# PYTS 411/511 – Cratering Mechanics and Morphologies

```Impact Cratering
Mechanics and Morphologies
PTYS 411/511 Geology and Geophysics of the Solar System
Shane Byrne – [email protected]
Background is from NASA Planetary Photojournal PIA00094
PYTS 411/511 – Cratering Mechanics and Morphologies
In This Lecture
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Crater morphologies
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Morphologies of impacts rim, ejecta etc
Energies involved in the impact process
Simple vs. complex craters
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Shockwaves in Solids
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Cratering mechanics
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Contact and compression stage
 Tektites
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Ejection and excavation stage
 Secondary craters
 Bright rays
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Collapse and modification stage
Atmospheric Interactions
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PYTS 411/511 – Cratering Mechanics and Morphologies
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Where do we find craters? – Everywhere!

Cratering is the one geologic process that every solid solar system body experiences…
Mercury
Earth
Venus
Moon
Mars
Asteroids
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PYTS 411/511 – Cratering Mechanics and Morphologies
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Morphology changes as craters get bigger
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Pit → Bowl Shape→ Central Peak → Central Peak Ring → Multi-ring Basin
Moltke – 1km
10 microns
Orientale – 970km
Euler – 28km
Schr&ouml;dinger – 320km
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PYTS 411/511 – Cratering Mechanics and Morphologies
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How much energy does an impact deliver?
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Projectile energy is all kinetic = &frac12;mv2 ~ 2 ρ r3 v2
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Most sensitive to size of object
Size-frequency distribution is a power law
 Slope close to -2
 Expected from fragmentation mechanics

Minimum impacting velocity is the escape velocity
Vesc 

GM p
Rp
Orbital velocity of the impacting body itself
2 1
Vesc  GM *   
r a
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Planet’s orbital velocity around the sun (~30 km s-1 for Earth)
Lowest impact velocity ~ escape velocity (~11 km s-1 for Earth)
Highest velocity from a head-on collision with a body falling from infinity
 Long-period comet
 ~78 km s-1 for the Earth
 ~50 times the energy of the minimum velocity case

A 1km rocky body at 12 kms-1 would have an energy of ~ 1020J
 ~20,000 Mega-Tons of TNT
 Largest bomb ever detonated ~50 Mega-Tons (USSR, 1961)
 Recent earthquake in Peru (7.9 on Richter scale) released ~10 Mega-Tons of TNT equivalent
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Harris et al.
PYTS 411/511 – Cratering Mechanics and Morphologies
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Planetary craters similar to nuclear test explosions
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Craters are products of point-source explosions
Oblique impacts still make round craters
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Overturned flap at edge
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Eject blanket
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Pulverized rock on crater floor
Shock metamorphosed minerals
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Continuous for ~1 Rc
Breccia
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Gives the crater a raised rim
Reverses stratigraphy
Shistovite
Coesite
Tektites
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Small glassy blobs, widely distributed
Meteor Crater – 1.2 km
Sedan Crater – 0.3 km
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PYTS 411/511 – Cratering Mechanics and Morphologies
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Differences in simple and complex
morphologies
Simple
Bowl shaped
Complex
Flat-floored
Central peak
Wall terraces
Little melt
Some Melt
d/D ~ 0.2
d/D much smaller
Diameter dependent
Small sizes
Larger sizes
Euler – 28km
Moltke – 1km
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PYTS 411/511 – Cratering Mechanics and Morphologies
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Simple to complex transition
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Simple craters
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In the strength regime
Most material pushed downwards
Size of crater limited by strength of rock
Energy ~ 2  r 3 Y
3 
Complex craters
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All these craters start as a transient hemispheric cavity
In the gravity regime
Size of crater limited by gravity
Energy ~ 2  r 3  g D
3


At the transition diameter you can use either method
2  r 3 Y ~ 2  rT 3  g DT
 i.e. Energy ~
3
3 T

Y   g DT
 
or DT  Y


So:

The transition diameter is higher when
g
 The material strength is higher
 The density is lower
 The gravity is lower
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Y ~ 100 MPa and ρ ~ 3x103 kg m-3 for rocky planets
DT is ~3km for the Earth and ~18km for the Moon
 Compares well to observations
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PYTS 411/511 – Cratering Mechanics and Morphologies
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PYTS 411/511 – Cratering Mechanics and Morphologies
Dimensional Analysis and Pi-Scaling
V – Volume of the crater
Projectile: a – radius
U – velocity
 - density
Target: - density
Y – strength
g – gravity acc.
By dimensional analysis we obtain:
or
The impactor act as a “point source”.
The coupling parameter:
Strength regime
Gravity regime
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PYTS 411/511 – Cratering Mechanics and Morphologies
Strength Regime
Cratering law
Gravity Regime
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PYTS 411/511 – Cratering Mechanics and Morphologies
Simple scaling model
Crater size = F [ {impactor prop}, {target prop}, {env. prop.} ]
V = F [ aUmn,
, Y,
Strength-regime:
g ]
Gravity-regime:
 2+m-6n
V
ga -3m/(2+m)
2+m
m  ( )
U2
 1-3n Y -3m/2
V
(U2)
m  
( )
( )
V
m
ga/U2
(from Housen 2003)
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Cratering in metals
Regression gives n=0.4, m=0.5
Ref: Holsapple and Schmidt (1982) JGR, 87, 1849-1870.
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PYTS 411/511 – Cratering Mechanics and Morphologies
Reg&iacute;menes de Impacto
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PYTS 411/511 – Cratering Mechanics and Morphologies
Reg&iacute;menes de Impacto II
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PYTS 411/511 – Cratering Mechanics and Morphologies
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PYTS 411/511 – Cratering Mechanics and Morphologies
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PYTS 411/511 – Cratering Mechanics and Morphologies
Radius of transient crater
depth
d=
Rfinal = 1.3 R
d/Dfinal ~ 0.2
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PYTS 411/511 – Cratering Mechanics and Morphologies
In the gravity regime
Diameter of
transient crater
Diameter of
final rim
Depth of
transient crater
Depth of
final rim
(Collins et al. 2005)
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PYTS 411/511 – Cratering Mechanics and Morphologies
Shockwaves in Solids
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Why impact craters are not just holes in the ground…
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Energy is transported through solids via waves
Away from free surfaces, two types of wave exist
Shear (S) waves with velocity vS  m 
Pressure (P) waves with velocity
vP 
K  4 3 m 

where K  
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P
 S
ρ is the density, μ is the shear modulus (rigidity), and K is the bulk modulus
P waves are faster, but typically only about 7 km s-1 in crustal rock
An impact transports energy faster than the sound speed
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Causes a shockwave in both target and projectile
v &gt;&gt; vp
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Projectile is slowed, target material is
accelerated downward
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Shockwaves cause irreversible
damage to material they pass through
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PYTS 411/511 – Cratering Mechanics and Morphologies
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Material can bounce back if it stays within the coulomb
failure envelope
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Hugoniot – a locus of shocked states
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Permanent deformation occurs when stress &gt; H.E.L.
Material flows plastically
Material fails outright when stress &gt; Y
When a material is shocked it’s pressure and density can be predicted
Need to know the initial conditions…
…and the shock wave speed
Rankine-Hugoniot equations
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Conservation equations for:
 Mass
 v  v p    o v
 Momentum
P  Po   o v p v
 Energy
E  Eo  1
2
P  Po Vo  V 
where V  1
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
and Vo  1
o
Need an equation of state (P as a function of T and ρ)
Equations of state come from lab measurements
Phase changes complicate this picture
Melosh, 1989
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PYTS 411/511 – Cratering Mechanics and Morphologies
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Material jumps into shocked state as compression wave passes through
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Decompression allows release of some of this energy (green area)
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Shock-wave causes near-instantaneous jump to high-energy state (along Rayleigh line)
Compression energy represented by area (in blue) on a pressure-volume plot
Decompression follows adiabatic curve
Used mostly to mechanically produce the crater
Difference in energy-in vs. energy-out (pink area)
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Heating of target material – material is much hotter after the impact
Irreversible work – like fracturing rock
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PYTS 411/511 – Cratering Mechanics and Morphologies
Contact and compression Stage
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Shockwave starts traveling backward through projectile
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Target material gets accelerated away from contact site
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Hemispheric cavity forms
Jets of material expelled
Projectile material deforms to line the cavity
Rarefaction wave follows shock
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In that time the projectile moves forward so it gets flattened
Shock takes &lt; 1sec to travel through object D/v
Some target material melted
Projectile usually vaporized
Vapor plume (fireball) expands upward
Material begins to move out of the crater
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Rarefaction wave provides the energy
Hemispherical transient crater cavity forms
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PYTS 411/511 – Cratering Mechanics and Morphologies
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Plume of molten silica expands
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Tektites
Drops of impact melt are swept up
Freeze during flight – aerodynamic forms
Cool quickly – glassy composition
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Minimum size
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Balance surface tension and velocity
Maximum size
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Balance surface tension with aerodynamic
forces
8
10

D

2
melt vJet
 gas v 2
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Surface tension (σ) typically 0.3 N/m
vJet is &lt; impact velocity
Δv is the difference between gas and droplet velocity in plume
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Minimum size close to 1 nm
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Maximum size depends on how well coupled the gas and particles are
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Tektites rain out over a large area
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PYTS 411/511 – Cratering Mechanics and Morphologies
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Vaporization and melting
Peak pressures of 100’s of GPa are common
Usually enough to melt material
Some target material also vaporized
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Shocked minerals produced
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Shock metamorphosed minerals produced from quartz-rich (SiO2) target rock
Shistovite – forms at 15 GPa, &gt; 1200 K
Coesite – forms at 30 GPa, &gt; 1000 K
Dense phases of silica formed only in impacts
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PYTS 411/511 – Cratering Mechanics and Morphologies
Ejection and Excavation Stage
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Material begins to move out of the crater
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Rarefaction wave provides the energy
Hemispherical transient crater cavity forms
Time of excavate crater in gravity regime:
t D
g
For a 10 Km crater on Earth, t ~ 32 sec
Material forms an inverted cone shape
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Fastest material from crater center
Slowest material at edge forms overturned flap
Ballistic trajectories with range:


 v 2 R p g sin  cos 

2 R p tan 
 1  v 2 R g cos2  
p


1
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

GM
P
Material escapes if ejected faster than ve 
RP
Craters on asteroids generally don’t have ejecta blankets
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PYTS 411/511 – Cratering Mechanics and Morphologies
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Only the top ~⅓ of the original material is ejected
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Most material is displaced downwards
Interaction of shock with surface produces spall zone
Large chunks of ejecta can cause secondary craters
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Commonly appear in chains radial to primary impact
Eject curtains of two secondary impacts can interact
 Chevron ridges between craters – herring-bone pattern
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Shallower than primaries: d/D~0.1
Asymmetric in shape – low angle impacts
Contested!
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Distant secondary impacts have considerable energy and are circular
Secondaries complicate the dating of surfaces
Very large impacts can have global secondary fields
 Secondaries concentrated at the antipode
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PYTS 411/511 – Cratering Mechanics and Morphologies
Unusual Ejecta
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Oblique impacts
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Rampart craters
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Crater stays circular unless projectile impact
angle &lt; 10 deg
Ejecta blanket can become asymmetric at angles
~45 deg
Fluidized ejecta blankets
Occur primarily on Mars
Ground hugging flow that appears to wrap
around obstacles
Perhaps due to volatiles mixed in with the
Martian regolith
Atmospheric mechanisms also proposed
Bright rays
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Occur only on airless bodies
Removed quickly by impact gardening
Associated with secondary crater chains
Brightness due to fracturing of glass spherules
on surface
…or addition of more crystalline material
Carr, 2006
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PYTS 411/511 – Cratering Mechanics and Morphologies
Collapse and Modification Stage
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Previous stages produces a hemispherical transient crater
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Simple craters collapse from d/D of ~0.5 to ~0.2
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Bottom of crater filled with breccia
Extensive cracking to great depths
Peak versus peak-ring in complex craters
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Central peak rebounds in complex craters
Peak can overshoot and collapse forming a peak-ring
Rim collapses so final crater is wider than transient bowl
Final d/D &lt; 0.1
Melosh, 1989
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Impact Cratering
Dating and the Planetary Record
PTYS 411/511 Geology and Geophysics of the Solar System
Shane Byrne – [email protected]
Background is from NASA Planetary Photojournal PIA00094
PYTS 411/511 – Cratering Mechanics and Morphologies
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Older surfaces have more craters
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Small craters are more frequent than large craters
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Relate crater counts to a surface age, if:
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Impact rate is constant
Landscape is far from equilibrium
i.e. new craters don’t erase old craters
No other resurfacing processes
Target area all has one age
You have enough craters
 Need fairly old or large areas
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Techniques developed for Lunar Maria
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Telescopic work established relative ages
Apollo sample provided absolute calibration
Mercury – Young and Old
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PYTS 411/511 – Cratering Mechanics and Morphologies
An ideal case…
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Crater population is counted
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Do  D  2Do
Size-frequency plot generated
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Need some sensible criteria
e.g. geologic unit, lava flow etc…
Tabulate craters in diameter bins
Bin size limits are some ratio e.g. 2&frac12;
In log-log space
Frequency is normalized to some area
Piecewise linear relationship:
N ( D, 2D)  kDb
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Slope (64km&lt;D,
b ~ 2.2
Slope (2km&lt;D&lt;64km), b ~ 1.8
Slope (250m&lt;D&lt;2km), b ~ 3.8
Primary vs. Secondary Branch
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Vertical position related to age
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These lines are isochrones
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Actual data = production function - removal
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PYTS 411/511 – Cratering Mechanics and Morphologies
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Cumulative plots
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Tend to mask deviations from the ideal
N cum ( D)  cDb


where N D, 2 D  N cum ( D)  N cum ( 2 D)
c 

k
1  2 b 


R-plots
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Size-frequency plot with -2 slope removed
Highlights differences from the ideal
2 3 4
R( D)  




 2
D N cum  D   Ncum  2 D

2 1 


Fractional area covered
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Area covered by craters of a certain size
Differs from R-plot by a numerical factor

F ( D)   2  D 2 N cum D   N cum
4


F D   



2 1

9  R D 
2 4

2D


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PYTS 411/511 – Cratering Mechanics and Morphologies
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Plotting styles compared for Phobos craters
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Hartmann and Neukum, 2001
Differential
Cumulative
R-plot
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PYTS 411/511 – Cratering Mechanics and Morphologies

Geometric saturation: N SAT / Area  Pf
4
D
2
 1.15D  2
P 4 
or log N SAT / Area  log f
   2 logD 

You can’t fit in more craters than the hexagonal packing (Pf = 90.5% efficiency) of area allows
A mix of crater diameters allows Ns ~ 1.54 D-2
No surface ever reaches this theoretical limit.
Saturation sets in long beforehand (typically a few % of the geometric value)
Mimas reaches 13% of geometric saturation – an extreme case
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Craters below a certain diameter exhibit saturation
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This diameter is higher for older terrain – 250m for lunar Maria
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PYTS 411/511 – Cratering Mechanics and Morphologies
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When a surface is saturated no more age information is added
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Number of craters stops increasing
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PYTS 411/511 – Cratering Mechanics and Morphologies
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Typical size-frequency curve
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Steep-branch for sizes &lt;1-2 km
Saturation equilibrium for sizes
&lt;250m
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PYTS 411/511 – Cratering Mechanics and Morphologies
Linking Crater Counts to Age
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Moon is divided into two terrain types
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Apollo and Luna missions
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Light-toned Terrae (highlands) – plagioclase feldspar
Dark-toned Mare – volcanic basalts
Maria have ~200 times fewer craters
Sampled both terrains
Mare ages 3.1-3.8 Ga
Terrae ages all 3.8-4.0 Ga
Lunar meteorites
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Confirm above ages are representative of most of the moon.
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PYTS 411/511 – Cratering Mechanics and Morphologies
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Crater counts had already established relative ages
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Samples of the impact melt with geologic context allowed
absolute dates to be connected to crater counts
Lunar cataclysm?
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Impact melt from large basins cluster in age
 Imbrium 3.85Ga
 Nectaris 3.9-3.92 Ga
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Cataclysm or tail-end of accretion?
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Highland crust solidified at ~4.45Ga
Lunar mass favors cataclysm
Impact melt &gt;4Ga is very scarce
Pb isotope record reset at ~3.8Ga
} weak
Cataclysm referred to as ‘Late Heavy Bombardment’
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PYTS 411/511 – Cratering Mechanics and Morphologies
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Last stages of planetary accretion
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Many planetesimals left over
Most gone in a ~100 Myr
We’re still accreting the last of these bodies today
Jupiter continues to perturb asteroids
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Mutual velocities remain high
Collisions cause fragmentation not agglomeration
Fragments stray into Kirkwood gaps
This material ends up in the inner solar system
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PYTS 411/511 – Cratering Mechanics and Morphologies

The worst is over…
Late heavy bombardment 3.7-3.9 Ga
Impacts still occurring today though
Jupiter was hit by a comet ~15 years ago
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Chain impacts occur due to Jupiter’s high
gravity
e.g. Callisto
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Crater-less impacts
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Impacting bodies can explode or be slowed in the atmosphere
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Significant drag when the projectile encounters its own mass in
atmospheric gas: i.e. Di  3PS 2 g P i
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Where Ps is the surface gas pressure, g is gravity and ρi is projectile density
If impact speed is reduced below elastic wave speed then there’s no
shockwave – projectile survives
Ram pressure from atmospheric shock
Pram  v 2  atmosphere
if
T  const. Pram  v
where H  kT

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2
gm ATM
If Pram exceeds the yield strength then projectile fragments
If fragments drift apart enough then they develop their own
shockfronts – fragments separate explosively (pancake
model)
Weak bodies at high velocities (comets) are susceptible
Tunguska event on Earth
Crater-less ‘powder burns’ on venus
m ATM
v 2 PS  z H
Pz  
e
kT
gH
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PYTS 411/511 – Cratering Mechanics and Morphologies
The sounds
Two sounds:
•Sonic Boom s&oacute;nico: minutes
after fireball
•Electrofonic noise: simultaneous
with fireball
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Infrasound records
Fireball of the
European
Network
Fireball Park
Forest
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Seismic records of the airblast
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Seismic detections of Carancas
First seismic detection of an
extraterrestrial impact on Earth
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Morphology
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Craters occur on all solar system bodies
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Crater morphology changes with impact energy
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Impact craters are the result of point source explosions
Mechanics
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Craters form from shockwaves
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Contact and compression &lt;1 s
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Excavation of material 10’s of seconds
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Craters collapse from a transient cavity to their final form
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Ejecta blankets are ballistically emplaced
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Low-density projectiles can explode in the atmosphere
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PYTS 411/511 – Cratering Mechanics and Morphologies
Summary of recognized impact features
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Primary crater
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Ejecta blanket
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Secondary impact craters
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Rays
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Rings and multirings
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Breccia
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Shock metamorphism: Planar Deformation Features (PDFs)
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Melt glasses
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Tektites
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Regolith
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Focusing effects in the antipodes

Erosion and catastrophic disruption
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Ejecta blanket
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Secondary craters
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Crater rays
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Rings and multirings
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Focusing in the antipoe
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