AGU Norman Sleep

RESEARCH ARTICLE

10.1002/2014GC005229

Physics of crustal fracturing and chert dike formation triggered

by asteroid impact, ~3.26 Ga, Barberton greenstone belt,

South Africa

Norman H. Sleep

and Donald R. Lowe

Department of Geophysics, Stanford University, Stanford, California, USA,

Department of Geological and Environmental

Sciences, Stanford University, Stanford, California, USA

Abstract Archean asteroid impacts, reﬂected in the presence of spherule beds in the 3.2–3.5 Ga Barber-

ton 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 dam-

aged 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

occurred from the surface and downward throughout the lithosphere. Shaking weakened the Onver-

wacht 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.

1. Introduction

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 struc-

tures 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 carbona-

ceous 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 [2013] 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 summa-

rize these results to examine the physics related to this process. We consider only data obtained south of

Key Points:

 Archean asteroid impact produced

extreme seismic waves

 Waves damaged shallow subsurface

at teleseismic distance

 Net movement of material by gravity

occurred during shaking

Correspondence to:

N. H. Sleep,

norm@stanford.edu

Citation:

Sleep, N. H., and D. R. Lowe (2014),

Physics of crusta l fracturing and chert

dike formation triggered by asteroid

impact, 3.26 Ga, Barberton

greenstone belt, South Africa,

Geochem. Geophys. Geosyst., 15, 1054–

1070, doi:10.1002/2014GC005229.

Received 6 JAN 2014

Accepted 27 FEB 2014

Accepted article online 3 MAR 2014

Published online 14 APR 2014

SLEEP AND LOWE

Geochemistry, Geophysics, Geosystems

PUBLICATIONS

the Inyoka Fault, as units north

of the fault are not closely corre-

lated 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 after-

math 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 unlithi-

ﬁed sediments capped the vol-

canic sequence at the time of

spherule deposition. Lowe

[2013] 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 pot-

ash contents suggest that these

were ﬁne tuffaceous and possi-

bly 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

Figure 1. Schematic diagram showing the four types of chert dikes and veins their rela-

tionships to one another and to stratigraphy. Type 1 large, irregular dikes extend down-

ward through both the sedimentary and volcanic parts of the Mendon Formation. They

cut across and are younger than the smaller, verti cal, Type 2 dikes that are largely

restricted to Mc1, the lower laminated part of the Mendon chert section, which was lithi-

ﬁed at the time of dike formation. Smaller Type 3 and 4 chert veins also occur mainly in

Mc3 and also associated with Type 1 dikes in Mc2. From Lowe [2013].

Geochemistry, Geophysics, Geosystems 10.1002/2014GC005229

SLEEP AND LOWE

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 precipi-

tative 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 ten-

sion fractures in the lower, lithiﬁed part of the sedimentary section (Mc1). Later seismic events triggered for-

mation 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 frac-

tures 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., W

€

unnemann 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 C.

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

Figure 2. Generalized strike-parallel cross section with faults F2 and F3. The stratigraphic complexity of the Fig Tree Group reﬂects crustal

disturbances associated with events at the Fig Tree-Onverwacht contact. The small fan delta (red) was derived from uplifts of the Mendon

cherts to north and lenses out to the south into ﬁner conglomerate and sandstone. The small minibasin developed at the Onverwacht-Fig

Tree contact is shown below the circled number 1. A chert dike complex is associated with fault F3. After Lowe [2013].

Geochemistry, Geophysics, Geosystems 10.1002/2014GC005229

SLEEP AND LOWE

Melosh [2012] 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 ini-

tial precurrent thickness is not precisely constrained. Johnson and Melosh [2012] 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

impact velocity, and equal projectile and target

densities from equations (22) and (27) of Collins et al. [2005]. We use the rounded value of 500 km in exam-

ple calculations. Our calculations are easily rescaled and do not depend critically on these values. See Bottke

et al. [2012] 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 se ismic waves. The mod ern mantle values are a good guide

to the Archean mantle. The main difference is that Earth’s interior has likely cooled som e 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 value s. These differences are similar to those between you ng and old oceanic lithosp here

on the modern Earth, a few percent in densi ty and seismic wave velocity [e.g., Weidner, 1974]. We do not

attemp t to obtain resu lts to the precision req uiring 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 A. The mantle P wave velocity a5

ﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ

ðk12GÞ=q

[Bullen and Bolt, 1985, pp. 88] is 8000 m s

and

S wave velocity b 5

ﬃﬃﬃﬃﬃﬃﬃﬃ

G=q

[Bullen and Bolt, 1985, pp. 88] is 4600 m s

. Mantle density q is 3300 kg m

The Lam



e constants are approximately equal in the mantle G  k.

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 pro-

vide 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

for both phase and group velocity in simple calculations.

Additional geometrical spreading occurs because Rayleigh waves are dispersive, that is, waves with differ-

ent frequencies have different group velocities and arrive at different times. In section 2.2, 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 [2005] and Senft and Stewart [2009] 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 hydro-

dynamic phase of cratering lasted for a time, T

, given by

50:54

ﬃﬃﬃﬃﬃﬃﬃﬃ

D=g

; (1)

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 fol-

low the calculation and compare related quantities.) For comparison, the time for the 180 km diameter

Geochemistry, Geophysics, Geosystems 10.1002/2014GC005229

SLEEP AND LOWE

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 B. We use the rounded value of 100 s in example cal-

culations for the dominant period of seismic waves on velocity seismograms that are relevant to dynamic

stress (Appendix A). 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

[1989] and Meschede et al. [2011, Figure 1] stated that about 10

of the impact energy (with the wide

range of 10

210

) becomes seismic waves that propagate away from crater (see Appendix B). Kinetic

energy W of a projectile scales with its mass and the cube of its diameter. Moment magnitude scales with

log

ðWÞ. Melosh [1989] gave that M 5 4.8 for a 30 m diameter projectile, so even a 30 km diameter pro-

jectile (with 10

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, Hugo-

niot 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). Con-

versely, 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., Timo-

shenko 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

21/2

of the peak velocity for a sinusoidal wave.

We apply these criteria using basic properties of seismic waves considered in Appendix A. 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. [2011] to account for

this difference.

Transient cavity

P-waves

1.6 Final crater diamter

Rayleigh wavesRayleigh waves

Nonlinear region

Transient cavity

Ejecta

Rock strength

Friction

Figure 3. Schematic diagram illustrates the generation of seismic waves during an impact. The shaded region below the transient cavity

behaves as a ﬂuid. Elastic seismic waves are generated at its edge where rock fails in friction. An inner boundary where dynamic stresses

exceed short-term rock strength (dashed) was also used to model P waves. Both approximations give similar values of far-ﬁeld P wave

amplitude for 45 km diameter projectiles. Rayleigh waves are generated about 0.8 crater diameters from the center and at shallower

depths than P waves.

Geochemistry, Geophysics, Geosystems 10.1002/2014GC005229

SLEEP AND LOWE

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 typi-

cally  0.1 G. [Poirier, 1990, pp. 38], here 7 GPa for b 5 4600 m s

in the upper mantle. The correspond-

ing particle velocity from (A4) and (A6) is 800 m s

. 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 r

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 par-

ticle velocity at this limit is 270 m s

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 fol-

lowing Meschede et al. [2011]. To the ﬁrst order, the projectile transfers its momentum to a hemispherical

shocked annulus of radius r

and thickness 2r

[Melosh, 1989, pp. 54],

4pq



Shock

½2pr

ð2r

Þq; (2)

where V

is the velocity of the asteroid at impact, V

Shock

is the particle velocity in the shocked region, q

the density of the asteroid, r

is the radius of the asteroid, and q 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 par-

ticle velocity is 270 m s

yields 112 km depth, assuming a 45 km diameter asteroid hitting at 20 km s

[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 qV

=2 [e.g., Timoshenko and Goodier, 1970, pp. 491]. This

energy is initially spread over part of a spherical shell of radius r

and surface area proportional to r

, when

by assumption its propagation became elastic. The energy in the shell is proportional to qV

Shock

. The

energy then spreads over a shell of radius r

prop

scaling with the propagation distance. The peak P wave

amplitude is thus approximately V

 V

Shock

prop

distance. The predicted peak amplitude is a modest

function of teleseismic distance. For example, the peak amplitude at 45



5 5000 km distance is 6 m s

A more accurate calculation would take account of actual raypaths in the mantle.

The experiments modeled by Ahrens and O’Keefe [1977] involved centimeter-sized projectiles where ambi-

ent pressure within the target is negligible compared with the Hugoniot elastic limit. The lithostatic pres-

sure 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

as the slip velocity for signiﬁcant fault weakening in their models

successful of Chicxulub. The calculations of Collins et al. [2008] also assume that such weakening in fact hap-

pens. The shear stress at frictional failure is then

frict

5lqgZ5

; (3)

where l  0.7 is the coefﬁcient of friction, Z is the depth, a is the P wave velocity, and V

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 r

. In analogy with (2), momentum conservation implies

Geochemistry, Geophysics, Geosystems 10.1002/2014GC005229

SLEEP AND LOWE

4pq



2pr

ð2r

Þq



3lgr



2pr

ð2r

Þq



; (4)

which yields 110 km with a particle velocity of 282 m s

and r

5 22.5 km is the asteroid radius. The parti-

cle velocity at 45



is 6 m s

, our previous estimate based on plasticity.

The computed particle velocity of 6ms

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

[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

suggested for Ordovician continental margin failure suggested by Parnell [2008]. It is comparable to 10 m s

computed by Ivanov [2005] for 300 km from the Chicxulub impact.

As a caveat, we summarize ways in which large craters differ from underground nuclear explosions. The per-

haps 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 fric-

tion 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. Compli-

cated 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 com-

pared 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 r

rad

sin ðh

rad

Þ, where R

is the radius of the Earth and h

rad

is the angular

separation. The total energy in the annulus is proportional to V

rad

, where V

rad

is the particle velocity at

the annulus. Ignoring dispersion, the wave annulus spreads out to angular separation h

prop

, where the total

energy is proportional to V

prop

sin ðh

prop

Þ, where the peak particle velocity is V

prop

. Hence, the peak parti-

cle velocity varies as

prop

rad

sqrt

sinðh

rad

sin ðh

prop



: (5)

It is thus not necessary to know the angular separation precisely. For example, the amplitude in (5)

decreases by 2

21/2

5 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 Ray-

leigh wave at that distance. The diameter of the crater D is a natural length scale. Melosh [1989] 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 pD or 1260 km.

Crustal earthquakes provide some analogy to faulting in the shallow annulus away from the crater that gen-

erates 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

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

Geochemistry, Geophysics, Geosystems 10.1002/2014GC005229

SLEEP AND LOWE

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 V

rad

from this inference should be around 10–15 m s

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. Non-

linear 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 p 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/c

Ray

, where V is the scalar particle

velocity and c

Ray

is the Rayleigh wave phase velocity. The dynamic shear stress is this quantity times the

shear modulus, s

 GV=c

Ray

5qb

V=c

Ray

, where density q and shear wave velocity b are evaluated at

points within the Earth. For reference, the dynamic stress is 174 MPa for mantle properties and 10 m s

particle velocity. The ratio of dynamic stress to frictional strength in (3) is

frict

Ray

lgZ

: (6)

Failure occurs when the ratio is greater than 1, for l 5 0.7 above the depth of 8 km. This depth is 6 km

assuming 4 km s

S 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

. We do not dis-

tinguish 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. Spher-

ules 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



5 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 con-

tinued 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

. They arrived at the top of the atmosphere 1600 s, 45



from

the impact using the code of Collins et al. [2005].

The tsunamis are much slower than seismic waves. Their velocity in the open ocean is

tsunami

ﬃﬃﬃﬃﬃﬃ

; (7)

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

. 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 C, spherules would have spent most of their transit time sinking through the ocean if it was deep,

Geochemistry, Geophysics, Geosystems 10.1002/2014GC005229

SLEEP AND LOWE

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 pla-

teau 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 hun-

dreds 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 tsu-

nami 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 pla-

teau, rather than abyssal depths much

greater than 1 km.

3.2. Incident Seismic Waves

The BGB site was several crater diame-

ters from the impact where static

strains (the permanent change before

and after the impact in distance

between two points per horizontal dis-

tance 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 ten-

sion 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 @U

=@x

had its mantle value, which is dimensionally V

for P waves where the particle velocity V

is 8ms

from the frictional model in section 3.3. 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 3ms

. Dynamic strain for Rayleigh waves is V

prop

Ray

where

prop

is 3 m s

and c

Ray

is phase velocity 4000 m s

. The dynamic strain in both cases was thus 10

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 subduc-

tion zone [Allmendinger and Gonz



alez, 2010; Arriagada et al., 2011]. These fractures formed and were reacti-

vated 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

Figure 4. (a) Schema tic diagram of the failure of a volcanic ediﬁce under gravity

during strong seismic shaking. Faults that cut the volcanic rocks and the overlying

sediments probably root within serpentine layers, which constitute the bulk of

the volcanic rocks in the Mendon Formation. Extreme vertical exaggeration. (b)

Type 1 veins formed near the outcrop of the fault. Type 2 veins are tension frac-

tures in stiff sedime nt.

Geochemistry, Geophysics, Geosystems 10.1002/2014GC005229

SLEEP AND LOWE

envision an analogous process of downslope movement through collapse along the edge of the Onver-

wacht 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 seis-

mic 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 [2008] proposed that strong seismic waves from cosmic impacts

destabilized continental margins in the Ordovician Period. Ivanov [2005] obtained 10 m s

particle veloc-

ity 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 trig-

gering 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

. 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 (q

sed

– q

water

)gZ,

where q

sed

and q

water

are sediment and water density. We show that vertical cracking is expected in shallow

stiff rocks for imposed horizontal extensional strain, here 10

. The formula for stresses from the extension

of a sheet in one direction provides a simple estimate of dynamic stress

ð12v





G; (8)

where E52ð11vÞG is Young’s modulus, m5k=2ðk1GÞ is Poisson’s ratio, and the approximate equality

assumes k 5 G [e.g., Turcotte and Schubert, 2002, pp. 114]. Our lithiﬁed sediments likely had an S wave veloc-

ity of 2000 m s

and a density of 2200 kg m

, so the shear modulus was 9 GPa using G 5 qb

strain of 10

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

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

) 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

and a density of 3000 kg m

yields a

shear modulus of 48 GPa. A strain of 10

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

Geochemistry, Geophysics, Geosystems 10.1002/2014GC005229

SLEEP AND LOWE

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 weak-

ened 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

D 

g sin ð/Þt

; (9)

where / is the dip of the slope and t is the duration of strong shaking. Signiﬁcant slip does occur on moder-

ate 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, respec-

tively. 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 vol-

canic 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 obser-

vations that average plate rates in Archean were less than modern rates [Korenaga,2008;Bra dley, 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 sepa-

rated 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 vol-

canic ediﬁce to orogenic clastic sedimentation and associated felsic volcanism of the Fig Tree Group sum-

marized by Lowe [2013] 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

Geochemistry, Geophysics, Geosystems 10.1002/2014GC005229

SLEEP AND LOWE

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 oce-

anic 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 per-

pendicular to the plateau margin and parallel to the ambient intraplate compressive stress. We know too lit-

tle 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 carry-

ing 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.

5. Conclusions

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 tsuna-

mis, 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 ampli-

tude of waves from ordinary earthquakes with particle velocities of 3 m s

. The duration of strong shaking

was over 1000 s, far longer than that of ordinary strong earthquake waves. Dynamic strains were 10

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 se ismic waves in Cartesian coordin ates for use in the main text follow-

ing the work of Bullen and Bolt [1985]. A P wave produces movement in its direction of propagation x

. The dis-

placement in this direction for a monochromatic wave with angular frequency x 5 2p/T

(where T

is period) is

exp ½iðk

2xtÞ ; (A1)

where U

is the scalar displacement amplitude, k

is the wave number for P waves, and t is the time. The P

wave propagates at a seismic velocity of a 5 x/k

. The particle velocity is

Geochemistry, Geophysics, Geosystems 10.1002/2014GC005229

SLEEP AND LOWE

5ixU

exp ½iðk

2xtÞ; (A2)

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

5ðk12GÞ

52ðk12GÞik

exp ½iðk

2xtÞ; (A3)

where G is shear modulus and k is the second Lam



e 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 V

, the

peak stress normal to the direction of propagation is

11Max

ðk12GÞk



qa; (A4)

where q is the density and the P wave velocity is a5

ﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ

ðk12GÞ=q

. The maximum scalar strain in the direc-

tion of propagation is V

/a.

A P wave also produces normal stresses

; (A5)

perpendicular to its direction of propagation. The resolved shear stress on planes 45



to the direction of

propagation. The maximum stress is



k12G



11Max



: (A6)

The second invariant of deviatoric stress

ﬃﬃﬃﬃﬃﬃﬃﬃ

(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 x

direction and produces

motion perpendicular to the propagation direction here x

exp ½iðk

2xtÞ ; (A7)

where U

is the peak particle displacement of the S wave, the wave number is, k

5 x/b and b 5

ﬃﬃﬃﬃﬃﬃﬃﬃ

G=q

the velocity of S waves. The maximum scalar shear traction on planes perpendicular to the direction of

propagation is



qb; (A8)

where V

is the peak S wave particle velocity.

Appendix B: Dynamic Model of Impact

Meschede et al. [2011] 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. [2011] 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

Geochemistry, Geophysics, Geosystems 10.1002/2014GC005229

SLEEP AND LOWE

f 5FSðtÞ; (B1)

where F 5 M

is the momentum of the asteroid of mass M

and impact velocity V

. Meschede et al. [2011]

assumed the normalized time function

SðtÞ5

ﬃﬃﬃﬃﬃ

exp ð2p

Þ: (B2)

The time scale T

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 domi-

nant period of dynamic stress is

ﬃﬃﬃ

The total energy of radiated seismic waves is

seis

3=2

5=2



; (B3)

where the material properties a, b, and q are those of the target [Meschede et al., 2011]. The kinetic energy

of the projectile is

: (B4)

Thus the seismic efﬁciency is

seis

kin

3=2



: (B5)

Meschede et al. [2011] argued that the seismic efﬁciency though unknown should not vary a lot over a moderate

range of projectile size. TheyprovidedexamplesforChicxulub with efﬁciencies of 10

and 3 3 10

and peri-

ods of 58 and 20 s. For reference , Ivanov [2005] obtained periods of 10–20 s at 300 km distance from numeri-

cally mod eling Chicxulub. Equation (B5) provides an estimate of the characteristic period T

of the Archean

impactor, scaling for its factor of 90 greater mass from the Chicxulub result. There is no cause to rescale for tar-

get physical parameters in (B5) given our ignorance of the Archean target geology and of the actual mass of

the projectile. Speciﬁcally, the period T

thus scales with M

1=3

. So the Archean event had a period a factor of 4.5

greater than the Chicxulub event. The 100 s period assumedincalculationsisthusgrosslyappropriate.The

dom inant 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

ﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ

drop

air

; (C1)

where q

drop

 3000 kg m

is the density of the drop, q

air

 1.3 kg m

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

Geochemistry, Geophysics, Geosystems 10.1002/2014GC005229

SLEEP AND LOWE

rate depends on its square root. Drops with 1 mm diameter fall at  5ms

. 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 atmos-

phere, so that the descent time L/U 5 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

The tephra studied by Carey [1997] fell at 5.6 3 10

kg m

(2 kg m

). This tephra was very ﬁne

grained. Individual particles sank at 0.2 cm s

and accumulated at shallow sea depths until density cur-

rents descended at 2cms

. 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

max

ﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ

drop

; (C2)

where c 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

[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.

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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

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