PYTS 411/511 – Cratering Mechanics and Morphologies
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Transcript 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
Crater morphologies
Morphologies of impacts rim, ejecta etc
Energies involved in the impact process
Simple vs. complex craters
Shockwaves in Solids
Cratering mechanics
Contact and compression stage
Tektites
Ejection and excavation stage
Secondary craters
Bright rays
Collapse and modification stage
Atmospheric Interactions
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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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Morphology changes as craters get bigger
Pit → Bowl Shape→ Central Peak → Central Peak Ring → Multi-ring Basin
Moltke – 1km
10 microns
Orientale – 970km
Euler – 28km
Schrödinger – 320km
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How much energy does an impact deliver?
Projectile energy is all kinetic = ½mv2 ~ 2 ρ r3 v2
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
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.
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Planetary craters similar to nuclear test explosions
Craters are products of point-source explosions
Oblique impacts still make round craters
Overturned flap at edge
Eject blanket
Pulverized rock on crater floor
Shock metamorphosed minerals
Continuous for ~1 Rc
Breccia
Gives the crater a raised rim
Reverses stratigraphy
Shistovite
Coesite
Tektites
Small glassy blobs, widely distributed
Meteor Crater – 1.2 km
Sedan Crater – 0.3 km
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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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Simple to complex transition
Simple craters
In the strength regime
Most material pushed downwards
Size of crater limited by strength of rock
Energy ~ 2 r 3 Y
3
Complex craters
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
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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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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Strength Regime
Cratering law
Gravity Regime
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Simple scaling model
Crater size = F [ {impactor prop}, {target prop}, {env. prop.} ]
V = F [ aUmn,
, 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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Regímenes de Impacto
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Regímenes de Impacto II
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Radius of transient crater
depth
d=
Rfinal = 1.3 R
d/Dfinal ~ 0.2
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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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Shockwaves in Solids
Why impact craters are not just holes in the ground…
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
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
Causes a shockwave in both target and projectile
v >> vp
Projectile is slowed, target material is
accelerated downward
Shockwaves cause irreversible
damage to material they pass through
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Material can bounce back if it stays within the coulomb
failure envelope
Hugoniot – a locus of shocked states
Permanent deformation occurs when stress > H.E.L.
Material flows plastically
Material fails outright when stress > 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
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
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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Material jumps into shocked state as compression wave passes through
Decompression allows release of some of this energy (green area)
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)
Heating of target material – material is much hotter after the impact
Irreversible work – like fracturing rock
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Contact and compression Stage
Shockwave starts traveling backward through projectile
Target material gets accelerated away from contact site
Hemispheric cavity forms
Jets of material expelled
Projectile material deforms to line the cavity
Rarefaction wave follows shock
In that time the projectile moves forward so it gets flattened
Shock takes < 1sec to travel through object D/v
Unloading of pressure causes massive heating
Some target material melted
Projectile usually vaporized
Vapor plume (fireball) expands upward
Material begins to move out of the crater
Rarefaction wave provides the energy
Hemispherical transient crater cavity forms
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Plume of molten silica expands
Tektites
Drops of impact melt are swept up
Freeze during flight – aerodynamic forms
Cool quickly – glassy composition
Minimum size
Balance surface tension and velocity
Maximum size
Balance surface tension with aerodynamic
forces
8
10
D
2
melt vJet
gas v 2
Surface tension (σ) typically 0.3 N/m
vJet is < impact velocity
Δv is the difference between gas and droplet velocity in plume
Minimum size close to 1 nm
Maximum size depends on how well coupled the gas and particles are
Tektites rain out over a large area
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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
Shocked minerals produced
Shock metamorphosed minerals produced from quartz-rich (SiO2) target rock
Shistovite – forms at 15 GPa, > 1200 K
Coesite – forms at 30 GPa, > 1000 K
Dense phases of silica formed only in impacts
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Ejection and Excavation Stage
Material begins to move out of the crater
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
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
GM
P
Material escapes if ejected faster than ve
RP
Craters on asteroids generally don’t have ejecta blankets
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Only the top ~⅓ of the original material is ejected
Most material is displaced downwards
Interaction of shock with surface produces spall zone
Large chunks of ejecta can cause secondary craters
Commonly appear in chains radial to primary impact
Eject curtains of two secondary impacts can interact
Chevron ridges between craters – herring-bone pattern
Shallower than primaries: d/D~0.1
Asymmetric in shape – low angle impacts
Contested!
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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Unusual Ejecta
Oblique impacts
Rampart craters
Crater stays circular unless projectile impact
angle < 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
Occur only on airless bodies
Removed quickly by impact gardening
Lifetimes ~1 Gyr
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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Collapse and Modification Stage
Previous stages produces a hemispherical transient crater
Simple craters collapse from d/D of ~0.5 to ~0.2
Bottom of crater filled with breccia
Extensive cracking to great depths
Peak versus peak-ring in complex craters
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 < 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
Older surfaces have more craters
Small craters are more frequent than large craters
Relate crater counts to a surface age, if:
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
Techniques developed for Lunar Maria
Telescopic work established relative ages
Apollo sample provided absolute calibration
Mercury – Young and Old
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An ideal case…
Crater population is counted
Do D 2Do
Size-frequency plot generated
Need some sensible criteria
e.g. geologic unit, lava flow etc…
Tabulate craters in diameter bins
Bin size limits are some ratio e.g. 2½
In log-log space
Frequency is normalized to some area
Piecewise linear relationship:
N ( D, 2D) kDb
Slope (64km<D,
b ~ 2.2
Slope (2km<D<64km), b ~ 1.8
Slope (250m<D<2km), b ~ 3.8
Primary vs. Secondary Branch
Vertical position related to age
These lines are isochrones
Actual data = production function - removal
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Cumulative plots
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
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
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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Plotting styles compared for Phobos craters
Hartmann and Neukum, 2001
Differential
Cumulative
R-plot
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Geometric saturation: N SAT / Area Pf
4
D
2
1.15D 2
P 4
or log N SAT / Area log f
2 logD
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
Craters below a certain diameter exhibit saturation
This diameter is higher for older terrain – 250m for lunar Maria
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When a surface is saturated no more age information is added
Number of craters stops increasing
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Typical size-frequency curve
Steep-branch for sizes <1-2 km
Saturation equilibrium for sizes
<250m
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Linking Crater Counts to Age
Moon is divided into two terrain types
Apollo and Luna missions
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
Confirm above ages are representative of most of the moon.
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Crater counts had already established relative ages
Samples of the impact melt with geologic context allowed
absolute dates to be connected to crater counts
Lunar cataclysm?
Impact melt from large basins cluster in age
Imbrium 3.85Ga
Nectaris 3.9-3.92 Ga
Cataclysm or tail-end of accretion?
Highland crust solidified at ~4.45Ga
Lunar mass favors cataclysm
Impact melt >4Ga is very scarce
Pb isotope record reset at ~3.8Ga
} weak
Cataclysm referred to as ‘Late Heavy Bombardment’
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Last stages of planetary accretion
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
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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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
Chain impacts occur due to Jupiter’s high
gravity
e.g. Callisto
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Crater-less impacts
Impacting bodies can explode or be slowed in the atmosphere
Significant drag when the projectile encounters its own mass in
atmospheric gas: i.e. Di 3PS 2 g P i
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
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
Pz
e
kT
gH
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The sounds
Two sounds:
•Sonic Boom sónico: 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
Craters occur on all solar system bodies
Crater morphology changes with impact energy
Impact craters are the result of point source explosions
Mechanics
Craters form from shockwaves
Contact and compression <1 s
Excavation of material 10’s of seconds
Craters collapse from a transient cavity to their final form
Ejecta blankets are ballistically emplaced
Low-density projectiles can explode in the atmosphere
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Summary of recognized impact features
Primary crater
Ejecta blanket
Secondary impact craters
Rays
Rings and multirings
Breccia
Shock metamorphism: Planar Deformation Features (PDFs)
Melt glasses
Tektites
Regolith
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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