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AGU Norman Sleep

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
1
and Donald R. Lowe
2
1
Department of Geophysics, Stanford University, Stanford, California, USA,
2
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
23
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
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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].
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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].
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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
21
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
p
[Bullen and Bolt, 1985, pp. 88] is 8000 m s
21
and
S wave velocity b 5
ffiffiffiffiffiffiffiffi
G=q
p
[Bullen and Bolt, 1985, pp. 88] is 4600 m s
21
. Mantle density q is 3300 kg m
23
.
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
21
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
f
, given by
T
f
50:54
ffiffiffiffiffiffiffiffi
D=g
p
; (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
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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
24
of the impact energy (with the wide
range of 10
23
210
25
) 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
2
3
log
10
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
9
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
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.
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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
21
in the upper mantle. The correspond-
ing particle velocity from (A4) and (A6) is 800 m s
21
. 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
11
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
21
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
S
and thickness 2r
A
[Melosh, 1989, pp. 54],
V
A
4pq
A
r
3
A
3

5V
Shock
½2pr
2
S
ð2r
A
Þq; (2)
where V
A
is the velocity of the asteroid at impact, V
Shock
is the particle velocity in the shocked region, q
A
is
the density of the asteroid, r
A
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
21
yields 112 km depth, assuming a 45 km diameter asteroid hitting at 20 km s
21
[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
P
=2 [e.g., Timoshenko and Goodier, 1970, pp. 491]. This
energy is initially spread over part of a spherical shell of radius r
S
and surface area proportional to r
2
S
, when
by assumption its propagation became elastic. The energy in the shell is proportional to qV
2
Shock
r
2
S
. 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
P
V
Shock
r
S
=r
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
21
.
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
21
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
s
frict
5lqgZ5
qV
F
a
3
; (3)
where l 0.7 is the coefficient of friction, Z is the depth, a is the P wave velocity, and V
F
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
F
. In analogy with (2), momentum conservation implies
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V
A
4pq
A
r
3
A
3

5V
F
2pr
2
F
ð2r
A
Þq

5
3lgr
F
a

2pr
2
F
ð2r
A
Þq

; (4)
which yields 110 km with a particle velocity of 282 m s
21
and r
A
5 22.5 km is the asteroid radius. The parti-
cle velocity at 45
is 6 m s
21
, our previous estimate based on plasticity.
The computed particle velocity of 6ms
21
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
ms
21
[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
21
suggested for Ordovician continental margin failure suggested by Parnell [2008]. It is comparable to 10 m s
21
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
5R
E
sin ðh
rad
Þ, where R
E
is the radius of the Earth and h
rad
is the angular
separation. The total energy in the annulus is proportional to V
2
rad
r
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
2
prop
R
E
sin ðh
prop
Þ, where the peak particle velocity is V
prop
. Hence, the peak parti-
cle velocity varies as
V
prop
5V
rad
sqrt
sinðh
rad
Þ
sin ðh
prop
Þ

: (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
21
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
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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
21
.
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
D
GV=c
Ray
5qb
2
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
21
particle velocity. The ratio of dynamic stress to frictional strength in (3) is
s
D
s
frict
5
b
2
V
c
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
21
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
21
. 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
21
. 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
U
tsunami
5
ffiffiffiffiffiffi
hg
p
; (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
21
. 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,
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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
1
=@x
1
had its mantle value, which is dimensionally V
P
/a
for P waves where the particle velocity V
P
is 8ms
21
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
21
. Dynamic strain for Rayleigh waves is V
prop
/c
Ray
where
V
prop
is 3 m s
21
and c
Ray
is phase velocity 4000 m s
21
. The dynamic strain in both cases was thus 10
23
.
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.
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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
21
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
23
. 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
23
. The formula for stresses from the extension
of a sheet in one direction provides a simple estimate of dynamic stress
r
11
5e
11
E
ð12v
2
Þ

8
3
e
11
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
21
and a density of 2200 kg m
23
, so the shear modulus was 9 GPa using G 5 qb
2
.A
strain of 10
23
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
21
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
23
) 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
21
and a density of 3000 kg m
23
yields a
shear modulus of 48 GPa. A strain of 10
23
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
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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
2
2
; (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
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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
21
. The duration of strong shaking
was over 1000 s, far longer than that of ordinary strong earthquake waves. Dynamic strains were 10
23
,
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
1
. The dis-
placement in this direction for a monochromatic wave with angular frequency x 5 2p/T
P
(where T
P
is period) is
U
1
5U
P
exp ½iðk
P
x
1
2xtÞ ; (A1)
where U
P
is the scalar displacement amplitude, k
P
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
P
. The particle velocity is
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V
1
5
@U
1
@t
5ixU
P
exp ½iðk
P
x
1
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
r
11
5ðk12GÞ
@U
1
@x
1
52ðk12GÞik
P
U
P
exp ½iðk
P
x
1
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
P
, the
peak stress normal to the direction of propagation is
r
11Max
5V
P
ðk12GÞk
P
x

5V
P
qa; (A4)
where q is the density and the P wave velocity is a5
ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
ðk12GÞ=q
p
. The maximum scalar strain in the direc-
tion of propagation is V
P
/a.
A P wave also produces normal stresses
r
22
5r
33
5k
@U
1
@x
1
; (A5)
perpendicular to its direction of propagation. The resolved shear stress on planes 45
to the direction of
propagation. The maximum stress is
s
P
5
r
11
2r
22
2
5
r
11
2r
33
2
5
G
k12G

r
11Max
jj
5
r
11Max
3
: (A6)
The second invariant of deviatoric stress
ffiffiffiffiffiffiffiffi
s
ij
s
ij
p
(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
1
direction and produces
motion perpendicular to the propagation direction here x
2
,
U
2
5U
S
exp ½iðk
S
x
1
2xtÞ ; (A7)
where U
S
is the peak particle displacement of the S wave, the wave number is, k
S
5 x/b and b 5
ffiffiffiffiffiffiffiffi
G=q
p
is
the velocity of S waves. The maximum scalar shear traction on planes perpendicular to the direction of
propagation is
s
S
5V
S
Gk
S
x

5V
S
qb; (A8)
where V
S
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
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f 5FSðtÞ; (B1)
where F 5 M
A
V
A
is the momentum of the asteroid of mass M
A
and impact velocity V
A
. Meschede et al. [2011]
assumed the normalized time function
SðtÞ5
ffiffiffiffi
p
T
2
A
r
exp ð2p
2
t
2
=T
2
A
Þ: (B2)
The time scale T
A
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
2
p
T
A
.
The total energy of radiated seismic waves is
E
seis
5
F
2
p
3=2
2
5=2
T
3
A
q
1
3a
3
1
2
3b
3

; (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
W5
m
A
V
2
A
2
: (B4)
Thus the seismic efficiency is
E
seis
E
kin
5
m
A
p
3=2
2
3=2
T
3
A
q
1
3a
3
1
2
3b
3

: (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
24
and 3 3 10
24
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
A
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
A
thus scales with M
1=3
A
. 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
U5
ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
q
drop
gd
q
air
s
; (C1)
where q
drop
3000 kg m
23
is the density of the drop, q
air
1.3 kg m
23
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
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rate depends on its square root. Drops with 1 mm diameter fall at 5ms
21
. 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
23
s
21
.
The tephra studied by Carey [1997] fell at 5.6 3 10
24
kg m
23
s
21
(2 kg m
23
h
21
). This tephra was very fine
grained. Individual particles sank at 0.2 cm s
21
and accumulated at shallow sea depths until density cur-
rents descended at 2cms
21
. 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
d
max
5
ffiffiffiffiffiffiffiffiffiffiffiffi
6c
q
drop
g
s
; (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
22
[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.
References
Ahrens, T. J., and J. D. O’Keefe (1977), Equations of state and impact-induced shock-wave attenuation on the moon, in Impact and Explosion
Cratering, edited by D. J. Roddy, R. O. Pepin, and R. B. Merrill, pp. 639–656, Pergamon, New York.
Allmendinger, R. W., and G. Gonz
alez (2010), Invited review paper: Neogene to Quaternary tectonics of the coastal Cordillera, nor thern
Chile, Tectonophysics, 495, 93–110.
Andrews, D. J., T. C. Hanks, and J. W. Whitney (2007), Physical limits on ground motion at Yucca Mountain, Bull. Seismol. Soc. Am., 97(6),
1771–1792, doi:10.1785/0120070014.
Arriagada, C., et al. (2011), Nature and tectonic significance of co-seismic structures associated with the Mw 8.8 Maule earthquake, central-
southern Chile forearc, J. Struct. Geol., 33, 891–897.
Artemieva, N., and J. Morgan (2009), Modeling the formation of the K–Pg boundary layer, Icarus, 201, 768–780.
Beeler, N. M., T. E. Tullis, and D. L. Goldsby (2008), Constitutive relationships and physical basis of fault strength due to flash heating, J. Geo-
phys. Res., 113, B01401, doi:10.1029/2007JB004988.
Bottke, W. F., et al. (2012), An Archaean heavy bombardment from a destabilized exte nsion of the asteroid belt, Nature, 485, 78–81, doi:
10.1038/nature10967.
Bradley, D. C. (2011), Secular trends in the geologic record and the supercontinent cycle, Earth Sci. Rev., 108, 16–33.
Brune, J. N. (2001), Shattered rock and precarious rock evidence for strong asymmetry in ground motions during thrust faulting, Bull. Seis-
mol. Soc. Am., 91(3), 441–447.
Bullen, K. E., and B. A. Bolt (1985), An Introduction to the Theory of Seismology, 4th ed., 499 pp., Cambridge Univ. Press, Cambridge, U. K.
Carey, S. (1997), Influence of convective sedimentation on the formation of widespread tephra fall layers in the deep sea, Geology, 25, 839–
842.
Coffin, M. F., M. S. Pringle, R. A. Duncan, T. P. Gladczenko, M. Storey, R. D. M
uller, and L. A. Gahagan (2002), Kerguelen hotspot output since
130 Ma, J. Petrol., 43(7), 1121–1139.
Collins, G. S., H. J. Melosh, and R. A. Marcus (2005), Earth impact effects program: A web-based computer program for calculating the
regional environmental consequences of a meteoroid impact on Earth, Meteorit. Planet. Sci., 40, 817–840.
Collins, G. S., J. Morgan, P. Barton, G. L. Christeson, S. Gulick, J. Urrutia-Fucugauchi, M. Warner, and K. W
unnemann (2008), Dynamic model-
ing suggests asymmetries in the Chicxulub crater are caused by target heterogeneity, Earth Planet. Sci. Lett., 270, 221–230.
Acknowledgments
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.
Geochemistry, Geophysics, Geosystems 10.1002/2014GC005229
SLEEP AND LOWE
V
C
2014. America n Geophysical Union. All Rights Reserved. 1068
Dor, O., C. Yildirim, T. K. Rockwell, Y. Ben-Zion, O. Emre, M. Sisk, and T. Y. Duman (2008), Geological and geomorphologic asymmetry across
the rupture zones of the 1943 and 1944 earthquakes on the North Anatolian Fault: Possible signals for preferred earthquake propaga-
tion direction, Geophys. J. Int., 173, 483–50 4, doi:10.1111/j.1365-246X.2008.03709.x.
Dunham, E. M., D. Belanger, L. Cong, and J. E. Kozdon (2011a), Earthquake ruptures with strongly rate-weakening friction and off-fault plas-
ticity: 1. Planar faults, Bull. Seismol. Soc. Am., 101(5), 2296–2307, doi:10.1785/0120100075.
Dunham, E. M., D. Belanger, L. Cong, and J. E. Kozdon (2011b), Earthquake ruptures with strongly rate-weakening friction and off-fault plas-
ticity: 2. Nonplanar faults, Bull. Seismol. Soc. Am., 101(5), 2308–2322, doi:10.1785/0120100076.
Gibbs, R. J., M. D. Matthews, and D. A. Link (1971), The relationship between sphere size and settling velocity, J. Sediment. Res., 41, 7–18.
Girty, G. H., M. A. Biggs, and R. W. Berry (200 8), An unusual occurrence of probable Pleistocene corestone with a Cretaceous dioritic
enclave, Peninsular Ranges, California, Catena, 74, 43–57.
Goldin, T. J., and H. J. Melosh (2009), Self-shie lding of thermal radiation by Chicxulub impact ejecta: Firestorm or fizzle?, Geology, 37 (12),
1135–1138, doi:10.1130/G30433A.1.
Hanks, T. C., N. A. Abrahamson, M. Board, D. M. Boore, J. N. Brune, and C. A. Cornell (Eds.) (2006), Report of the workshop on extreme
ground motions at Yucca Mountain, August 23–25, 2004, Open File Rep. 2006-1277, 234 pp., U.S. Geol. Surv., Reston, Va.
Herzberg, C., K. Condie, and J. Korenaga (2010), Thermal history of the Earth and its petrological expression, Earth Planet. Sci. Lett., 292, 79–
88.
Hill, D. P. (2008), Dynamic stresses, Coulomb failure, and remote triggering, Bull. Seismol. Soc. Am., 98(1), 66–92, doi:10.1785/0120070049.
Ingle, S., D. Weis, and F. A. Frey (2002), Indian continental crust recovered from Elan Bank, Kerguelen Plateau (ODP Leg 183, Site 1137), J.
Petrol., 43(7), 1241–1257.
Ivanov, I. V. (2005), Numerical modeling of the largest terrestrial meteorite craters, Solar System Research, 39, 381–409. Translated from
Astronomicheskii Vestnik, Vol. 39, No. 5, 2005, pp. 426–456.
Johnson, B. C., and H. J. Melosh (2012), Impact spherules as a record of an ancient heavy bombardment of Earth, Nature, 485, 75–77, doi:
10.1038/nature10982.
Korenaga, J. (2008), Urey ratio and the structure and evolution of Earth’s mantle, Rev. Geophys., 46, RG2007, doi:10.1029/2007RG000241.
Kreslavsky, M. A., and J. W. Head (2012), New observational evidence of global seismic effects of basin-forming impacts on the Moon from
Lunar Reconnaissance Orbiter Lunar Orbiter Laser Altimeter data, J. Geophys. Res., 117, E00H24, doi:10.1029/2011JE003975.
Kyte, F. T., A. Shukolyukov, G. W. Lugmair, D. R. Lowe, and G. R. Byerly (2003), Early Archean spherule beds: Chromium isotopes confirm ori-
gin through multiple impacts of projectiles of carbonaceous chondrite type, Geology, 31, 283–286.
Lowe, D. R. (1999), Petrology and sedimentology of cherts and related silicified sedimentary rock s in the Swaziland Supergroup, in Geologic
Evolution of the Barberton Greenstone Belt, South Africa, Geol. Soc. Am. Spec. Pap. 329, edited by D. R. Lowe and G. R. Byerly, pp. 83–114,
Geol. Soc. of Am., Boulder, Colo.
Lowe, D. R. (2013), Crustal fracturing and chert dike formation triggered by large meteorite impacts, 3.260 Ga, Barberton greenstone
belt, South Africa, Geol. Soc. Am. Bull., 125
, 894–912.
Lowe, D. R., and G. R. Byerly (1999), Stratigraphy of the west-central part of the Barberton Greenstone Belt, South Africa, in Geologic Evolu-
tion of the Barberton Greenstone Belt, South Africa, Geol. Soc. Am. Spec. Pap. 329, edited by D. R. Lowe and G. R. Byerly, pp. 1–36, Geol.
Soc. of Am., Boulder, Colo.
Lowe, D. R., and G. R. Byerly (2010), Did LHB end not with a bang but a whimper? The Geologic Evidence, paper presented at 41st Lunar
and Planetary Science Conference, Lunar and Planetary Institute, Houston, Texas.
Lowe, D. R., G. R. Byerly, F. T. Kyte, A. Shukolyukov, F. Asaro, and A. Krull (2003), Spherule beds 3.47–3.24 billion years old in the Barberton
Greenstone Belt, South Africa: A record of large meteorite impacts and their influence on early crustal and biological evolution, Astrobi-
ology, 3(1), 7–48.
Makris, N., and C. J. Black (2004), Evaluation of peak ground velocity as a ‘‘good’’ intensity measure for near-source ground moti ons, J. Eng.
Mech., 130(9), 1032–1044, doi:10.1061/(ASCE)0733–9399(2004)130:9(1032).
McCalpin, J. P., and E. W. Hart (2003), Ridge-top spreading features and relationship to earthquakes, San Gabriel Mountains Region, Part B:
Paleoseismic investigations of ridgetop depressions, in Ridge-Top Spreading in California, California, Geol. Surv. Open File Rep. 1, Contrib.
4 [CD-ROM], edited by E. W. Hart, 51 pp., California Geological Survey, Sacramento, California.
Melosh, H. J. (1989), Impact Cratering: A Geologic Process, 245 pp., Oxford Univ. Press, New York.
Melosh, H. J., and B. A. Ivanov (1999), Impact crater collapse, Ann. Rev. Earth Planet. Sci., 27, 385–415.
Meschede, M. A., C. L. Myhrvold, and J. Tromp (2011), Antipipodal focusing of seismic waves due to large meteorite impacts on Earth, Geo-
phys. J. Int., 187, 529–537.
Morelli, A. A., and M. Dziewonski (1993), Body wave traveltimes and a spherically symmetric P- and S-wave velocity model, Geophys. J. Int.,
112(2), 178–194.
Morgan, J. K., D. A. Clague, D. C. Borchers, A. S. Davis, and K. L. Milliken (2007), Mauna Loa’s submarine western flank: Landsliding, deep vol-
canic spreading, and hydrothermal alteration, Geochem. Geophys. Geosyst., 8, Q05002, doi:10.1 029/2006GC001420.
Noda, H., E. M. Dunham, and J. R. Rice (2009), Earthquake ruptures with thermal weakening and the operation of major faults at low overall
stress levels, J. Geop hys. Res., 114, B07302, doi:10.1029/2008JB006143.
Parnell, J. (2008), Global mass wasting at continental margins during Ordovician high meteorite influx, Nat. Geosci., 2, 57–61, doi:10.1038/
NGEO386.
Patton, H. J., and S. R. Taylor (2011), The apparent explosion moment: Infere nces of volumetric moment due to source medium damage by
underground nuclear explosions, J. Geophys. Res., 116, B03310, doi:10.1029/2010JB007937.
Pho, H. T., and L. Behe (1972), Extended distances and angles of incidence of P-waves, Bull. Seismol. Soc. Am., 62(4), 885–902.
Poirier, J.-P. (1990), Creep of Crystals, High-Temperature Deformation Processes in Metals, Ceramics and Minerals, 260 pp., Cambridge Univ.
Press, Cambridge, U. K.
Prakash, V. (1998 ), Frictional response of sliding interfaces subjected to time varying normal pressures, J. Tribol., 120, 97–102.
Proussevitch, A. A., and D. L. Sahagian (1998), Dynamics and energetics of bubble growth in magmas: Analytical formulation and numerical
modeling, J. Geophys. Res., 103(B8), 18,223–18,251, doi:10.1029/98JB00906.
Replogle, C. T. (2011), Corestone and saprock development in a zone of precariously balanced rocks, Peninsular Ranges, southern Califor-
nia: Speculations on the effects of ground shaking during earthquakes, MS thesis, 67 pp., San Diego State Univ., Calif.
Rotstein, Y., R. Schlich, M. Munschy, and M. F. Coffin (1992), Structure and tectonic history of the Southern Kerguelen Plateau (Indian
Ocean) deduced from seismic reflection data, Tectonics, 11(6), 1332–1347, doi:10.1029/91TC02909.
Sleep, N. H. (2011a), Seismically damaged regolith as self-organized fragile geological feature, Geochem. Geophys. Geosyst., 12
, Q12013, doi:
10.1029/2011GC003837.
Geochemistry, Geophysics, Geosystems 10.1002/2014GC005229
SLEEP AND LOWE
V
C
2014. America n Geophysical Union. All Rights Reserved. 1069
Sleep, N. H. (2011b), Deep-seated down-slope slip during strong seismic shaking, Geochem. Geophys. Geosyst., 12, Q12001 , doi:10.1029/
2011GC003838.
Senft, L. E., and S. T. Stewart (2009), Dynamic fault weakening and the formation of large impact craters, Earth Planet. Sci. Lett., 287, 471–
482.
Timoshenko, S. P., and J. N. Goodier (1970), Theory of Elasticity, 567 pp., McGraw-Hill, New York.
Turcotte, D. L., and G. Schubert (2002), Geodynamics, 2nd ed., 456 pp., John Wiley, New York.
Villermaux, E., and B. Bossa (2009), Single-drop fragmentation determines size distribution of raindrops, Nat. Phys., 5, 697–702, doi:10.1038/
NPHYS1340.
Wechsler, N., T. K. Rockwell, and Y. Ben-Zion (2009), Application of high resolution DEM data to detect rock damage from geomorphic sig-
nals along the central San Jacinto Fault, Geomorphology, 113, 82–96.
Weidner, D. J. (1974), Rayleigh-wave phase velocities in Atlantic Ocean, Geop hys. J. R. Astron. Soc., 36, 105–139.
W
unnemann, K., G. S. Collins, and R. Weiss (2010), Impact of a cosmic body into Earth’s ocean and the generation of large tsunami waves:
Insight from numerical modeling, Rev. Geophys., 48, RG4006, doi:10.1029/2009RG000308.
Zoback, M. D., and J. Townend (2001), Implications of hydrostatic pore pressures and high crustal strength for the deformation of intra-
plate lithosphere, Tectonophysics, 336, 19–30.
Geochemistry, Geophysics, Geosystems 10.1002/2014GC005229
SLEEP AND LOWE
V
C
2014. America n Geophysical Union. All Rights Reserved. 1070

 

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