## Supershear rupture down below

Deep earthquakes occur in complex fault zones more than 70 kilometers below Earth's surface. Although they do not pose much of a hazard, they can still provide valuable insight into how earthquakes rupture. Zhan *et al.* found that a magnitude 6.7 aftershock of the largest deep earthquake recorded to date—the 2013 magnitude 8.3 Sea of Okhotsk earthquake—ruptured faster than the velocity of its seismic waves. This so-called “supershear” rupture shows that deep earthquakes have diverse rupture mechanisms and have several routes to dissipate energy.

*Science*, this issue p. 204

## Abstract

Earthquake rupture speeds exceeding the shear-wave velocity have been reported for several shallow strike-slip events. Whether supershear rupture also can occur in deep earthquakes is unclear, because of their enigmatic faulting mechanism. Using empirical Green's functions in both regional and teleseismic waveforms, we observed supershear rupture during the 2013 moment magnitude (*M*_{w}) 6.7 deep earthquake beneath the Sea of Okhotsk, an aftershock of the large deep earthquake (*M*_{w} 8.3). The *M*_{w} 6.7 event ruptured downward along a steeply dipping fault plane at an average speed of 8 kilometers per second, suggesting efficient seismic energy generation. Comparing it to the highly dissipative 1994 *M*_{w} 8.3 Bolivia earthquake, the two events represent end members of deep earthquakes in terms of energy partitioning and imply that there is more than one rupture mechanism for deep earthquakes.

Most earthquakes rupture at speeds less than the shear-wave speed (*V _{S}*). Theory and laboratory experiments indicate that rupture speeds in excess of

*V*are possible (

_{S}*1*–

*3*), and supershear ruptures have now occasionally been reported for large strike-slip events (mode II), including the 1979 Imperial Valley (

*4*), 1999 Izmit (

*5*), 2001 Kunlun (

*6*–

*8*), 2002 Denali (

*7*,

*9*), 2010 Yushu (

*10*), and 2013 Craig (

*11*) earthquakes. All of these documented occurrences were shallow earthquakes with a simple fault geometry (

*12*), and mostly with surface breaks, which is consistent with theoretical studies that the free surface helps promote supershear rupture (

*13*,

*14*).

No definitive evidence has yet been obtained for supershear rupture in deep earthquakes (depth > 300 km) (*15*). However, the rupture speeds of these events are difficult to estimate because of a general absence of near-field observations, and they appear highly variable. For example, the rupture speeds of the two largest deep earthquakes observed to date, the 1994 moment magnitude (*M*_{w}) 8.3 Bolivia earthquake and the 2013 *M*_{w} 8.3 Sea of Okhotsk earthquake (*16*–*18*), were about 0.2 to 0.4 and 0.7 *V _{S}*, respectively. About 80% of the rupture velocities for deep earthquakes fall between 0.3 and 0.9

*V*(

_{S}*19*), a greater range than is seen for shallow earthquakes (

*15*). The rupture speed may depend on the slab thermal state (

*20*,

*21*), with ruptures propagating more slowly in warm slabs than in cold slabs, but seismic observations have been inconclusive (

*22*,

*23*). The one previous example of observed supershear rupture during the 1990

*M*

_{w}7.1 Sakhalin deep earthquake neglected to take into account waveform changes from attenuation and the high-velocity subducted slab (

*24*,

*25*).

The 24 May 2013 *M*_{w} 8.3 Sea of Okhotsk event (depth, 607 km) was the largest deep earthquake ever recorded (Fig. 1), slightly larger than the 1994 Bolivia earthquake. On the same day, an *M*_{w} 6.7 earthquake at a depth of 642 km occurred about 300 km southwest of the mainshock and was recorded by many teleseismic stations and one regional station (Fig. 1). An extraordinary feature of the *M*_{w} 6.7 event was its sharp teleseismic *P* waves, which had displacement pulse widths at most azimuths of 1 to 2 s (Fig. 1). These are much less than the expected source duration of 8 s, based on its magnitude and previous studies of scaled durations of deep earthquakes (*26*, *27*). If taken as a rough estimate of the *M*_{w} 6.7 earthquake’s source duration, these very short teleseismic *P*-wave durations imply extremely high stress drops in a range from 157 MPa to 5.856 GPa (*17*). On the other hand, the regional station PET (distance ≈ 495 km) on the Kamchatka Peninsula to the east displayed a much longer direct *P* wavetrain of about 5 s (Fig. 1). Because the *P* wave to the PET station left the source along an upgoing ray path, instead of the downgoing rays for the teleseismic stations, this longer *P*-wave duration at PET suggests possible downward rupture directivity during the *M*_{w} 6.7 earthquake. However, to test this possibility we first need to account for possible path effects such as wave diffractions along the high-velocity slab in which the earthquake occurred and site effects at the stations.

We used waveforms from two nearby smaller earthquakes (Fig. 1; the 24 June 2013 *M*_{w} 4.3 event and the 30 August 1996 *M*_{w} 5.5 event) as empirical Green’s functions (EGFs) to calibrate the paths. The *M*_{w} 4.3 earthquake’s small moment, similar depth, and probably similar focal mechanism as the *M*_{w} 6.7 earthquake (fig. S1) make it an ideal EGF event. Its direct *P* wave recorded at the PET station displays two distinct arrivals separated by about 2 s (Fig. 2), due to diffraction along the dipping high-velocity slab in the upper mantle (*25*). Therefore, the apparent 5-s *P *duration of the *M*_{w} 6.7 earthquake at the PET station was partly caused by the structural path effect. We deconvolved the EGF waveform from the *M*_{w} 6.7 earthquake* P* wave to remove the path effect and obtained a more accurate source-time function (STF) (*28*). Most of the energy then concentrated in the first ~2 s, which we measured as the STF duration at the PET station (Fig. 2; red shading in top STF).

Because teleseismic records of the *M*_{w} 4.3 event are noisy, we used the 1996 *M*_{w} 5.5 event at somewhat shallower depth (~590 km) with a slightly rotated focal mechanism (Fig. 1) as the teleseismic EGF event. Because we only used teleseismic direct *P* waveforms (no absolute amplitude), these small differences in depth and radiation pattern did not significantly affect the accuracy of the EGFs. The *M*_{w} 4.3 and 5.5 EGF events had highly similar waveforms at the regional station PET and several quiet teleseismic stations (fig. S2), despite their difference in moment. This suggests that both EGF events can be regarded as delta-function–like point sources and their waveforms are mostly controlled by path effects. We chose teleseismic stations with clean direct *P* waves from both the *M*_{w} 6.7 and the *M*_{w} 5.5 earthquakes (Fig. 1 inset) and then deconvolved to estimate STFs and their durations (Fig. 2 and fig. S3). The resulting teleseismic STF durations range from ~0.5 to ~1 s. For both regional and teleseismic stations, relatively simple and compact STFs convolved with the EGFs produce good fits to the direct *P* and *P*-coda waveforms of the *M*_{w} 6.7 earthquake, which suggests effective correction of the path effects. We also attempted to include two more stations, MA2 and YSS, at distances of about 818 and 858 km, respectively (fig. S4). Direct *P* waves from these stations left the source along approximately horizontal ray paths. However, because of waveform complexities caused by triplications due to the 660-km discontinuity (figs. S4 to S6), we were unable to find an appropriate EGF event to correct for these structural effects.

After removing the path effects with EGFs, we inverted the resulting STF durations for earthquake rupture parameters. The path-corrected STF duration of the PET station (~2.1 s) is still more than two times longer than those of the teleseismic stations (0.5 to ~1 s), suggesting downward rupture directivity. For three-dimensional unilateral rupture (fig. S7), the STF duration of the -th station can be written as a function of rupture duration , horizontal rupture azimuth θ* _{r}*, and horizontal and vertical dimensions

*L*and

*H,*as

*T*= τ +

_{i}*x*(θ

_{i}*)*

_{r}*L*+ η

_{i}

*H*, where

*x*(θ

_{i}*)*

_{r}*L*and η

_{i}

*H*are the corrections for azimuthal and vertical directivity, respectively. Note that is the horizontal directivity parameter for the

*i*-th station with azimuth θ

*and*

_{i}*P-*wave phase velocity (

*18*

*,*

*29*). Here ϕ

*is the takeoff angle for the*

_{i}*i*-th station, and α is the

*P*-wave speed. Therefore, the azimuthal variations in STF durations resolve the rupture direction θ

*and horizontal extent*

_{r}*L*. In the final term, is the vertical slowness, negative for teleseismic stations (with down-going rays) and positive for regional stations (with up-going rays). This sign difference in η

*accounts for the major observed difference between teleseismic and regional STF durations.*

_{i}We used a grid-search method to invert for the rupture parameters (τ, θ* _{r}*,

*L*, and

*H*). The least-squares misfit of the STF durations, as a function of rupture vertical extent and rupture azimuth θ

*, has a well-defined global minimum at*

_{r}*H*= 11 km and θ

*= 130° (Fig. 3A). With these optimal values, the STF durations corrected for the downward vertical directivity (Fig. 3B) fall near a straight line with a slope of*

_{r}*L*= 4 km and zero-crossing duration of τ = 1.5 s. With

*L*= 4 km and = 11 km, we estimated the rupture dip to be ~70°, coincident with the steeper fault plane's dip of ~69° (

*17*). Because the rupture direction θ

*= 130° is roughly perpendicular to the fault strike (~26°), we conclude that the*

_{r}*M*

_{w}6.7 earthquake features a downward mode II rupture on the fault plane dipping steeply to the southeast (Fig. 4A). The rupture propagated or ~12 km in τ = 1.5 s, from which we estimate an average rupture speed of about 8 km/s. This speed is about , which is substantially higher than the local shear wave speed (

*V*~5.5 km/s, based on the Preliminary Reference Earth Model). Contouring the average rupture speeds for all grid-searched rupture parameters (Fig. 3A) shows that within the region with reasonable misfit (inside the dark blue contours), the rupture speed is always higher than

_{S}*V*and lower than

_{S}*V*. Within 95% confidence limits, the average rupture speed is 8.0 ± 0.7 km/s. Anomalously broad teleseismic depth phases (

_{P}*pP*) also are roughly consistent with the downward supershear rupture model (figs. S8 and S9). However,

*pP*pulse widths exhibit much larger scatter than

*P*pulse widths, and their behavior appears to be heavily influenced by complicated path effects, thus we cannot invert the

*pP*waveforms for rupture parameters with any confidence.

Previously identified extremely high-stress drops (157 MPa to 5.856 GPa) of the *M*_{w} 6.7 earthquake and subsequently low radiation efficiency (0.005 < η_{R} < 0.15) (*16*, *17*) depict this event as mechanistically distinct from the Okhotsk *M*_{w} 8.3 mainshock (Δσ ≈ 15 MPa, η_{R} ≈ 0.6) and more similar to the 1994 *M*_{w} 8.3 Bolivia earthquake (Δσ ≈ 114 MPa, η_{R} ≤ 0.036) in a warmer slab (Fig. 4B). This complexity suggests strong stress heterogeneity in subducted slabs (*17*). However, supershear rupture during the *M*_{w} 6.7 earthquake brings its stress drop down to 32 MPa and its radiation efficiency to about 1.0 (Fig. 4B), which are much closer to values for the *M*_{w} 8.3 Okhotsk mainshock. Therefore, strong stress heterogeneity inside subducted slabs is not required to explain the 2013 Okhotsk mainshock and its *M*_{w} 6.7 aftershock. However, the difference in rupture speed (subshear versus supershear) indicates substantial spatial heterogeneity in the fracture strength or fracture energy within the slab.

Compared with shallow supershear events, this deep event has a relatively small rupture dimension and higher static stress drop (by a factor of ~10). Our estimate of high radiation efficiency (η_{R} ≈1.0) during the *M*_{w} 6.7 event is also consistent with theoretical predictions of low fracture energy during supershear ruptures (*30*). This constraint of low fracture energy bears on the question of deep earthquake faulting mechanisms, which is still enigmatic (*15*, *19*). The 1994 Bolivia earthquake involved a large amount of fracture/thermal energy and radiated relatively little energy in seismic waves (*16*). In terms of energy partitioning, the supershear *M*_{w} 6.7 earthquake represents the opposite end member from the Bolivia earthquake, with almost all the available strain energy being radiated as seismic waves. This contrast is consistent with the idea of more than one rupture mechanism for deep earthquakes in slabs with different thermal states (*18*, *20*, *21*). The Okhotsk mainshock and aftershock in a cold slab ruptured with the transformational faulting mechanism, whereas the Bolivia earthquake in a warm slab was dominated by shear melting (*18*).

## Supplementary Materials

## References and Notes

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**Acknowledgments:**We thank two anonymous reviewers for their helpful comments. The Incorporated Research Institutions for Seismology (IRIS) provided the seismic data. This work was supported by NSF (grants EAR-1142020 and EAR-1111111). All data used are available from the IRIS data center at www.iris.edu.