the rupture front at successive 0.5 ms time steps for (Figure 9a) the rupture displayed in Figure 3 (homogeneous interface), (Figure 9b) the rupture displayed in Figure 6b (linear barrier, represented by grey circles), and the rupture displayed in Figure 8 (distributed barrier, limit represented by the dashed grey line), respectively. (The rupture fronts position has been detected by a maximum gradient detection algorithm applied on each snapshot of the particle velocity field. Dashed lines correspond to a manual detection, applied in cases of failure of the algorithm). The straight lines (blue and red) materialize the directions in which the rupture velocities are measured. (d f) Position of the rupture fronts along the rupture propagation direction as a function of time for the events displayed in Figures 9a 9c, respectively. The black curves correspond to an identical measurement of the S wave velocity. (g i) Probability density functions (PDF) of the rupture velocity for the events displayed in Figures 9a 9c, respectively. The histograms allow to quantify the uncertainty on the velocities measurements. 7. Discussion 7.1. Complexity and Variability of Slip Events [40] One of the most striking features in our experiments is the high variability of the rupture dynamics. Successive events, during the same experiment, can be highly different one from another, whereas normal stress and loading velocity remain the same. The knowledge of the frictional properties of the fault is therefore not sufficient to predict the dynamics of its rupture. We therefore interpret that some memory effects at the interface play a key role. A possible explanation could be that the prestress distribution, resulting from the loading process and the previous events, has a role just as important as the friction properties. [41] Ben-David et al. [2010] and Rubinstein et al. [2011] demonstrated experimentally the influence of the prestress distribution on rupture velocities and quantified it. It may be argued that the frictional properties of the fault also govern the stress loading, and thus should determine the prestress conditions. In such a case, with a constant tectonic loading (constant glass plate velocity in our experiments), the seismic cycle should show some regularity. However, in our results, no clear regular pattern in the succession of the different classes of rupture was observed. [42] Such variability of the effects of a barrier, which can either limit an earthquake size by stopping its propagation, or be broken and lead to a larger earthquake, has also been observed in natural faults. Indeed, paleoseismicity studies in some seismic regions can quantify, for a given fault, the length that ruptured for each historical earthquake. For example, the historical seismicity along the Nankai trough shows a segmentation in two zones that in some cases break together and in some cases break separately [Kumagai, 1996], very similar to the results of the experiments with a linear barrier. Dynamic simulation of rupture on the Nankai through stopping at the barrier and of rupture propagating through it were proposed in Hok et al. [2011], who showed that whether a rupture would break or not through the barrier is dependent on the location of the nucleation zone of the rupture. Oglesby and Mai [2012] performed dynamic simulation of the north Anatolian fault and also showed that the effects of the bends of the fault are strongly dependent of the initial stress conditions and of the position of the nucleation. [43] In the present experimental model, the notion of a characteristic event and of a regular seismic cycle is 5899

13 clearly not valid. Other experimental data were published that show that the stick-slip cycle cannot be fit by timeor slip-predictable cycle models [Rubinstein et al., 2012a, 2012b]. On the other hand, some published experimental results, obtained with homogeneous interfaces, show data in which a certain regularity of the stick-slip cycle is observed [Rubinstein et al., 2011; Corbi et al., 2011]. Thus, it seems that the validity of a model with regular seismic cycle and characteristic events depend on the conditions of loading and on the heterogeneity of the interface. This raises the interesting issue of which level of heterogeneity, in the prestress and in the friction properties, is necessary to switch from regular to irregular stick-slip cycle. [44] Some numerical studies have shown that a high complexity of the rupture cycle was produced by the introduction of heterogeneous fault properties, even when they are very simple [Dragoni, 1990; Dragoni and Santini, 2012; Zoller et al., 2005; Nielsen and Knopoff, 1998; Dublanchet et al., 2013]. Nielsen et al. [1995, 2000] identified three regimes, namely periodic, aperiodic, and dynamically complex that can occur on a fault. They showed that the transition between these regimes on homogeneous faults can depend on the size or aspect ratio of the fault. A numerical study [van Dinther et al., 2013] coupled to an experimental study [Corbietal., 2013] showed that in a analog experimental subduction zone, complexity arises in the seismic cycle due to the very simple heterogeneity of the fault friction properties, presenting some velocity-weakening and some velocity strengthening areas. It is not surprising then that adding barriers on faults, thus adding further limitation to the rupture propagation, can lead to an aperiodic, seemingly chaotic behavior. This phenomenon was studied numerically by Lapusta and Liu [2009] in the case of a single circular barrier, based on simulations of numerous complete seismic cycles. They show that the barrier introduces a complexity in the seismic cycle, due to the redistribution of stress during each slip event Effect of Heterogeneities on Rupture Velocity Effect of a Single Barrier [45] The effect of the strength of a barrier has been studied in 2-D and 3-D numerical simulations, which can be related to the barrier distribution presented in Figures 1b and 1c. Das and Aki [1977] proposed a 2-D numerical model where a zone with a strength higher than the rest of the fault was able, depending on the initial stress, to stop the rupture front or to be crossed by it. They showed also, that in some cases, the barrier could break after the passage of the rupture front. We observed those three behaviors in the point-like and linear geometries in our experiments. [46] In the present work, we could study the effect of the linear barrier on rupture velocities. We observed that the barrier could either slow down or accelerate the rupture propagation. The decrease of rupture velocity is rather intuitive, because the barrier can be seen as an obstacle to propagation. An interesting example is the rupture of the 2004 Sumatra earthquake: The inversion of continuous GPS data has shown that the rupture, propagating northward with an estimated velocity of 3.7 km s 1, was delayed at 7 ı N and then continued later with a velocity decreased down to 2 km s 1 [Vigny et al., 2005]. The position of this change in rupture velocity corresponds to a minimum in the inverted 5900 seismic total slip. This minimum may be interpreted as a barrier, which delayed and slowed down the rupture and did not break. This would correspond to our observation where the rupture is slowed down when the barrier does not break. [47] However, in the experiments, we also observe the opposite, nonintuitive behavior that the rupture velocity may increase after interacting with the barrier. This increase can be due to the energy release due to the barrier breaking. We can note that, usually, the second rupture occurs after a delay, which means that even with a higher rupture velocity in the second part of the fault, the total rupture time can be increased by the barrier, highlighting the anelastic process that occurred in the breaking of the interface. The acceleration of a rupture due to the breaking of a barrier was studied in Dunham et al. [2003], using 3-D numerical simulations. They proposed that a point-like barrier can favor the transition from subshear to supershear rupture when breaking. Page et al. [2005] have studied the effect of such a dynamic effect on the ground motion. Liu and Lapusta [2008] have performed 2-D numerical simulation and proposed a parametric study to characterize the effect of a linear barrier, in which they showed the same effect. Our data therefore provide an experimental observation with the linear barrier (Figure 6b) of this phenomenon that is, so far, discussed only in the framework of numerical simulations. It is evidenced here that a subshear rupture can become supershear because of a barrier. More generally, a rupture either subshear or supershear can be accelerated by a mechanical barrier, up to rupture velocities that are either subshear or supershear Effect of a Heterogeneous Frictional Domain on the Rupture Velocity [48] Concerning the change in rupture velocities, we observe that the rupture velocity is either decreased or remains constant when entering a domain with heterogeneous frictional properties (distributed barrier). These results can be interpreted in light of numerical simulations. Many numerical studies focused on the effect of a heterogeneous zone containing a distribution of barrier on rupture propagation [Mikumo and Miyatake, 1978; Fukuyama and Madariaga, 2000; Latour et al., 2011a]. In contrast, we study here a rupture that first propagated into a homogeneous zone and then entered a heterogeneous area. This was done because of the high variability of rupture speed, even for completely homogeneous interfaces, that would have made it impossible to compare directly the velocities of the homogeneous case to the velocities of the heterogeneous case. In our experiments, we can therefore compare the velocities of the same rupture in the homogeneous and heterogeneous zones. [49] Our experimental results on heterogeneous zones can be compared to numerical studies that analyze the propagation on a globally homogeneous spatial distribution of frictional properties, except for some localized zones where the strength of the interface is much higher. For example, Mikumo and Miyatake [1978] showed that with this kind of heterogeneity, the rupture velocity was lower than for homogeneous or slightly heterogeneous cases. In addition, Fukuyama and Madariaga [2000] showed that a periodic spatial distribution of heterogeneities could slow down the rupture, and prevent it to propagate at supershear velocity, because the distribution of barriers