Scaling of crater formation numerical modeling of impact processes on
continental targets
Kai Wünnemann
Museum für Naturkunde, Leibniz-Institute at the
Humboldt Universität, Berlin
Scaling of crater formation - numerical modeling of impact processes on continental targets
How
do
the
observed
shape
and
size
of
an
impact
crater
depend
on
properties
of
the
impactor...
•
size
•
composition
L
•
velocity
U
•
angle
θ
...and
the
underlying
geology?
•
lithology
•strength
•
layering
•
gravity
D
d
V
Image from:http://www.meteorcrater.com
Scaling
Laws
Gardnos-Gol Workshop, 10. June, 2009
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Scaling of crater formation - numerical modeling of impact processes on continental targets
Crater
morphometry
and
morphology
varies
on
different
planetary
surfaces
as
a
function
of
size
effect
of
target
properties
(e.g.
strength)
and
gravity
on
crater
morphometry
Crater Depth (km)
Crater Diameter (km)
Simple-Complex transition
Gravity (cm/s2)
Pike, 1977
Garvin et al., 2003
Schenk, 1991,2002
Moon
s
Mar
de
nyme
Ga
Simple Craters
d = 0.196 D1.01
d = 0.21 D0.81
Complex Craters
d = 1.044 D0.301
d = 0.360 D0.49
d = 0.227 D0.446
Crater Diameter (km)
Gardnos-Gol Workshop, 10. June, 2009
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Scaling of crater formation - numerical modeling of impact processes on continental targets
Simple question:
What is the size of a crater resulting from the impact of a
projectile of a given size, mass, velocity, and angle?
Image from:http://www.meteorcrater.com
The question can only be answered by
➡ Impact and explosion experiments
➡ Theoretical solutions
➡ Numerical modeling
Scaling
Laws
Gardnos-Gol Workshop, 10. June, 2009
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Scaling of crater formation - numerical modeling of impact processes on continental targets
Impactor properties:
m=mass
θ=angle
U=velocity L=Diameter
δ=density
θ
Transient crater parameter:
D=diameter
d=depth
V=volume
D
d
V
Image from:http://www.meteorcrater.com
Target properties:
ρ
g
Y
=f (Φ,Yc)
α
density, strength (=friction+cohesion), porosity, gravity
Scaling law:
crater size = F [ {impactor properties}, {target properties}]
{D,d,V}
{δ,m,r,U,θ}
{ρ,Y=f(Φ,Yc),α,g}
Gardnos-Gol Workshop, 10. June, 2009
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Scaling of crater formation - numerical modeling of impact processes on continental targets
The size of the so-called „transient crater“ is the best
measure of the energy that was released by an impact event!
Maximum depth of
the crater
Gardnos-Gol Workshop, 10. June, 2009
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Scaling of crater formation - numerical modeling of impact processes on continental targets
The size of the transient crater is the best measure of the
energy that was released by an impact event!
Gardnos-Gol Workshop, 10. June, 2009
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Scaling of crater formation - numerical modeling of impact processes on continental targets
The size of the transient crater is the best measure of the
energy that was released by an impact event!
Kink in ejecta
curtain
Transient crater diameter
Gardnos-Gol Workshop, 10. June, 2009
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Scaling of crater formation - numerical modeling of impact processes on continental targets
The size of the transient crater is the best measure of the
energy that was released by an impact event!
Final crater diameter
Gardnos-Gol Workshop, 10. June, 2009
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Scaling of crater formation - numerical modeling of impact processes on continental targets
Simple crater - gravity dominated
(craters > 10th of meters on earth and all craters in
granular material - no cohesion)
slumping of oversteepened crater rim causes
the formation of a breccia lens inside the
crater and slightly enlarges crater diameter
and reduces crater depth
Gardnos-Gol Workshop, 10. June, 2009
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Scaling of crater formation - numerical modeling of impact processes on continental targets
Simple crater - gravity dominated
(craters > 10th of meters on earth and all craters in
granular material - no cohesion)
slumping of oversteepened crater rim causes
the formation of a breccia lens inside the
crater and slightly enlarges crater diameter
and reduces crater depth
1.5
1.0
0.5
0
0.5
1.0
1.5
Simple crater - strength dominated
(laboratory-size craters in competent rock)
material strength stops crater growth,
final crater corresponds almost exactly to the
transient crater
0.2
Gardnos-Gol Workshop, 10. June, 2009
0
0.2
11
Scaling of crater formation - numerical modeling of impact processes on continental targets
Impact experiments in sand (1978-1981),
NASA Ames Vertical Gun Facility
Courtesy by Dieter Stöffler
Gardnos-Gol Workshop, 10. June, 2009
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Scaling of crater formation - numerical modeling of impact processes on continental targets
MEMIN-experiments
courtesy EMI
Laboratory
experiments
‐
high
technical
demands
Range
of
material
properties
is
limited
and
cannot
be
varied
independently
The
effect
of
gravity
on
crater
growth
can
be
only
investigated
in
granular
target
materials
Pierazzo et al., 2008
Boeing quarter space laboratory experiment
To
vary
gravity
large
centrifuges
are
required
Schmidt & Housen, 1984
→
only
vertical
impacts
can
be
simulated
Impact
velocity
is
limited
to
~10
km/s
at
most;
however,
most
experiments
are
carried
out
at
2‐5
km/s
Gardnos-Gol Workshop, 10. June, 2009
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Scaling of crater formation - numerical modeling of impact processes on continental targets
vertical impact
Numerical
modeling
‐
development
of
oblique impact
appropriate
codes
Crater
formation
can
be
studied
in
the
course
of
time
Simulation
of
crater
formation
at
realistic
size‐scale,
gravity
conditions,and
arbitrary
impact
angle
and
velocity
are
possible
All
parameters
can
be
varied
independently,
thus
the
effect
of
a
single
material
property
can
be
studied
separate
from
other
effects
Numerical
models
are
„cheap“;
however,
simulation
of
laboratory‐size
experiments
can
be
computationally
very
expensive
Codes
(hydrocodes)
must
be
validated
against
experiments
to
assure
accuracy
Gardnos-Gol Workshop, 10. June, 2009
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Scaling of crater formation - numerical modeling of impact processes on continental targets
To compare small-scale laboratory experiments, large-scale
natural craters and numerical modeling dimensionless measures
of crater dimensions are required
Boeing quarter space laboratory experiment,
Pierazzo et al., 2008
Lunar complex crater „Euler“,
diameter 28 km, depth 2.5 km,
© NASA/JPL
iSALE 2D hydrocode simulation of a complex
impact crater
Most successful approach in dimesnional analysis uses the so-called
„Pi-theorem“1 which has bee used the develop so-called Pi-group
scaling2 for impact cratering
1Buckingham
(1914), Bridgman (1949);
2e.g. Schmidt (1980), Schmidt & Housen (1987), Holsapple(1993)
Gardnos-Gol Workshop, 10. June, 2009
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Scaling of crater formation - numerical modeling of impact processes on continental targets
Dimensionless ratios for crater morphometry
!

volume V 
= F (U, ρ, δ, Y, g, m)
diameter D

depth d
6
variables


gravity‐scaled
size
strength‐scaled
size
!
πV
!
dimensionless
πD
= F (π2 , π3 , π4 )

ratios
πd
3
variables
gL
π2 = 1.61 2
U
Y
π3 =
δU 2
Gardnos-Gol Workshop, 10. June, 2009
(Holsapple
&
Schmidt
1987)
dimensionless
geometric
parameters
ρV crater
πV =
efficiency
m
! ρ "1/3
πD = D
m
! ρ "1/3
πd = d
m
other
scaling
parameters
ρ
π4 =
δ
16
Scaling of crater formation - numerical modeling of impact processes on continental targets
Annual Reviews
www.annualreviews.org/aronline
Analog impact experiments in water
344
HOLSAPPLE
5
lO
~/~
~
-
~
Hyperveloct-ty Impact
(].Gto G km/sec)
Water
impacts,
__0.648 . 1.928
1‐3
km/s
ee~Fit to
GaultDataOnly
~
104
1:333-373. Downloaded from arjournals.annualreviews.org
itat Berlin on 07/17/07. For personal use only.
~
Power-law
103
Water‐drop
experiments
(1‐20
m/s)
Wa
ter
~
10
101
x Olevson(1969)
0 Engel (1961)
)aterTd~
~ Worthington (18970908)
0
10
10-11
I
10"10
I
10-9
I
10"8
I
"7
10
|
-6
10
1i?. GIL~VITY-SCALED
Y 1ELD
I
10-5
1
"4
10
1
"3
10
I
10"2
lo’l
( ~.~ [~]1/3)
Figure2 Datafor crateringin waterfor velocitiesfrom1 m/secto 6 km/sec.Asinglepowerlaw fit through the hypervelocity data goes right through the low speed data. Thus, a single
power-law fit holds for over 8 decades of impactor radius (24 decades of mass), 4 decades
after
Holsapple
(1993)
impact velocity, and 8 decades in gravity.
Gardnos-Gol Workshop, 10. June, 2009
Scaling of crater formation - numerical modeling of impact processes on continental targets
Centrifuge experiments in different materials
Experimental range
Water
impacts,
1‐3
km/s
Quar
tz
sa
nd
Wat
er
Water‐drop
experiments
(1‐20
m/s)
Cohesive
soil
Power-law: πD~π2x
π2-Range of real
craters
Schmidt
(1980),
Schmidt
&
Housen
(1987),
Holsapple
(1993),
Gault
&
Wedekind
(1977),
Gault
&
Sonett
(1982)
Gardnos-Gol Workshop, 10. June, 2009
Scaling of crater formation - numerical modeling of impact processes on continental targets
Numerical experiments in different materials
Experimental range
Numerical range
Depends on
numerical solver
Quar
tz
sa
nd
Cohesive
soil
Wat
er
π2-Range of real
craters
Wünnemann
et
al.,
2007,
2008
Gardnos-Gol Workshop, 10. June, 2009
Scaling of crater formation - numerical modeling of impact processes on continental targets
Theoretical
solution:
Impacts
can
be
approximated
by
a
„point
source“.
L
Dienes
&
Walsh,
1970;
Holsapple
&
Schmidt,
1987;
Schmidt
&
Housen,
1984
„Point‐Source“
Impactor
U
dPS
Excavation
Flow
Coupling
Zone
Transfer
of
Energy
/
Momentum
to
the
Target
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Scaling of crater formation - numerical modeling of impact processes on continental targets
Point‐Source
analogous
to
detonation
centre
of
an
explosive
source
〉
near‐field
point‐source
approximation
fails
dPS
=
depth
of
burial
of
an
explosive
source
Impactor
Coupling
Zone
far‐field
point‐source
approximation
is
satisfied
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Scaling of crater formation - numerical modeling of impact processes on continental targets
The
coupling
parameter
At
sufficient
distance
point‐source
approximation
holds
true
and
energy/momentum
transfer
by
the
impactor
can
be
described
by
a
single
parameter,
the
coupling
parameter
C =L·U ·δ
µ
ν
(Holsapple,
1993)
If
the
size
of
an
event
scales
with
energy
"1/3
!
1
1
3
2/3
1/3
2
1/3
=
π·L
·
U
·
δ
=
mU
C ∼ E
"#
$
12 !
2
=C
If
the
size
of
an
event
scales
with
momentum
1
1/3
3
1/3
1/3
1/3 = [mU ]
= π · !L · U "# · δ $
C ∼ M
6
=C
Gardnos-Gol Workshop, 10. June, 2009
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Scaling of crater formation - numerical modeling of impact processes on continental targets
The
coupling
parameter
is
the
sole
measure
of
the
coupling
of
energy
and
momentum
of
the
impactor
into
the
target
C =L·U ·δ
µ
ν
(Holsapple,
1993)
energy‐momentum
2/3
‐
1/3
Implications
and
physical
meaning:
‣Impact
events
with
same
C
produce
same‐sized
craters
‣All
far‐field
processes
(e.g.
crater
growth)
are
related
by
power‐laws
‣The
velocity
exponent
μ
depends
on
dissipative
target
properties,
e.g.
porosity,
friction,
...?
‣The
angle
of
impact
is
not
considered
in
the
coupling
parameter
Gardnos-Gol Workshop, 10. June, 2009
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Scaling of crater formation - numerical modeling of impact processes on continental targets
point‐source
approximation
enables
derivation
of
power‐
laws
to
scale
crater
size
(and
other
processes,
e.g.
ejection,
crater
growth,
...)
point‐source
approximation
applies
to
both
regimes,
gravity
and
strength
dominated
crater
formation
Note,
the
coupling
zone
has
to
be
„small“
in
comparison
to
the
crater
size
so
that
point‐source
approximation
holds
true
→projectile
small
in
comparsion
to
the
size
of
transient
crater
(at
least
2‐3
times
smaller
in
diameter;
Holsapple,
1993)
This
is
satisfied
for
most
hypervelocity
impacts
with
some
restrictions
to
very
large
impacts
...
Gardnos-Gol Workshop, 10. June, 2009
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Scaling of crater formation - numerical modeling of impact processes on continental targets
Scaling‐laws
for
gravity
regime
applies
to
almost
all
crater
structures
on
planetary
surfaces;
critical
size
depends
on
material
strength
and
gravity
crater
efficiency
crater
diameter
3µ
− 2+µ
(π4 )
πV = KV (π2 )
µ
− 2+µ
πD = KD (π2 )
ρV
πV =
m
πD
= −β
(π4 )
! ρ "1/3
gL
π2 = 1.61 2
=D
U
m
ρ
π4 =
δ
2+µ−6ν
2+µ
2+µ−6ν
3(2+µ)
(for
ρ=δ)
μ,
KD,
KV
need
to
be
determined
in
laboratory
or
numerical
experiments
and
depend
on
material
properties
(friction,
porosity
...).
Note,
μ
and
ν
are
the
same
parameters
for
strength
and
gravity
regime!
(e.g.
Housen
&
Holsapple,
2003)
Gardnos-Gol Workshop, 10. June, 2009
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Scaling of crater formation - numerical modeling of impact processes on continental targets
Scaling‐laws
for
strength
regime
applies
to
laboratory‐sized
craters
in
cohesive
material
and
very
small
natural
craters
in
competent
rock
crater
efficiency
crater
diameter
3µ
− 2
πV = QV (π3 )
µ
−2
πD = QD (π3 )
ρV
πV =
m
πD
3µ
1−3ν+ 2
(π4 )
(π4 )
! ρ "1/3
Y
π3 =
=D
δU 2
m
µ
1
3 −ν+ 2
ρ
π4 =
δ
(for
ρ=δ)
μ,
QD,
QV
need
to
be
determined
in
laboratory
or
numerical
experiments
and
depend
on
material
properties
(friction,
porosity
...).
(e.g.
Housen
&
Holsapple,
2003)
Gardnos-Gol Workshop, 10. June, 2009
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Scaling of crater formation - numerical modeling of impact processes on continental targets
It
is
possible
to
formulate
one
equation
that
satisfies
both
regimes,
strength
and
gravity
(Holsapple
&
Housen,
2007)
&
− 2+µ
# $ % 2ν "
# 2+µ
ν(2+µ)
$ρ% µ
2
D
gL
ρ µ
Y
= JD
1.61 2
+
L
U
δ
ρU 2
δ
µ
!
"
−
ν(2+µ)
2+µ
2ν
2+µ
D
= JD π2 π4µ + π3 2 π4 µ
L
µ
{
crater
diameter
!"
=0,
If
strength
negligible
(Y=0)
"
!
µ
2ν
− 2+µ − 2+µ
D
= JD π2
π4
L
!
"
! " 31 #
$
2+µ−6ν
µ
− 2+µ − 3(2+µ)
D
ρ
6
= JD
π2
π4
1
L 6 Πδ
Π
πD = KD (π2 )
πD = KD (π2 )−β
− 2+µ−6ν
3(2+µ)
(π4 )
{
µ
− 2+µ
multiply
both
sides
of
the
!
"
ρ
equation
with 1 Πδ
6
assuming
spherical
projectile!
=1,
if
ρ=δ
(π4=1)
β=0.25
for
energy‐scaling
β=0.14
for
momentum‐scaling
Gardnos-Gol Workshop, 10. June, 2009
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Scaling of crater formation - numerical modeling of impact processes on continental targets
Numerical experiments in different materials
Scaled
crater
diameter
πD
100
Water
slope
μ=0.57
10
πD =
KD (
π2 ) −β
close
to
pure
energy‐
scaling
with
μ=0.67
Quartz
Sand
friction=0.8
porosity=30%
slope
μ=0.44
closer
to
momentum‐
scaling
with
μ=0.33
1
1e-07
1e-06
Difference
in
slope
may
be
due
to
porosity
or
friction?
1e-04
1e-03
1e-05
Gravity
scaled
size
π2
Gardnos-Gol Workshop, 10. June, 2009
Scaling of crater formation - numerical modeling of impact processes on continental targets
Scaled
crater
diameter
πD
100
Water
Quartzite
5
km/s
1
km/s
friction=0.8
5
km/s
10
craters
in
compact
rock
(nonporous)
scale
similar
as
craters
in
sand
(same
slope)
but
they
are
~30%
larger
(friction
coef.
0.8)
Quartz
Sand
friction=0.8
porosity=30%
5
km/s
1
km/s
Porosity
reduces
crater
efficiency
(vertical
shift
of
scaling
line)
1
1e-07
1e-06
Friction
changes
scaling
exponent
μ
1e-04
1e-03
1e-05
(change
in
slope
of
scaling
line)
Gravity
scaled
size
π2
Gardnos-Gol Workshop, 10. June, 2009
Scaling of crater formation - numerical modeling of impact processes on continental targets
The fact that craters in porous targets can be smaller than in
competent rock may seem a bit unintuitive at first glance
fric=0.4,
v=5
km/s
fric=0.8,
v=5
km/s
Competent rock
porosity=30%
fric=0.4,
v=5
km/s
porosity=30%
fric=0.8,
v=5
km/s
Porous rock
Note, crater excavation is a result of release from shock compression.The
crushing of pore space consumes a lot of energy, thus shock pressure and
therefore crater size is smaller!
Gardnos-Gol Workshop, 10. June, 2009
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Scaling of crater formation - numerical modeling of impact processes on continental targets
Summary: scaling of transient crater size (vertical impacts)
Dimensionless form
Absolute parameters
(Note difference
between KD, JD, K1, ...)
µ
− 2+µ
πD = KD (π2 )
!
D
gL
= JD 1.61 2
L
U
where KD
µ
"− 2+µ
! " 13
µ
6
and β =
= JD
2+µ
Π
{
If strength is
negligible and
density of projectile
and target are
equal
Scaling exponent μ as a function of friction
Numerical modeling enables
determination of KD, μ, ν, ... as a
function of friction and porosity.
Scaling exponent μ
0.73
0.67
energy scaling limit μ=2/3
0.5
0.33
momentum scaling limit μ=1/3
0.31
friction coefficient
Gardnos-Gol Workshop, 10. June, 2009
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Scaling of crater formation - numerical modeling of impact processes on continental targets
All scaling laws discussed so far apply only to vertical impact!
Probability
What about the effect of the impact
angle on crater efficiency?
Impact angle
Impact angle
30°-60°
:
20-70°
:
<15° :
>5° :
Gardnos-Gol Workshop, 10. June, 2009
Probability
50%
76.6%
6.7 %
0.75%
32
Scaling of crater formation - numerical modeling of impact processes on continental targets
90°
75°
60°
Computation
time much
higher;
parameter
studies time
consuming
gravity cannot be
varied in oblique
impact experiments
1978LPSC....9.3843G
To simulate
oblique impacts
3D hydrocodes
are required
Oblique impact
experiments by
Gault & Wedekind
(1978)
45°
30°
Gardnos-Gol Workshop, 10. June, 2009
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Scaling of crater formation - numerical modeling of impact processes on continental targets
Comparison between numerical model of
vertical and oblique impact
vertical
oblique
Gardnos-Gol Workshop, 10. June, 2009
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Scaling of crater formation - numerical modeling of impact processes on continental targets
Comparison if the size of the transient crater
between vertical and oblique impact
vertical
oblique
Gardnos-Gol Workshop, 10. June, 2009
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Scaling of crater formation - numerical modeling of impact processes on continental targets
Crater volume decreases with
decreasing impact angle
Normalized crater volume V/V90
1.1
Strength-dominated
1.0
Impact exp. in granite
0.9
(Gault and Wedekind,1978 )
sin(θ)
0.8
0.0
=
Φ
tion
c
i
r
f
No
.7
0
=
nΦ
o
i
t
Fric
sin2(θ)
Impact exp. in quartz sand
0.7
(Gault and Wedekind,1978 )
0.6
Gravity-dominated
0.5
0.4
Numerical models, gravity regime with π2=1.6×10-4 ,
Impact velocity U=6.5 km/s
30
40
50
60
impact angle
70
80
90
Elbeshausen
&
Wünnemann,
2007,
2008
Gardnos-Gol Workshop, 10. June, 2009
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Scaling of crater formation - numerical modeling of impact processes on continental targets
Impact angle
Elbeshausen
&
Wünnemann,
2008
90°
75°
60°
45°
30°
0.0
0.2
0.5 Coefficient of friction
Gardnos-Gol Workshop, 10. June, 2009
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Scaling of crater formation - numerical modeling of impact processes on continental targets
The effect of impact angle on crater efficiency
does not depend on π2
Normalized crater volume V/V90
1.1
1.0
0.9
sin(θ)
0.8
π2= 10-4 - 10-3
sin2(θ)
0.7
0.6
0.5
0.4
30
40
50
60
impact angle
70
Gardnos-Gol Workshop, 10. June, 2009
80
90
38
Scaling of crater formation - numerical modeling of impact processes on continental targets
How can we consider the impact
angle in the scaling equations?
θ
Scaling for crater efficiency for vertical impacts
3µ
− 2+µ
πV = KV (π2 )
3µ
!
"− 2+µ
gL
πV = KV 1.61 2
U
Chapman and McKinnon (1986) suggested to replace U by the vertical component U sin(θ)
πV = K V
πV = K V
!
3µ
"− 2+µ
gL
1.61 2
U sin(θ)2
κ = 1 or 2
3µ
!
"− 2+µ
3µ
gL
κ 2+µ
1.61 2
· sin(θ)
U
Gardnos-Gol Workshop, 10. June, 2009
{
Depending on
material (?),
friction (?), ...
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Scaling of crater formation - numerical modeling of impact processes on continental targets
The effect of impact angle on crater scaling
30°- 90°
µ=0.56 - 0.52
.0
90
75
60
45
30
Fri
ctio
nΦ
=0
.7
=0
nΦ
tio
fric
No
Crater efficiency
πV = V/Vp
30°- 90°
µ=0.47- 0.48
Impact velocity U=6.5 km/s
Gravity scaled size π2 = (1.61⋅L⋅g)/U2
Gardnos-Gol Workshop, 10. June, 2009
Scaling of crater formation - numerical modeling of impact processes on continental targets
Summary: scaling the diameter of the transient crater size
µ
− 2+µ
πD = KD (π2 )
! ρ "1/3
= KD
D
m
#
gL
U2
µ
κ 2+µ
sin(θ)
µ
$− 2+µ
(π4 )
µ
κ 2+µ
sin(θ)
Considering
impact angle
2+µ−6ν
2+µ
! ρ " 2+µ−6ν
2+µ
δ
Considering
density ratio
projectile/target
There is a big difference between the size of the transient
crater and the diameter of the final crater in particular for
complex crater morphology
Gardnos-Gol Workshop, 10. June, 2009
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Scaling of crater formation - numerical modeling of impact processes on continental targets
Chesapeake Bay crater formation model
Impactor diameter 3.2
km; Impact velocity 18 km/s
Peak/inner ring
Outer rim
Incoherent reflectors
Weak sediments
Strong crystalline basement
transient crater
Collins and Wünnemann, 2005
• Final crater (~85 km) is enlarged by inwards collapsing
weak, water-saturated sediments
• more diagnostic crater size ~36 km in diameter
• transient crater size ~28 km in diameter
Gardnos-Gol Workshop, 10. June, 2009
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Scaling of crater formation - numerical modeling of impact processes on continental targets
Chicxulub crater formation model
transient crater
Peak ring
Outer rim
Wünnemann, Collins and Ivanov
Gardnos-Gol Workshop, 10. June, 2009
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Scaling of crater formation - numerical modeling of impact processes on continental targets
Scaling from the transient crater size to the final
crater diameter
Dt
Scaling based on
complex lunar craters
D=
Dt1.13
1.17 0.13
Dc
Transient crater
28.0 km
40.0 km
Scaling
43.4 km
Observed
36-85 km
Chesapeake Bay
142.2 km
180.0 km
Chicxulub
McKinnon and Schenk, 1985
with Dc = 3.2 km for the earth
Scaling laws provide only a
very rough estimate
Gardnos-Gol Workshop, 10. June, 2009
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Scaling of crater formation - numerical modeling of impact processes on continental targets
Take-Home-Messages
• Almost all impact craters on planetary surfaces are „gravity dominated“ - crater
size is controlled by gravity not strength!
• Scaling laws relate the kinetic energy of an impact to the size of the transient
crater (crater diameter, depth, efficiency)
• Scaling laws apply only to processes, such as crater growth, that take place in the
„far-field“ - sufficiently far enough from the „coupling zone“
• Scaling parameters (velocity exponent μ, intercept K) can be determined by
laboratory or numerical experiments and depend on material properties such as
friction and porosity
• Only numerical experiments can be used to study the effect of the impact angle on
crater scaling (diameter, depth, ...) → using the vertical component of the impact
velocity holds true only for frictional targets comparable to sand
• Final crater size can be roughly estimated from the transient crater by empirical
estimates from the lunar crater record; however, more precise estimates can only
be obtained from numerical modeling
Gardnos-Gol Workshop, 10. June, 2009
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Scaling of crater formation - numerical modeling of impact processes on continental targets
Thanks
to
Henning, Elin, and NiR
Gardnos-Gol Workshop, 10. June, 2009
46
Scaling of crater formation - numerical modeling of impact processes on continental targets
Thanks
to
Henning, Elin, and NiR
Projectile
Gardnos-Gol Workshop, 10. June, 2009
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Scaling of crater formation - numerical modeling of impact processes on continental targets
Gardnos-Gol Workshop, 10. June, 2009
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