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As the recent 2011 moment magnitude (Mw) 9.0 Tohoku-Oki event clearly demonstrated, the shallow portion (up to several tens of kilometres down-dip from the trench axis) of a subduction zone can not only slip seismically but can also slip to a large distance of about 50 m (ref. 3). A similar observation was made during the 1999 Mw 7.7 Chi-Chi earthquake in Taiwan, during which the shallow part of the fault slipped as much as 15 m (ref. 4). The lack of shallow seismicity and laboratory evidence showing that shallow parts of these faults are frictionally stable5 has introduced an apparent paradox about the behaviour of thrust faults in the wake of the above observations. Thrust fault events also show significant asymmetry in ground motion6 and fracture damage across the two sides of the fault, with more damage and larger accelerations on the hanging wall compared to the footwall7,8,9. This is due to the break in symmetry of the fault geometry and interaction of the stress waves, with respect to the free surface10,11,12.

Brune and colleagues13 attempted to resolve these observations and paradoxes by showing the existence of a torquing mechanism of thrust fault ruptures near the free surface in laboratory experiments conducted on foam rubber. However, foam rubber is not a suitable analogue material to represent Earth’s upper crust, as it is not brittle, linear elastic, and hence this mechanism has remained unexplored. Of note, theoretical arguments from linear elastic fracture mechanics have supported this possibility13,14,15,16. The torquing mechanism, however, is geometrical in nature and allows for natural reduction in elastic compressive normal stress at shallow depths, up to a few kilometres down-dip a shallow subduction zone fault, owing to dynamic rupture. It even promotes fault opening in extreme situations (contrary to the assumptions of traditional theoretical and numerical models of thrust fault ruptures that the fault interface remains fully in contact during rupture). The purpose of the present work is to explore this torquing mechanism through highly instrumented, fully dynamic earthquake rupture experiments and detailed finite-element elastodynamic calculations, which allow for spontaneous fault opening.

Thrust fault rupture experiments were conducted at the Caltech Earthquake Laboratory17 (see Methods for details). Dynamic photoelasticity and laser velocimetry were used to extract mechanical information during the simulated earthquake rupture (Fig. 1).

Figure 1: A thrust fault modelled by dividing a rectangular plate with an angled cut.
figure 1

The schematic draws analogy to forces and geometrical elements of earthquakes. A rupture nucleates at the hypo-centre and is guided up-dip towards the simulated Earth surface. a–c, Dynamic photoelasticity (a) and laser velocimetry (b) extract full-field and discrete mechanical measurements to study free-surface effects on rupture dynamics, particularly the existence of the fault-opening phenomena (c). FN, fault normal; FP, fault parallel.

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Three snapshots of a laboratory thrust earthquake (tectonic pressure (P) = 2.5 MPa, fault dip = 61°) collectively elucidate the rupture dynamics: experimental results (Fig. 2a, d, g), accompanying schematics (Fig. 2b, e, h), and the output of the numerical calculations mimicking experimental conditions (Fig. 2c, f, i). At around 58.5 μs after nucleation, the rupture tip arrives to station x1 = 10 mm (Fig. 2a, white circles), as indicated by a rise in the recorded slip and opening velocities. Minute negative opening rates measured ahead of the rupture tip imply pinching of the interface before the concurrent initiation of both opening and slip. The fault re-locks after the rupture tip sweeps past the stations; however, reflected P and S waves from the free surface feed back stress waves onto the fault and introduce additional features in the records. In the schematic (Fig. 2b), red and green portions of the fault signify locked and slipping regions, respectively. These locked and slipping regions can be clearly seen in the numerical simulation (Fig. 2c). The up-dip propagating left-lateral rupture induces a counter-clockwise torque on the hanging-wall wedge.

Figure 2: A typical sub-Rayleigh rupture (P = 2.5 MPa) is chronologically portrayed at experimental times t = 58.5, 63.5, and 93.5 μs.
figure 2

a–i, Experimental results (a, d, g), schematic representations (b, e, h), and numerical results (c, f, i) summarize the simulated earthquake. The deformation in the numerical simulations is exaggerated by a factor of 40. The rupture speed (vr) and phase velocities of bulk wave intersections with the fault are identified for both up-dip (vP,S) and reflected down-dip phases (). Up-dip rupture propagation (a) is accompanied by opening (vopen) and slip pulses (vslip), which are significantly amplified at the fault trace station (d). The reflected S wave re-ruptures the locked fault at supershear speeds (cS <), emitting a Mach front (g). Trailing behind the down-dip rupture is an opening–shutting pulse generated at the free surface.

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At around 63.5 μs, the rupture tip arrives at the free surface, x1 = 0 mm, breaking the simulated Earth surface (Fig. 2d). The recorded slip and opening velocities (v) exhibit significant amplification in peak values at the free surface ( ≈ 4 m s−1 and  ≈ 6 m s−1). Peak negative values associated with the pinching precursor are also amplified and are at this stage accompanied by an in-phase negative slip signature, both approximately equal to −2 m s−1. Numerical simulations suggest that the above effect is due to the release of the counter-clockwise torque that has built up on the hanging-wall wedge before the rupture breaks the free surface (Fig. 2f). Owing to the absence of material above the free surface, the fault is unable to counteract the pinching motion ahead of the rupture, resulting in immediate compression and release of the stress on the interface through opening and slip. Separation of the fault surfaces generates an opening pulse propagating down-dip at speed and two surface Rayleigh waves travelling, with a velocity cR, on either side of the fault, along the simulated Earth surface (Fig. 2e, daggered insert); the latter claim has been verified with previous measurements along the free surface18. The opening pulse trails behind the reflected S-wave front and propagates at  = 1.20 km s−1 ≈ cR. Oscillations in the records persist past the arrival of the rupture tip, extending the slip and opening process durations near the free surface. Theoretical work on thrust faults discusses the instantaneous emergence of a Boussinesq point force at the fault trace: the sudden inability of the system to sustain a moment upon rupture tip arrival to the free surface is balanced by this point force12. The measured fault-opening phenomenon is strong evidence in support of this claim.

At the deepest station, x1 = 20 mm, at time t = 68.5 μs, recorded slip and velocity indicate that the reflected S-wave front re-ruptures the fault (Fig. 2g). The photograph at t = 93.5 μs shows a shear Mach front emanating from the intersection of the reflected S wave and the fault, that is, the rupture tip (). Measurements from consecutive frames confirm that the average rupture tip speed is indeed supershear,  ≈ 1.6 km s−1 (1.24 cS). The geometric relation (β) = cS / sinβ and Mach angle β = 47° verify supershear speeds (47°) ≈ 1.7 km s−1. Trailing behind the down-dip rupture are the pair of fringes that correspond to the opening and shutting of the fault at the free surface , as seen in the opening velocity records. In fact, the numerical simulations reveal that the trailing-Rayleigh pulse is mixed mode in nature, having both both opening and slipping modes (Fig. 2i). The down-dip supershear slip pulse has larger slip velocity than the up-dip rupture slip pulse (Fig. 2h), due to the fact that a downward propagating rupture (which can be roughly seen as an upward propagating rupture reflecting off of the free surface) now encounters a region of much lower frictional resistance. This leads to greater slip rates in the down-dip direction. Because of this reduced frictional resistance, we expect the down-dip supershear rupture to exist at higher confining stresses.

Fault slip and opening velocity records measured at stations x1 = 0, 2, 4, 10, 20 mm are collectively plotted in Fig. 3 for experimental loads P = 2.5 MPa and P = 7.5 MPa. Timing lines bound the arrivals of up-dip P (and S) waves, tP,S, up-dip rupture tip, tr, down-dip P (S) waves, , and the down-dip trailing Rayleigh signatures, . In the P = 2.5 MPa data set (Fig. 3a), before the arrival of the first reflected P wave (t < ), the rupture process is blind to the presence of the free-surface boundary. Reflected P waves continuously feed back onto the fault with nearly no effect on the slip and opening velocity. However, the reflected S-wave front, with an arrival time of , re-ruptures the fault as it propagates back down-dip. This is clearly seen for station x1 = 20 mm at around t = 70 μs. Although the up-dip rupture is sub-Rayleigh, 0 < vr < cR, appearance of shear Mach fronts (Fig. 2g) and the geometry-driven inequality, cS < , together validate the existence of a down-dip supershear rupture, cS <  < cP. For stations within x1 ≈ 10 mm, the up-dip and down-dip ruptures coalesce, broadening the slip–velocity pulse near the free surface. In response to the opening and subsequent shutting of the fault at the free surface, the system sends an opening–closing pulse back down-dip at the Rayleigh wave speed (timing lines correspond to the leading and trailing edges). The leading supershear slip pulse is broadened by the decrease in normal stress of the fault from this trailing-Rayleigh signature. Oscillations in the records after rupture tip arrival are unique to stations near the free surface. The recorded slip and opening velocity for P = 7.5 MPa experiments (Fig. 3b) show similar results, with several key differences. The magnified driving shear stress enhances slip at every station. The fault has a lower tendency to lock; in fact, the down-dip supershear rupture is crack-like rather than pulse-like. Whereas slip is enhanced, fault opening is nearly absent in the higher-load experiments, except very close to the free surface. Unlike in the P = 2.5 MPa results, the down-dip opening–closing pulse is absent in the P = 7.5 MPa records, showing that higher confinement loads tend to enhance slip and suppress opening. It is worth noting that amplification of slip and opening rates near the free surface is largely due to the preferential enhancement of hanging-wall ground motions for both parallel and normal components of the fault.

Figure 3: Recorded fault slip (vslip) and opening velocity (vopen).
figure 3

a, b, Measured at stations x1 = 0, 2, 4, 10, 20 mm along the fault for both experimental loads P = 2.5 MPa (a) and 7.5 MPa (b). Up-dip rupture tip arrival, tr, induces a slip pulse for both loads; however, the opening pulse is attenuated in the higher-load experiment. The down-dip supershear rupture, , is pulse-like for P = 2.5 MPa and crack-like for P = 7.5 MPa experiments: increased confinement loads enhance slip but inhibit fault opening. Ground motions amplify towards the free surface as the up-dip and down-dip ruptures coalesce, elongating the slip and opening velocity pulses for stations within x1 ≈ 10 mm.

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High-resolution, controlled experimental and numerical results conclusively validate the hypothesis that certain thrust faults (collisional and subduction) suffer significant reduction in compressional normal stress owing to free surface effects and that they might open when an up-dip propagating rupture breaks that surface. This reduction in normal stress is essentially a geometrical phenomenon that is expressed whenever a dynamic rupture runs through a thrust fault and approaches the surface of the earth. The 2011 Tohoku-Oki earthquake occurred on a bimaterial interface where the material on the hanging wall was softer than that on the footwall19,20. This naturally results in reduction of normal stress around the up-dip propagating rupture. The mechanism that we propose, when correctly accounted for in the numerical models, will further reduce the normal stress, making the possibility of opening even more likely. Indeed, any other physical mechanism that is invoked to reduce normal stress, when coupled with the mechanism we propose, would only enhance the effect of normal stress reduction as our mechanism is geometrical in nature.

The laboratory experiments show that there is a small, but non-negligible, opening at confining pressure of P = 7.5 MPa. This corresponds to a normal stress of σ = 5.7 MPa that acts on the fault plane. It can be shown, using reasonable values of the state of stress in fluid-rich sedimentary upper crust21, that the corresponding down-dip extent l along a shallow subduction fault (5o < dip (δ) < 10o), where the normal stress corresponds to laboratory conditions, is between 2 km and 4 km (l ≈ 6.10−5σ / sinδ). These correspond to depths at which large shallow slip was observed in the 1999 Chi-Chi earthquake, around 15 m, and the 2011 Tohoku-Oki earthquake, around 50 m. Further evidence of fault opening comes from the lack of high-frequency radiation from the shallow part of the thrust ruptures, observed for both the Tohoku-Oki22 and the Chi-Chi7,23 earthquakes. Geological evidence for this mechanism has been observed during the Chi-Chi earthquake, when the toe of the fault was propelled forward and crumpled during its passage, with no overshoot7. During the 1971 San Fernando Earthquake, a large volume of asphalt covering the surface trace of the thrust fault was seemingly coherently translated about 1.5 m by motions associated with thrust-fault displacement24. High-resolution mapping of the 2013 Mw 7.7 Balouchistan earthquake (dominant strike-slip with local dip-slip component) shows significant tensile cracks on certain sections of the hanging wall of the fault9. This fault had an average dip angle of approximately 60o, as in our experiments. These latter observations may be explained by the mechanism we propose, by which the hanging wall undergoes significant rotations in both directions as the rupture approaches and breaks the free surface, resulting in complete reduction of compressive normal stress.

Once the rupture breaks the free surface, it reverses course and propagates down-dip as a supershear rupture (with higher slip rates) that is trailed by an opening and a sliding pulse, which propagates at the Rayleigh wave speed. This effect could explain the observed enhanced slip pulse propagating down-dip during the Tohoku-Oki earthquake22,25.

In conclusion, this work shows that accounting for this mechanism of dynamic normal stress reduction, with possible opening, along with dynamic frictional weakening processes and bimaterial effects, helps to resolve the majority of the paradoxes associated with surface-breaking earthquakes in thrust faults.

Methods

Thrust fault rupture experiments were conducted at the Caltech Earthquake Laboratory facility17. This facility and setup is the same used by Gabuchian et al. in the previous publications18. In this setup, dynamic photoelasticity (Fig. 1a) and laser velocimetry (Fig. 1b) are used to record deformations occurring during the simulated earthquake ruptures. Digital cameras capture a sequence of images with 50 ns exposure times, providing a full-field view of the rupture process. Photoelasticity yields isochromatic fringe patterns related to magnitudes of maximum shear stress averaged through the thickness of the specimen, |τmax(x1, x2, t)|. Complementary use of full-field images and discrete velocity records identifies the effects of various dynamic features of ground motion and slip history. The laser velocimeter systems function as laboratory seismometers, each outputting a temporally resolved velocity record for a single component of ground motion at a discrete point on the specimen26.

A thrust fault is modelled in the laboratory by means of a rectangular plate with dimensions height = 360 mm, width = 180 mm, and thickness = 9.52 mm (Fig. 1). The surrogate material is Homalite H-100, a brittle linear elastic, transparent, optically bi-refringent polymer with the dilatational (P) wave speed, cP = 2.59 km s−1 and the shear (S) wave speed cS = 1.27 km s−1. An angled cut divides the specimen into the hanging wall and footwall plates: this interface represents a thrust fault with a 61° dip angle. We can currently model only steep faults in the laboratory, but in the future maybe be able to model shallower faults; this would have a direct application to the physics of shallow thrust faults in the earth.

The characteristic double-lobe fringe structure trailing behind the S wave (Fig. 1a) is the signature of a sub-Rayleigh rupture tip propagating up-dip with a nearly constant speed, vr = 1.14 km s−1 (<cR = 1.18 km s−1, the Rayleigh wave speed). The origin of the coordinate system is set at the intersection of the fault with the free surface with the x1 component collinear to the fault (x2 = 0). The two surfaces are frictionally held together and the resulting interface experiences compression and shear under the action of the remote load. Far-field uniaxial compression of the plate mimics far-field tectonic stress in the earth: the applied load, P (MPa), resolves into fault parallel (x1) and normal (x2) components along the angled interface. At a distance x1 = 74.3 mm from the free surface, a pre-fabricated notch houses a NiCr wire of diameter 127 μm. Discharge of a capacitor bank across the wire converts the filament to plasma, locally decreasing the fault strength such that the driving shear stress is sufficient to initiate slip. This mechanism nucleates a bilateral rupture propagating away from the hypo-centre (Fig. 1, marked by a star). Confined to the fault plane, the rupture tips unzip the fault, continuously emitting P and S stress waves into the bulk, and this process simulates an earthquake17.

By focusing four different velocimeters just to the left and right of the fault at an offset distance, ε ≈ 200 − 300 μm, four components of ground motion are recorded in each experiment: two fault parallel, v1(x1, x2 = 0 ± ε, t) = (x1), and two fault normal, v2(x1, x2 = 0 ± ε, t) = (x1) components of particle velocity. For any given along-fault distance x1, slip and opening rates are determined by taking the difference between the paired hanging wall and footwall station records: and . Rupture evolution is tracked by a series of experiments with measurements conducted at distances x1 = 0, 2, 4, 10, 20 mm along the fault (Fig. 1c) for applied loads of P = 2.5 MPa and P = 7.5 MPa.

The numerical simulations were conducted using a commercial finite element software, ABAQUS (Dassault Systèmes Simulia Corp.), using a kinematic contact algorithm. The frictional constitutive response is modelled using a slip-weakening law with static friction, fs = 0.6, dynamic friction, fd = 0.2, and critical slip, Dc = 10 μm (ref. 27). Elastic properties, loading and frictional parameters were chosen to closely represent the laboratory earthquake. In addition to sliding, the simulation allows for the possibility of opening across the fault. The aim of the simulation is to qualitatively explain the experiments at this stage.

Data availability

All relevant data are available from the authors upon reasonable request.