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From Sub-Rayleigh to Supershear Ruptures During Stick-Slip Experiments on Crustal Rocks

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Science  07 Jun 2013:
Vol. 340, Issue 6137, pp. 1208-1211
DOI: 10.1126/science.1235637

Sonic Boom from Below

Seismic shear waves released by an earthquake typically far outpace motion along the fault surface. Occasionally, however, earthquakes along strike-slip faults appear to propagate so that the rupture velocity is faster than shear waves, creating a sort of sonic boom along the fault surface. Passelègue et al. (p. 1208) were able to reproduce and measure these so-called supershear ruptures in stick-slip experiments with two pieces of granite under high applied normal stress. Much like during a sonic boom when a plane travels faster than the speed of sound, the ruptures created a shock wave in the form of a Mach cone around the rupture front.

Abstract

Supershear earthquake ruptures propagate faster than the shear wave velocity. Although there is evidence that this occurs in nature, it has not been experimentally demonstrated with the use of crustal rocks. We performed stick-slip experiments with Westerly granite under controlled upper-crustal stress conditions. Supershear ruptures systematically occur when the normal stress exceeds 43 megapascals (MPa) with resulting stress drops on the order of 3 to 25 MPa, comparable to the stress drops inferred by seismology for crustal earthquakes. In our experiments, the sub-Rayleigh–to–supershear transition length is a few centimeters at most, suggesting that the rupture of asperities along a fault may propagate locally at supershear velocities. In turn, these sudden accelerations and decelerations could play an important role in the generation of high-frequency radiation and the overall rupture-energy budget.

Earthquake damage depends, in part, on the velocity of the rupture front (1). In 1973, Burridge demonstrated theoretically that in-plane shear ruptures (mode II) could propagate at velocities higher than the shear wave velocity (Cs) and up to the compressional wave velocity (Cp) (2). Since then, so-called supershear ruptures (Vr > Cs, where Vr is rupture velocity) have been observed during large strike-slip earthquakes (38). The stress and geometric conditions leading to the transition between sub-Rayleigh and supershear ruptures have been investigated with photoelasticity, both theoretically (9, 10) and experimentally, on brittle polymers (1115). Although these experiments successfully illustrate supershear ruptures, the lack of experiments on rock samples limits the ability to understand these rare events observed in nature. In a recent experimental study, a photoelastic setup was coupled with an acoustic high-frequency–recording multistation array during stick-slip experiments on polycarbonate sheets. This allowed Schubnel et al. to use high-frequency acoustics to identify unequivocally the signature of both sub-Rayleigh and supershear ruptures (15). This advance has opened the possibility of revisiting experimental work performed on rocks (1619).

Here, we report results from stick-slip experiments conducted on saw-cut Westerly granite samples (fig. S1), which serve as proxies for crustal rocks, during triaxial loading (where the principal stresses σ1 > σ2 = σ3). Stick-slip experiments and earthquake mechanisms are analogous in nature because they both result from rapid frictional sliding along preexisting faults, leading to partial or total stress drop (16). In our experiments, the stress conditions were typical of the upper crust, ranging from 10 to 150 MPa in normal stress acting on the preexisting fault. In total, we recorded more than 200 stick-slip events (Fig. 1). For each event, we inverted the rupture velocity directly from our experimental records, using high-frequency acoustics as a tracking tool (fig. S2).

Fig. 1 Stress release during microearthquakes.

Evolution of shear stress (solid lines) and displacement (dashed lines) is represented for two stick-slip experiments conducted at 10- and 50-MPa confining pressure.

We used recorded accelerograms to track the Mach wavefront arrival. Theoretical arrival time of the Mach wavefront radiated away from the rupture tip was predicted using (i) the position of the rupture front determined from the inverted rupture velocity (fig. S2) and (ii) the shear wave velocity and the distance between the Mach front antenna (MFA) sensors to the fault, as defined in Fig. 2A (15). Our calculation assumes that the rupture velocity is constant. Importantly, we looked for ruptures with Vr greater than the shear wave speed but different that Embedded Image, for in this case, no Mach cone is expected (20).

Fig. 2 Mach wavefront arrival.

(A) Schematic of the Mach cone arrival at MFA stations. The red star represents the nucleation zone of the event. Arrows indicate the sense of shear (here, right lateral). The positions of the MFA stations a to d are shown relative to the fault plane. θ, is the angle of the Mach cone, a function of the ratio between the rupture and shear wave velocities. (B) Waveforms recorded on the MFA array during a supershear event that occurred at τ = 84 and σn = 99 MPa. Blue and red solid lines represent the first P-wave front and the S-wave Mach front, respectively. The Mach front is shaded in red.

We compared our calculation with waveforms recorded by the MFA array for a stick-slip event during which a supershear rupture velocity was predicted by the inversion (Fig. 2B). In agreement with theory (21), we first observed a weak P-wave arrival, which corresponds to the continuous emission of P waves by the rupture tip as it propagates. However, the signal is dominated by the arrival of a large-amplitude, coherent wavefront just after the diffuse P-wave arrival. The relative amplitude of this wavefront, when compared to the first P-wave amplitude, increases with distance to the fault. This is expected because the geometric attenuation of a conic wavefront is smaller than that of spherical one. At each station, the arrival time of this wavefront is consistent with the predicted arrival time of the Mach wavefront.

To confirm our estimations of the rupture velocity, we used two-dimensional (2D) steady-state rupture model to conduct simulations (21). We observe an excellent fit, both in relative amplitude and for the general waveform shape, when comparing the experimental waveforms recorded on the MFA sensors during a subshear event and the synthetics obtained by our numerical simulation (Fig. 3B). We observed similar good correspondence between experimental waveforms and simulation of a supershear rupture (Fig. 3C). In both cases, we obtained the best fit between analytical and experimental records by using the rupture velocity estimated experimentally, confirming that our experimental estimate of the rupture velocity is accurate. Furthermore, we show that dynamic rupture models that can accurately simulate strong ground motions on the kilometric scale can also simulate accelerations in the kilohertz range on centimetric sized samples. In other words, dynamic rupture propagation is truly a self-similar mechanism.

Fig. 3 Comparison of experimental waveforms with synthetics.

(A) Description of the distance-weakening rupture model used by Dunham and Archuleta (21). R and L are, respectively, the length of the breakdown zone and the length of the crack. Comparison of the analytical particle accelerations with the waveforms recorded during a sub-Rayleigh event (B) and during a supershear event (C). The best fit is obtained using the inverted rupture velocity.

Our experimental results demonstrate that the ruptures were dominantly mode II (fig. S3). For this mode, the transition between sub-Rayleigh and supershear rupture has been extensively discussed in theoretical and experimental studies (9, 1215). Following 2D numerical studies, this transition is generally explained in terms of the seismic ratio S = (τp – τo)/(τo – τr) where τp, τo, and τr are the peak frictional strength, the initial shear stress, and the residual frictional strength, respectively. The ratio τon (where σn is the normal stress), employed by Ben-David et al. (14), is equivalent to S, and both quantities are simply related by τon = (fsfd)/(1 + S) + fd (where fs and fd are the static and dynamic friction coefficients, respectively) (Fig. 4). In our experiments, τo was continuously measured (Fig. 1). Taking fs = 0.85 and fd = 0.1, S could be estimated for each individual stick-slip. Supershear propagation may happen under both of the following conditions: (i) S < Sc (where Sc , the critical value of S allowing supershear transition, is equal to 1.77 or 1.119 in 2D and 3D, respectively), which was always the case in our experiments (Fig. 4A), and (ii) when the rupture length exceeds the transition length L, estimated following the semi-empirical relation (9) Embedded Image (1)where υ, μ, and G are, respectively, the Poisson ratio, the shear modulus, and the fracture energy. In our case, condition (ii) can be met only if L < Lf, where Lf is the finite length of the experimental fault. In our experiments, G may range from the lower bound 10 J/m2, as given by single-crystal fracture energy values and stick-slip experiments performed at low normal stress (19), to the upper bound 104 J/m2, measured for intact Westerly granite samples at high confining pressures (22). From Eq. 1, L was calculated as a function of normal stress in two cases: (i) S = 1 and G = 10 J/m2 and (ii) S = 0 and G = 1000 J/m2 (Fig. 4A). Experiments performed at the lowest normal stresses are compatible with G ≈ 10 J/m2. However, experiments performed at intermediate normal stresses can be explained only by using larger fracture energy. This is consistent with our observation of an intense production of fine gouge particles at intermediate and high normal stresses. Indeed, for spherical particles, the ratio between G and surface energy of single crystals (γ) is G/γ ≈ 3w/d, where w is the fault thickness and d is the average particle size. Our observation of gouge particles of 1-μm diameter and smaller is consistent with a fault roughness of less than 30 μm. The match between the measured rupture velocities and the prediction that the minimum transition length L drops to a few centimeters (comparable to our sample size) at high normal stress (Fig. 4A) explains why, in our experiments, supershear rupture becomes a "normal" phenomena for σn > 60 MPa. It also explains why supershear ruptures were not clearly observed in previous experimental studies on rocks conducted at low normal stress (most often in biaxial conditions) (18, 19).

Fig. 4 The transition to supershear ruptures.

(A) Correlation between normal stress and rupture velocity. Color-coding corresponds to the value of S. Red and blue solid lines represent L as a function of normal stress, assuming two combinations of S and G. (B) Correlation between rupture velocity and stress drop. Color-coding corresponds to the value of τon. Lf is the length of the experimental fault and Embedded Image is the transition length as a function of the normal stress.

Finally, we observe a double correlation between the rupture velocity, the initial stress ratio τon, and the final stress drop (Fig. 4B). Subshear ruptures occurred for stress ratios τon < 0.6 and resulted in stress drops generally lower than 1.5 MPa. Conversely, supershear ruptures occurred for stress ratios τon > 0.7 and resulted in stress drops generally larger than 3 MPa. These results not only make sense physically but are also compatible with values previously observed on brittle polymers (14) and with field observations for the Kunlunshan earthquake (23). Importantly, our findings are comparable to the average stress drops inferred by seismologists for most large crustal earthquakes. Note that our direct measurement of the stress drop is comparable to what a seismological estimate would be using the final slip u (fig. S4).

Based on our experimental results, why is there a paucity of supershear ruptures observed in nature? A first straightforward explanation is related to the difference in fault geometry between our experiments and seismogenic faults. Our experiments consisted of a perfectly planar fault geometry with very low initial roughness at high normal stress, leading to uniform and large stresses on the fault plane. Seismogenic faults, on the other hand, are most often nonplanar and exhibit self-affine roughness (24). The occurrence of kinks and dilatational jogs could slow down or even arrest locally the propagation of seismic ruptures (25). The few documented examples of supershear earthquakes are on very smooth, planar fault sections (38). In addition, the presence of a gouge layer along the fault interface may slow the propagation of the rupture, as well as thermo-hydro-mechanical coseismic processes within the breakdown zone [such as thermal pressurization (26), frictional melting (27), mineral reactions (28), and off fault damage, including pulverization (29)], which dissipate part of the released strain energy available, resulting in a deceleration of the rupture front. Alternatively, the paucity of supershear rupture observation in nature might also be due to limitations in instrumentation and/or spatial coverage. Nevertheless, the experimental values of L and stress drops reported here for a classical crustal lithology (Westerly granite) under upper-crustal conditions (<150 MPa) demonstrate that rupture velocity may exhibit important variations at the scale of small (centimetric) asperities, so that the seismological estimate of rupture velocities over long fault segments is an average that could well have little importance at the scale of an asperity. Our experimental results strongly suggest that, despite the scarcity of compelling measurements on natural earthquakes, supershear ruptures may frequently occur at the local scale of asperities, for which the stress drop generally inferred is quite large. In turn, these sudden accelerations and decelerations of the rupture front should play an important role in generating high-frequency radiation, which will influence the total rupture-energy budget.

Supplementary Materials

www.sciencemag.org/cgi/content/full/340/6137/1208/DC1

Materials and Methods

Figs. S1 to S4

Table S1

References

References and Notes

  1. Acknowledgments: We thank Y. Pinquier for technical support and two reviewers and the associate editor for their constructive remarks, which helped to enhance this paper. F.X.P., A.S., and S.N. acknowledge support from the French and Italian Ministry of Foreign affairs program GALILEO, project no. 26019WJ. This work was supported by the Institut National des Sciences de l'Univers. Data are available in the supplementary materials.

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