Supershear transition due to a free surface in 3-D simulations of spontaneous dynamic rupture on vertical strike-slip faults
Research Highlights
► A free surface promotes supershear rupture transition and propagation. ► Minor near-surface supershear rupture can occur due to a supershear loading field. ► Dominant near-surface supershear rupture can occur due to SV-P phase conversion. ► Local near-surface supershear transition occurs regardless of the level of prestress. ► Local supershear rupture causes global supershear transition for larger prestress.
Introduction
Recent improvements in availability and quality of strong-motion data revealed variability of rupture speeds in large crustal earthquakes. Seismological inversions show that average rupture speeds of many earthquakes are about 80% of the S wave speed of the surrounding medium (Heaton, 1990), i.e. earthquakes have subshear rupture speeds on average. However, supershear rupture speeds that exceed the S wave speed of the medium have been inferred for several large strike-slip earthquakes, including the 1979 Imperial Valley earthquake (Archuleta, 1984, Spudich and Cranswick, 1984), the 1999 Kocaeli (Izmit) earthquake (Bouchon et al., 2000, Bouchon et al., 2001), the 1999 Duzce earthquake (Bouchon et al., 2001, Konca et al., 2010), the 2001 Kokoxili (Kunlun) earthquake (Bouchon and Vallée, 2003, Robinson et al., 2006, Vallée et al., 2008, Walker and Shearer, 2009), and the 2002 Denali earthquake (Dunham and Archuleta, 2004, Ellsworth et al., 2004). The possibility of the occurrence of such phenomena has been confirmed in laboratory studies (Rosakis et al., 1999, Xia et al., 2004, Lu et al., 2007, Lu et al., 2009).
Variability of earthquake rupture speeds, either subshear or supershear, has important implications for seismic radiation and the resulting ground motion. In the case of supershear ruptures, radiating S waves can constructively form a Mach front that transports large seismic stress and particle velocity far from the fault (Bernard and Baumont, 2005, Dunham and Archuleta, 2005, Bhat et al., 2007, Dunham and Bhat, 2008). The directivity pattern of supershear rupture can also be different from that of subshear rupture (Aagaard and Heaton, 2004). Bouchon and Karabulut (2008) showed that earthquakes with inferred supershear speeds have a characteristic pattern of aftershocks, with almost no aftershocks on the fault plane and clusters of them on secondary structures off the fault plane. Hence it is important to understand the conditions controlling the transition of earthquake ruptures from sub-Rayleigh to supershear speeds during destructive large earthquakes.
The problem of sub-Rayleigh-to-supershear transition has been theoretically analyzed in a number of studies (e.g., Burridge, 1973, Andrews, 1976, Das and Aki, 1977, Day, 1982, Madariaga and Olsen, 2000, Fukuyama and Olsen, 2002, Festa and Vilotte, 2006, Dunham, 2007, Liu and Lapusta, 2008, Shi et al., 2008, Lapusta and Liu, 2009). Based on an earlier analytical work of Burridge, 1973, Andrews, 1976 numerically showed that supershear transition can be produced by nucleating a daughter crack at the S wave shear stress peak ahead of the Mode II main rupture on faults governed by a linear slip-weakening friction law (Fig. 1) in which friction linearly decreases from static strength τs to dynamic strength τd over a characteristic slip dc. This mechanism of supershear transition is often called ‘the Burridge–Andrews mechanism.’
For the Burridge–Andrews mechanism of the supershear transition to occur on homogeneously prestressed faults in 2-D models, the level of prestress defined as must be high enough (i.e., ). Equivalently, the seismic ratio S defined as S = (τs − τo)/(τo − τd) must be smaller than the critical value, Scrit = 1.77. Recently, Dunham (2007) showed that the critical level of prestress on homogeneously prestressed faults in 3-D models is given by or, equivalently, Scrit = 1.19. This means that 3-D models generally require much larger prestress to allow the Burridge–Andrews mechanism to occur than 2-D models do (Day, 1982, Fukuyama and Olsen, 2002, Dunham, 2007).
Since the work of Burridge, 1973, Andrews, 1976, a number of theoretical and numerical studies have addressed the issue of sub-Rayleigh-to-supershear transition on faults with non-uniformly distributed prestress or strength (e.g., Day, 1982, Olsen et al., 1997, Fukuyama and Olsen, 2002, Dunham et al., 2003, Liu and Lapusta, 2008, Lapusta and Liu, 2009). Under such circumstances, sub-Rayleigh-to-supershear transition and the subsequent supershear propagation can sometimes occur under background prestress levels that are lower than the ones predicted by the Burridge–Andrews mechanism. Examples include sub-Rayleigh rupture propagating into a region of increased stress drop (Fukuyama and Olsen, 2002) or a region of pre-existing quasi-statically expanding secondary crack (Liu and Lapusta, 2008), or sub-Rayleigh rupture breaking a strong heterogeneity on a fault (Dunham et al., 2003, Lapusta and Liu, 2009). Liu and Lapusta (2008) showed that the Burridge–Andrews mechanism belongs to a general case of sub-Rayleigh-to-supershear transition that subjects secondary cracks to a supershear loading field between the S-wave peak and earliest P waves propagating in front of a spontaneously expanding Mode II crack. Here we refer to such transition mechanism as ‘the generalized Burridge–Andrews mechanism.’ Heterogeneities in prestress and fault friction properties, therefore, play an important role on whether a rupture speed does or does not transition to a supershear speed and on its transition distance, i.e., the distance between the location of the hypocenter and the location of supershear transition.
Heterogeneities on natural faults that can potentially influence earthquake rupture speeds and induce transition to supershear speeds include the presence of the free surface and the variations in stress with depth. Supershear rupture propagation near the free surface has been reported in a number of simulations of spontaneous dynamic ruptures (Olsen et al., 1997, Aagaard et al., 2001, Day et al., 2008, Kaneko et al., 2008, Olsen et al., 2008). In particular, Olsen et al. (1997) noted that, in a dynamic rupture simulation of the 1992 Landers earthquake, supershear rupture propagation at shallow depths is caused by the free surface, which promotes “the generation of S to P converted head waves.” However, supershear transition at shallow depth and its consequences for dynamic rupture have not been explored in more detail. This is because near-surface transition to supershear speeds has been mostly treated as an inconvenience to be avoided in numerical simulations, in the light of the general observations that most ruptures remain subshear. However, accumulating evidence suggests that most large strike-slip earthquakes have supershear speeds over parts of the fault rupture.
In this work, we explore the details of supershear transition induced by the free surface using simulations of spontaneous dynamic rupture on a vertical strike-slip fault embedded in an elastic half-space. We find two types of supershear transition mechanisms that can potentially act in the shallow portions of natural faults: one caused by the generalized Burridge–Andrews mechanism and the other related to the combined supershear loading fields generated by (a) the geometric effect of the rupture arrival at the free surface and (b) the free-surface phase conversion. To understand supershear rupture generation next to the free surface, we create several scenarios that remove one of more of these effects. As a result, we show that the additional stress field produced by the phase conversion of SV to P-diffracted waves at the free surface plays a key role in sustained supershear propagation next to the free surface (Section 5). Finally, we discuss the resulting global supershear transition over the entire fault depth and conditions and fault properties that favor or diminish the effectiveness of the supershear transition next to the free surface (Section 6).
Section snippets
Fault models and parameters
We simulate dynamic rupture scenarios on a vertical strike-slip fault embedded into an elastic half-space (Fig. 2) with the P-wave speed of 6.0 km/s and S-wave speed of 3.46 km/s. The fault is governed by a linear slip-weakening friction law (Ida, 1972, Palmer and Rice, 1973), where its shear strength Γ linearly decreases from its static value τs to the dynamic value τd over the a characterize slip dc:
The static strength τs and dynamic strength τd can be
Numerical simulations of supershear rupture propagation near the free surface
Fig. 3 shows snapshots of spontaneously propagating dynamic rupture and the emergence of the secondary rupture front next to the free surface that propagates with a supershear speed. Since the level of absolute prestress and resulting stress drop are relatively low at shallow depths, this supershear rupture is initially only local and has a relatively small peak slip velocity of 0.5 m/s compared to the main rupture front with its peak slip velocity of 5 m/s (the snapshot at t = 8.5 s Fig. 3a).
Origin of earlier, weaker supershear arrival: the generalized Burridge–Andrews mechanism of supershear transition
The weaker supershear arrival in Fig. 4b is caused by the generalized Burridge–Andrews mechanism of supershear transition. Fig. 5 illustrates the evolution of shear traction at different fault depths and how the earlier supershear slip is induced as a result of such transition mechanism. Once the main rupture front is initiated at the nucleation patch, a part of rupture front propagates towards the free surface. As the rupture front progresses into shallower depths, it propagates into the
Origin of dominant supershear pulse: relation to phase conversion of SV to P-diffracted waves
Here we investigate the origin of the second, dominant supershear pulse (Fig. 4). To eliminate the earlier, weaker supershear slip and hence to focus on the dominant supershear rupture, we consider scenarios with uniform prestress in this section.
The dominant supershear pulse has several interesting properties distinct from the traditional Burridge–Andrews mechanism. First, the dominant supershear rupture next to the free surface is not nucleated from a daughter crack, or a secondary crack,
Factors that affect supershear transition due to the free surface
Given that global supershear rupture transition related to phase conversion can occur under a wide range of prestress conditions, it is important to understand whether such supershear rupture transition and subsequent supershear propagation would be favored on natural faults. As we discuss in the following, there are several potentially important factors on natural faults that can influence the effectiveness of such transition.
Conclusions
We have analyzed the occurrence of supershear transition induced by the free surface using simulations of spontaneous dynamic rupture on a fault governed by a linear slip-weakening friction law. We have shown that locally supershear rupture near the free surface can occur due to (i) the supershear loading field between P- and SV-wave arrivals radiated by rupture propagation at depths, and (ii) the supershear loading field caused by the amplified slip and phase conversion of SV to P-diffracted
Acknowledgements
This study was supported by the National Science Foundation (grant EAR0548277) and the Southern California Earthquake Center (SCEC). SCEC is funded by NSF Cooperative Agreement EAR-0106924 and USGS Cooperative Agreement 02HQAG0008. The SCEC contribution number for this paper is 1324. The numerical simulations for this research were performed on Caltech Division of Geological and Planetary Sciences Dell cluster. We thank Don Helmberger, Daoyuan Sun, and Steve Day for helpful discussions.
References (64)
Evidence for and implications of self-healing pulses of slip in earthquake rupture
Phys. Earth Planet. Inter.
(1990)- et al.
Transition of mode II cracks from sub-Rayleigh to intersonic speeds in the presence of favorable heterogeneity
J. Mech. Phys. Solids
(2008) - et al.
Properties of dynamic rupture and energy partition in a two-dimensional elastic solid with a frictional interface
J. Mech. Phys. Solids
(2008) - et al.
Near-source ground motions from simulations of sustained intersonic and supersonic fault ruptures
Bull. Seismol. Soc. Am.
(2004) - et al.
Dynamic earthquake ruptures in the presence of lithostatic normal stresses: implications for friction models and heat production
Bull. Seismol. Soc. Am.
(2001) - Aki K., Richards P.G., 2002. University Science Books, Sausalito,...
- Ampuero J.-P., 2002. Etude physique et numérique de la nucléation des séismes. Ph.D. thesis, Univ. Paris 7, Denis...
Rupture velocity of plane strain shear cracks
J. Geophys. Res.
(1976)Rupture dynamics with energy loss outside the slip zone
J. Geophys. Res.
(2005)A faulting model for the 1979 imperial valley earthquake
J. Geophys. Res.
(1984)
Dynamic simulations of slip on a smooth fault in an elastic solid
J. Geophys. Res.
Shear Mach wave characterization for kinematic fault rupture models with constant supershear rupture velocity
Geophys. J. Int.
Off-fault damage patterns due to supershear ruptures with application to the 2001 Mw 8.1 Kokoxili (Kunlun) Tibet earthquake
J. Geophys. Res.
The aftershock signature of supershear earthquakes
Science
Observation of long supershear rupture during the magnitude 8.1 Kunlunshan earthquake
Science
Seismic imaging of the 1999 Izmit (Turkey) rupture inferred from the near-fault recordings
Geophys. Res. Lett.
How fast is rupture during an earthquake? New insights from the 1999 Turkey earthquakes
Geophys. Res. Lett.
Admissible speeds for plane-strain shear cracks with friction but lacking cohesion
Geophys. J. R. Astron. Soc.
Internal structure and weakening mechanisms of the San Andreas Fault
J. Geophys. Res.
A numerical study of two-dimensional spontaneous rupture propagation
Geophys. J. R. Astron. Soc.
Three-dimensional finite difference simulation of fault dynamics: rectangular faults with fixed rupture velocity
Bull. Seismol. Soc. Am.
Comparison of finite difference and boundary integral solutions to three-dimensional spontaneous rupture
J. Geophys. Res.
Scale-model and numerical simulations of near-fault seismic directivity
Bull. Seismol. Soc. Am.
Inelastic strain distribution and seismic radiation from rupture of a fault
J. Geophys. Res.
Conditions governing the occurrence of supershear ruptures under slip-weakening friction
J. Geophys. Res.
Evidence for a supershear transition during the 2002 Denali fault earthquake
Bull. Seismol. Soc. Am.
Near-source ground motion from steady state dynamic rupture pulses
Geophys. Res. Lett.
Attenuation of radiated ground motion and stresses from three-dimensional supershear ruptures
J. Geophys. Res.
A supershear transition mechanism for cracks
Science
Near-field ground motion of the 2002 Denali Fault, Alaska, earthquake recorded at Pump Station 10
Earthquake Spectra
Influence of the rupture initiation on the intersonic transition: crack-like versus pulse-like modes
Geophys. Res. Lett.
Structural properties and deformation patterns of evolving strike-slip faults: numerical simulations incorporating damage rheology
Pure Appl. Geophys.
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