Archean asteroid impacts, reflected in the presence of spherule beds in the 3.2–3.5 Ga Barberton greenstone belt (BGB), South Africa, generated extreme seismic waves. Spherule bed S2 provides a field example. It locally lies at the contact between the Onverwacht and Fig Tree Groups in the BGB, which formed as a result of the impact of asteroid (possibly 50 km diameter). Scaling calculations indicate that very strong seismic waves traveled several crater diameters from the impact site, where they widely damaged Onverwacht rocks over much of the BGB. Lithified sediments near the top of the Onverwacht Group failed with opening-mode fractures. The underlying volcanic sequence then failed with normal faults and opening-mode fractures. Surficial unlithified sediments liquefied and behaved as a fluid. These liquefied sediments and some impact-produced spherules-filled near-surface fractures, today represented by swarms of chert dikes. Strong impact-related tsunamis then swept the seafloor. P waves and Rayleigh waves from the impact greatly exceeded the amplitudes of typical earthquake waves. The duration of extreme shaking was also far longer, probably hundreds of seconds, than that from strong earthquakes. Dynamic strains of ∼10−3 occurred from the surface and downward throughout the lithosphere. Shaking weakened the Onverwacht volcanic edifice and the surface layers locally moved downhill from gravity accommodated by faults and open-mode fractures. Coast-parallel opening-mode fractures on the fore-arc coast of Chile, formed as a result of megathrust events, are the closest modern analogs. It is even conceivable that dynamic stresses throughout the lithosphere initiated subduction beneath the Onverwacht rocks.
Asteroids of many tens of kilometers in diameter struck and modified the Earth's lithosphere during the Archean [Lowe et al., 2003; Lowe and Byerly, 2010]. In this work, we physically model the effects of these impacts at several to many crater diameters from the impact site. We concentrate on the effects of seismic waves. Impact basins on the Moon provide general analogs. Shaking from strong waves from the Orientale impact caused ground failure, smoothing preexisting topographic roughness [Kreslavsky and Head, 2012]. Furthermore, extreme seismic waves from rare, catastrophic events are potential hazards to critical structures that are designed to persist for long times, such as nuclear waste depositories [e.g., Hanks et al., 2006; Andrews et al., 2007]. Examination of ancient sites affected by extreme seismic waves bears on recognizing the effects of putative extreme shaking in the recent geological record.
The ∼3.26 Ga contact between the largely volcanic Onverwacht Group and overlying largely sedimentary Fig Tree Group in the Barberton greenstone belt (BGB), South Africa, is marked by the S2 spherule bed [Lowe et al., 2003]. This bed includes abundant sand-sized spherules that condensed from a rock vapor cloud formed during a large asteroid impact at approximately 3.26 Ga [Lowe et al., 2003]. This deposit has a significant iridium concentration and chromium isotope anomalies indicating cosmic origin from a carbonaceous chondrite body [Kyte et al., 2003]. We proceed on the inference that associated features of ground damage and strong seafloor (water) currents share causes associated with the impact.
Lowe  summarized field evidence of rock damage likely caused by seismic waves from this event, as well as impact-related tsunamis. The main present-day features related to this damage are a series of chert dikes formed by the downward flowage of sediments into fractures formed on the seafloor. These dikes are especially well developed and exposed in an area of the BGB termed Barite Valley [Lowe, 2013]. We summarize these results to examine the physics related to this process. We consider only data obtained south of the Inyoka Fault, as units north of the fault are not closely correlated with those south of it. In particular, another later spherule bed S3 widely overlies the Onverwacht Group north of the fault.
Lithology influenced the mechanical behavior of the Onverwacht Group in the aftermath of the S2 impact. The Onverwacht Group consists mostly of basaltic and komatiitic volcanic rocks with some felsic and sedimentary units. Its uppermost unit, the Mendon Formation, 300–1000 m thick, is a series of cyclically interbedded units of komatiitic volcanic rock and thin sedimentary layers composed mostly of black chert, banded black-and-white chert, and banded ferruginous chert [Lowe and Byerly, 1999; Lowe, 1999]. A 40–60 m sequence of sedimentary rocks and unlithified sediments capped the volcanic sequence at the time of spherule deposition. Lowe  defined three lithological and mechanical units in this interval (Figure 1). The lower zone (Mc1) consists of 25–30 m of thinly bedded and laminated chert. Its even, fine laminations and layering, lack of current structures, fine sediment size, and moderate alumina and potash contents suggest that these were fine tuffaceous and possibly chemical sediments deposited under quiet, relatively deep water conditions. This unit shows extensive brittle fracturing associated with dike formation and was apparently at least partially lithified at the time of the impact. The overlying 15–25 m (Mc2) is composed of massive to thickly bedded black chert. This unit was extensively disturbed by postdepositional liquefaction and mobilization but, where intact, it shows common fine lamination, some banding, and rare cross laminations, again indicating deposition well below wavebase. The uppermost 3–5 m of Mendon chert (Mc3) represents fine volcaniclastic sediments, were also deposited mostly under quiet water conditions.
Four types of dikes and veins indicate that shallow Onverwacht rocks failed during the arrival of spherules at the seafloor and before the arrival of the proposed tsunami (Figure 1). Type 1 irregular dikes up to 8 m wide extend downward across as much as 100 m of stratigraphy (Figure 2). These dikes formed initially as open fractures but soft seafloor sediments, liquefied sediments of Mc2, and subordinate ashes of Mc3 rapidly flowed downward into the open fractures, often through multiple passive fill and injection events through continuing movement and adjustment of the shattered blocks of the uppermost volcanic and sedimentary sequence. Type 2 small vertical dikes, mostly <1 m wide, are restricted to Mc1 marking the lower half of the Mendon chert section. Type 3 small crosscutting veins are mostly <50 cm across and filled with precipitative silica. Type 4 small bedding-parallel to irregular veins are mostly <10 cm wide, filled with translucent precipitative silica. Type 2 dikes formed first and reflect a short-lived event that locally decoupled the sedimentary section at the top of the Mendon Formation from underlying volcanic rocks and opened narrow vertical tension fractures in the lower, lithified part of the sedimentary section (Mc1). Later seismic events triggered formation of the larger Type 1 fractures throughout the sedimentary and upper volcanic section, widespread liquefaction of soft, uppermost Mendon sediments (Mc2 and Mc3), and flowage of the liquefied sediments and loose impact-generated spherules into the open fractures. The overall strain (opening of dikes per unit horizontal length) is a few percent. Late stage circulation of shallow subsurface fluids through still-open fractures and cavities resulted in complete filling of the fractures and veins by precipitative silica.
The Onverwacht locality was below wavebase and hence likely within an ocean basin. Large impacts within deep ocean basins produce giant tsunamis [e.g., Wünnemann et al., 2010]. Such an event is a prime suspect for everywhere eroding and reworking the spherule layer immediately after its deposition. Spherules locally comprise part of the dike fill, indicating that the strong currents arrived when cracks were still open and spherules still loose. Alternative explanations for reworking seafloor material include currents driven by local seafloor failure and density currents driven by spherule-filled seawater. We cannot exclude currents driven by local massive, nonimpact related, seafloor failure, but we have no evidence of them in the composition of sediments associated with the spherules. We discuss the physics of density currents in Appendix Descent Time of Rock RainC.
We examine two issues with regard to the hypothesis that strong seismic waves from the asteroid impact caused the observed shallow rock failure. We obtain scaling relationships to estimate the size of seismic waves that impinged on the Onverwacht rocks and show that these extreme waves likely caused the observed brittle failure of shallow rocks accommodated by opening-mode dikes and normal faults. We also constrain the relative timing of the arrival of seismic waves, spherules, and tsunamis.
2 Scaling Relationships for Seismic Waves From a Large Asteroid Impact
We proceed by using crater diameter as a length scale to estimate the strength and duration of seismic shaking. Evidence from outcrops in the Barite Valley in the central BGB suggests that this area was several crater diameters away from the crater center [Lowe, 2013]. Our locality is neither within the crater nor within coarse ejecta blanket. The latter observation does not yield good estimate of distance from the crater, as the finite depth of open ocean water at the S2 impact site in analogy to Chicxulub limited the reach of coarse ejecta [Artemieva and Morgan, 2009]. As already stated, tsunami deposits indicate a direct oceanic path from crater to outcrop site and thus a moderate distance.
The spherules beds were thoroughly mixed by currents likely from tsunamis and hence provide no precise information on the impactor and crater sizes. In round numbers, we follow the estimate of Johnson and Melosh  that the S2 impactor was between 37 and 58 km in diameter, a size several times larger than the bolide that ended the Cretaceous period. The estimated impactor for bed S2 is similar to that of other better-constrained impactors. However, intense currents perturbed all known exposures of bed S2, so its initial precurrent thickness is not precisely constrained. Johnson and Melosh  estimated bolide properties from their estimate of the effective thickness of spherules. We use 45 km bolide diameter. We obtain 478 km for final crater diameter for vertical incidence, 20 km s−1 impact velocity, and equal projectile and target densities from equations (22) and (27) of Collins et al. . We use the rounded value of 500 km in example calculations. Our calculations are easily rescaled and do not depend critically on these values. See Bottke et al.  for discussion of the relevance of the spherule beds to the late heavy bombardment in general.
2.1 Ambient Material Properties
The sizes of the bolide and the resulting crater were large enough that cratering in an oceanic region mainly involved the mantle, so did propagation of strong seismic waves. The modern mantle values are a good guide to the Archean mantle. The main difference is that Earth's interior has likely cooled some since the Archean [e.g., Korenaga, 2008; Herzberg et al., 2010], causing Archean mantle density and elastic constants to be modestly less than the present values. These differences are similar to those between young and old oceanic lithosphere on the modern Earth, a few percent in density and seismic wave velocity [e.g., Weidner, 1974]. We do not attempt to obtain results to the precision requiring this resolution. Neither do we know the age of the oceanic lithosphere and ocean depths at the target and along the path to our site. We note that typical oceanic crust was likely thicker than present, perhaps similar to that beneath modern oceanic plateau [Herzberg et al., 2010].
We obtain relationships in terms of seismically measurable parameters for the modern mantle in Appendix Properties of Seismic WavesA. The mantle P wave velocity [Bullen and Bolt, 1985, pp. 88] is ∼8000 m s−1 and S wave velocity [Bullen and Bolt, 1985, pp. 88] is ∼4600 m s−1. Mantle density ρ is ∼3300 kg m−3. The Lamé constants are approximately equal in the mantle G ≈ λ.
With forethought, we need the phase and group velocity of Rayleigh waves to estimate strains in shallow rock near the target and near our outcrop site. At long wavelengths, a mantle half-space wave with group and phase velocities equal to 0.92 of S wave velocity of the mantle [Bullen and Bolt, 1985, pp. 113] will provide an approximation. The ocean has some effect so the phase velocity is somewhat higher and the group velocity is somewhat lower than 0.92 times the mantle S wave velocity [Bullen and Bolt, 1985, pp. 271]. We use the rounded estimate of ∼4000 m s−1 for both phase and group velocity in simple calculations.
Additional geometrical spreading occurs because Rayleigh waves are dispersive, that is, waves with different frequencies have different group velocities and arrive at different times. In section 'Time Scale of Impact', we estimate that extreme seismic waves with periods of ∼100 s radiated from the impact site for over 1000 s. Modest amounts of dispersion thus affected waveforms by rearranging energy within a long wave train. They did not cause significant geometrical spreading of the wave train in its direction of propagation.
2.2 Time Scale of Impact
Physicists have not extrapolated numerical calculations of large asteroid impacts on the Earth through to the time of generation of seismic waves. Ivanov  and Senft and Stewart  studied the smaller Chicxulub impact. Still physicists have developed useful scaling relationships that we apply to this process [Melosh, 1989; Collins et al., 2005; Meschede et al., 2011]. We wish to infer the type of seismic waves, their dominant period T, and their amplitude in terms of dynamic stresses that cause ground failure, both at the impact site and in the far field.
Qualitatively in chronological order, the projectile initially penetrated into the Earth over a distance scaling with its diameter over a time of a few seconds. The stresses in the shock wave greatly exceeded the short-term strength of rock. The material then behaved as an inviscid fluid in the presence of gravity. This hydrodynamic phase of cratering lasted for a time, Tf, given by
where D is the crater diameter and g is the acceleration of gravity [Melosh, 1989, pp. 123]. For example, this time is 120 s for a 500 km diameter crater. (We retain insignificant digits where it may help the reader to follow the calculation and compare related quantities.) For comparison, the time for the 180 km diameter Chicxulub crater [e.g., Melosh and Ivanov, 1999] is 70 s. Numerical modeling of Chicxulub indicates that major rock deformation and hence generation of extreme seismic waves continued for 600 s [Collins et al., 2008]. Extrapolating to the Archean event using (1) indicates that extreme seismic waves radiated for over 1000 s.
We discuss a more sophisticated dynamical model for impacts that gives a characteristic time of ∼100 s extrapolating from the Chicxulub impact in Appendix BDynamic Model of Impact. We use the rounded value of 100 s in example calculations for the dominant period of seismic waves on velocity seismograms that are relevant to dynamic stress (Appendix AProperties of Seismic Waves). For reference, this time is comparable to the kinematic times for waves cross a 500 km crater. For example, a mantle P wave takes ∼60 s and a mantle Rayleigh wave takes ∼120 s.
2.3 Methodology for Strength of Radiated Seismic Waves
We begin by obtaining an estimate of the equivalent earthquake magnitude for a large impact. Melosh  and Meschede et al. [2011, Figure 1] stated that about 10−4 of the impact energy (with the wide range of 10−3−10−5) becomes seismic waves that propagate away from crater (see Appendix Dynamic Model of ImpactB). Kinetic energy W of a projectile scales with its mass and the cube of its diameter. Moment magnitude scales with . Melosh  gave that M = 4.8 for a 30 m diameter projectile, so even a 30 km diameter projectile (with 109 times the mass) produces M ≈ 10.8. This result suffices to show that shaking from large impacts exceeds that from ordinary great earthquakes.
We obtain separate estimates for the amplitude of P waves and Rayleigh waves by considering the strength of rock. We base model a P wave on the transition pressure of shocks waves to linear elastic waves, Hugoniot elastic limit and P wave and Rayleigh wave models on frictional failure. We estimate the radius from the center of the impact where this transition occurred. We estimate the strength of the wave by noting that this transition occurs when dynamic stresses drop below the elastic limit of the material (Figure 3). Conversely, the maximum amplitude of a seismic wave that actually propagates to teleseismic distances cannot cause stresses that exceed the strength of the rock along the way. We take advantage of the principle that the local kinetic energy is equal to the local elastic strain energy for both P waves and S waves [e.g., Timoshenko and Goodier, 1970, pp. 491]. Peak stresses thus scale with and occur at the time of peak particle velocities for elastic waves. We then consider the effects of geometrical spreading along the wave path. Note that the root mean square particle velocity is 2−1/2 of the peak velocity for a sinusoidal wave.
We apply these criteria using basic properties of seismic waves considered in Appendix AProperties of Seismic Waves. In particular, the Coulomb frictional strength of rocks increases rapidly with depth. P waves are generated efficiently deep in the mantle below the crater where rock is strong. Surface waves are generated at shallower depths where rock is weaker. We dimensionally modify the dynamical approach of Meschede et al.  to account for this difference.
2.4 P Wave Amplitude
We obtain an extreme upper limit for the amplitude of a P wave that can propagate through the mantle without strong attenuation, as dynamic stress cannot exceed the short-term strength of the rock. We obtain this amplitude in terms of peak particle velocity and its distance from the center of the impact in two ways. That is, we model rock failure as plasticity and as Coulomb friction. We then account for geometrical spreading.
Beginning with plasticity that transition into elasticity, the short-term shear strength of silicates is typically ∼0.1 G. [Poirier, 1990, pp. 38], here 7 GPa for β = 4600 m s−1 in the upper mantle. The corresponding particle velocity from (A4) and (A6) is 800 m s−1. This behavior applies within the outermost shock wave (Figure 3). Calculations based on shock wave experiments [Ahrens and O'Keefe, 1977] yield a lower estimate of the Hugoniot elastic limit where the dynamic pressure σ11 in (A3) is ∼0.1 G. In this case, the experimental and model target was gabbro with G ≈ 50 Ga and Hugoniot elastic limit of 5 Ga. The particle velocity at this limit is 270 m s−1 for mantle parameters. We use this value to estimate the depth to the Hugoniot elastic limit.
We obtain the radius of the shock wave when it has this stress by conserving momentum, dimensionally following Meschede et al. . To the first order, the projectile transfers its momentum to a hemispherical shocked annulus of radius rS and thickness 2rA [Melosh, 1989, pp. 54],
where VA is the velocity of the asteroid at impact, VShock is the particle velocity in the shocked region, ρA is the density of the asteroid, rA is the radius of the asteroid, and ρ is the density of the target region of the Earth, which we assume is also that of the asteroid for simplicity. Solving for the depth that the shocked particle velocity is 270 m s−1 yields 112 km depth, assuming a 45 km diameter asteroid hitting at 20 km s−1 [Johnson and Melosh, 2012].
The elastic P wave then spreads crudely radially, and must conserve energy. The total energy, the kinetic energy, and the elastic strain energy all scale to [e.g., Timoshenko and Goodier, 1970, pp. 491]. This energy is initially spread over part of a spherical shell of radius rS and surface area proportional to , when by assumption its propagation became elastic. The energy in the shell is proportional to . The energy then spreads over a shell of radius rprop scaling with the propagation distance. The peak P wave amplitude is thus approximately distance. The predicted peak amplitude is a modest function of teleseismic distance. For example, the peak amplitude at 45° = 5000 km distance is 6 m s−1. A more accurate calculation would take account of actual raypaths in the mantle.
The experiments modeled by Ahrens and O'Keefe  involved centimeter-sized projectiles where ambient pressure within the target is negligible compared with the Hugoniot elastic limit. The lithostatic pressure at the computed depth of 112 km of 4 GPa is comparable to the Hugoniot elastic limit. We construct and alternative model where a radial region exists farther from the impact center where stresses do not exceed short-term strength but Coulomb failure in shear occurs on planes (Figure 3). Although it is not clear how to formulate frictional failure criteria in a very strong P wave, we proceed with the inference from experiments that the strength depends on the previous ambient pressure from lithostatic stress [Prakash, 1998] and that Coulomb failure once started greatly weakens the material allowing continued failure [Senft and Stewart, 2009]. They used 5–10 m s−1 as the slip velocity for significant fault weakening in their models successful of Chicxulub. The calculations of Collins et al.  also assume that such weakening in fact happens. The shear stress at frictional failure is then
where μ ≈ 0.7 is the coefficient of friction, Z is the depth, α is the P wave velocity, and VF is the particle velocity at the radius of frictional failure. The second equality arises from the relationship between particle velocity and dynamic stress in (A4) and (A6). Directly beneath the impact the depth Z equals the radius of frictional failure rF. In analogy with (2), momentum conservation implies
which yields 110 km with a particle velocity of 282 m s−1 and rA = 22.5 km is the asteroid radius. The particle velocity at 45° is 6 m s−1, our previous estimate based on plasticity.
The computed particle velocity of ∼6 m s−1 beneath the crater implied by frictional failure is a few times greater than that of near-field (with a few kilometers of the fault) velocity pulses in strong earthquakes 1–2 m s−1 [e.g., Makris and Black, 2004]. High particle velocities also persist for much larger times, hundreds of seconds rather than a few seconds. Our computed amplitude is much greater than the value of 0.5 m s−1 suggested for Ordovician continental margin failure suggested by Parnell . It is comparable to 10 m s−1 computed by Ivanov  for 300 km from the Chicxulub impact.
As a caveat, we summarize ways in which large craters differ from underground nuclear explosions. The perhaps attractive scaling from explosions is not straightforward and hence here unproductive. Engineers planned these explosions so that they did not generate surface craters and thereby release radioactivity to the environment. Nonlinear interaction of the seismic wave with the free surface generated strong seismic waves [Patton and Taylor, 2011]. The burial depths were shallow ∼1 km where rocks are quite weak in friction from (2) and in dynamic tension. Teleseismic waves were generated in a fraction of a second, rather than ∼100 s and over a tiny area compared to that of the Earth. Gravitational collapse and rebound after the explosion did not generate strong amplitudes at long periods. In contrast, hydrodynamic processes were important in large craters. Impacts-generated P waves with initial outward particle motion. The crater then rebounded from gravity toward the surface generating P waves with the opposite polarity. Complicated generation of S waves and Rayleigh waves followed.
2.5 Rayleigh Wave Amplitude
Processes near the edge of the S2 crater generated Rayleigh waves with initial radial transport from the impact center and vertical motion. For completeness, real impacts were likely oblique to the Earth's surface and likely released any tectonic stresses stored in the cratered region. These effects generated some Love waves with horizontal motions circumferential to the source, which we ignore as second-order effects compared with P waves and Rayleigh waves.
We begin with the effects of geometrical spreading of surface waves over the spherical Earth. As with P waves, the distance from the center where material behaves elastically (analogous with Hugoniot elastic limit) acts as a radiating distance , where RE is the radius of the Earth and θrad is the angular separation. The total energy in the annulus is proportional to , where Vrad is the particle velocity at the annulus. Ignoring dispersion, the wave annulus spreads out to angular separation θprop, where the total energy is proportional to , where the peak particle velocity is Vprop. Hence, the peak particle velocity varies as
It is thus not necessary to know the angular separation precisely. For example, the amplitude in (5) decreases by 2−1/2 = 0.7 from 30° to 90°.
To apply (5), it is necessary to constrain both the effective radius of radiation and the amplitude of the Rayleigh wave at that distance. The diameter of the crater D is a natural length scale. Melosh  suggested a “rule of thumb” where strong nonlinear behavior extends 0.8 D near the surface from the crater center, 400 km for our crater (Figure 3). We note that the equivalent source's lateral dimension is comparable to that of great earthquakes. The source length on the near side of our crater is 0.8 πD or 1260 km.
Crustal earthquakes provide some analogy to faulting in the shallow annulus away from the crater that generates Rayleigh waves. Crustal earthquakes nucleate in a small source region with high shear stresses expected for frictional failure. The rupture then propagates into less stressed regions with ambient shear stresses of ∼10 MPa. High particle velocities ∼10–15 m s−1 and stresses occur briefly at the rupture tip; most of the slip occurs at low stresses <<10 MPa and low particle velocities [Beeler et al., 2008; Noda et al., 2009; Dunham et al., 2011a, 2011b]. In contrast, shock waves arrive at the entire shallow annulus at about the same time causing large strains and large stresses. Rupture of faults at the effective radiating distance thus nucleates at numerous places at the peak stress levels for earthquake crack tips. Particle velocities Vrad from this inference should be around 10–15 m s−1.
A further constraint is that Rayleigh waves propagate outward over several wavelengths, here 400 km for 100 s waves; 5000 km distance from the crater center is 11.5 wavelengths from the radiating annulus. Nonlinear rock failure over any significant fraction of the depth interval where elastic strain occurs would sap the wave over several periods precluding such propagation. The energy of Rayleigh waves is distributed over scale depth L/0.78 π where L is the wavelength [Bullen and Bolt, 1985, pp. 113]. This depth is 160 km for 100 s period waves. The dynamic shear strain at depth is crudely V/cRay, where V is the scalar particle velocity and cRay is the Rayleigh wave phase velocity. The dynamic shear stress is this quantity times the shear modulus, , where density ρ and shear wave velocity β are evaluated at points within the Earth. For reference, the dynamic stress is 174 MPa for mantle properties and 10 m s−1 particle velocity. The ratio of dynamic stress to frictional strength in (3) is
Failure occurs when the ratio is greater than 1, for μ = 0.7 above the depth of 8 km. This depth is 6 km assuming 4 km s−1S wave velocity in the crystalline crust. Both depths are small compared to the scale depth of 160 km for the Rayleigh wave, so the wave should propagate with modest nonlinear attenuation. Using a radiation radius of 400 km, the amplitude in (5) at 45° angular separation is 3 m s−1. We do not distinguish components of the wave in our dimensional approach. Note that the horizontal amplitude of a half-space wave is 0.68 of the vertical amplitude [Bullen and Bolt, 1985, pp. 113].
3 Shaking and Shallow Rock Failure Resulting From Large Asteroid Impacts
Given the uncertainties in the calculations, we conclude that P wave and Rayleigh wave amplitudes were comparable and exceeded the amplitudes at teleseismic distances of waves from great earthquakes. The duration ∼1000 s and period ∼100 s of the waves are many times longer than those of strong earthquake waves. The hypothesis that impact-generated seismic waves could have damaged rock that had been exposed unscathed to seismic waves from ordinary great earthquakes for millions of years is thus feasible.
We propose from outcrop evidence that impact-generated seismic waves damaged shallow rocks. Spherules reached the seabed, but it is not clear that shaking was continuing when the first spherules arrived. The spherules moved downward into the fractures along with surface sediments, but any role played by tsunamis in this process is unclear.
3.1 Timing of Events
We use a distance of 45° = 5000 km from the center of the crater to examine the sequence of events. Rapid arrival of P waves in ∼500 s is expected [e.g., Morelli and Dziewonski, 1993]. Reverberating body waves continued to arrive for a few times this interval. Direct Rayleigh waves took ∼1250 s. Surface waves continued to circle the Earth. For reference, it takes ∼10,000 s for each circumnavigation. Ejecta and rock vapor moved at a fraction of orbital velocity ∼8000 m s−1. They arrived at the top of the atmosphere ∼1600 s, 45° from the impact using the code of Collins et al. .
The tsunamis are much slower than seismic waves. Their velocity in the open ocean is
where h is the water depth [Bullen and Bolt, 1985, pp. 464]. Little is known about Archean ocean depth; for reference, modern abyssal water depths of 4–6 km yields velocities of 0.200–0.245 km s−1. It took 20,000–25,000 s for the waves to arrive at 5000 km distance well after the seismic waves. In analogy to earthquake-generated tsunamis, strong waves continued to arrive for a comparable time.
Spherules reached the seafloor before the tsunami arrived, providing a constraint on water depth. From Appendix CDescent Time of Rock Rain, spherules would have spent most of their transit time sinking through the ocean if it was deep, and it is thus not necessary to consider their travel through space and air in detail. It is feasible that spherules did reach the seafloor on a submarine plateau before the tsunami. We do not have good constraints on water depth other than it was below wavebase. The minimum likely depth of a few hundreds of meters is attractive, as uplift of nearby regions immediately following the impact provided a flux of clastic sediments at the start of Fig Tree Group deposition. For reference, the sinking time is 6500 s in 1 km deep water. Hence, spherules could have reached the seafloor before the tsunami only at a significant distance from the crater, which we infer from the lack of coarse ejecta. We infer that our site was most likely on a submarine plateau, rather than abyssal depths much greater than 1 km.
3.2 Incident Seismic Waves
The BGB site was several crater diameters from the impact where static strains (the permanent change before and after the impact in distance between two points per horizontal distance in the region of our outcrop) were negligible relative to dynamic strains from seismic waves. The initial pulse from the impact produced movement away from the crater and horizontal compression. Later pulses produced comparable velocities toward the impact and horizontal tension so that the impinging particle velocity averaged to near zero with little net movement relative to the crater center.
We quantify rock damage from these incident waves applying two basic principles. First, the wavelength >100 km of the waves was much greater than the depth below seafloor where we infer rock failure. The horizontal strain in the direction of propagation had its mantle value, which is dimensionally VP/α for P waves where the particle velocity VP is ∼8 m s−1 from the frictional model in section 'Analogous Failure in the Shallow Subsurface'. Dikes opened when this strain was tensile. So only the horizontal component of the incident P wave caused this strain; the total strain needs to be multiplied by the sine of the angle of incidence in the mantle, for example, 25° at 45° distance [Pho and Behe, 1972], so the estimated velocity causing horizontal strain was a factor of ∼2 less than for the full particle velocity or ∼3 m s−1. Dynamic strain for Rayleigh waves is Vprop/cRay where Vprop is 3 m s−1 and cRay is phase velocity ∼4000 m s−1. The dynamic strain in both cases was thus ∼10−3. We continue using this rounded estimate to avoid implying spurious precision. Importantly, seismic waves transmitted through the mantle did not directly produce the few percent anelastic strains that we infer from outcrops.
3.3 Analogous Failure in the Shallow Subsurface
We make analogy with three processes related to ordinary earthquakes where the shallow subsurface becomes anelastic (Figure 4): (1) Opening-mode fractures occur parallel to the coast of the Chilean subduction zone [Allmendinger and González, 2010; Arriagada et al., 2011]. These fractures formed and were reactivated during numerous megathrust events over geological time. The slope toward the subduction zone is ∼7°. The net effect involves fractured fore-arc material moving downward and toward the trench. We envision an analogous process of downslope movement through collapse along the edge of the Onverwacht plateau. (2) Strong seismic waves damaged rocks on the Onverwacht seafloor and produced minor Type 3 and 4 veins (Figure 1). This process is analogous to the formation of regolith by repeated strong seismic waves in the near field of faults and within sedimentary basins that trap strong surface waves [Brune, 2001; Dor et al., 2008; Girty et al., 2008; Wechsler et al., 2009; Replogle, 2011; Sleep, 2011a]. (3) Strong shaking over hundreds of seconds destabilized the Onverwacht volcanic edifice that failed in an apparent tectonic manner under ambient gravity. Parnell  proposed that strong seismic waves from cosmic impacts destabilized continental margins in the Ordovician Period. Ivanov  obtained ∼10 m s−1 particle velocity ∼300 km from the center of the Chicxulub crater, where the continental margin failed in massive landslides.
The Onverwacht features are analogous seismically triggered sackungen, which, also extend only to shallow depths, 10 to ∼100 s of meters [Sleep, 2011b]. They move ∼1 m per strong shaking event and have the net effect of slow deep landslide over numerous earthquake cycles [McCalpin and Hart, 2003]. Earthquake triggering by strong seismic waves at ambient tectonic stresses at greater depths is analogous [Hill, 2008] in the sense that gravity maintains ambient stresses within broad edifices.
3.4 Failure During Shallow Dynamic Stress
We consider the strain in the shallow subsurface and the dynamic stresses that caused failure. In particular, the observed shallow anelastic strain was much greater than the elastic strain in the incident seismic waves ∼10−3. Parallel vertical cracks opened in the lithified sediment layer. Shallower unlithified sediment failed in a ductile manner.
We apply a simple mechanical criterion for the opening of vertical cracks: The dynamic extensional stress needs to exceed the ambient normal stress on vertical planes. To the first order, the normal stress is the lithostatic stress from the weight of the overlying sediment minus hydrostatic pressure (ρsed – ρwater)gZ, where ρsed and ρwater are sediment and water density. We show that vertical cracking is expected in shallow stiff rocks for imposed horizontal extensional strain, here 10−3. The formula for stresses from the extension of a sheet in one direction provides a simple estimate of dynamic stress
where is Young's modulus, is Poisson's ratio, and the approximate equality assumes λ = G [e.g., Turcotte and Schubert, 2002, pp. 114]. Our lithified sediments likely had an S wave velocity of ∼2000 m s−1 and a density of ∼2200 kg m−3, so the shear modulus was ∼9 GPa using G = ρβ2. A strain of 10−3 would produce 24 MPa of dynamic stress in (8), which would exceed the difference between lithostatic and fluid pressure down to 2 km depth.
The overlying soft sediments likely had an S wave velocity of ∼300 m s−1 so the stress in them was ∼0.6 MPa, but still enough for tensional failure in the upper ∼50 m. Most likely the shallow soft sediment failed through liquefaction and/or in a ductile manner, without obvious opening-mode cracks.
3.5 Failure of the Volcanic Pile Under Gravity
Faults with displacements of up to ∼40 m cut the volcanic edifice and its sediments and appear to have formed during or shortly after the S2 impact (Figures 2 and 4). As with shallow stiff sediments, dynamic stresses could bring the uppermost ∼1 km of the volcanic edifice to failure, but the observed strains were again much greater than reasonable dynamic strains (∼10−3) from incidence seismic waves. We suggest that seismic shaking led to cracking that greatly weakened the stiff sediments and the underlying volcanic edifice. The edifice failed under gravity producing large displacements and strains. Faults in the underlying rock became opening-mode fractures at shallow depths, including within the sediments.
The seismic velocity and density of the uppermost komatiite were higher than that for the stiff sediments so failure is expected. Assuming an S wave velocity of 4000 m s−1 and a density of 3000 kg m−3 yields a shear modulus of 48 GPa. A strain of 10−3 would produce 128 MPa of extensional stress that would exceed lithostatic minus hydrostatic pressure down to 32 km depth. (The simple model with a free surface is not valid at that depth.) Still, the upper few kilometers of the edifice could fail even if our estimated dynamic stresses and strains are high by a factor of a few. Overall, reasonable dynamic strains from the impact likely brought the komatiite pile to extensional and frictional failure.
We envision a process analogous to downslope movement of sackungen on moderate slopes, for example, near the San Andreas Fault [McCalpin and Hart, 2003; Sleep, 2011b] and continental margins from impact-generated waves [Parnell, 2008]. The observed event displacement ∼1 m of sackungen near the San Andreas Fault exceeds the dynamic displacement across the shallow layer within strong seismic waves from nearby earthquakes. Physically, the strong seismic waves took the material in the upper 10 s of meters beyond its frictional elastic limit. The failed material was quite weak as long as shaking persisted. The weakened material did not distinguish remote sources of stress and systematically slid downhill from forces from gravity while strong shaking persisted, on the order of 1 s for San Andreas events [Sleep, 2011b]. The well-known movement of an object down a vibrating ramp is analogous. Our impact differed from earthquakes on the San Andreas Fault in that shaking lasted far longer >100 s and that anelastic failure occurred within the komatiite pile not just within shallow regolith. Crosscutting relationships indicate that the major faults developed late when some spherules were already on the seafloor [Lowe et al., 2013]. Once damaged by the initial seismic waves, the edifice was likely unstable. It may have continued to fail on its own or when subsequent strong seismic waves arrived.
Returning to basic physics, considering downslope movement of very weak material from gravity on a slope provides an upper limit for displacements
where ϕ is the dip of the slope and t is the duration of strong shaking. Significant slip does occur on moderate slopes; we use 19° from sackungen in the San Gabriel Mountains near the San Andreas Fault [McCalpin and Hart, 2003], for example. Movement of 160, 620, and 1400 m would occur in 10, 20, and 30 s, respectively. The movements on a 2° slope are a factor of 10 less. Still material would move 1600 m in 100 s. It is thus reasonable that this process could produce ∼40 m of throw observed on our faults. We suspect that failure occurred on preexisting weaknesses in the volcanic edifice. Preexisting faults, sediment beds, and serpentinized regions are attractive (Figure 4).
Our site was likely a submarine plateau at the time of the impact. We do not have a modern geological analog, as our site persisted in an oceanic environment for ∼300 Ma with periods of ultramafic, mafic, and felsic volcanic and intrusive activity. Submarine plateaus and oceanic crust of this age do not exist on the modern Earth. This duration observation is compatible with the general inference from thermal modeling or geological observations that average plate rates in Archean were less than modern rates [Korenaga, 2008; Bradley, 2011].
The Kerguelen plateau in the southern Indian Ocean is an attractive mechanical and geological analog. It formed at 120 Ma from a starting plume head. Seafloor spreading on the Southeast Indian Ridge has separated the plateau from Broken Ridge that now lies west of the southern margin of Australia. The plume has subsequently backtracked across the plateau and now lies beneath it [Coffin et al., 2002]. Periods of volcanism alternated with periods of quiescence and sediment deposit at given sites, in analogy to our Onverwacht locality. There is some continental crust within Elan Bank [Ingle et al., 2002]. The plateau is complicated, escarpments with sustained slopes to ∼4° exist locally including around the Elan Bank [Rotstein et al., 1992].
Hawaii is another possible mechanical analog. The edifice spreads gravitationally with sedimentary rocks forming weak layers with the net effect of a fold and thrust belt at the toe of the edifice [Morgan et al., 2007]. The slope is ∼0.2 or 11°. Catastrophic slope failure has also occurred producing very large landslides.
4 Fig Tree Group Tectonic Aftermath
Even the general change in tectonic environment from the inactive mafic and ultramafic Onverwacht volcanic edifice to orogenic clastic sedimentation and associated felsic volcanism of the Fig Tree Group summarized by Lowe  is conceivably an effect of strong seismic waves from the impact. The lithosphere needs to fail and connect with other plate boundaries to start a new subduction zone. The scale depth of 100 s Rayleigh waves of ∼160 km implies significant dynamic stresses throughout the full lithospheric thickness. Far-field dynamic displacements and stresses approach those in the near field of earthquake faults that are known to continue rupture. High dynamic stresses persisted for over 100 s.
The pre-3.1 Ga geodynamic regime is poorly constrained, even to the point of evaluating the role of subduction-related tectonics in Archean. However, if some form of plate tectonics was effective at that early point in Earth history, we would speculate that large impacts like S2 could trigger activity along preexisting plate-boundary faults. In fact, much lower dynamic stresses in the far field of ordinary earthquakes suffice to trigger events [e.g., Hill, 2008]. With regard to starting new plate boundaries, intraplate stresses generally maintain midplate lithosphere near to frictional failure [e.g., Zoback and Townend, 2001], so dynamic stresses that are a significant fraction of the frictional strength suffice to trigger events. In our case, old oceanic lithosphere was likely under horizontal compression, perhaps from ridge-push effects, and the edge of the Onverwacht plateau produced local stress concentrations. Seismic waves could well have arrived perpendicular to the plateau margin and parallel to the ambient intraplate compressive stress. We know too little about global paleogeography to determine if this scenario had any relevance to the crustal damage observed at the time of the S2 impact, but note that there would then be a tendency for thrust faults carrying ocean lithosphere under the plateau to nucleate during times of strong dynamic compression. These faults could then have evolved into a subduction zone dipping beneath the plateau, perhaps associated with the initiation of felsic volcanism that was characteristic of Fig Tree time.
Opening-mode dikes deformed the uppermost Onverwacht Group soon before impact spherules arrived at the seafloor. Deformation continued while spherules arrived. Strong currents, likely associated with tsunamis, then swept the seafloor. This sequence is expected several crater diameters from the impact site, but we have no way to obtain a precise estimate.
Calculations indicate that both P waves and Rayleigh waves from the impact greatly exceeded the amplitude of waves from ordinary earthquakes with particle velocities of 3 m s−1. The duration of strong shaking was over 1000 s, far longer than that of ordinary strong earthquake waves. Dynamic strains were ∼10−3, which greatly exceeded the elastic limit for opening-mode dikes in stiff, lithified sedimentary rock and the limit for opening-mode dikes and faulting observed in the upper volcanic section. This deformation occurred preferentially when dynamic stresses and strains produced horizontal tension.
The anelastic observed strain (dike opening per horizontal length) of a few percent is much greater than the computed dynamic strain. Rock weakened by the strong seismic waves likely moved downslope under the influence of gravity. This process required that the Onverwacht rocks were near an edge of a submarine plateau. Furthermore, seismic waves arriving perpendicular to bathymetric contours would preferentially produce dynamic downslope motions. We do not have good constraints on the local paleogeography of Onverwacht rocks at the time of the impact.
Sedimentation changed from fine-grained deep water sediments of the uppermost Onverwacht Group to clastic sediments at the start of Fig Tree time. These Fig Tree sediments were, in part, derived by erosion of Mendon Formation rocks (Figure 2). Local uplift along faults does occur within seismically driven sackungen [e.g., McCalpin and Hart, 2003], so it is not unexpected during gravitational failure of a volcanic edifice. The main mechanical requirement is that the net movement of mass was downhill, for example, in the tilting of a large mostly intact block.
Appendix A: Properties of Seismic Waves
We summarize well-known properties of seismic waves in Cartesian coordinates for use in the main text following the work of Bullen and Bolt . A P wave produces movement in its direction of propagation x1. The displacement in this direction for a monochromatic wave with angular frequency ω = 2π/TP (where TP is period) is
where UP is the scalar displacement amplitude, kP is the wave number for P waves, and t is the time. The P wave propagates at a seismic velocity of α = ω/kP. The particle velocity is
where i indicates that the velocity is 90° out-of-phase with the displacement. The dynamic normal stress on a plane perpendicular to the direction of propagation is proportional to the dynamic strain
where G is shear modulus and λ is the second Lamé constant. Compression is negative in the traditional sign convention. Hence P wave motion polarity in the direction of propagation produces compression. From (A2) and (A3), stress is in-phase with particle velocity. In terms of scalar peak particle velocity VP, the peak stress normal to the direction of propagation is
where ρ is the density and the P wave velocity is . The maximum scalar strain in the direction of propagation is VP/α.
A P wave also produces normal stresses
perpendicular to its direction of propagation. The resolved shear stress on planes 45° to the direction of propagation. The maximum stress is
The second invariant of deviatoric stress (normalized so that it yields the shear stress in simple shear) is the basis of more sophisticated failure criteria that are not needed at our attempted level of precision.
The derivation for S waves is analogous. The plane wave again propagates in the x1 direction and produces motion perpendicular to the propagation direction here x2,
where US is the peak particle displacement of the S wave, the wave number is, kS = ω/β and is the velocity of S waves. The maximum scalar shear traction on planes perpendicular to the direction of propagation is
where VS is the peak S wave particle velocity.
Appendix B: Dynamic Model of Impact
Meschede et al.  presented a dynamic model for seismic waves based on conservation of momentum. We discuss this model to rescale its results from the Chicxulub impactor to an Archean impactor with ∼90 times its mass and similar velocity.
Meschede et al.  represent the net effect of the impact as a spatial point force with amplitude that varies over the time. Retaining scalars with the intent of obtaining dimensional relationships, the point force is
where F = MAVA is the momentum of the asteroid of mass MA and impact velocity VA. Meschede et al.  assumed the normalized time function
The time scale TA denotes the period below which the amplitude of radiated waves is decreased by 1/e from the long period limit. The dominant period of waves on a velocity seismogram and hence the dominant period of dynamic stress is .
The total energy of radiated seismic waves is
where the material properties α, β, and ρ are those of the target [Meschede et al., 2011]. The kinetic energy of the projectile is
Thus the seismic efficiency is
Meschede et al.  argued that the seismic efficiency though unknown should not vary a lot over a moderate range of projectile size. They provided examples for Chicxulub with efficiencies of 10−4 and 3 × 10−4 and periods of 58 and 20 s. For reference, Ivanov  obtained periods of 10–20 s at ∼300 km distance from numerically modeling Chicxulub. Equation (B5) provides an estimate of the characteristic period TA of the Archean impactor, scaling for its factor of ∼90 greater mass from the Chicxulub result. There is no cause to rescale for target physical parameters in (B5) given our ignorance of the Archean target geology and of the actual mass of the projectile. Specifically, the period TA thus scales with . So the Archean event had a period a factor of 4.5 greater than the Chicxulub event. The 100 s period assumed in calculations is thus grossly appropriate. The dominant period for teleseismic P waves generated at great depth is likely to be less than that for surface waves generated at shallower depths if their seismic efficiency in fact increases with wave generation depth.
Appendix C: Descent Time of Rock Rain
We apply basic physics of the behavior of water rain to obtain the descent time of rock rain following an impact. The main differences are that rock rain forms high (∼70 km) in the atmosphere and is optically thick to thermal radiation after a major impact [Goldin and Melosh, 2009]. Rock rain likely freezes like sleet as it falls [see Goldin and Melosh, 2009], which locks in the drop size. The physical properties of rock rain and rock sleet also differ modestly from those of water. We use the typical diameter ∼1 mm of our spherules for example calculation using analogies with water rain.
Droplets descend at a velocity where their flux of kinetic energy into the air balances the energy flux from gravity
where ρdrop ≈ 3000 kg m−3 is the density of the drop, ρair ≈ 1.3 kg m−3 near the surface, and d is the drop diameter [Villermaux and Bossa, 2009]. It is not critical to precisely know Archean air density as the descent rate depends on its square root. Drops with 1 mm diameter fall at ∼5 m s−1. The density of air decreases upward with a scale length L of now ∼8 km. Falling drops spend most of their time in the lower atmosphere, so that the descent time L/U = 1600 s gives an estimate. Frozen spherules descended to the seabed. Quartz grains of 1 mm diameter sinking through water provide a proxy [Gibbs et al., 1971]. The descent rate is 15.34 cm/s or 6500 s to sink 1000 m.
It is conceivable that the sinking particles organized into density currents in analogy to tephra falling into the deep sea [e.g., Carey, 1997]. We consider this possibility unlikely. The impact spherules did not all arrive at the top of atmosphere at the same time at our site as they had different orbits [Collins et al., 2005]. They did not settle through the atmosphere at the same rate, as they were not all the same size. Our computed orbital time and atmospheric descent times, both 1600 s, give a crude duration of the arrival of spherules at the sea surface. Accumulation rate of a (rounded) 0.1 m thick layer of spherules was thus ∼0.2 kg m−3 s−1. The tephra studied by Carey  fell at 5.6 × 10−4 kg m−3 s−1 (2 kg m−3 h−1). This tephra was very fine grained. Individual particles sank at ∼0.2 cm s−1 and accumulated at shallow sea depths until density currents descended at ∼2 cm s−1. Our individual particles sank at a faster rate than these currents. They were dispersed over a depth range of at least 100 m. They changed the density of this water column by ∼0.23%. This change may have been insufficient to overcome ambient stratification of the Archean ocean. (We do not attempt to deduce Archean oceanography.) For reference, the density of water changes by 0.27% between 10°C and 25°C and 0.9% between 40°C and 60°C. Still our computed settling rate should be regarded as a minimum.
The spherules while liquid had to descend without fragmenting. The balance between surface tension and drag forces a maximum drop size
where γ is equivalently surface tension and surface free energy; excessively large drops rarely collide with other drops before they become unstable [Villermaux and Bossa, 2009]. The critical size in (C2) does not involve the density of air and hence elevation. The surface free energy of mafic silicate liquid is 0.36 J m−2 [Proussevitch and Sahagian, 1998], somewhat greater than that of water 0.06 [Villermaux and Bossa, 2009]. The maximum drop size 8.5 mm for rock rain is modestly greater than that of water rain 3 mm. Survival of the observed ∼1 mm rock drops during their descent is thus reasonable.
Gareth Collins critically reviewed an earlier draft and the final version. John Spray critically reviewed the final version. This work was performed as part of collaboration with the NASA Astrobiology Institute Virtual Planetary Laboratory Lead Team. Grants from the NASA Exobiology Program contributed to this research during its earliest stages. This research was supported by the Southern California Earthquake Center. SCEC is funded by NSF Cooperative Agreement EAR-0106924 and USGS Cooperative Agreement 02HQAG0008. The SCEC contribution number for this paper is 1915.