Meteoritics & Planetary Science 40, Nr 6, 817–840 (2005)
Abstract available online at http://meteoritics.org

Earth Impact Effects Program: A Web-based computer program for calculating theregional environmental consequences of a meteoroid impact on Earth
Gareth S. COLLINS,1* H. Jay MELOSH,2 and Robert A. MARCUS2
1Impacts and Astromaterials Research Centre, Department of Earth Science and Engineering, Imperial College London,

South Kensington Campus, London, SW7 2AZ, UK
2Lunar and Planetary Laboratory, University of Arizona, 1629 East University Boulevard, Tucson, Arizona 85721–0092, USA*Corresponding author. E-mail: g.collins@imperial.ac.uk(Received 29 July 2004; revision accepted 14 April 2005)

Abstract–We have developed a Web-based program for quickly estimating the regional
environmental consequences of a comet or asteroid impact on Earth (www.lpl.arizona.edu/
impacteffects). This paper details the observations, assumptions and equations upon which theprogram is based. It describes our approach to quantifying the principal impact processes that might
affect the people, buildings, and landscape in the vicinity of an impact event and discusses theuncertainty in our predictions. The program requires six inputs: impactor diameter, impactor density,
impact velocity before atmospheric entry, impact angle, the distance from the impact at which theenvironmental effects are to be calculated, and the target type (sedimentary rock, crystalline rock, ora water layer above rock). The program includes novel algorithms for estimating the fate of the
impactor during atmospheric traverse, the thermal radiation emitted by the impact-generated vapor
plume (fireball), and the intensity of seismic shaking. The program also approximates various
dimensions of the impact crater and ejecta deposit, as well as estimating the severity of the air blastin both crater-forming and airburst impacts. We illustrate the utility of our program by examining thepredicted environmental consequences across the United States of hypothetical impact scenarios
occurring in Los Angeles. We find that the most wide-reaching environmental consequence is seismic
shaking: both ejecta deposit thickness and air-blast pressure decay much more rapidly with distancethan with seismic ground motion. Close to the impact site the most devastating effect is from thermalradiation; however, the curvature of the Earth implies that distant localities are shielded from direct
thermal radiation because the fireball is below the horizon.
INTRODUCTION
Asteroid and comet impacts have played a major role in
the geological and biological history of the Earth. It is
widely accepted that one such event, 65 million years ago,
perturbed the global environment so catastrophically that amajor biological extinction ensued (Alvarez 1980). As aresult, both the scientific community and the general
populace are increasingly interested in both the threat tocivilization and the potential environmental consequences ofimpacts. Previous papers have examined, in detail, thenatural hazard associated with the major environmental
perturbations caused by impact events (Toon et al. 1994,
1997). To provide a quick and straightforward method for
estimating the severity of several of these environmental
effects, we have developed a free-of-charge, easy-to-use
Web page maintained by the University of Arizona, which islocated at: www.lpl.arizona.edu/impacteffects. Our program
focuses on the consequences of an impact event for theregional environment; that is, from the impact location to a
few thousand km away. The purpose of this paper is topresent and justify the algorithm behind our program so thatit may be applied more specifically to important terrestrial
impact events and its reliability and limitations may beunderstood.
Before describing our program in detail, we will briefly
review the impact process and the related environmental
consequences. The impact of an extraterrestrial object on
Earth begins when the impactor enters the tenuous upper
atmosphere. At this moment, the impactor is traveling at a
speed of between 11 and 72 km s1 on a trajectory anywhere
between normal incidence (90° to the Earth’s surface) and agrazing impact, parallel to the Earth’s surface. The most likely
impact angle is 45° (Shoemaker 1962). The impactor’s

817© The Meteoritical Society, 2005. Printed in USA.

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G. S. Collins et al.

traverse of the atmosphere may disrupt and decelerate theimpactor significantly—a process that greatly affects theenvironmental consequences of the collision. Small impactors
are disrupted entirely during their atmospheric traverse,
depositing their kinetic energy well above the surface andforming no crater. Larger objects, however, retain sufficient
momentum through the atmosphere to strike the Earth withenough energy to excavate a large crater and initiate several
processes that affect the local, regional, and even global
environment.
The formation of an impact crater is an extremelycomplicated and dynamic process (Melosh 1989). The abrupt
deceleration of a comet or asteroid as it collides with the Earthtransfers an immense amount of kinetic energy from theimpacting body to the target. As a result, the target andimpactor are rapidly compressed to very high pressures andheated to enormous temperatures. Between the compressed
and uncompressed material, a shock wave is created that
propagates away from the point of impact. In the wake of the
expanding shock wave, the target is comprehensively
fractured, shock-heated, shaken, and set in motion—leading
to the excavation of a cavity many times larger than theimpactor itself. This temporary cavity (often termed thetransient crater; Dence et al. 1977) subsequently collapses
under the influence of gravity to produce the final crater form.
As the crater grows and collapses, large volumes of rockdebris are ejected onto the surface of the Earth surrounding
the crater. Close to the crater rim, this “ejecta deposit” forms
a continuous blanket smothering the underlying terrain;
further out, the ejecta lands as a scattered assortment of finegrained dust and larger bombs that may themselves form
small secondary craters.
In addition to cratering the surface of the earth, an
impact event initiates several other processes that may havesevere environmental consequences. During an impact, thekinetic energy of the impactor is ultimately converted into
thermal energy (in the impactor and target), seismic energy,
and kinetic energy of the target and atmosphere. The increasein thermal energy melts and vaporizes the entire impactor andsome of the target rocks. The hot plume of impact-generated
vapor that expands away from the impact site (referred to as
the “fireball”) radiates thermal energy that may ignite fires
and scorch wildlife within sight of the fireball. As the impactgenerated shock wave propagates through the target, it
eventually decays into elastic waves that travel great
distances and cause violent ground shaking several crater
radii away. In addition, the atmosphere is disturbed in asimilar manner to the target rocks; a shock wave propagatesaway from the impact site compressing the air to highpressures that can pulverize animals and demolish buildings,
vehicles, and infrastructure, particularly where constructional
quality is poor. Immediately behind the high-pressure front,
violent winds ensue that may flatten forests and scatterdebris.

All of these impact-related processes combine and interact
in an extremely complicated way that requires detailed
observation, laboratory experiments, or computer models to
fully simulate and understand. However, with certain
simplifying assumptions, we can derive reasonable estimatesof their consequences for the terrestrial environment. In thefollowing sections, we describe each of the steps that allow us
to achieve this in the Earth Impact Effects Program. We discuss
how our program estimates: 1) the impact energy and averagetime interval between impacts of the same energy, somewhere
on Earth; 2) the consequences of atmospheric entry; 3) for
crater forming events, the resulting crater size and volume of
the melt produced; 4) the thermal radiation damage from thefireball; 5) the impact-induced seismic shaking; 6) the extent
and nature of the ejecta deposit; and 7) the damage caused by
the blast wave. To clearly identify our algorithm in thefollowing discussion, all of the equations that we implement in
the code are labeled with an asterisk (*).
To make the program accessible to the broadest range ofusers, it was written with as few input parameters as possible.
The program requests six descriptors, which are illustrated
schematically in Fig. 1: the diameter of the impactor L0 (we use
the term impactor to denote the asteroid, comet or otherextraterrestrial object considered), the impactor density Ui, theimpact velocity v0, the angle that the trajectory of the impactor
subtends with the surface of the Earth at the impact point T, thetarget type, and the distance away from the impact at which theuser wishes to calculate the environmental consequences r.
Three target types are possible: sedimentary rock, for which we
assign a target density of Ut 2500 kg m3, crystalline rock (Ut2750 kg m3), or a marine target, for which the program
requests a water-layer depth dw and assigns a density of Uw
1000 kg m3 for the water and a target density of Ut 2700 kgm3 for the rock layer below. The program offers the user avariety of options for units; however, in this paper, the units for
all variables are the SI units (mks) unless otherwise stated.
IMPACT ENERGY AND RECURRENCE INTERVAL
The most fundamental quantity in assessing theenvironmental consequences of the impact is the energy
released during the impact, which is related to the kinetic
energy of the impactor E before atmospheric entry begins. At
normal solar system impact speeds, E is approximately given
as one half times the impactor mass mi times the square of the
impactor velocity v0, which can be rewritten in terms of themeteoroid’s density Ui and diameter L0, assuming that themeteoroid is approximately spherical:
2
3 2
1
S
E = --- m i v 0 = ------ U i L 0 v 0
2
12

(1*)

In fact, the program uses the relativistic energy equationto accommodate the requests of several science fiction
writers. The program does not limit the impact velocity toEarth Impact Effects Program

819

Science Definition Team 2003; their Fig. 2.3) and multiplying
by the number of asteroids of a given potential impact energythat are estimated to be circling the sun with potentiallyhazardous, Earth-crossing orbits. We found that a simple
power-law relationship adequately represents these data:
TRE | 109EMt0.78

Fig. 1. Diagram illustrating the input parameters for the Earth Impact
Effects Program: L0 is the impactor diameter at the top of theatmosphere, v0 is the velocity of the impactor at the top of theatmosphere, Ui is the impactor density, Ut is the target density, and T
is the angle subtended between the impactor’s trajectory and thetangent plane to the surface of the Earth at the impact point. The
distance r from the impact site at which the environmental
consequences are determined is measured along the surface of the
Earth; the epicentral angle ' between the impact point and thisdistance r is given by ' = r/RE, where RE is the radius of the Earth.

72 km s1, the maximum possible for an impactor bound to
the Sun; however, we have limited the maximum velocity to
the speed of light, in response to attempts of a few users toinsert supra-light velocities!
Natural objects that encounter the Earth are either
asteroids or comets. Asteroids are made of rock (Ui ~2000–
3000 kg m3; Hilton 2002) or iron (Ui ~8000 kg m3) andtypically collide with the Earth’s atmosphere at velocities of
12–20 km s1 (Bottke et al. 1994). Detailed knowledge of thecomposition of comets is currently lacking; however, they areof much lower density (Ui ~500–1500 kg m3) and are composed
mainly of ice (Chapman and Brandt 2004). Typical velocities
at which comets might encounter the Earth’s atmosphere are in
the range of 30–70 km s1 (Marsden and Steel 1994). Thus, anasteroid or comet typically has 4–20 times the energy per unit
mass of TNT at the moment atmospheric entry begins.
Therefore, impact events have much in common with chemical
and nuclear explosions, a fact that we will rely on later in ourestimates of the environmental effects of an impact.
Observations of near-Earth objects made by several
telescopic search programs show that the number of nearEarth asteroids with a diameter greater than Lkm (in km) may
be expressed approximately by the power law (Near-Earth
Object Science Definition Team 2003):
N(>L) | 1148Lkm2.354(2)These data may also be represented in terms of therecurrence interval TRE in years versus the impact energy EMt
in megatons of TNT by assuming a probability of a singleobject collision with Earth (~1.6 × 109 yr1; Near-Earth Object(3*)

Thus, for a given set of user-input impact parameters (L0,v0, Ui, Ut, and T), the program computes the kinetic energy(EMt, in megatons; 1 Mt = 4.18 × 1015 J) possessed by the
impacting body when it hits the upper atmosphere and defines
an average time interval between impacts of that energy,
somewhere on the Earth. Furthermore, we estimate therecurrence interval TRL for impacts of this same energy withina certain specified distance r of the impact. This is simply the
product of the recurrence interval for the whole Earth and thefraction of the Earth’s surface area that is within the distance r:
T RE
T RL = ---------- 1 – cos '2(4*)

where ' is the epicentral angle from the impact point to arange r (given in radians by: ' = r/RE, where RE is the radiusof the Earth; Fig. 1).
Currently, the relative importance of comets to the Earthcrossing impactor flux is not well-constrained. The Near-Earth
Object Science Definition Team (2003) suggests that comets
comprise only about 1% of the estimated population of small
NEOs; however, there is evidence to suggest that, at larger
sizes, comets may comprise a significantly larger proportion of
the impactor flux (Shoemaker et al. 1990). Of the asteroids thatcollide with the Earth’s atmosphere, the current best estimate
is that approximately 2–10% are iron asteroids (Bland andArtemieva 2003), based on NEO and main-belt asteroid
spectroscopy (Bus et al. 2002; Binzel et al. 2003), meteorite
composition, and the impactor types in large terrestrial craters.
ATMOSPHERIC ENTRY
Atmospheric entry of asteroids has been discussed indetail by many authors (Chyba et al. 1993; Ivanov et al. 1997;
Krinov 1966; Melosh 1981; Passey and Melosh 1980; Svetsov
et al. 1995; Korycansky et al. 2000, 2002; Korycansky and
Zahnle 2003, 2004; Bland and Artemieva 2003) and is now
understood to be a complex process, involving interaction of
the atmosphere and fragmenting impactor in the Earth’s
gravitational field. For the purposes of a simple program of thetype that we have created, many of the refinements now
understood are too complex to be included. Therefore, wehave opted to make a number of drastic simplifications that,
we believe, will still give a good description of the basic
events during atmospheric entry for most cases. Of course, forrefined predictions, a full simulation using all of the known
processes and properties must be undertaken. Atmosphericentry has no significant influence on the shape, energy, or820

G. S. Collins et al.

momentum of impactors with a mass that is much larger thanthe mass of the atmosphere displaced during penetration. For
this reason, the program procedure described below is applied
only for impactors less than 1 km in diameter.
For the purposes of the Earth Impact Effects Program, we
assume that the trajectory of the impactor is a straight linefrom the top of the atmosphere to the surface, sloping at aconstant angle to the horizon given by the user. Accelerationof the impactor by the Earth’s gravity is ignored, as isdeviation of the trajectory toward the vertical in the case thatterminal velocity is reached, as it may be for small impactors.
The curvature of the Earth is also ignored. The atmosphere isassumed to be purely exponential, with the density given by:U(z)U0ez/H(5)

where z is the altitude above the surface, H is the scale height,
taken to be 8 km on the average Earth, and U0 is the surface
atmospheric density, taken to be equal to 1 kg/m3.
During the first portion of the impactor’s flight, its speed
is decreased by atmospheric drag, but the stresses are too
small to cause fragmentation. Small meteoroids are often
ablated to nothing during this phase, but in the current
program implementation, we ignore ablation on the grounds
that it seldom affects the larger impactors that reach thesurface to cause craters. Thus, this program should not be
used to estimate the entry process of small objects that may
cause visible meteors or even drop small meteorites to thesurface at terminal velocity.
While the body remains intact, the diameter of theincoming impactor is constant, equal to the diameter L0 givenby the user. The rate of change of the velocity v is given by theusual drag equation (corrected from Melosh 1989, chapter 11):
3UzC D 2
dv------ = – ----------------- v
dt
4U i L 0(6)

where CD is the drag coefficient, taken to equal 2, and Ui is theimpactor density (an input parameter). This equation can begreatly simplified by making the replacement dt = dz/v sinT
(justified by our assumption that the impactor travels in astraight line) and rearranging:
3U z C D
d ln v------------- = -------------------------dz
4U i L 0 sin T

log 10 Y i = 2.107 + 0.0624 U i(9*)

where the impactor density Ui is in kg m3. Note that, even atzero density, this implies a non-zero strength of about 130 Pa.
Thus, this empirical formula should not be applied too far outof the range of 1000 to 8000 kg m3, over which it wasestablished.
Using this estimate of strength and comparing it to thestagnation pressure, we can compute an altitude of breakup z*
by solving the transcendental equation:
Yi = U(z*)v2(z*)(10)

Rather than solving this equation in the program directly,
an excellent analytic approximation to the solution was foundand implemented:§ Yi ·
z * | – H ln ¨ ----------2-¸ + 1.308 – 0.314I f – 1.303 1 – I f© U0 vi ¹(11*)

where If is given by:(7)

Integration of this equation using the exponential density
dependence gives the velocity of the impactor as a function ofaltitude:­ 3U z C D H ½
v z = v 0 exp ® – --------------------------- ¾¯ 4U i L 0 sin T ¿the leading edge of the impactor, Ps
U(z) v(z)2, rises.
Eventually, this exceeds the strength of the impactor, and it
begins to break up. Observed meteoroids often undergo
several cascades of breakup, reflecting components of widely
varying strengths. The entire subject of meteoroid strength ispoorly understood, as measured crushing strengths of
specimens collected on the ground are often a factor of 10 lessthan strengths inferred from observed breakup (Svetsov et al.
1995). Clearly, strong selection effects are at work. For the
purposes of our program, we decided not to embroil the user
in the ill-defined guesswork of estimating meteoroid crushingstrength. Instead, we found a rough correlation between
density and estimated strength for comets (about 15 Pa in
tension from the tidal breakup of SL-9; Scotti and Melosh1993), chondrites (Chyba et al. 1993), and iron or stone
objects (Petrovic 2001). Based on four simplified estimatesfor comets, carbonaceous, stony, and iron meteorites, weestablished an empirical strength-density relation for use in
the program. The yield strength Yi of the impactor in Pa is thus
computed from:(8*)

where T is the entry angle, and v0 is the impact velocity at the
top of the atmosphere, given by the user.
As the impactor penetrates the atmosphere theatmospheric density increases and the stagnation pressure at

C D HY i
I f = 4.07 --------------------------2
U i L 0 v i sin T(12*)

In certain specific instances (i.e., small, strong
impactors), the impactor may reach the surface intact; in thiscase, If >1, and Equation 11 does not apply. The properly
decremented velocity, calculated using Equation 8, is used tocompute a crater size. (If this velocity happens to be less than
the terminal velocity, then the maximum of the two is usedinstead.) The velocity at the top of the atmosphere and at thesurface is reported.
Most often, the impactor begins to break up well above
the surface; in this case, If <1, and Equation 11 is used toEarth Impact Effects Program
compute the breakup altitude z*. After breakup, the fragments
begin to disperse in a complex series of processes (Passey andMelosh 1980; Svetsov et al. 1995) that require detailed
numerical treatment. However, a simple approximation to thiscascade was found (Chyba et al. 1993; Melosh 1981), called
the pancake model, that does a good job for Tunguska-classevents. The basic idea of this model is that the impactor, once
fractured, expands laterally under the differential pressure
between the front and back surfaces. The front of the impactor
is compressed at the stagnation pressure, and the rear isessentially in a vacuum with zero pressure. The sides squirt
out at a rate determined by force balance in an inviscid fluid.
This leads to a simple equation for the expansion of the
impactor diameter L, now a function of time:2

2
CD U z v z
CD Ps
d L
--------2- = ------------- = -------------------------------Ui L
U
L
i
dt

(13)

The initial condition is that L = L0 at z = z*. If L does notincrease too much over the scale height H, the time
derivatives can be replaced with altitude derivatives (Chyba
et al. 1993) and a nonlinear differential equation can beconstructed that does not contain v(z):2
CD U zd L
L --------2- = -----------------2
dz
U i sin T­ z* – z ½ ·2H 2 §
L z = L 0 1 + § -------· ¨ exp ® ------------- ¾ – 1¸
© l ¹ ©
¯ 2H ¿ ¹

suffer one, or more, further pancake fragmentation events.
However, Chyba et al (1993) obtained good agreement with
Tunguska-class events using pancake factors as large as 5–10.
In this work, we experimented with different factors andsettled on a value of 7 to terminate the dispersion of the
impactor. The altitude at which this dispersion is obtained iscalled the “airburst altitude” (zb; see Fig. 2a); it is given by
substituting fp = L(z)/L0 into Equation 15 and rearranging:l2z b = z * – 2H ln 1 + ------- f p – 1
2H

2

(15*)

where the dispersion length scale l is given by:
Ui
l = L 0 sin T --------------------CD U z*

(16*)

The velocity as a function of altitude is then given by
inserting this expression for L(z) into the drag equation andintegrating downward from the breakup altitude z*. Becauseof the rapid expansion of the pancake, the drag rises rapidly as
well, and the velocity drops as a double exponential:z*­½
z* – z e H 2° 3 CD U z*°
v z = v z * exp ® – --- ---------------------e
L z dz ¾³
34° U i L 0 sin T
°
z
¯
¿

z*

³ e

z* – z e H 2

L z dz =z burst2
lL 0-------- D 8 3 + D
24

2

(19*)

l
2
+ 3D ---- 2 + D
H2with the definition D { f p – 1 . The surface impact velocityof the remnants from the airburst vi is also reported as the
maximum of the terminal velocity of a fragment half thediameter of the original impactor or the velocity of theswarm as a whole. The spreading velocity at airburst
multiplied by the time to impact is added to the breadth of
the swarm to estimate the dispersion of what will be a strewn
field on the surface. The principal environmental
consequence of such an event is a strong blast wave in theatmosphere (see below).
On the other hand, if the pancake does not spread to thelimiting size before it reaches the ground (zb d0 inEquation 19; Fig. 2b), the swarm velocity at the moment of
impact is computed using Equation 17. In this case, theintegral in the exponent, evaluated from the surface (z = 0) to
the disruption altitude, is given by:
z*

³e
6e

2z * e H

3 2

H L0 §
l 2 z* e H+
L z dz = ------------ 34 + § ----· e
2 ©
© H¹
3l

z* – z e H 2

0

(17*)

The crushed impactor spreads laterally until the ratio
L(z)/L0 reaches a prescribed limit, which we call the “pancake
factor” fp. In reality, this should be no larger than 2 to 4
(Ivanov et al. 1997), after which the fragments are sufficiently
separated that they follow independent flight paths and may(18*)

If the airburst occurs above the surface (Fig. 2a), most of
the energy is dissipated in the air. We report the airburst
altitude zb and the residual velocity of the swarm, which iscomputed using Equation 17. In this case, the integral in the
exponent, evaluated from the airburst altitude to thedisruption altitude, is given by:(14)

Again, we construct an analytic approximation to the full
solution of this equation, which is adequate for the purposesof the program:

821

– 16e

3z * e 2H

(20)

l 2
– 3 § ----· – 2·
© H¹¹

The dispersion of the swarm at impact is compared to theestimated transient crater size (see below) and, if it iscomparable or larger, then the formation of a crater field isreported, similar to that actually observed at Henbury,
Australia. Otherwise, we assume the impact to be a crater-

822

G. S. Collins et al.

Fig. 2. Schematic illustration of two atmospheric entry scenarios considered in the Earth Impact Effects Program: a) the impactor (initial
diameter L0) begins to break up at an altitude z*; from this point the impactor spreads perpendicular to the trajectory due to the differentpressures on the front and back face. We define the airburst altitude zb to be the height above the surface at which the impactor diameter L(z)= 7L0. All the impact energy is assumed to be deposited at this altitude; no crater is formed, but the effects of the blast wave are estimated; b)
the impactor breaks up but the critical impactor diameter is not reached before the fragmented impactor strikes the surface (z* >0; zb <0). The
cluster of fragments impacts the target surface with a velocity vi, forming a single crater or crater field depending on the lateral spread of thecluster, L(z = 0)/sinT.

forming event and use the velocity at the surface to computea crater size. In either case, the environmental consequencesof these events are calculated based on an impact energy
equal to the total kinetic energy of the swarm at the moment it
strikes the surface.
Although simple, we have found the prescription above
to give a fairly reasonable account of atmospheric entry overa wide range of impactor sizes and compositions. As
mentioned above, a much more complex treatment must be
made on a case-by-case basis if more exact results are needed.
In particular, our program is not capable of providing a massor velocity-distribution for fragmented impactors and,
therefore, cannot be used to model production of terrestrial
crater fields where the size of the largest crater is related to thelargest surviving fragment.
CRATER DIMENSIONS AND MELT PRODUCTION
Determining the size of the final crater from a given
impactor size, density, velocity, and angle of incidence is nota trivial task. The central difficulty in deriving an accurate
estimate of the final crater diameter is that no observational orexperimental data exist for impact craters larger than a few
tens of meters in diameter. Perhaps the best approach is to use
sophisticated numerical models capable of simulating the
propagation of shock waves, the excavation of the transient
crater, and its subsequent collapse; however, this method isbeyond the scope of our simple program. Instead, we use a setof scaling laws that extrapolate the results of small-scale
experimental data to scales of interest or extend observationsof cratering on other planets to the Earth. The first scaling law
we apply is based on the work of Holsapple and Schmidt(1982), Schmidt and Housen (1987), and Gault (1974) andcombines a wide range of experimental cratering data (forexample, small-scale hypervelocity experiments and nuclear
explosion experiments). The equation relates the density ofthe target Ut and impactor Ui (in kg m3), the impactor
diameter after atmospheric entry L (in m), the impact velocity
at the surface vi (in m s1), the angle of impact T (measured tothe horizontal), and the Earth’s surface gravity gE (in m s2),

Earth Impact Effects Program

823

Fig. 3. Symbols used in the text to denote the various dimensions of an impact crater. a) Transient crater dimensions: Dtc is the transient crater
diameter measured at the pre-impact surface; Dtr is the diameter of the transient crater measured from rim crest to rim crest; htr is the rim heightof the transient crater measured from the pre-impact surface; dtc is the depth of the transient crater measured from the pre-impact surface (weassume that Dtc = 2 2 dtc); b) simple crater dimensions (the transient crater outline is shown by the dotted line): Dfr is the rim-to-rim diameter;
hfr is the rim height above the pre-impact surface; tbr is the breccia lens thickness; dfr is the crater depth measured from the crater floor (above
the breccia lens) to the rim crest. We assume that the base of the breccia lens coincides with the floor of the transient crater at a depth of dtc
below the pre-impact surface; therefore, dfr = dtc + hfr  tbr; c) complex crater dimensions: Dfr is the rim-to-rim diameter; hfr is the rim height
above the pre-impact surface; tm is the melt sheet thickness; dfr is the crater depth measured from the crater floor (above the melt sheet) to therim crest.

to the diameter of the transient crater Dtc (in m) as measured
at the pre-impact target surface (Fig. 3a):U i 1 e 3 0.78 0.44 –0.22 1 e 3
D tc = 1.161 § ----· L v i g E sin T© U t¹(21*)

This equation applies for impacts into solid rock targets
where gravity is the predominant arresting influence in crater
growth, which is the case for all terrestrial impacts larger thana couple of hundred meters in diameter. For impacts into
water, the constant 1.161 must be replaced by 1.365 (Schmidt
and Housen 1987). In reality, these constants are not known tothree decimal places; the values quoted serve as a best
estimate within a range of 0.8 to 1.5.
The transient crater is only an intermediate step in thedevelopment of the final crater (Fig. 3). To estimate the final
crater diameter, we must consider the effect of the transient

crater’s collapse using another scaling law. For craters
smaller than ~3.2 km in diameter on Earth (classified byDence [1965] as “simple” based on their intuitive
morphology), the collapse process is well-understood:
highly brecciated and molten rocks that were originally
pushed out of the opening crater slide back down the steep
transient cavity walls forming a melt-and-breccia lens at thebase of the crater (Grieve et al. 1977; Fig. 3a). To derive an
estimate of the final crater diameter for simple craters, weapplied an analytical model for the collapse of simple
craters originally developed by Grieve and Garvin (1984) totwo terrestrial craters for which good observational data on
breccia-lens volume and final crater dimensions exist. In
matching the observational data to model predictions wefound that an excellent first order approximation is that the
final rim-to-rim diameter Dfr for a simple crater is given
approximately by:824

G. S. Collins et al.
Dfr | 1.25Dtc(22*)

if the unbulked breccia lens volume Vbr (i.e., the observed
volume of the breccia lens multiplied by a 90–95% bulking
correction factor; Grieve and Garvin 1984) is assumed to berelated to the final crater diameter by:
Vbr | 0.032Dfr3(23*)

This approximate relationship is based on estimates ofunbulked breccia-lens volumes at Meteor Crater and Brent
Crater (Grieve and Garvin 1984).
The model may also be used to estimate the thicknessof the breccia lens, the depth to the base of the breccia lens,and the final depth of the crater. Assuming that the top
surface of the breccia lens is parabolic and that the
brecciation process increases the bulk volume of thismaterial by 10%, the thickness of the breccia lens tbr isgiven approximately by:§ d tc + h fr·
t br = 2.8V br ¨ -------------------¸© d tc D 2fr ¹(24*)

where dtc is the transient crater depth (below the original
ground plane), and hfr is the rim height (above the original
ground plane) of the final crater (see the section below onejecta deposits). The depth to the base of the breccia lens istaken to be the same as the transient crater depth dtc, which we
assume is given by:
d tc = D tc e 2 2(25*)

based on observations by Dence et al. (1977). The depth of
the final crater from the rim to the crater floor dfr is thensimply (see Fig. 3b):dfr

dtc  hfr  tbr(26*)

For craters larger than 3.2 km on Earth (termed complex
because of their unintuitive morphology after Dence [1965]),
the collapse process is less well-understood and involves thecomplicated competition between gravitational forces
tending to close the transient crater and the strength
properties of the post-impact target rocks. Several scalinglaws exist for estimating the rim-to-rim diameter of acomplex crater from the transient crater diameter, or viceversa, based on reconstruction of the transient craters oflunar complex craters (see, for example, Croft 1985;
McKinnon and Schenk 1985; Holsapple 1993). We use thefunctional form:
1.13

D tc
D fr = 1.17 ----------0.13
Dc

(27*)

established by McKinnon and Schenk (1985), which lies
intermediate between the estimates of Croft (1985) andHolsapple (1993). In this equation, Dc is the diameter atwhich the transition from simple to complex crater occurs(taken to be 3.2 km on Earth); both Dtc and Dfr are in km (SeeFig. 3b). If the transient crater diameter is greater than
2.56 km, we apply Equation 27 to determine the final crater
diameter and report that a “complex” crater is formed;
otherwise, we apply Equation 22 and report that a “simple”
crater is formed. It is worth emphasizing that the final crater
diameter that the program reports is the diameter of the fresh
crater measured from rim crest to rim crest (see Figs. 3b and3c). The topographic rim is likely to be strongly affected bypost-impact erosion. Furthermore, multiple concentric zones
of structural deformation are often observable at terrestrial
impact structures—a fact that has led to uncertainty in therelationship between the structural (apparent) andtopographic (rim-to-rim) crater diameter (Turtle et al. 2005).
Therefore, the results of the scaling arguments above should
be compared with caution to apparent diameters of known
terrestrial impact structures.
To estimate the average depth dfr (in km) from the rim tofloor of a complex crater of rim-to-rim diameter Dfr (in km),we use the depth-to-diameter relationship of Herrick et al.
(1997) for venusian craters:
dfr = 0.4Dfr0.3(28*)

The similarity in surface gravity between Earth andVenus as well as the large number of fresh complex craters on
Venus makes this relationship more reliable than that basedon the limited and erosion-affected data for terrestrial
complex craters (Pike 1980; Grieve and Therriault 2004).
We also estimate the volume of melt produced during
the impact event, based on the results of numerical modelingof the early phase of the impact event (O’Keefe and Ahrens
1982b; Pierazzo et al. 1997; Pierazzo and Melosh 2000) andgeological observation at terrestrial craters (Grieve andCintala 1992). Provided that: 1) the impact velocity is inexcess of ~12 km s1 (the threshold velocity for significant
target melting, O’Keefe and Ahrens 1982b); 2) the densityof the impactor and target are comparable; and 3) all impacts
are vertical, these data are well-fit by the simple expression:2vi
V m = 0.25 ------ V i
Hm

(29)

where Vm is the volume of melt produced, Vi is the volume of
the impactor, and Hm is the specific energy of the RankineHugoniot state from which the isentropic release ends at the
1 bar point on the liquidus. To avoid requiring further input
parameters in our program, we use Hm = 5.2 MJ/kg for granite(see Pierazzo et al. 1997), which we take as representative of
upper-crustal rocks, and assume an impactor and target
density of 2700 kg m3. This allows us to rewrite Equation 29,
giving the impact melt volume Vm (in m3) in terms of just the
impact energy E (in J): Vm = 8.9 × 1012 E.
To account for the effect of impact angle on impact melt

Earth Impact Effects Program
production, we assume, based on numerical modeling work
(Pierazzo and Melosh 2000; Ivanov and Artemieva 2002), thatthe volume of impact melt is roughly proportional to thevolume of the transient crater. In our program, the diameterand depth of the transient crater are proportional to sin1/3T(Equations 21 and 25); hence, the volume of the transient
crater is proportional to sinT. The equation used in our
program to compute the impact melt volume is, therefore:
Vm = 8.9 × 1012 E sinT

(30*)

This expression works well for all geologic materials
except ice. In this case, Vm is about ten times larger than forrock (Pierazzo et al. 1997). Equation 30 neglects the effect ofgeothermal gradient on melt production. For very large
impacts, which affect rocks deep in the Earth where ambient
temperatures are much closer to the melting point, thisexpression will underestimate the volume of melt produced.
Equation 30 agrees well with model predictions (Pierazzo andMelosh 2000) of impact melt volume versus impact angle for
impact angles greater than ~15q to the horizontal; for impact
angles of ~15q or less, Equation 30 probably overestimates
the volume of impact melt produced by a factor of ~2.
In simple craters, the melt is well-mixed within the
breccia lens on the floor of the crater; in larger complex
craters, however, the melt forms a coherent sheet, whichusually has an approximately uniform thickness across thecrater floor (Grieve et al. 1977). Here we assume that thecrater floor diameter is similar to the transient crater diameter(Croft 1985). Thus, we estimate the average thickness of thissheet tm as the ratio of the melt volume to the area of a circle
equal in diameter to the transient crater:
tm = 4Vm/SDtc2(31*)

In extremely large terrestrial impact events (Dtc
>1500 km), the volume of melt produced, as predicted by
Equation 30, is larger than the volume of the crater. In this case,
we anticipate that the transient crater would collapse to ahydrostatic, almost-featureless surface and, therefore, ourprogram does not quote a final crater diameter. Instead of a
topographically observable crater, the program postulates thata large circular melt province would be formed. We note,however, that no such feature has been unequivocally
identified on Earth. Our program also compares the volume of
impact-generated melt to the volume of the Earth and reports
the fraction of the planet that is melted in truly gigantic impacts.
THERMAL RADIATIONAs alluded to above, the compression of the target andimpactor during the initial stages of an impact event
drastically raises the temperature and pressure of a small
region proximal to the impact site. For impacts at a velocity
greater than ~12 km s1, the shock pressures are high enoughto melt the entire impactor and some target material;

825

vaporization also occurs for impacts at velocities greater than
~15 km s1. Any vapor produced is initially at very highpressure (>100 GPa) and temperature (>10,000 K) and, thus,
begins to rapidly inflate; the expanding hot vapor plume istermed the “fireball.” The high temperatures imply that
thermal radiation is an important part of the energy balance ofthe expanding plume. Initially, the fireball is so hot that the air
is ionized and its radiation absorption properties aresubstantially increased. As a result, the fireball is initiallyopaque to the emitted radiation, which remains bottled up
within the ball of plasma. The actual process is much more
complex than the simple description here and we refer theinterested reader to Glasstone and Dolan (1977) for a more
complete exposition. With continued expansion, the fireballcools; as the temperature approaches a critical temperature,
known as the transparency temperature T* (Zel’dovich andRaizer 1966, p. 607), the opacity rapidly diminishes and thethermal radiation escapes, bathing the Earth’s surface in heatfrom the fireball. The thermal radiation lasts for a few seconds
to a few minutes; the radiation intensity decays as the
expanding fireball rapidly cools to the point where radiationceases. For Earth’s atmosphere, the transparency temperatureis ~2000–3000 K (Nemtchinov et al. 1998); hence, thethermal radiation is primarily in the visible and infrared
wavelengths—the fireball appears as a “second sun” in thesky. The transparency temperature of silicate vapor is about
6000 K (Melosh et al. 1993), so that the limiting factor for
terrestrial impacts is the transparency temperature of air
surrounding the silicate vapor fireball.
Provided that the impact velocity is in excess of 15 km s1,
we estimate the fireball radius Rf* at the moment thetransparency temperature is achieved, which we consider to be
the time of maximum radiation. Numerical simulations of vapor
plume expansion (Melosh et al. 1993; Nemtchinov et al. 1998)
predict that the fireball radius at the time of maximum radiation
is 10–15 times the impactor diameter. We use a value of 13 andassume “yield scaling” applies to derive a relationship between
impact energy E in joules and the fireball radius in meters:
Rf*

0.002E1/3(32*)

Yield scaling is the empirically derived concept thatcertain length and time scales measured for two different
explosions (or impacts) are approximately identical if divided
by the cube root of the yield (or impact) energy. Yield scaling
can be justified theoretically, provided that gravity and ratedependent processes do not strongly influence the measured
parameters (Melosh 1989, p. 115). The constant inEquation 32 was found by dividing the fireball radius (given
by Rf* 13L0) by the cube root of the impact energy (given by
Equation 1), for a typical impactor density (2700 kg m3) andterrestrial impact velocity (20 km s1).
The time at which thermal radiation is at a maximum Tt isestimated by assuming that the initial expansion of the fireballoccurs at approximately the same velocity as the impact:

826

G. S. Collins et al.

R f*
T t = -------vi(33*)

To calculate the environmental effects of the thermalradiation from the fireball, we consider the heating at alocation a distance r from the impact site. The total amount ofthermal energy emitted as thermal radiation is some small
fraction K (known as the “luminous efficiency”) of the impact
energy E. The luminous efficiency for hypervelocity impacts
is not presently well-constrained. Numerical modeling results(Nemtchinov et al. 1998) suggest that K scales as some powerlaw of impact velocity. The limited experimental,
observational, and numerical results that exist indicate thatfor typical asteroidal impacts with Earth, K is in the range of
104–102 (Ortiz et al. 2000); for a first-order estimate weassume K = 3 × 103 and ignore the poorly-constrained
velocity dependence.
The thermal exposure ) quantifies the amount of heating
per unit area at our specified location. ) is given by the total
amount of thermal energy radiated KE divided by the area
over which this energy is spread (the surface area of ahemisphere of radius r, 2Sr2):KE) = ----------22Sr(34*)

The total thermal energy per unit area ) that heats our
location of interest arrives over a finite time period between
the moment the fireball surface cools to the transparency
temperature and is unveiled to the moment when the fireballhas expanded and cooled to the point where radiation ceases.
We define this time period as the “duration of irradiation” Wt.
Without computing the hydrodynamic expansion of the vapor
plume this duration may be estimated simply by dividing thetotal energy radiated per unit area (total thermal energy
emitted per unit area of the fireball) by the radiant energy
flux, given by VT*4, where V = 5.67 × 108 W m2 K4 is the
Stefan-Bolzmann constant. In our program, we use T* =3000 K. Then, the duration of irradiation is:KE
W t = ------------------------2
4
2SR f* VT *(35*)

For situations where the specified distance away from theimpact point is so far that the curvature of the Earth implies thatpart of the fireball is below the horizon, we modify the thermal
exposure ) by multiplying by the ratio f of the area of thefireball above the horizon to the total area. This is given by:2hf = --- § G – -------- sin G·
¹
S©
R f*

(36*)

In this equation, h is the maximum height of the fireballbelow the horizon as viewed from the point of interest, givenby:h(1  cos')RE(37*)

where ' is the epicentral angle between the impact point andthe point of interest, and RE is the radius of the Earth. If
h tRf*, then the fireball is entirely below the horizon; in thiscase, no direct thermal radiation will reach our specified
location. The angle G in Equation 36 is half the angle of thesegment of the fireball visible above the horizon, given by
G cos1 h/Rf*. We presently ignore atmospheric refractionand extinction for rays close to the horizon (this effect isimportant only over a small range interval).
Whether a particular material catches fire as a result of
the fireball heating depends not only on the corrected thermal
exposure f) but also on the duration of irradiation. The
thermal exposure )ignition (J m2) required to ignite a material,that is, to heat the surface to a particular ignition temperature
Tignition, is given approximately by:) ignition | T ignition Uc p NW t

(38)

where U is the density, cp is the heat capacity, and N is thethermal diffusivity of the material being heated. This
expression equates the total radiant energy received per unit
area, on the left, to the heat contained in a slab of unit area
perpendicular to the fireball direction, on the right. The
thickness of the slab is estimated from the depth, NW t ,penetrated by the thermal wave during the irradiation time Wt.
Analysis of Equation 35 shows that Wt is proportional to thethermal exposure divided by the fireball radius squared.
Hence, the duration of irradiation is proportional to E1/3, andthe thermal exposure required to ignite a given material is
proportional to E1/6. This simple relationship is supported byempirical data for the ignition of various materials by thermalradiation from nuclear explosion experiments over a range ofthree orders of magnitude in explosive yield energy(Glasstone and Dolan 1977, p. 287–289). Thus, although amore energetic impact event, or explosion, implies a greater
total amount of thermal radiation, this heat arrives over alonger period of time, and hence, there is more time for heatto be diluted by conduction through the material. This results
in a greater thermal exposure being required to ignite thesame material during a more energetic impact event.
To account for the impact-energy dependence of thethermal exposure required to ignite a material (or cause skindamage), we use a simple scaling law. We estimate thethermal exposure required to ignite several different
materials, or burn skin, during an impact of a given energy bymultiplying the thermal exposure required to ignite thematerial during a 1 Mt event (see Table 1; data from
Glasstone and Dolan 1977, p. 287–289) by the impact energy(in MT) to the one-sixth power:)ignition(E))ignition(1 Mt)EMt1/6(39*)

To assess the extent of thermal radiation damage at our
location of interest, we compute the thermal radiation

Earth Impact Effects Program

Table 1. Ignition factors for various materials.a827

Table 2. Seismic magnitude/Modified Mercalli Intensity.aMaterial

Thermal exposure required to ignite
material during a 1 Mt explosion()ignition(1 Mt), MJ m2)

Clothing
Plywood
Grass
Newspaper
Deciduous trees
Third degree burns
Second degree burns
First degree burns

1.0
0.67
0.38
0.33
0.25
0.42
0.25
0.13

Richter magnitude

Modified Mercalli Intensity

0–1
1–2
2–3
3–4
4–5
5–6
6–7
7–8
8–9
9+

–
I
I–II
III–IV
IV–V
VI–VII
VII–VIII
IX–X
X–XI
XII

a Data extracted from Glasstone and Dolan (1977).

a Based on data from Richter (1958).

exposure f) and compare this with )ignition (calculated using
Equation 39) for each type of damage in Table 1. For thermal
exposures in excess of these ignition exposures, we report thatthe material ignites or burns.
Our simple thermal radiation model neglects the effect ofboth atmospheric conditions (cloud, fog, etc.) and thevariation in atmospheric absorption with altitude above thehorizon. Experience from nuclear weapons testing (Glasstone
and Dolan 1977, p. 279) suggests that, in low visibility
conditions, the reduction in direct (transmitted) radiation iscompensated for, in large part, by indirect scattered radiation
for distances less than about half the visibility range. Thisobservation led Glasstone and Dolan (1977) to conclude that“as a rough approximation, the amount of thermal energy
received at a given distance from a nuclear explosion may be
assumed to be independent of the visibility.” Hence, although
the above estimate should be considered an upper estimate on
the severity of thermal heating, it is probably quite reliable,
particularly within half the range of visibility.

To estimate the extent of devastation at a given distancefrom a seismic event of this magnitude we determine theintensity of shaking I, as defined by the Modified Mercalli
Intensity Scale (see Table 2), the most widely-used intensity
scale developed over the last several hundred years toevaluate the effects of earthquakes. We achieve this bydefining an “effective seismic magnitude” as the magnitudeof an earthquake centered at our specified distance away fromthe impact that produces the same ground motion amplitude
as would be produced by the impact-induced seismic shaking.
We then use Table 3, after Richter (1958), to relate theeffective seismic magnitude to the Modified Mercalli
Intensity. A range of intensities is associated with a given
seismic magnitude because the severity of shaking depends
on the local geology and rheology of the ground and the
propagation of teleseismic waves; for example, damage inalluviated areas will be much more severe than on wellconsolidated bed rock.
The equations for effective seismic magnitude use curves
fit to empirical data of ground motion as a function of distancefrom earthquake events in California (Richter 1958, p. 342).
We use three functional forms to relate the effective seismic
magnitude Meff to the actual seismic magnitude M and the
distance from the impact site rkm (in km), depending on the
distance away from the impact site. For rkm <60 km:

SEISMIC EFFECTS
The shock wave generated by the impact expands andweakens as it propagates through the target. Eventually, allthat remains are elastic (seismic) waves that travel through theground and along the surface in the same way as those excitedby earthquakes, although the structure of the seismic waves
induced by these distinct sources is likely to be considerably
different.
To calculate the seismic magnitude of an impact event,
we assume that the “seismic efficiency” (the fraction of the
kinetic energy of the impact that ends up as seismic wave
energy) is one part in ten thousand (1 × 104). This value is themost commonly accepted figure based on experimental data
(Schultz and Gault 1975), with a range between 105–103.
Using the classic Gutenberg-Richter magnitude energy
relation, the seismic magnitude M is then:M

0.67log10 E  5.87

(40*)

where E is the kinetic energy of the impactor in Joules(Melosh 1989, p. 67).

Meff

M  0.0238rkm(41a*)

for 60 drkm <700 km:
Meff

M  0.0048rkm  1.1644(41b*)

and for rkm t700 km:
Meff

M  1.66log10 '  6.399(41c*)

To compute the arrival time Ts of the most violent seismic
shaking, we assume that the main seismic wave energy is thatassociated with the surface waves. Then, Ts is simply the userspecified distance rkm (in km) divided by the typical surfacewave velocity of upper-crustal rocks (~5 km s1):
r km
T s = -------5

(42*)

828

G. S. Collins et al.

Table 3. Abbreviated version of the Modified Mercalli Intensity scale.
Intensity

Description

I
II
III

Not felt except by a very few under especially favorable conditions.
Felt only by a few persons at rest, especially on upper floors of buildings.
Felt quite noticeably by persons indoors, especially on upper floors of buildings. Many people do not recognize it as anearthquake. Standing motor cars may rock slightly. Vibrations similar to the passing of a truck.
Felt indoors by many, outdoors by few during the day. At night, some awakened. Dishes, windows, doors disturbed; walls
make cracking sound. Sensation like heavy truck striking building. Standing motor cars rocked noticeably.
Felt by nearly everyone; many awakened. Some dishes, windows broken. Unstable objects overturned. Pendulum clocks
may stop.
Felt by all, many frightened. Some heavy furniture moved; a few instances of fallen plaster. Damage slight.
Damage negligible in buildings of good design and construction; slight to moderate in well-built ordinary structures;considerable damage in poorly built or badly designed structures; some chimneys broken.
Damage slight in specially designed structures; considerable damage in ordinary substantial buildings with partial collapse.
Damage great in poorly built structures. Fall of chimneys, factory stacks, columns, monuments, and walls. Heavy furniture
overturned.
General panic. Damage considerable in specially designed structures; well-designed frame structures thrown out of plumb.
Damage great in substantial buildings, with partial collapse. Buildings shifted off foundations. Serious damage to reservoirs.
Underground pipes broken. Conspicuous cracks in ground. In alluviated areas sand and mud ejected, earthquake fountains,
sand craters.
Most masonry and frame structures destroyed with their foundations. Some well-built wooden structures and bridges
destroyed. Serious damage to dams, dikes, and embankments. Large landslides. Water thrown on banks of canals, rivers,
lakes, etc. Sand and mud shifted horizontally on beaches and flat land. Rails bent slightly.
As X. Rails bent greatly. Underground pipelines completely out of service.
As X. Damage nearly total. Large rock masses displaced. Lines of sight and level distorted. Objects thrown into the air.

IV
V
VI
VII
VIII
IX

X
XI
XII

EJECTA DEPOSIT
During the excavation of the crater, material originallysituated close to the target surface is either thrown out of thecrater on ballistic trajectories and subsequently lands to form
the ejecta deposit, or is merely displaced upward and outward
to form part of the crater rim. This uplifted portion of thecrater-rim material is significant close to the transient craterrim but decreases rapidly with distance such that, outside twotransient-crater radii from the crater center, the material
above the pre-impact target surface is almost all ejecta
deposit. For simplicity, we ignore the uplifted fraction of thecrater rim material. We estimate the thickness of ejecta at agiven distance from an impact by assuming that the material
lying above the pre-impact ground surface is entirely ejecta,
that it has a maximum thickness te htr at the transient crater
rim, and that it falls off as one over the distance from thecrater rim cubed:
h tr d tr 3
t e = ------ § ------·
8© r¹

(43)

The power of 3 is a good approximation of data from
explosion experiments (McGetchin et al. 1973) and asatisfactory compromise for results from numericalcalculations of impacts and shallow-buried nuclear
explosions, which show that the power can vary between 2.5
and 3.5.
The ejecta thickness at the transient crater rim (assumed
to be equal to the transient crater rim height htr) may be
calculated from a simple volume conservation argument
where we equate the volume of the ejecta deposit and uplifted

transient crater rim Ve with the volume of the transient crater
below the pre-impact surface Vtc. For this simple model, we
assume that the transient crater is a paraboloid with a depth todiameter ratio of 1:2 2 . Ve is given by:
3h tr D tr
V e = -------------8

f³
D tr e 2

2Srdr-------------+
3r
4

D tr e 2§ 4d tc 2·- r – d tc¸ dr³ 2Sr ¨© --------2¹
Dtc

D tc e 2
42

2

D tr – D tc D tr – D tc ·S§
2
= --- ¨ h tr D tr + d tc --------------------- – ---------------------- ¸
2
2©
2
¹
4D

(44)

tc

where Dtr is the diameter of the transient crater at the transient
crater rim (see Fig. 3a), which is related to Dtc by:d tc + h tr
D tr = D tc ------------------d tc(45)

The volume of the transient crater is given by:3

SD tc
V tc = ------------16 2(46)

Equating Ve with Vtc and rearranging to find the rimheight gives htr = Dtc/14.1. Inserting this result into
Equation 43 gives the simple expression used in the program:
4

D tc
t e = -------------3
112r

(47*)

Earth Impact Effects Program
As this model ignores any “bulking” of the ejecta deposit
and entrainment of the substrate on which the ejecta lands, it
provides a lower bound on the probable ejecta thickness. The
use of transient crater diameter instead of final crater diameteravoids the need for a separate rim height equation for simple
and complex craters. Rim heights of complex craters, as afraction of the final crater diameter, are significantly smaller
than the scaled rim heights of simple craters because, forcomplex craters, the thickest part of the ejecta blanket
collapses back into the final crater during the late stages of thecratering process. As this collapse process is not fully
understood, we only report the ejecta thickness outside thefinal crater rim. The final rim height of the crater, which is
required for our estimate of the breccia-lens thickness in
simple craters (above) is found by inserting r = Dfr/2 into
Equation 31:
4

D tc
h fr = 0.07 ------3
D fr

(48*)

The outward flight of rock ejected from the crater occurs
in a transient, rarefied atmosphere within the expanding
fireball. In large impacts (E >200 Mt), the fireball radius iscomparable to the scale height of the atmosphere; hence, theejecta’s trajectory takes it out of the dense part of theatmosphere, allowing it to reach distances much in excess ofthe fireball radius. For smaller impacts, however, the ejecta’s
outward trajectory is ultimately stifled at the edge of thefireball, where the atmospheric density returns to normal. We
incorporate these considerations into our program by limiting
the spatial extent of the ejecta deposit to the range of thefireball for impact energies less than 200 Mt.
The ejecta arrival time is determined using ballistic travel
time equations derived by Ahrens and O’Keefe (1978) for aspherical planet. Using a mean ejection angle of 45° to the
Earth’s surface allows us to estimate the approximate arrival
time of the bulk of the ejecta. In reality, material is ejectedfrom the crater at a range of angles, and consequently, thearrival of ejecta at a given location does not occur
simultaneously. However, this assumption allows us to write
down an exact (although complex) analytical expression for
the average travel time of the ejecta Te to our specified
location:
1.5
2
–1
2a
1–e
' § e 1 – e sin ' e 2 ·T e = ----------------- 2 tan § ------------ tan ---· – ¨ ---------------------------------------------¸ (49*)© 1+e
4 ¹ © 1 + e cos ' e 2 ¹2
gE RE

where RE is the radius of the Earth, gE is the gravitational
acceleration at the surface of the Earth, and ' is the epicentral
angle between the impact point and the point of interest. The
ellipticity e of the trajectory of ejecta leaving the impact site atan angle of 45° to the horizontal and landing at the point ofinterest is given by:

829

2

2

·
1 § vee = --- ¨ ------------- – 1¸ + 1
2 © gE RE ¹
2

(50*)

where ve is the ejection velocity, and e is negative when ve2/
gERE d1. The semi-major axis a of the trajectory is given by:2ve
a = ---------------------------2
2g E 1 – e(51*)

To compute the ejection velocity of material reaching thespecified range r 'RE, we use the relation:
2g E R E tan ' e 22v e = -----------------------------------1 + tan ' e 2(52*)

which assumes that all ejecta is thrown out of the crater fromthe same point and at the same angle (45°) to the horizontal.
Equation 49 is valid only when ve2/gERE d1, whichcorresponds to distances from the impact site less than about
10,000 km (1/4 of the distance around the Earth). For
distances greater than this, a similar equation exists (Ahrens
and O’Keefe 1978); however, we do not implement it in our
program because, in this case, the arrival time of the ejecta ismuch longer than one hour. Consequently, an accurate
estimate of ejecta thickness at distal locations must take into
account the rotation of the Earth, which is beyond the scope of
our simple program. Furthermore, ejecta traveling along these
trajectories will be predominantly fine material thatcondensed out of the vapor plume and will be greatly affectedby reentry into the atmosphere, which is also not consideredin our current model. For ejecta arrival times longer than one
hour, therefore, the program reports that “little rocky ejecta
reaches our point of interest; fallout is dominated bycondensed vapor from the impactor.”
We also estimate the mean fragment size of the fineejecta at our specified location using results from a study ofparabolic ejecta deposits around venusian craters (Schallerand Melosh 1998). These ejecta deposits are thought to formby the combined effect of differential settling of fine ejecta
fragments through the atmosphere depending on fragment
size (smaller particles take longer to drop through theatmosphere), and the zonal winds on Venus (Vervack andMelosh 1992). Schaller and Melosh (1998) compared atheoretical model for the formation of the parabolic ejecta
deposits with radar observations and derived an empirical law
for the mean diameter of impact ejecta d (in m) on Venus as afunction of distance from the crater center rkm (in km):D fr Dd = d c § -----------·© 2r km¹(53*)

where Dfr is the final crater diameter measured from rim torim (in km); D 2.65, and dc 2400(Dfr/2)1.62. This relationneglects the effects of the atmosphere and windtransportation on Earth, which will be more significant for830

G. S. Collins et al.

smaller fragment sizes, and the disintegration of ejecta
particles as they land. Thus, the uncertainty in thesepredictions is greatest very close to the crater, where ejecta
fragments are large and will break up significantly during
deposition, and at great distances from the impact point,where the predicted fragment size is small. We circumvent
this problem at small distances by not calculating the mean
fragment size for ranges less than two crater radii, whichroughly corresponds to the extent of the continuous ejecta
blanket observed around extra-terrestrial craters (Melosh
1989, p. 90). We also emphasize that the predicted fragment
size is a rough mean value of the ejecta fragment size. At any
given location, there will be a range of fragment sizes aroundthis mean including large bombs and very fine-grained dust,
which will arrive at different times depending on how easily
they traverse the atmosphere.

from ground zero (the location on the Earth directly below the
airburst) is more complex than for a surface burst due to theinteraction between the blast wave direct from the source andthe wave reflected off the surface. Within a certain distancefrom ground zero, the delay between the arrival of the direct
wave and the reflected wave is sufficient for little constructive
interference of the waves to occur; this region is known as theregular reflection region. Beyond this zone, however, the two
waves merge in what is known as the “Mach reflection
region;” this effect can increase the overpressure at a given
location by as much as a factor of two (Glasstone and Dolan
1977, p. 38). Within the Mach region, we found that Equation
54 holds approximately, provided that the crossover distancerx is increased slightly as a function of burst altitude (rx 289
 0.65zb). At distances inside the regular reflection region, we
found that the peak overpressure decreases exponentiallywith distance from ground zero:

AIR BLAST
The impact-induced shock wave in the atmosphere isreferred to as the air blast or blast wave. The intensity of theblast depends on the energy released during the impact andthe height in the atmosphere at which the energy is deposited,which is either zero for impacts where a crater is formed or
the burst altitude for airburst events. The effects of the blast
wave may be estimated by drawing on data from US nuclear
explosion tests (Glasstone and Dolan 1977; Toon et al. 1994,
1997; Kring 1997). The important quantities to determine are
the peak overpressure, that is, the maximum pressure inexcess of the ambient atmospheric pressure (1 bar = 105 Pa),and the ensuing maximum wind speed. With these data, tables
compiled by the US Department of Defense may be used to
predict the damage to buildings and structures of varying
constructional quality, vehicles, windows, and trees.
To estimate the peak overpressure for crater-forming
impacts, we assume that the impact-generated shock wave in
the air is directly analogous to that generated by an explosive
charge detonated at the ground surface (surface burst). We
found that the expression:px rx
r x 1.3
p = ---------- § 1 + 3 § ----· ·© r 1¹ ¹
4r 1 ©

(54*)

is an excellent fit to empirical data on the decay of peak
overpressure p (in Pa) with distance r1 (in m) for a 1 kiloton(kt) surface burst (Glasstone and Dolan 1977; their Fig. 3.66,
p. 109). In this equation, the pressure px at the crossover pointfrom ~1/r2.3 behavior to ~1/r behavior is 75000 Pa(0.75 bars); this occurs at a distance of 290 m.
The peak overpressure resulting from an airburst is
estimated using a similar suite of equations fit to empirical
data on the peak overpressure experienced at different
distances away from explosions detonated at various heights
above the surface (Glasstone and Dolan 1977, p. 113). The
relationship between peak overpressure and distance awayp = p0 e– Er 1(55*)

where p0 and E are both functions of burst altitude:p0

3.14 × 1011zb2.6
E 34.87zb1.73(56a*)(56b*)To extrapolate these relationships to explosions (impacts)of greater energy, we again rely on yield scaling, which
implies that a specific peak overpressure occurs at a distancefrom an explosion that is proportional to the cube root of theyield energy. In other words, the ratio of the distance at whicha certain peak overpressure occurs to the cube root of the
impact energy (r(p)/E1/3) is constant for all impacts.
Therefore, the peak overpressure at the user-specified
distance r away from an impact of energy Ekt (in kilotons) is
the same as that at a distance r1 away from an impact ofenergy 1 kt, where r1 is given by:r
r 1 = ---------1e3
E kT

(57*)

The equivalent burst altitude in a 1 kt explosion zb1 isrelated to the actual burst altitude by a similar equation zb1
zb/Ekt1/3.
To compute the peak overpressure, we substitute thescaled-distance r1 into Equation 54 or 55, depending onwhether the distance r1 lies within the Mach region or the
regular reflection region for a 1 kt explosion. The distancefrom ground zero to the inner edge of the Mach region rm1 insuch an explosion depends only on the altitude of burst zb1;
we found a good fit to the observational data with the simple
function:
550z b1
r m1 = ----------------------------------1.2 550 – z b1

(58*)

Earth Impact Effects Program

831

Table 4. Air blast damage.aDistance from a 1 kt explosion(d1 in m)Over pressure(p in Pa)

126

426000133149379000297000155273000229
251121000100000

389
411

42600
38500

502
549

26800
22900

1160

6900

Description of air blast-induced damage
Cars and trucks will be largely displaced and grossly distorted
and will require rebuilding before use.
Highway girder bridges will collapse.
Cars and trucks will be overturned and displaced, requiring major
repairs.
Multistory steel-framed office-type buildings will suffer extreme
frame distortion, incipient collapse.
Highway truss bridges will collapse.
Highway truss bridges will suffer substantial distortion ofbracing.
Multistory wall-bearing buildings will collapse.
Multistory wall-bearing buildings will experience severe
cracking and interior partitions will be blown down.
Wood frame buildings will almost completely collapse.
Interior partitions of wood frame buildings will be blown down.
Roof will be severely damaged.
Glass windows shatter.

a Data extracted from Glasstone and Dolan (1977).

Note that for surface bursts (zb1 0), the Mach region isassumed to begin at the impact point (rm1 0); for scaled
burst-altitudes in excess of 550 m, there is no Mach region.
The calculated peak overpressure can then be compared withdata presented in Table 4 to assess the extent of the air blast
damage.
The characteristics of a blast wave in air at the shock
front are uniquely related by the Hugoniot equations whencoupled with the equation of state for air. The particle velocity(or peak wind velocity) behind the shock front u is given by:
c05p
u = --------- --------------------------------------7P 0 1 + 6p e 7P 0.5
0

(59*)

where P0 is the ambient pressure (1 bar), c0 is the ambient
sound speed in air (~330 m s1), and p is the overpressure(Glasstone and Dolan 1977, p. 97). If the calculated
maximum wind velocity is greater than 40 m s1, experiencefrom nuclear weapons tests suggests that “about 30% of trees
are blown down; the remainder have some branches andleaves blown off” (Glasstone and Dolan 1977, p. 225). If the
maximum wind velocity is greater than 62 m s1, devastation
is more severe: “Up to 90 percent of trees blown down;
remainder stripped of branches and leaves.”
The blast wave arrival time is given by:rdr
T b = ³ ----------U rr
T b = ----c0(64*)

This simplification results in large errors only very close
to the crater rim.
The air blast model we use extrapolates from data
recorded after a very small explosion (in impact crateringterms) in which the atmosphere may be treated as being of
uniform density. Furthermore, at this scale of explosion, thepeak overpressure decays to zero at distances so small (<1km) that the curvature of the Earth may be ignored. Neither ofthese assumptions applies to larger impacts; thus, thereliability of our predictions decreases as impact energy
increases. In the future, we hope to examine the effect of avariable-density atmosphere and a curved Earth on the blast
wave decay using numerical modeling. Such sophisticatedcalculations of the interaction between a hot ejecta plume anda realistic atmosphere by Zahnle (1990) and Toon et al.
(1994), which included blast wave formation, are in good
agreement with our simple model in the 1–10000 Mt range;
for impact energies greater than this, Equation 44 probably
overestimates the blast wave effects by a factor of 2–5.
EFFECT OF A WATER LAYER

(62)

0

where U is the shock velocity in air, given formally by:
6p r 0.5
U r = c 0 § 1 + -------------·©
7P 0 ¹For convenience, however, we assume that the shock
wave travels at the ambient sound speed in air c0. In this case,the air blast arrival time at our specified distance r is simply:(63)

The rationale discussed above for predicting theenvironmental consequences of an asteroid collision with
Earth assumes that the impact occurs on land. In fact, marine
impacts are more than twice as likely to occur as land impacts
on Earth. The influence of a water layer on the impact process
has been the subject of many recent field studies (Tsikalas et832

G. S. Collins et al.

al. 1998, 1999; Ormö and Lindström 2000), laboratory
experiments (McKinnon and Goetz 1981; Gault and Sonnett
1982), and numerical simulations (O’Keefe and Ahrens
1982a; Roddy et al. 1987; Ormö and Miyamoto 2002;
Shuvalov et al. 2002; Artemieva and Shuvalov 2002;
Wünnemann and Lange 2002), which have led to aqualitative paradigm for submarine cratering in both the deep
ocean (Wünnemann and Lange 2002) and shallow seas
(Oberbeck et al. 1993; Poag et al. 2004). However, like manyother aspects of impact cratering, an accurate quantitative
treatment of the effect of a water layer on the cratering
process requires complicated numerical methods beyond thescope of our program. Consequently, our program employs
only a rudimentary algorithm for estimating the effect of awater column on the environmental consequences of an
impact. We estimate the change in velocity of the impactor at
the seafloor vi|seafloor from that at the surface vi|surface byintegrating the drag equation (Equation 7) over the depth of
the water column:viseafloor= vi­ 3U w C D d w ½
exp ® – ------------------------- ¾
surface¯ 2U i L sin T ¿(65*)

In this equation, dw is the thickness of the water layer, L
is the diameter of the impactor after the atmospheric traverse,
and CD is the drag coefficient for a rigid sphere of water in the
supersonic regime, which we set equal to 0.877 (Landau andLifshitz 1959). This simple expression ignores both theflattening of the impactor during penetration and the
propagation of the shock wave through the water column;
however, it agrees quite favorably with numerical simulationsof deep sea impact events (Wünnemann and Lange 2002).
For marine impact scenarios, we calculate theapproximate kinetic energy of the impactor at the moment it
strikes the surface of the water layer Esurface and when it reaches
the seafloor Eseafloor. Using Equation 16, we compute andreport two transient crater diameters: one in the water layer and
one in the seafloor. For the transient crater diameter in thewater layer, we use the impact velocity at the surface (vivi|surface), replace the constant 1.161 with 1.365, and use a target
density equal to the density of water (Ut Uw 1000 kg m3).
For the transient crater diameter in the seafloor we assume thatthe impact velocity is that of the impactor at the seafloor (vi =
vi|seafloor) and use a target density of Ut = 2700 kg m3.
From this point, the program continues as before,
calculating the dimensions of the crater in the seafloor,
whether it is simple or complex, the volume of the target
below the seafloor that is melted, etc. The air blast andthermal radiation calculations proceed assuming that the
impact energy is that released at the surface of the water layer(E Esurface); the seismic shaking and ejecta calculations, on
the other hand, assume that the impact energy is the kinetic
energy of the impactor at the moment it reaches the sea floor(E
Eseafloor). As a result, our program predicts that thethermal radiation and air blast effects are unchanged by thepresence of the water column relative to a land impact of thesame energy. However, a deep enough water layer could
entirely suppress the seismic shaking and excavation of rocky
ejecta that would occur in an impact of the same size on dry
land.
The current version of the program does not compute theeffects of impact-generated tsunamis for water impacts. There
are several reasons for this omission, in spite of requests bymany users for this feature. The first set of reasons ispractical. A plausible tsunami computation requires not only
the depth of the water at the impact site, but also the depth ofthe ocean over the entire path from the impact to the observer.
The observer must, of course, be on a coastline with anunobstructed great circle path to the impact site. The observed
tsunami height and run up depends on the local shoreline
configuration and slope, the presence or absence of offshore
bars, etc. The sheer number of input parameters required
would daunt most potential users. This sort of computation
requires a professional effort of the scale of Ward andAsphaug (2000, 2003); it is far beyond the capability of oursimple program. The other set of reasons centers around thecurrent uncertainty of the size of tsunamis generated by
impacts. Following some initial spectacular estimates oftsunami heights, heights that greatly exceed the depth of theocean itself (Hills et al. 1994), a reaction occurred (Melosh2003) based on a newly-unclassified document (Van Dorn etal. 1968) that suggests that impact-tsunami waves break on
the continental shelf and pose little threat to coastal locations(the “Van Dorn” effect). The present situation with regard to
this hazard is thus confused, and we decided against including
such an estimate in our code until the experts have sorted out
the actual size of the effect.
GLOBAL EFFECTS
In addition to the regional environmental consequencesof the impact event, we also compute some global
implications of the collision. We compare the linear
momentum of the impactor at the moment it strikes the target
surface, Mi mivi, with the linear momentum of the Earth, ME
mEvE, where mE is the mass of the Earth (5.83 × 1024 kg) andvE is the mean orbital velocity of the Earth (29.78 km s1).
Depending on the ratio Mi/ME, the program reports the likely
effect of the impact on the orbit of the Earth. Our choice oflimits on Mi/ME and the corresponding degree to which theorbit changes is presented in Table 5. We compare the angularmomentum imparted by the impact *i = miviREcosT to the
angular momentum of the Earth *E = 5.86 × 1033 kg m3 s1 ina similar manner. Table 5 also presents the ranges of the ratio*i/*E for which we assume certain qualitative changes to the
Earth’s rotation period and the tilt of its axis as a result of the
impact. Finally, we compare the volume of the transient crater
Vtc with the volume of the Earth VE. In the event that the ratio

Earth Impact Effects Program
Vtc/VE is greater than 0.5, we assume that the Earth iscompletely disrupted by the impact and forms a new asteroid
belt between Venus and Mars. If Vtc/VE is in the range of 0.1–
0.5, the program reports that the Earth is strongly disturbed by
the impact but loses little mass. Otherwise, the program
reports that the Earth is not strongly disturbed by the impact
and loses negligible mass.
Currently, we do not make any estimates regarding thepotentially global environmental consequences of large
impact events. In such catastrophes, dust, melt droplets, andgas species generated during the impact event are ejected outof the Earth’s atmosphere and dispersed all over the globe(Alvarez1980).
Severalpotentiallydevastating
environmental consequences could result from the re-entry
and prolonged settling though the atmosphere of this material(Toon et al. 1982, 1994, 1997; Zahnle 1990; Kring 2000).
Thermal radiation generated during the re-entry of high speed
ejecta may be strong enough to ignite wildfires over large
areas of the globe (Alvarez 1980; Melosh et al. 1990; Toon etal. 1994, 1997). Dust loading in the atmosphere may block out
light and restrict photosynthesis for months after the impact(Toon et al. 1982, 1994, 1997; Covey et al. 1990; Zahnle1990). Furthermore, the presence of carbonate or anhydrite
rocks in the sedimentary target sequence may add additional
environmental consequences due to the production ofclimatically active gas species (Lewis et al. 1982; Prinn andFegley 1987; Zahnle 1990; Brett 1992; Pope et al. 1997;
Pierazzo et al. 1998; Kring 1999). These compounds may
produce aerosols that further reduce the amount of light thatreaches the surface of the Earth, condense with water to formacid rain, react with and deplete ozone levels, and cause“greenhouse” warming. To make reasonable estimates of theseverity of these effects requires detailed, time-consuming
computations involving a large suite of model parameters (forexample, target chemistry and mass-velocity distributions forthe ejected material; Toon et al. 1997). Such calculations arewell beyond the scope of our simple program; we direct
readers interested in these processes to the above references
for further information.
APPLICATIONS OF THE EARTH IMPACT EFFECTS
PROGRAMWe have written a computer program that estimates theenvironmental consequences of impact events both past andfuture using the analytical expressions presented above. To
illustrate the utility of our program, consider the hypotheticaldevastation at various locations within the United States if
asteroids of various sizes were to strike Los Angeles. The firstevent worthy of consideration is the impact of a ~75-m
diameter stony asteroid (density
2000 kg m3), which
occurs somewhere on earth every 900 years on average. In
this case, our program determines that the impactor would
begin to disrupt at an altitude of ~66 km and deposit the833

Table 5. Global implications of an impact event.
Ratio

Qualitative global change

Mi/ME <0.001
0.001 <Mi/ME <0.01
0.01 <Mi/ME <0.1
Mi/ME >0.1
*i/*E <0.01

No noticeable change in orbit.
Noticeable change in orbit.
Substantial change in orbit.
Totally changes orbit.
No noticeable change in rotation period
and tilt of axis.
Noticeable change in rotation period andtilt of axis.
Substantial change in rotation period andtilt of axis.
Totally changes rotation period and tilt of
axis.

0.01 <*i/*E <0.1
0.1 <*i/*E <1.0

*i/*E >1.0

majority of its kinetic energy in the atmosphere at a burst
altitude of ~5 km. The air blast from this event would bestrong enough to cause substantial damage to woodenbuildings and blow down 90% of trees to a radius of ~15 km,
which agrees well with the extent of forest damage observed
after the Tunguska airburst event in Siberia in 1908.
Next, let us examine the environmental consequences ofthree impact events of drastically different magnitudes at a
fixed distance of 200 km away from our impact site in Los
Angeles, which is the approximate distance from L.A. to San
Diego. The three impacts we will consider are a 40-m diameteriron asteroid (density 8000 kg m3) impacting at 20 km s1
into a sedimentary target (density 2500 kg m3), which is theapproximate scenario of the event that formed Barringer
Crater in northern Arizona; a 1.75-km diameter stony asteroid(density
2700 kg m3) impacting at 20 km s1 into acrystalline target (density 2750 kg m3), which corresponds
approximately to the magnitude of the impact event thatformed the Ries crater in Germany; and an 18-km diameterstony asteroid also impacting at 20 km s1 into a crystalline
target, which represents a reasonable estimate of the scale of
the Chicxulub impact event in the Gulf of Mexico. For each
impact we assume identical impact angles (T = 45°). Table 6
presents a comparison of the important parameters discussed
in this paper for each impact event at a distance of 200 km
away from our hypothetical impact center in Los Angeles.
Note the substantial variation in impact energy between each
impact event, which results in very different estimatedenvironmental effects 200 km away in San Diego. The average
recurrence interval is for the entire Earth; the two larger
impact scenarios are both extremely rare events. All of these
impactors are large enough (or strong enough) to traverse theatmosphere and create a single impact crater; however, theBarringer-scale impactor is slowed considerably by theatmosphere.
In the case of the small iron asteroid impact, San Diego isa very safe place to be. As little to no vapor is generated
during this event, there is no significant thermal radiation.
The impact crater formed is only 1.2 km in diameter; theatmosphere would prevent much if any ejecta thrown out of

834

G. S. Collins et al.

Table 6. Comparison of environmental effects 200 km away from various impacts.
Impactor size (km)0.04 (iron)

1.75

18

50

–

–

1.3 × 1016
3.2
1000a

1.5 × 1021
3.6 × 105
2.1 × 106

1.65 × 1024
3.9 × 108
4.6 × 108

1.2 (Simple)

23.7 (Complex)

186 (Complex)

–
–

23
1.2

236
–

Equation 34, 36, 37
Equation 35
Equation 39; Table 1––
No fireball created due
to low impact velocity.

Equation 42

40

14.8
300
Third degree burns;
many combustible
materials ignited.
40––
Within the fireballradius, everything
incinerated!
40

4.9
I–II (III)b

8.3
VII–VIII (VIII)b

10.4
X–XI (XI)b

Arrival time of bulk ejecta (s)Equation 40
Equation 41; Tables 2
and 3
Equations 49–52

206

206

Average ejecta thickness (m)Mean fragment diameter (cm)
Arrival time of air blast (s)Peak overpressure (bars)
Maximum wind velocity (m/s)
Air blast damage

Equation 47
Equation 53
Equation 64
Equations 54 and 57
Equation 59
Table 4Ejecta blocked byatmosphere.
–
–
606
0.004
0.96
Blast pressure
insufficient to cause
damage.

.09
2.4
606
0.80
145
Wooden and tall
unstable buildings
collapse; glass
windows shatter; 90%
trees blown down.

137
–
606
77
2220
Collapse of almost allbuildings and bridges;
damage andoverturning ofvehicles; 90% of trees
blown down.

Percentage reduction in velocity
during atmospheric entry
Impact energy (J)(megatons; 1 Mt = 4.2 × 1015 J)
Recurrence interval (years;
whole Earth)Final crater diameter (km)Fireball radius (km)Time at which radiation begins(s)Thermal exposure (MJ m2)
Duration of irradiation (s)Thermal radiation damage
Arrival time of major seismic
shaking (s)Richter scale magnitude
Modified Mercalli Intensity

Equations 9, 11, 12,
15, 16, 17, 20
Equation 1
Equation 3
Equations 21 and 22 or
27
Equation 32
Equation 33

a Note that the recurrence interval is based on impact energy alone. Iron asteroids represent only ~5% of the known NEOs; therefore, the real recurrence interval

for an impact of this sort is ~20 times longer.
b Estimates of seismic intensity according to Toon et al. (1997).

the crater from reaching San Diego. Furthermore, the air blast
would be extremely weak at a radius of 200 km: the change inatmospheric pressure would be barely discernible at a rise ofless than one part in a hundred with ensuing wind speeds ofunder a meter per second. The only noticeable consequencesfrom this scale of impact would be from seismic shaking,which would be most obvious around 40 sec after the impact
occurred. The impact would be analogous to an earthquake ofRichter magnitude 4.9 centered in L.A. The Modified
Mercalli Intensity of the shaking in San Diego would be in therange of I–II, depending on the local geology, meaning thatthe disturbance would be felt only in favorable circumstances
and would not cause any permanent damage.
In stark contrast, San Diego would not be an attractive
location in the event that either of the two larger impacts
occurred in L.A. In the case of a 1.75-km diameter asteroid
impact, the thermal exposure at a range of 200 km would be
sufficient to ignite most combustible materials and cause third
degree burns to unfortunate San Diegans, particularly if
visibility was good. The seismic surface waves emanatingfrom the impact site would arrive half a minute later andwould be violent enough to damage poorly constructedstructures, topple tall chimneys, factory stacks, andmonuments, and overturn furniture in homes and offices. A
relatively thin layer of ejecta would arrive a few minutes after
the impact and begin to rain down through the atmosphere
covering the city in a few cm of ejecta fragments. During thistime, the air blast wave would propagate across the city
flattening any poorly constructed structure that remained
standing and kicking up 150 m/s winds capable of blowing
over most trees.
In the case of a Chicxulub-scale event, the environmental
consequences in San Diego would be extreme. Seconds after
the impact, the fireball would engulf the city of San Diego,
incinerating all combustible materials. The seismic shaking
that would arrive moments later would be as violent as thatcaused by the most severe earthquake recorded on Earth. Ifanything remained standing after this episode, it would soon
be smothered and suffocated by the arrival of a huge amountof rock debris thrown out of the growing crater. Finally, aEarth Impact Effects Program

835

Fig. 4. Thermal exposure from the impact-generated fireball, divided by the impact energy (in Mt) to the one-sixth power, as a function of
distance from the impact center, for three hypothetical impacts in Los Angeles. (Dividing f) by EMt1/6 allows us to more easily compare theextent of thermal radiation damage for impacts of different energies. Plotted in this way, the scaled thermal exposure required to ignite a given
material does not depend on impact energy; thus, values on the ordinate can be compared directly with the data in Table 1.) The solid line
represents an impact of an 18-km diameter stony asteroid; the dashed line represents an impact of a 1.75-km stony asteroid; no line appears
for the 40-m iron asteroid because little to no vapor is produced during the impact and no significant thermal radiation occurs. The verticallines represent four distances from the impact center that correspond to the approximate distances from L.A. to four major U.S. cities. Greyarrows indicate the radial extent of fires ignited by thermal radiation from the fireball as predicted by Toon et al. (1997). See the text for further
details.

strong pressure wave nearly 80 times greater than atmosphericpressure would pass through San Diego flattening any
remaining erect buildings; winds over 2 km per second would
follow, violently scattering debris and ripping up trees.
The algorithm presented in this paper also allows us toextend our study of potential impact-related disasters over arange of distances away from the impact. Figures 4–7
illustrate how each of the major environmental consequences
depends on the distance away from the impact site for thethree different scales of impact; in each figure, the dotted line
represents the 40-m diameter iron asteroid impact, the dashedline represents the 1.75-km diameter asteroid impact, and thesolid line represents the 18-km diameter asteroid impact. Also
marked on the figures are the approximate locations of four
major U.S. cities with respect to Los Angeles, the location of
our impact site. Figure 4 shows the reduction in thermal
exposure with distance away from the edge of the fireball.
The change in slope of the curves is caused by the curvatureof the Earth, which acts to hide more and more of the fireballbelow the horizon with increasing distance away from theimpact. As a result, the thermal radiation damage from even a
Chicxulub-scale impact is restricted to a range of ~1500 km;
in the event that an 18-km diameter asteroid struck L.A.,
Denver would probably escape any thermal radiation damage.

The horizontal positions of the grey arrows in Fig. 4 denote
the radial extent of thermal radiation damage for the twolarger impacts, according to Toon et al. (1997). Comparing
our predictions and those of Toon et al. illustrates theapproximate uncertainty of both estimates. Figure 5 shows theimpact ejecta thickness for each potential impact event as afunction of distance. Figure 6 shows the drop in effective
seismic magnitude with distance away from the impact,which can be related to the intensity of shaking using Table 2.
The graph illustrates that impact-related seismic shaking
would be felt by all as far as Denver if a Ries-scale impact
occurred in L.A.; and significant tremors would be felt as fara-field as New York City following a Chicxulub-scale impact
in L.A. The decay in peak overpressure with distance from theimpact associated with the impact air blast wave is depicted inFig. 7. In the case of a 40-m diameter iron asteroid, the air
blast damage would be confined to a few km away from theimpact site. However, the blast wave from a Chicxulub-scale
impact centered in L.A. may be strong enough to level steel
framed buildings in San Francisco and wooden buildings as
far away as Denver. For comparison, the grey squares inFig. 7 illustrate the approximate radial extent of airblast
damage for each impact event, as predicted by Toon et al.
(1997). For the two larger impacts, the disagreement between

836

G. S. Collins et al.

Fig. 5. The effective seismic magnitude as a function of distance away from three hypothetical impacts in Los Angeles. The solid line
represents an impact of an 18-km diameter stony asteroid; the dashed line represents an impact of a 1.75-km stony asteroid; the dotted line
represents the impact of a 40-m diameter iron asteroid. The vertical lines represent four distances from the impact center that correspond to
the approximate distances from L.A. to four major U.S. cities. See the text for further details.

Fig. 6. The variation in ejecta-deposit thickness with increasing distance from the impact point for three hypothetical impacts centered in Los
Angeles. The solid line represents an impact of an 18-km diameter stony asteroid; the dashed line represents an impact of a 1.75-km stonyasteroid; the dotted line represents the impact of a 40-m diameter iron asteroid. The vertical lines represent four distances from the impact
center that correspond to the approximate distances from L.A. to four major U.S. cities. See the text for further details.

Earth Impact Effects Program

837

Fig. 7. The peak airblast overpressure as a function of distance from three hypothetical impacts centered in Los Angeles. The solid line
represents an impact of an 18-km diameter stony asteroid; the dashed line represents an impact of a 1.75-km stony asteroid; the dotted line
represents the impact of a 40-m diameter iron asteroid. The dash-dotted line illustrates the decay of peak overpressure with distance away froman airburst resulting from the impact of a 75-m diameter stony object (density = 2000 kg m3) at 17 km s1, as discussed in the text. The verticallines represent four distances from the impact center that correspond to the approximate distances from L.A. to four major U.S. cities. The greysquares show the extent of the airblast damage as predicted by Toon et al. (1997). See the text for further details.

our predictions and those of Toon et al. (1997) is due to ourneglect of the effects of Earth curvature and a variable density
atmosphere, as discussed earlier.
DISCUSSION
The Earth Impact Effects Program provides a
straightforward method for estimating the regional
environmental consequences of the collision of extraterrestrial
objects with the Earth. To implement such a program, it isnecessary to make some simplifying assumptions that limit theaccuracy of any predictions. Nevertheless, some important
conclusions may be drawn from our simple model. Of theenvironmental consequences that we consider, the seismic
shaking poses the most significant threat at large distancesfrom the impact site; effects of ejecta fallout and the air blast
decrease much more rapidly with distance away from theimpact site. Moreover, the curvature of the Earth ensures that,even in the case of very rare ~20-km scale impact events, thethermal radiation will be confined to a maximum range of1500 km, at which point the fireball is completely hidden
below the horizon. Closer to the impact site, however, the air
blast, thermal radiation, and ejecta deposition combine toseverely affect the local environment and should all beconsidered in any hazard assessment.

We believe that we have developed a valuable tool foruse both within the scientific community and the population
at large. We anticipate that within the field of impact cratering
our program will serve the function of providing a quick
assessment of the hazard risk for potential future impact
scenarios and enable those studying particular terrestrial
impact events to estimate the regional environmental
consequences associated with the impact. We welcome anysuggestions for improvements or additions to the algorithm
presented here.
Acknowledgments–Many members of the impact crateringcommunity and users of the Earth Impact Effects Program
have offered helpful advice for improvements to our model.
In particular, we gratefully acknowledge input from Bevan
French, Boris Ivanov, Natasha Artemieva, Ivan Nemtchinov,
Kai Wünnemann, Lori Styles, Al Harris, Alexander Reid, andBlake Morlock. We are indebted to the thorough andinsightful reviews of Erik Asphaug and an anonymous
reviewer, and the editorial handling of Elisabetta Pierazzo.
This work was supported by NASA grant NAG5–11493. This
is IARC publication number 2005-0414.
Editorial Handling—Dr. Elisabetta Pierazzo

838

G. S. Collins et al.
REFERENCES

Ahrens T. J. and O’Keefe J. D. 1978. Energy and mass distributionsof impact ejecta blankets on the moon and Mercury. Proceedings,
9th Lunar and Planetary Science Conference. pp. 3787–3802.
Alvarez L. W., Alvarez W., Asaro F., and Michel H. V. 1980.
Extraterrestrial cause for the Cretaceous-Tertiary extinction.
Science 208:1095–1108.
Artemieva N. A. and Shuvalov V. V. 2002. Shock metamorphism on
the ocean floor (numerical simulations). Deep Sea Research Part
II: Topical Studies in Oceanography 49:959–968.
Binzel R. P., Lupishko D. F., Di Martino M., Whiteley R. J., and Hahn
G. J. 2003. Physical properties of near-Earth objects. In Asteroids
III, edited by Bottke W. F., Cellino A., Paolicchi P., and Binzel P.
R. Tucson: The University of Arizona Press. pp. 255–271.
Bland P. A. and Artemieva N. A. 2003. Efficient disruption of small
asteroids by the Earth’s atmosphere. Nature 424:288–291.
Bottke W. F. Jr., Nolan M. C., Greenberg R., and Kolvoord R. A.
1994. Collisional lifetimes and impact statistics of near-Earthasteroids. In Hazards due to comets and asteroids, edited byGehrels T. Tucson: The University of Arizona Press. pp 337–357.
Brett R. 1992. The Cretaceous-Tertiary extinction: A lethal
mechanism involving anhydrite target rocks. Geochimica et
Cosmochimica Acta 56:3603–3606.
Bus S. J. and Binzel R. P. 2002. Phase II of the small main-belt
asteroid spectroscopic survey: A feature-based taxonomy. Icarus
158:146–177.
Chapman C. R. and Brandt J. C. 2004. Introduction to comets, 2ndedition. New York: Cambridge University Press.
Chyba C. F., Thomas P. J., and Zahnle K. J. 1993. The 1908 Tunguska
explosion: Atmospheric disruption of a stony asteroid. Nature
361:40–44.
Covey C., Ghan S. J., Walton J. J., and Weissman P. R. 1990. Global
environmental effects of impact-generated aerosols: Resultsfrom a general circulation model. In Global catastrophes inEarth history, edited by Sharpton V. S. and Ward P. D. Special
Paper 247. Boulder: Geological Society of America. pp. 263–
270.
Croft S. K. 1985. The scaling of complex craters. Journal ofGeophysical Research 90:C828–C842.
Dence M. R. 1965. The extraterrestrial origin of Canadian craters.
Annual New York Academy of Science 123:941–969.
Dence M. R., Grieve R. A. F., and Robertson P. B. 1977. Terrestrial
impact structures: Principal characteristics and energy
considerations. In Impact and explosion cratering, edited by
Roddy D. J., Pepin R. O., and Merrill R. B. New York: Pergamon
Press. pp 247–275.
Gault D. E. 1974. Impact cratering. In A primer in lunar geology,
edited by Greeley R. and Shultz P. H. Moffett Field: NASA Ames
Research Center. pp. 137–175.
Gault D. E. and Sonett C. P. 1982. Laboratory simulation of pelagic
asteroid impact: Atmospheric injection, benthic topography, andthe surface wave radiation field. In Geological implications ofimpacts of large asteroid and comets on the Earth, edited by
Silver L. T. and Schultz P. H. Special Paper 190. Boulder:
Geological Society of America. pp. 69–92.
Glasstone S. and Dolan P. J. 1977. The effects of nuclear weapons,
3rd edition. Washington D.C.: United States Department of
Defense and Department of Energy.
Grieve R. A. F. and Cintala M. J. 1992. An analysis of differential
melt-crater scaling and implications for the terrestrial impact
record. Meteoritics 27:526–538.
Grieve R. A. F. and Garvin J. B. 1984. A geometric model for
excavation and modification at terrestrial simple impact craters.
Journal of Geophysical Research 89:11,561–11,572.

Grieve R. A. F., Dence M. R., and Robertson P. B. 1977. Cratering
processes: As interpreted from the occurrence of impact melts. In
Impact and explosion cratering, edited by Roddy D. J., Pepin R.
O., and Merrill R. B. New York: Pergamon Press. pp 791–814.
Grieve R. A. F. and Therriault A. M. 2004. Observations at terrestrial
impact structures: Their utility in constraining crater formation.
Meteoritics & Planetary Science 39:199–216.
Herrick R. R., Sharpton V. L., Malin M. C., Lyons S. N., and Freely
K. 1997. Morphology and morphometry of impact craters. In
Venus II, edited by Bougher S. W., Hunten D. M., and Phillips R.
J. Tucson: The University of Arizona Press. pp. 1015–1046.
Hills J. G., Nemchinov I. V., Popov S. P., and Teterev A. V. 1994.
Tsunami generated by small asteroid impacts. In Hazards fromcomets and asteroids, edited by Gehrels T. Tucson: The
University of Arizona Press. pp. 779–789.
Hilton J. L. 2002. Asteroid masses and densities. In Asteroids III,edited by Bottke W. F. Jr., Cellino A., Paolicchi P., and Binzel P.
Tucson: The University of Arizona Press. pp. 103–112.
Holsapple K. A. and Schmidt R. M. 1982. On the scaling of crater
dimensions II—Impact processes. Journal of GeophysicalResearch 87:1849–1870.
Holsapple K. A. 1993. The scaling of impact processes in planetarysciences. Annual Review of Earth and Planetary Sciences 21:
333–373.
Ivanov B. A. and Artemieva N. A. 2002. Numerical modeling of theformation of large impact craters. In Catastrophic events andmass extinctions: Impacts and beyond, edited by Koeberl C. and
MacLeod K. G. Special Paper 356. Boulder: Geological Societyof America. pp. 619–630.
Ivanov B. A., Deniem D., and Neukum G. 1997. Implementation of
dynamic strength models into 2D hydrocodes: Applications foratmospheric breakup and impact cratering. International Journalof Impact Engineering 20:411–430.
Korycansky D. G., Zahnle K. J., and Mac Low M. M. 2000. Highresolution simulations of the impacts of asteroids into thevenusian atmosphere. Icarus 146:387–403.
Korycansky D. G., Zahnle K. J., and Mac Low M. M. 2002. Highresolution simulations of the impacts of asteroids into thevenusian atmosphere II: 3D Models. Icarus 157:1–23.
Korycansky D. G. and Zahnle K. J. 2003. High-resolution
simulations of the impacts of asteroids into the venusian
atmosphere III: Further 3D models. Icarus 161:244–261.
Korycansky D. G. and Zahnle K. J. 2004. Atmospheric impacts,
fragmentation, and small craters on Venus. Icarus 169:287–299.
Krinov E. L. 1966. Giant meteorites. New York: Pergamon Press.
397 p.
Kring D. A. 1997. Air blast produced by the Meteor Crater impact
event and a reconstruction of the affected environment.
Meteoritics & Planetary Science 32:517–530.
Kring D. A. 1999. Ozone-depleting chlorine and bromine producedby the Chicxulub impact event. Meteoritics & Planetary Science
34:A67–A68.
Kring D A. 2000. Impact events and their effect on the origin,evolution, and distribution of life. GSA Today 10:1–7.
Landau L. D. and Lifshitz E. M. 1959. Fluid mechanics. New York:
Pergamon Press. 536 p.
Lewis J. S., Watkins G. H., Hartman H., and Prinn R. G. 1982.
Chemical consequences of major impact events on Earth. In
Geological implications of impacts of large asteroid and cometson the Earth, edited by Silver L. T. and Schultz P. H. Special Paper
190. Boulder: Geological Society of America. pp. 215–221.
Marsden B. G. and Steel D. I. 1994. Warning times and impact
probabilities for long-period comets. In Hazards due to comets
and asteroids, edited by Gehrels T. Tucson: The University of
Arizona Press. pp. 221–239.

Earth Impact Effects Program

McGetchin T. R., Settle M., and Head J. W. 1973. Radial thickness
variation in impact crater ejecta: Implications for lunar basin
deposits. Earth and Planetary Science Letters 20:226–236.
McKinnon W. B. and Goetz P. 1981. Impact into the Earth’s ocean
floor during the last billion years: Preliminary experiments,
theoretical models, and possibilities for geological detection.
Conference on Large Body Impacts and Terrestrial Evolution:
Geological, Climatological, and Biological Implications. pp. 1–
34.
McKinnon W. B. and Schenk P. M. 1985. Ejecta blanket scaling on
the Moon and Mercury—Inferences for projectile populations(abstract). Proceedings, 16th Lunar and Planetary Science
Conference. pp. 544–545.
Melosh H. J. 1981. Atmospheric breakup of terrestrial impactors. In
Multi-ring basins, edited by Schultz P. H. and Merrill R. B. New
York: Pergamon Press. pp. 29–35.
Melosh H. J. 1989. Impact cratering: A geologic process. New York:
Oxford University Press. 245 p.
Melosh H. J. 2003. Impact tsunami: An over-rated hazard (abstract#1338). 34th Lunar and Planetary Science Conference. CD-ROM.
Melosh H. J., Schneider N. M., Zahnle K. J., and Latham D. 1990.
Ignition of global wildfires at the Cretaceous/Tertiary boundary.
Nature 343:251–254.
Melosh H. J. Artemieva N. A., Golub A. P., Nemchinov I. V.,
Shuvalov V. V., and Trubetskya I. A. 1993. Remote visual
detection of impacts on the lunar surface (abstract). Proceedings,
24th Lunar and Planetary Science Conference. pp. 975–976.
Near-Earth Object Science Definition Team. 2003. Study todetermine the feasibility of extending the search for near-Earthobjects to smaller limiting diameters. NASA Technical Report.
Nemtchinov I. V., Shuvalov V. V., Artemieva N. A., Ivanov B. A.,
Kosarev I. B., and Trubetskaya I. A. 1998. Light flashes causedby meteoroid impacts on the lunar surface. Solar System
Research 32:99–114.
Oberbeck V. R., Marshall J. R., and Aggarwal H. 1993. Impacts,tillites, and the breakup of Gondwanaland. Journal of Geology
101:1–19.
O’Keefe J. D. and Ahrens T. J. 1982a. The interaction of theCretaceous/Tertiary extinction bolide with the atmosphere,
ocean, and solid Earth. In Geological implications of impacts oflarge asteroid and comets on the Earth, edited by Silver L. T. and
Schultz P. H. Special Paper 190. Boulder: Geological Society ofAmerica. pp. 103–109.
O’Keefe J. D. and Ahrens T. J. 1982b. Cometary and meteorite
swarm impact on planetary surfaces. Journal of GeophysicalResearch 87:6668–6680.
Ormö J. and Lindström M. 2000. When a cosmic impact strikes theseabed. Geological Magazine 137:67–80.
Ormö J. and Miyamoto M. 2002. Computer modeling of the water
resurge at a marine impact: The Lockne crater, Sweden. DeepSea Research Part II 49:983–994.
Ortiz J. L., Sada P. V., Bellot Rubio L. R., Aceituno F. J., Aceituno J.,
Gutierrez P. J., and Thiele U. 2000. Optical detection of
meteoroid impacts on the Moon. Nature 405:921–923.
Passey Q. and Melosh H. J. 1980. The effects of atmospheric breakup
on crater field formation. Icarus 42:211–233.
Petrovic J. J. 2001. Mechanical properties of meteorites and theirconstituents. Journal of Materials Science 36:1579–1583.
Pierazzo E. and Melosh H. J. 2000. Melt production in obliqueimpacts. Icarus 145:252–261.
Pierazzo E., Vickery A. M., and Melosh H. J. 1997. A re-evaluationof impact melt production. Icarus 127:408–423.
Pierazzo E., Kring D. A., and Melosh H. J. 1998. Hydrocode
simulation of the Chicxulub impact event and the production ofclimatically active gases. Journal of Geophysical Research 103:
28,607–28,625.

839

Pike R. J. 1980. Control of crater morphology by gravity and target
type: Mars, Earth, Moon. Proceedings, 11th Lunar and Planetary
Science Conference. Geochimica et Cosmochimica Acta 3:2159–
2190.
Poag C. W., Koeberl C., and Reimold W. U. 2004. The Chesapeake
Bay Crater—Geology and geophysics of a Late Eocene
submarine impact structure. Heidelberg: Springer. 522 p.
Pope K. O., Baines K. H., Ocampo A. C., and Ivanov B. A. 1997.
Energy, volatile production, and climatic effects of the Chicxulub
Cretaceous-Tertiary impact. Journal of Geophysical Research
102:21,645–21,654.
Prinn R. G. and Fegley B. 1987. Bolide impacts, acid rain, andbiosphere traumas at the Cretaceous-Tertiary boundary. Earthand Planetary Science Letters 83:1–15.
Richter C. F. 1958. Elementary seismology. San Francisco: W. H.
Freeman. 768 p.
Roddy D. J., Schuster S. H., Rosenblatt M., Grant L. B., Hassig P. J.,
and Kreyenhagen K. N. 1987. Computer simulation of large
asteroid impacts into oceanic and continental sites-preliminary
results on atmospheric, cratering, and ejecta dynamics.
International Journal of Impact Engineering 5:525–541.
Schaller C. J. and Melosh H. J. 1998. Venusian ejecta parabolas:
Comparing theory with observations. Icarus 131:123–137.
Schmidt R. M. and Housen K. R. 1987. Some recent advances in thescaling of impact and explosion cratering. International Journalof Impact Engineering 5:543–560.
Schultz P. H. and Gault D. E. 1975. Seismic effects from majorbasin formation on the Moon and Mercury. The Moon 12:159–
177.
Scotti J. and Melosh H. J. 1993. Estimate of the size of comet
Shoemaker-Levy 9 from a tidal breakup model. Nature 365:733–
735.
Shoemaker E. M. 1962. Interpretation of lunar craters. In Physics andastronomy of the Moon, edited by Kopal Z. New York: Academic
Press. pp. 283–359.
Shoemaker E. M., Ruth F. W., and Shoemaker C. S. 1990. Asteroid
and comet flux in the neighborhood of Earth. In Global
catastrophes in Earth history, edited by Sharpton V. L. and Ward.
P. D. Special Paper 247. Boulder: Geological Society of America.
pp. 155–170.
Shuvalov V. V., Dypvik H., and Tsikalas P. 2002 Numericalsimulations of the Mjølnir marine impact crater. Journal ofGeophysical Research 107, doi:10.1029/2001JE001698.
Svetsov V. V., Nemtchinov I. V., and Teterev A. V. 1995.
Disintegration of large meteoroids in the Earth’s atmosphere:
Theoretical models. Icarus 116:131–153.
Toon O. B., Pollack J. B., Ackerman T. P., Turco R. P., McKay C. P.,
and Liu M. S. 1982. Evolution of an impact-generated dust cloudand its effects on the atmosphere. In Geological implications ofimpacts of large asteroids and comets on the Earth, edited by
Silver L. T. and Schultz P. H. Boulder: Geological Society ofAmerica. pp. 187–200.
Toon O. B., Zahnle K., Turco R. P., and Covey C. 1994.
Environmental perturbations caused by impacts. In Hazards due
to comets and asteroids, edited by Gehrels T. Tucson: The
University of Arizona Press. pp. 791–826.
Toon O. B., Zahnle K., Morrison D., Turco R. P., and Covey C. 1997.
Environmental perturbations caused by the impacts of asteroids
and comets. Reviews of Geophysics 35:41–78.
Tsikalas F., Gudlaugsson S. T., Eldholm O., and Faleide J. I. 1998.
Integrated geophysical analysis supporting the impact origin of
the Mjølnir structure, Barents Sea. Tectonophysics 289:257–
280.
Tsikalas F., Gudlaugsson S. T., Faleide J. I., and Eldholm O. 1999.
Mjølnir Structure, Barents Sea: A marine impact crater
laboratory. In Impact cratering and planetary evolution II, edited

840

G. S. Collins et al.

by Dressler B. O. and Sharpton V. L. Special Paper 339. Boulder:
Geological Society of America. pp. 193–204.
Turtle E. P., Pierazzo E., Collins G. S., Osinski G. R., Melosh H. J.,
Morgan J. V., and Reimold W. U. 2005. In Large meteorite
impacts III, edited by Kenkmann T., Hörz F., and Deutsch A.
Geological Society of America Special Paper #384. pp. 1–24.
Van Dorn W. G., LeMéhauté B., and Hwang L. S. 1968. Handbook of
explosion-generated water waves, volume I—State of the art.
Pasadena: Tetra Tech.
Ward S. N. and Asphaug E. 2000. Asteroid impact tsunami: A
probabilistic hazard assessment. Icarus 145:64–78.
Ward S. N. and Asphaug E. 2003. Asteroid impact tsunami of 2880
March 16. International Journal of Geophysics 153:F6–F10.

Vervack R. J. and Melosh H. J. 1992. Wind interaction with falling
ejecta: Origin of the parabolic features on Venus. GeophysicalResearch Letters 19:525–528.
Wünnemann K. and Lange M. A. 2002. Numerical modeling of
impact-induced modifications of the deep-sea floor. Deep SeaResearch Part II 49:969–982.
Zahnle K. J. 1990. Atmospheric chemistry by large impacts. In
Global catastrophes in Earth history, edited by Sharpton V. L.
and Ward P. D. Special Paper 247. Boulder: Geological Societyof America. pp. 271–288.
Zel’dovich Ya. B. and Raizer Yu. P. 1966. Physics of shock waves andhigh-temperature hydrodynamic phenomena. New York:
Academic Press. 916 p.

Errata and Improvements in Earth Impact E↵ects Program
Gareth Collins and Jay Melosh
May 13, 2013

1

ErrataTwo equations in Collins et al. [2005] contain typographic errors. Equation 4 should be:
TRL =

2(1

TRE
cos

(1)

)

Equation 20 should be:
Z z⇤
0

e

H 3 L20
L (z)dz =3l 2(z⇤ z)/H 2

2

Improvements

2.1

Length of day

( "

3 4+

✓

l
H

◆2 #

e

z⇤ /H

+ 6e

2z⇤ /H16e3z⇤ /2H

3

✓

l
H

◆2

2

)
(2)

To estimate the maximum change in Earth’s rotation rate we use conservation of angular momentum.
The change in angular momentum L is given by:
L = r ⇥ m i vi

(3)

where mi and vi are the mass and velocity of the impactor, respectively, and r is the position vectorof the impact site. For the change in angular momentum to have the largest possible e↵ect on
the rotation rate, the impact must occur at the equator and in the equatorial plane. In this case,r ⇥ mi vi = mi vi RE cos ✓ where ✓ is the impact angle. Assuming the moment of inertia for Earth IE
is given as IE = 25 ME RE2 , where ME and RE are the mass and radius of the Earth, respectively, andthe angular velocity of the Earth is given by T2⇡E , we can rewrite Eq. 3 as:
✓
◆
1
1
2⇡IE
= mi vi RE cos ✓(4)
TE + TE
TE
or

For

✓

1
TE + TE

1
TE

◆

=

5 mi
vi cos ✓4⇡RE ME(5)

TE << TE this can be rearranged to give the equation used in the program:
TE =

5 mi
cos (✓) vi TE2
4⇡RE ME(6)

where RE , ME and TE are the Earth’s radius (m), mass (kg) and rotation period (s). Note that
this equation predicts a maximum period change for a grazing impact ✓ = 0. In reality, such an
1

Figure 1: Maximum possible change in length of day caused by impacts on Earth.
impact would not impart any momentum on the Earth. Moreover, shallow angle impacts that resultin impactor decapitation would not impart all the impactors momentum into the target. Hence, inreality, the maximum would probably occur at an impact angle of ⇠ 15 .
The change in length of day as a function of impactor diameter is given in Fig. 1 assuming an
impact velocity of 20 km/s and an impactor density of 3000 kg/m3 .

2.2

Crater depth

The original equation used by the Impact E↵ects program to estimate the depth of a complex crater(Eq. 28) was based on the depth-to-diameter relationship of Herrick et al. [1997]
dfr = 0.4Dfr0.3(7)

Extraterrestrial depth measurements must be used as the terrestrial data is a↵ected by erosion.
However, the Venusian depth data has a large amount of scatter [Herrick, 2006] and extracting ameaningful scaling law from it seems impossible. As fresh lunar craters still seem to be the cleanest
data set, we instead use that data but scale it to be relevant for the Earth. This includes someassumptions about how craters collapse and is discussed in Holsapple [1993] and in McKinnon and
Schenk [1985]. In essence, starting with the scaling law for the moon:
dfr = 1.04Dfr0.301(8)

We scale the constant at the front (1.04) by dividing by the factor: 0.7gearth /gmoon , which is about
3.5
dfr = 0.294Dfr0.301(9)2Hence, the new equation predicts a shallower depth; the 0.294/0.4 factor di↵erence is about 74%.

2.3

Tsunami hazard

Many users have requested that the program estimate the amplitude and arrival time of tsunami
waves generated by impact into a water-covered target. When the program was first developed we
did not include such a calculation due to the lack of consensus on how to best estimate tsunami wave
generation and propagation as well as the fact that any such estimate requires several additionalparameters to be specified by the user. Recent work has provided new insight into wave generation
by impact, which allows us to make a crude estimate of tsunami amplitude and arrival time for
an impact into a given water depth [see Wünnemann et al., 2010, for a recent review]. As wave
amplitude is a function of water depth, a proper estimate of wave height a given distance fromthe impact must account for the change in water depth along the wave path. Incorporating suchinformation into the program is beyond its scope, so instead we estimate the amplitude and arrival
time a given distance from the impact by assuming that the water depth is constant. As water depth
is already an input paramter to the program, this requires no additional input form the user.
Recent numerical simulations of impacts in water suggest that impact generates water waves by
two distinct mechanisms [Wünnemann et al., 2010]: (a) rim uplift and ejecta curtain collapse; and(b) oscillations caused by cavity collapse, overshoot, collapse, overshoot, etc. Waves formed by the
first mechanism have been termed rim waves; whereas waves formed by the second mechanims havebeen termed collapse waves. Some numerical calculations suggest that rim waves are generated only
when the water depth is less than twice the impactor diameter; however, other calculations show
rim wave generation even in deep water. Here we will assume that a rim wave is always generated
by oceanic impact. Collapse waves, however, are only generated in deep-water impacts, when thedepth of the water layer is more than twice the impactor diameter.
2.3.1

Rim wave amplitude

According to numerical impact simulations, rim waves are formed by the uplift of the transient craterin the water and the subsequent outward collapse of the curtain of material ejected from the crater.
The rim wave appears to reach a maximum amplitude at a radial distance between 1 and 2 transient
crater radii. The wave is soliton-like in form and typically has a wavelength similar to the transient
crater diameter Dtc . A suitable estimate of the maximum amplitude of the rim wave Amax
rw is thetransient crater rim height in the water [Collins et al., 2005]
Amax
rw = htr =

Dtc
.
14.1

(10)

Here, we assume that this maximum rim-wave amplitude occurs at a radial distance Rrw = 3Dtc /4;i.e., half way between the transient crater rim and the edge of the zone within which most ejecta
lands. We also assume that the wave amplitude cannot be larger than the depth of the water layer,
so that in shallow-water impacts
✓
◆
Dtc
max
Arw = min
,H ,
(11)
14.1
where H is the water depth.
Oceanic impact simulations also suggest that the rim wave decays with radial distance as 1/r 1 .
1Their appears to be some dependence of the wave attenuation on the ratio of impactor diameter to water depth,
but assuming 1/r decay is adequate for our purposes3

We therefore estimate the rim-wave amplitude Arw at a distance r from the point of impact as:✓◆
Rrw
Arw = Amax
for r > Rrw
(12)
rw
r
If r < Rrw we inform the user that their present location is within the wave-generation zone.
2.3.2

Collapse wave amplitude

Rim wave amplitude is reported for all impacts into a water layer. Collapse wave amplitude isreported only if the water depth is more than twice the impactor diameter H > 2L. Collapse waves
are generated by the complex oscillations in water height near the impact zone as the transient
crater collapses, overshoots the pre-impact surface, collapses to form a secondary crater, overshootsa second time, etc. Very large amplitude waves can be generated by this process, which subsequently
break as they propagate away from the impact site. Numerical impact models suggest that the zoneof collapse-wave breaking has a radius as large as five transient crater radii and that the amplitudeof the largest collapse wave at this point is given by:
Amax
cw = 0.06 min (dtc , H) ,(13)

where dtc is the depth of the transient crater in the water, which is related to the transient crater
depth by dtc = Dtc /2.828. We assume that this maximum collapse-wave amplitude occurs at aradial distance Rcw = 5Dtc /2.
The collapse wave decays in amplitude more rapidly than the rim wave. Here we define theamplitude of the collapse wave Acw at a distance r from the point of impact as:
✓
◆
Rcw q
max
Acw = Acw
for r > Rcw(14)r
where q is an attenuation factor. If r < Rcw we inform the user that their present location is within
the collapse wave-generation zone.
Numerical impact simulations suggest that the collapse wave amplitude attenuation factor q
depends on the ratio of impactor diameter to water depth L/H. A reasonable fit to available
calculation results is
q = 3e 0.8L/H for L/H < 0.5
(15)
2.3.3

Rim- and Collapse-wave arrival time

As described above, rim waves are soliton-like in form and have a typical wavelength similar to
the transient crater diameter. Collapse waves, on the other hand are generally not soliton-like;the collapse process generates a complex wave signal with several characteristic wavelengths, thelargest of which is of order Dtc . For simplicity, here we make the assumption that there is only one
collapse wave, that it is also soliton-like and that its wavelength is also similar to the transient crater
diameter. To estimate the arrival time of both the rim wave and the collapse wave we use simple
surface gravity wave theory.
In general, the phase speed of surface gravity waves depends on the gravitational accelerationg , the water depth H, the wavelength and the amplitude of the wave A. In the small amplitude
limit (A << H, ) the phase speed is independent of A:
r
g
2⇡H
c=
tanh
.
(16)
2⇡
4

In the long-wave limit,>> H, this simplifies topc ⇡ gH.

On the other hand, in the short-wave limit,

(17)

<< H,
r
g
c⇡
.
2⇡

(18)

If the amplitude of the wave is a significant fraction of the wavelength or water depth, the shortand long wave limits are instead:✓◆pAc ⇡ gH 1 +for >> H
(19)
2H
and

s

c⇡

g
2⇡

✓

1+

2⇡ 2 A2
2

◆

for

<< H

(20)

According to the analysis above, rim waves have a maximum amplitude-to-wavelength ratio of
0.07; collapse waves have a smaller maximum amplitude-to-wavelength ratio. Consequently, when
first generated, rim-wave and collapse-wave amplitudes are sufficiently large that their approximate
wave speeds should be estimated using Eqs. 19 & 20; however, as the waves decay in amplitude
their speeds are better approximated by Eqs. 17 & 18 or Eq. 16. Rather than derive an equation
for finite amplitude collapse- and rim-wave speed as a function of distance and integrate this to findtravel times, we use Eqs. 19 & 20 to estimate a lower limit on the arrival time of the collapse or rim
wave and use Eq. 16 to estimate an upper limit on the arrival time of the same waves. This should
give the user some idea of the uncertainty in these estimates. Hence, the minimum estimated arrival
time of the collapse or rim wave at distance r is given by:
Twmin =mins

1.56Dtc✓

1 + 39.5

r
⇣

A
Dtc

⌘2 ◆ pA, 9.8H 1 + 2H

!

(21)

and the maximum estimated arrival time is given byr
Twmax = r⇣⌘
1.56Dtc tanh 6.28H
Dtc

(22)

where A is the maximum amplitude of the collapse or rim wave.

References
Collins, G. S., H. J. Melosh, and R. A. Marcus, Earth impact e↵ects program: A web-based computer
program for calculating the regional environmental consequences of a meteoroid impact on earth,
Meteoritics & Planetary Science, 40 (6), 817–840, doi:10.1111/j.1945-5100.2005.tb00157.x,
2005.
Herrick, R. R., Updates regarding the resurfacing of venusian impact craters, in Lunar and Planet.
Sci. Conf. XXXVII, p. Abs. 1588, Lunar and Planetary Institute, Houston, Texas, 2006.

5

Herrick, R. R., V. L. Sharpton, M. C. Malin, S. N. Lyons, and K. Feely, Morphology and Morphometryof Impact Craters, in Venus II: Geology, Geophysics, Atmosphere, and Solar Wind Environment,edited by S. W. Bougher, D. M. Hunten, and R. J. Phillips, p. 1015, 1997.
Holsapple, K. A., The scaling of impact processes in planetary sciences., Ann. Rev. Earth Planet.
Sci., 21, 333–373, 1993.
McKinnon, W. B., and P. M. Schenk, Ejecta blanket scaling on the Moon and Mercury - inferences
for projectile populations, in Lunar and Planet. Sci. Conf. Proceedings XVI, pp. 544–545, Lunarand Planetary Institute, Houston, Texas, 1985.
Wünnemann, K., G. S. Collins, and R. Weiss, Impact of a cosmic body into earth’s ocean andthe generation of large tsunami waves: Insight from numerical modeling, Reviews of Geophysics,
48 (4), doi:10.1029/2009RG000308, 2010.

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