Impact Cratering Lecture 4

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Impact CrateringLecture 4

• Excavation

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The impact cratering process is divided into
three basic stages

• Contact and Compression
• Excavation of the crater
• Modification (collapse) of the crater

(not a real division, just a convenient one)
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Excavation
Begins as the rarefaction wave starts following
the shock wave in the target, leaving behind
material with a residual velocity
The residual velocity sets material in motion,
initiating the excavation flow and the ejecta
curtain
(OKeefe Ahrens, 1975)
Excavation flow continues as the
shock/rarefaction waves move down into the
target, opening the crater
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Characterized by

• Expansion of the shock wave, shocking target
  material to different levels as it expands and
  weakens while engulfing more target material
• Excavation flow, which follows the passage of the
  shock/rarefaction wave and opens the crater
  cavity
• Ends when excavation is halted by either strength
  or gravity. For planetary scale impacts
• TE (DTC/g)1/2
• Material is ejected ballistically from the target
  into an ejecta curtain that starts at the edge of
  the growing crater

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Shock in the Target
Rarefaction wave quickly catches up with the
shock wave, forming an isolated or detached
shock As the shock wave expands (roughly)
hemispherically in the target its intensity (peak
pressure and particle velocity) decrease roughly
as 1/r2 Eventually, the shock degrades to a
strong stress wave (with an elastic precursor)
ending into an elastic wave
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Shock Wave Decay
Contact Compression
Excavation

• 0lt d ltDpr
• Max. peak shock pressure
• given by the Planar Impact
• approximation small decrease in shock
• pressure with distance
• d gt Dpr
• Detached shock decays
• With distance with a slope
• 1.5?3.0

Similar behavior goes for particle velocity
(Pierazzo et al., 1997)
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Excavation Schematic
Interference zone
(French, 1998)

• Shock wave appears to radiate from below the
  target surface
• (parallel with shallow burial explosions)

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Equivalent Depth of Burial
A rough estimate of the equivalent depth of
burial (penetration of the projectile into the
target) are obtained from the classic supersonic
jet-penetration formula
Penetration at high speed is close to the
projectile diameter
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Modeling Results

• Melting regions in the target have the shape of a
  truncated sphere
• Contact/compression region is a spheroid within
  the target (equivalent depth of burial varies
  with impact velocity)

20 km/s
50 km/s
(Dunitic impactor, 2 km in diameter on Dunite
target)
(Pierazzo et al., 1997)
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Near-Surface Region

• In the interference zone the shock wave is
  quickly followed by rarefaction from the the
  surface, limiting the maximum pressure excursion
• A tensional wave following the stress wave causes
  material to shatter (when higher than the
  materials dynamic tensile strength)
• Pressure gradient is responsible for material
  acceleration to high speeds Spallation

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Excavation Schematic
Interference zone
(French, 1998)

• Shock wave distribution in the original
  (undeformed) target provides a way to determine
  amount of melting and vaporization

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Melting and Vaporization

• Oblique impacts produce asymmetric (directional)
  shock waves near the impact point

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Melting and Vaporization

• Oblique impacts produce asymmetric (directional)
  shock waves near the impact point

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Melting and Vaporization Vertical Impacts

• Volume of material within the appropriate peak
  pressure contours give amount of melt/vapor
  (caveat mixtures!)

Good agreement with estimated terrestrial data
(Pierazzo et al., 1997)
(Wünnemann Collins, subm.)
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Melting and Vaporization Oblique Impacts

• In oblique impacts less energy is transferred to
  the target
• (weaker shock smaller crater)

Use a volumetric pressure-decay regime to
average out directional effects due to obliquity
(for V gt Vpr the detached shock decays with a
slope 0.6?0.7)
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Melting/Vaporization in the Projectile
Like in the target, the shock in the projectile
weakens with decreasing angle of impact (from the
surface)
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Excavation Schematic
Interference zone
(French, 1998)

• After the passage of the shock/rarefaction wave,
  material has a residual velocity, (1/3 ?1/5)uP,
  away from the impact point

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Excavation Flow

• Material beneath the impact site continues moving
  downward
• Rarefaction waves from the free surface add an
  upward-directed pressure gradient, adding an
  extra upward component to the materials residual
  velocity
• Excavation flow causes material to be ejected
  above the pre-impact surface
• Ejecta Curtain

Material ejected along a given streamline
contains a mixture of shock levels
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Ejecta Curtain

• 2D laboratory experiments show that the ejecta
  curtain forms an inverted cone that expands with
  time

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Maxwell-Z Model of Crater Excavation
Simple analytical model for the excavation flow
of explosive craters

• r r0(1-cos?)1/(Z-2)
• Modified for impact cratering by Croft (1980)

Best fit to cratering
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Ejecta Curtain Experiments

• Use of lasers to produce stroboscopic photographs
  of individual grains allow for measurements of
  ejecta position, speed and directions

(Cintala et al., 1999)
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Ejecta Curtain

• Speed of ejecta is related to the launch position
  
• Ejection angle ranges between 40º and 55º
• Neither ejecta speed nor ejection angle depend on
  the projectile impact velocity

(Cintala et al., 1999)
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Ejecta Curtain in Oblique Impacts

• Oblique impacts also create an ejecta curtain
  with a similar inverted cone shape

And again, the use of a laser allows to measure
particles speed, angle and position over time
during cratering
(Anderson et al., 2003)
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Maxwell-Z Model of Crater Excavation
Does not work for oblique impacts! Problem The
center of the flow field appears to migrate
downrange and downward during cratering (Anderson
et al., 2004, 2006)
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What about the Projectile?
Projectile
Projectile stays inside the crater in the early
stages of cratering only in impacts close to
vertical
(Pierazzo Melosh, 2000)
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Projectile Tracers during early stages of
excavation
(Pierazzo Melosh, 2000)
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Crater Growth Impact in water
(Pierazzo et al., 2007)
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Crater Growth
An hemispherical cavity grows at a steadily
decreasing rate Maximum depth is reached when
material strength and increasing lithostatic
pressure from surrounding rock halt the growing
vertical motion Resistance to crater growth is
lower near the surface and the crater continues
growing in width until material velocity does not
allow ejection anymore ? Transient Crater
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Transient Crater and Excavation
Transient Crater is generally used to refer to
the idealized theoretical construct defined by
the maximum extent to which excavation proceeds
in every direction (Turtle et al., 2005)
Dtc
MeltVapor
Spallation
Hexc
Htc
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• The transient crater is not the end of the
  cratering story
• One more stage, modification, is needed to reach
  the final crater that we see on planetary surfaces