Seismic Characteristics of Supershear and Sub-Rayleigh Earthquakes: Implication from Simple Cases, Geophys

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Geophysical Research Letters

RESEARCH LETTER Seismic characteristics of supershear and sub-Rayleigh 10.1002/2017GL074158 earthquakes: Implication from simple cases

Key Points: • The common conclusion that Zhenguo Zhang1 , Jiankuan Xu1 , Hanqing Huang2 , and Xiaofei Chen1 supershear earthquake transmits farther distance than subshear one is 1Department of Earth and Space Sciences, Southern University of Science and Technology, Shenzhen, China, 2School of conﬁrmed by numerical simulations • Shaking of subshear earthquake Earth and Space Sciences, University of Science and Technology of China, Hefei, China is more intensive than that of supershear one at short distance to the fault plane Abstract Numerous investigations of supershear earthquakes make a conclusion that a supershear • The supershear earthquake has earthquake produces a seismic shock wave on the ground that may increase the resulting destruction. relatively quiet aftershock potential based on Coulomb We investigate a supershear rupture promoted by the free surface and ﬁnd out that although the seismic failure stress analysis energy of a supershear earthquake can be transmitted further with large amplitudes, the peak slip velocity on a fault near the free surface is smaller than that caused by a subshear rupture earthquake. Our results

Correspondence to: show that the free-surface-induced supershear rupture mitigates the amplitudes of ground motions near X. Chen, the fault plane compared with the subshear rupture. The Coulomb failure change derived from dynamic [email protected] modeling further suggests that this free-surface-induced supershear reduces aftershock potential compared to a subshear rupture. Both ground motion at near-fault and aftershock possibility show low Citation: risk for the free-surface-induced supershear rupture earthquake than subshear earthquake, contrary to the Zhang, Z., J. Xu, H. Huang, and traditional concept. X. Chen (2017), Seismic characteristics of supershear and sub-Rayleigh earthquakes: Implication from simple cases, Geophys. Res. Lett., 44, 6712–6717, doi:10.1002/ 1. Introduction 2017GL074158. The rupture speed of an earthquake is an important parameter that results in high frequencies and strong seismic radiation, particularly the transition from a speed slower than Rayleigh wave speeds (subshear rupture) Received 14 MAY 2017 to that faster than shear wave speeds (supershear rupture) of the surrounding medium [Madariaga, 1983]. Accepted 26 JUN 2017 Earthquake simulations with specific rupture velocities indicate that supershear rupture, compared with the Accepted article online 28 JUN 2017 Published online 11 JUL 2017 subshear case, radiates S waves as a Mach front that causes extensive shaking at places far away the fault [Aagaard and Heaton, 2004; Bernard and Baumont, 2005; Dunham and Archuleta, 2005]. This Mach cone effect is further supported by dynamic modeling [Andrews, 2010], laboratory earthquakes [Rosakis et al., 1999; Xia et al., 2004], and supershear earthquake observations [Vallée et al., 2008]. Theoretical analysis and numerical experiments have demonstrated that the rupture pattern of an earthquake depends primarily on the rela- tionship between the shear stress and strength of the fault, which can be denoted by the quantitative seismic ratio S. For a planar fault embedded in a homogeneous medium, a sufficiently small S can accelerate a rupture to a supershear one [Burridge, 1973; Andrews, 1976; Das and Aki, 1977; Dunham, 2007]. This mechanism of supershear transition is usually called the Burridge-Andrews mechanism (BAM). Moreover, recent numerical simulations also prove the existence of another rupture type that increases the speed to supershear [Liu et al., 2014]. It has been identified that the rupture speeds of a few crustal earthquakes exceed the shear wave velocities [Archuleta, 1984; Bouchon et al., 2000, 2001; Bouchon and Vallée, 2003; Dunham and Archuleta, 2004; Wang and Mori, 2012; Wang et al., 2012; Yueetal., 2013]. These crustal supershear earthquakes are all strike-slip and reach the Earth’s surface, which is consistent with the theoretical studies that the flat free surface will always induce the supershear transition given a long enough propagation distance for a strike-slip rupture [Xu et al., 2015]. This free-surface-induced (FSI) supershear rupture, which is caused by the SV-P phase conversion at the free surface [Kaneko and Lapusta, 2010], behaves quite differently compared to those induced by BAM and can be prevented by inhomogeneities such as low velocity media [Kaneko and Lapusta, 2010], an irregular surface [Zhang et al., 2016], or a barrier [Xu et al., 2016]. It is necessary to evaluate the seismic hazard characteristics of a FSI supershear rupture because it is common for faults to reach the Earth’s surface. Is the ground motion caused by a FSI supershear earthquake stronger than that caused by a subshear earthquake? We report the

©2017. American Geophysical Union. characteristics of a FSI supershear rupture in this study and ﬁnd that the answer for this question is negative All Rights Reserved. from both near-source ground motion and aftershock triggering.

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2. Models and Method This work focuses on the seismic hazards caused by a free-surface-induced supershear earthquake. For a strike-slip fault, a supershear rupture is promoted from subshear rupture at the free surface due to SV-P wave conversion [Kaneko and Lapusta, 2010; Xu et al., 2015]. To discuss seismic hazards, a subshear rupture, with initial conditions and dynamic parameters identical to those of the supershear rupture, must be compared and analyzed. Then, the free-surface-induced supershear rupture must be prevented without changing the initial conditions and parameters. Numerical experiments indicate that an irregular topography can prevent the supershear rupture transition [Zhang et al., 2016]. In this work, this supershear transition is prevented by a topographical perturbation, causing a subshear on the entire fault plane. The supershear and subshear have the same initial stress, dynamic stress drop, and other parameters, but they have different rupture velocities. Note that the model of earthquake faulting is relative simple, it considers a vertical planar fault surrounded by a homogeneous media and driven by uniform stress field except for the nucleation patch. The conditions that trigger an earthquake might have much complexity in stress, media, fault geometry, and so on. However, to differentiate the seismic radiations between supershear and subshear rupture earthquakes, the simplified model is chosen to run simulation and analyze the associated phenomena. Moreover, all the supershear earthquakes observed in the upper crust are all the strike-slipping faults reaching Earth’s surface. Three-dimensional (3-D) numerical simulations indicate that a long enough fault in the strike direc- tion is required to accelerate rupture from subshear to supershear speed. With these considerations, we choose the following 3-D models to compare the seismic dangers between subshear and supershear rupture earthquakes. We investigate supershear rupture induced by interaction with Earth’s surface using 3-D rupture dynamics modeling. A vertical planar fault with 110 km length and 20 km width is modeled under the slip-weakening . friction law [Ida, 1972]. In the dynamic modeling, the critical distance d0 = 0 4 m, the static and dynamic 𝜇 . 𝜇 . frictions are set to s = 0 677 and d = 0 525, respectively. The medium is homogeneous with P wave speed 𝜌 3 vp = 6000 m/s, S wave speed vs = 3464 m/s, and density = 2670 kg/m . A homogeneous initial stress field (the normal and shear stresses are 120 MPa and 70.0 MPa, respectively) is employed over the whole fault plane except for the nucleation patch with a size of 3 km × 3 km, within which a stress slightly higher than the strength of the fault is used to trigger the dynamic rupture. The square nucleation zone, located 10 km away from the left, bottom, and flat free-surface boundaries, initializes the dynamic rupture. The subsequent rupture spontaneously propagates over the entire fault plane until it is stopped by surrounding barriers with sufficiently high strength. For the supershear rupture model, a vertical planar fault of 110 km length and 20 km width is considered. The flat surface is used to generate FSI supershear rupture. A canyon, defined by z(r)=1000 exp(−r2/15002), where r is the distance to the canyon center, is added to prevent the free-surface-induced supershear rupture. The fault plane crosses the center of canyon. We use the curved grid finite-difference method (CG-FDM) [Zhangetal., 2014] to simulate the dynamic rupture dynamic on a fault with flat and canyon-shaped surfaces. This method was verified by modeling benchmarks released by the Southern California Earthquake Center [Harris et al., 2009]. By using curvilinear grids that can fit the irregular interfaces and adopting of split nodes to represent the discontinuous condition across the two sides of a fault, the CG-FDM can model the rupture dynamics on a generic fault with complex geometry, including one with irregular surface topographies.

3. Results Previous investigations have indicated that a strike-slip earthquake rupture with a flat free surface would be accelerated into a supershear rupture, given a long enough propagating distance [Xu et al., 2015]. However, when the free surface is topographically irregular, the same strike-slip ruptures propagating speed would remain subshear [Zhang et al., 2016]. In this study, a canyon-shaped surface is added to model a subshear rupture in a half-space because the irregular surface breaks the condition required for the supershear transition [Zhang et al., 2016]. All of the conditions are the same for the supershear and subshear ruptures, except the topography of the free surfaces. The differences in consequent seismic radiation and strong ground motion between the simulations are caused by different rupture speeds.

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Figure 1. Maps of peak slip velocity on the fault planes in the (top) supershear and (bottom) subshear ruptures, respectively.

3.1. Seismic Radiation The rupture with the maximum slip velocity, which is a short distance after the rupture front, produces large-amplitude seismic radiation. The derived peak slip velocities (PSV) on faults are quite different between the supershear and subshear rupture cases (Figure 1). For the supershear model, the overlapping of the original rupture front radiating from the nucleation patch and the induced supershear rupture front propagating from the free surface contributes to the large-amplitude PSV at the merging point, which causes a subduction-zone-shaped bend with a large PSV and a small PSV for the remaining area of the fault. For the subshear model, however, because no second rupture front is induced at the free surface, the rupture front on fault plane uniformly expands, and no coalescence of the PSV as the bend appears in the supershear case. Moreover, for the subshear model, the area with a large PSV is concentrated near the Earth’s surface that would contribute great ground shaking near fault. Both the seismic wave radiation and the resulting ground motion distribution depend on the rupture pattern. The characteristics of PSV distribution on the fault (Figure 1) cause different shaking in the 3-D space. Figure 2 illustrates the 3-D distribution of the maximum absolute values of three-component particle velocity. Note that the vertical striking slice is 250 m away from the fault plane. One important discrepancy in the motion distribution between the supershear and subshear earthquakes is the shaking amplitude in the near-fault filed. For the supershear rupture earthquake, the maximum absolute values of three-component particle velocity along strike slice have a pattern similar to that of the PSV on the fault plane (Figure 1). However, the seismic shaking on the striking slice for the subshear earthquake is much stronger than that for the supershear earthquake. This large-amplitude seismic shaking could cause extensive damage in the near-fault field for the subshear earthquake. Another difference between supershear and subshear earthquakes is the horizontal extent Figure 2. Three-dimensional distributions of maximum absolute of the seismic energy. As observed for the values of three-component particle velocity in the supershear and 3-D distribution of shaking (Figure 2), seis- subshear earthquakes. mic waves with high energy are radiated to

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Figure 3. Normalized ΔCFS distributions at a 5 km depth resolved onto a fault parallel to the main shock fault for (top) supershear and (bottom) subshear ruptures.

a farther distance in the supershear earthquake than in the subshear earthquake, in agreement with previous simulations [Aagaard and Heaton, 2004; Bernard and Baumont, 2005; Dunham and Archuleta, 2005]. Compar- ing the ground motion caused by the supershear and subshear ruptures, it is clear that the supershear rupture induced by the free surface reduces the most intense ground motion near the fault and radiates moderate ground motion at a greater distance. When this supershear transition is blocked by irregular topography, the resulting ruptures radiate much stronger seismic wave and contribute extensive ground motion within a short distance from the fault plane. The comparison of maximum values of velocity on the vertical slices in Figure 2 suggests that the subshear rupture generates more intensive shaking in the near ﬁeld than FSI supershear rupture does. Note that in this work we are discussing the FSI supershear rupture, and it causes weaker ground motion near the fault compared to the subshear rupture. The case for supershear rupture generated by a high stress drop is diﬀerent, in which situation, extensive ground motion will be caused, and large-amplitude ground motion can travel a long distance, thus supporting the conclusions from kinematic simulations with prescribed rupture velocities [Aagaard and Heaton, 2004; Bernard and Baumont, 2005; Dunham and Archuleta, 2005].

3.2. Implication for Aftershocks The probability of aftershock occurrence is another parameter that is used to evaluate the hazards related to an earthquake. The earthquake redistributes background stress, changes the stress load acting on the potential fault, and brings in aftershocks. The Coulomb failure stress changes (ΔCFS) of an earthquake could be used to predict the behavior of its aftershock distribution. Mathematically, the ΔCFS is evaluated as ΔCFS = 𝜏 𝜇 𝜎 𝜇 𝜇 𝜎 Δ + sΔ n and is normalized by the dynamic stress drop ( s− d) n. For a location with increasing ΔCFS, aftershocks are highly probable, whereas regions with decreasing ΔCFS have reduced probabilities of aftershocks. The distributions of ΔCFS at a 5 km depth, resolved onto a fault plane parallel to the main shock fault for the supershear and subshear ruptures (Figure 3), show diﬀerent aftershock probabilities. There is a wider range with negatively normalized ΔCFS (≤1.0, exactly) in the supershear rupture segment than in the subshear case, indicating that the fault rupturing at supershear speed would have quiet aftershock clusters at a greater distance than at subshear speed. This agrees with the observations that supershear rupture segments have relatively quiet aftershock clusters [Bouchon and Karabulut, 2008; Bouchon et al., 2010]. The aftershock analysis shows that the FSI supershear rupture earthquake is safer than the corresponding subshear earthquake in the capability of trigging aftershocks.

4. Discussion and Conclusions We modeled and compared the dynamic rupture with diﬀerent rupture speeds on a vertical fault due to varying free surfaces. For the strike-slip fault with a free surface, a subshear rupture can be promoted into a supershear one at the free surface due to SV-P wave conversion. This FSI supershear causes severer ground

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motion at a wide range. When this conversion mechanism is interrupted, for example, a canyon in this work, the following subshear rupture generates great shaking concentrated in a beam within a small distance to the fault plane. Comparing the rupture and ground motion patterns of these two rupture, we can find that at a very short distance to the fault plane, the subshear earthquake generates much stronger ground motion than FSI supershear does, which means subshear earthquake is more dangerous in the near field. At the farther distance, because of the ability transmitting seismic energy to large distance, the supershear earthquake brings in more intensive ground motion, thus, is more dangerous than subshear earthquake. We also analyze the seismic hazard performances of subshear and supershear earthquakes based on Coulomb failure stress changes to infer their aftershock potentials. The synthetic results show that the supershear earthquake will more unlikely to host the aftershock clusters than a subshear earthquake does. This conclusion agrees with the aftershock observations [Bouchon and Karabulut, 2008; Bouchon et al., 2010]. This work reveals that the free-surface-induced supershear earthquake is less dangerous than subshear earthquake from the viewpoint of near-fault field ground motion and aftershock implication. However, the factor that supershear earthquake can transmit large seismic energy at a great distance must be noted. Note that the model discussed in this work is simple, i.e., a vertical planar fault plane embedded within homogeneous media and driven by uniform tectonic background stress fields. The environment of real earthquake may be much more complex. However, this simple model reveals the basic physics of supershear and sub-Rayleigh earthquakes. More extended work in the future work can be investigated based on the reliable conditionals of real earthquakes.

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