Cratering as a Geological Process
Part 1：
(a) Simple and complex craters;
(b) Fundamental concepts of stress waves,
plastic waves, and shock waves;
(c) Impact and crater modifying processes
Importance of Crater Studies:
1. Principal process in shaping planetary surfaces.
2. Principal means of determining relative and for some
planetary bodies the absolute ages of planetary surfaces.
3. Major impact events may have affected the tectonic, chemical
and biological evolution of planetary bodies (e.g., initiation of
plate tectonics; alternate mantle convection; extensive
melting in the mantle; removal mantle and crustal materials
of target planets during major impacts, extinction and
possible delivery of organism of planets).
4. Crater morphology may tell us about the rheological
structures of the crust and mantle of planetary bodies.
5. Large impacts may have affected planetary rotations and
orbits.
Basic Classification:
(1) Simple craters: strength controlled formation process with
smooth bowl shapes; relatively higher depth-to-diameter ratios.
(2) Complex craters: gravity-dominated modification process, clear
sign of wall and floor modifications expressed as central peaks,
peak-ring structures; relatively low depth-to-diameter ratios (i.e.,
relatively shallower basins than simple craters).
(3) Multi-ring basins: having peaks in concentric rings on flat floors.
Moltke Crater (D = 7km):
Simple crater with a bowlshaped interior and smooth
walls.
Such craters typically have
depths that are about 20
percent of their diameters
(Apollo 10 photograph
AS10-29-4324.)
Tycho crater (D = 83 km):
Complex crater with terraced rim and a
central peak.
Bessel Crater (D = 16 km h = 2km)
A transitional-type crater between
simple and complex shapes.
Slumping of material from the inner
part of the crater rim destroyed the
bowl-shaped structure seen in smaller
craters and produced a flatter,
shallower floor. However, wall
terraces and a central peak have not
developed. (Part of Apollo 15
Panoramic photograph AS15-9328.)
Young lava flow
Mare Orientale (D = 930 km)
A lunar multiring basin
An outer ring has a D = 930 km
Three inner rings with D= 620,
480, and 320 km.
Radial striations in lower right
may be related to low-angle
ejection of large blocks of
excavated material.
Transition size from simple to complex craters on various
planetary bodies:
(1) Europa: 5 km
(2) Mars: 8-10 km
(3) Moon: 15-20 km
(4) Venus: No craters with diameters < 10 km are scarce,
possibly due to thick atmosphere; dominantly complex
craters and multi-ringed basins.
(5) Earth: 2-4 km
(6) Mercury: 10 km
Simple-to-complex crater transition occurs when the yield strength is related to
the gravity (g), density (rho), transient crater depth (h), and a constant c that is
less than 1:
or
Where Dtr is the transient crater diameter that can be related to the final
crater diameter by
That is, D is proportional to yield strength (Y) and
inversely proportionally to density (rho) and gravity (g).
Transverse and longitudinal waves are related to
bulk modulus K0, shear modulus m, and density r0.
Wave-induced longitudinal and transverse or
perpendicular stress components are
UL is particle velocity
C is wave velocity
=
Poisson’s ratio
Relative importance of longitudinal and transverse waves:
Transverse waves are not important in the cratering process,
because the shear strength of materials limits the strength
of the wave.
The strength of the longitudinal waves have no limit, the
strength of compression has no upper bound.
In most cratering modeling, transverse waves are neglected.
Compressional and tensional waves are converted at a free surface
Free surfaces require both normal
and shear stresses are zero, but the
particle velocity can be non zero.
UL at the free surfaces for compressive
wave is:
UL = sL /CL r0
For tensional waves, sL and CL have the
opposite sign, and thus
UL = sL /CL r0
Thus, at the interface, UL is doubled.
Deformation generated by this process is
called “spalling”.
Three stages of cratering:
(1) Contact and compression stage (initiation
of shock waves)
(2) Excavation stage (shockwave expansion
and attenuation; crater growth; ejection
of impactor and target materials)
(3) Post-impact modification
Reflection at an interface from
high-velocity material to lowvelocity material:
Reflected wave is tensile waves
and the rest continues into the
low-velocity material as
compressive wave.
Reflection at an
interface from lowvelocity material to highvelocity material:
Reflected wave is
compressive wave and
the rest continues into
the high-velocity material
as compressive wave.
Plastic Yielding at “HEL”— the Hugoniot Elastic Limit
When stress in the stress wave reached the plastic limit, irreversible deformation
will occur. This plastic yield strength affects both the speed and shape of the stress
wave. The onset of this behavior is indicated by a characteristic kind in the Hugoniot
P-V plot. The corresponding pressure is known as the Hugoniot Elastic Limit (HEL).
In the continuum and fracture mechanics sense, when the
differential stress
sL – sp = - Y,
Y is the yield strength, the material begins to experience
“plastic flow”.
Shear stress t = - (sL – sp)/2
Pressure P = - (sL + 2sp)/3
HEL
At the failure point, when t = - Y/2, the longitudinal stress
equals to HEL, that is
Idealized cross section of a simple crater
1. Once the wave-induced stress reaches HEL, the shear
stress t = - (sL – sp)/2 remains constant, and thus the
increase in sL and sp must also maintain in such a way
that its difference is the same as -2t.
2. When P is much greater than t, we neglect the differential
stress term and corresponding stress wave becomes
strong pressure wave.
Cautions for the HEL:
1. For porous medium, there might be two HEL points,
one for the collapse of the pores, and the other for
the onset of ductile flow.
2. Yield strength may not be constant, but a pressuredependent envelope.
3. Yield strength may be rate-dependent.
Elastic Wave: sL < sHEL Longitudinal wave depends on both bulk
and shear muduli
Plastic Wave: sL = sHEL Longitudinal wave depends almost
completely on the bulk modulus. The wave propagates much
slower than the elastic wave and at a speed of the “bulk wave
speed” defined by
CB = [K(P)/r0]1/2
Where bulk modulus increases with pressure. Thus, the bulk
speed of plastic wave is much higher under high-pressure
condition.
This segment is called strong or shock wave,
which is a plastic wave travels faster than
elastic wave
Strong compressive waves: The Hugoniot Equations
Conservation of mass
Conservation of momentum
Conservation energy
P = P(V, E) is equation of state for shock waves. There are two ways to represent
the equation of state for shock waves (P-V and U-up plots)
Shock pressure as a function of
specific volume
Shock wave velocity as a function
of particle velocity
Release wave or rarefaction wave
1. The high-pressure state induced by an impact is transient, ranging from 10-3 to 10-1 sec
for projectile of 10 m and 1 km size.
2. The high-pressure in a shock wave is relieved by the propagation of rarefaction, or
release waves from free surfaces into the shocked materials. This type of wave from
strong compression generally moves faster than the shock wave and is proportional to
the slope of the adiabatic release curve on the P-V diagram
Stage 1: Contact and compression (shockwave generation and projectile
deformation): this stage only lasts a few seconds. Rarefaction waves cause
projectile to transform into vapor and melts instantaneously.
From O’Keefe and Ahrens (1975)
Impact of 46-km-diameter projectile
at a speed of 15 km/s 1 s after the
impact.
Formation of simple craters
Examples of Complex craters
Peak-ring crater on the Moon (Schrodinger crater, D = 320 km)
Young lava flow
Mare Orientale (D = 930 km)
A lunar multiring basin
An outer ring has a D = 930 km
Three inner rings with D= 620,
480, and 320 km.
Radial striations in lower right
may be related to low-angle
ejection of large blocks of
excavated material.
c: Cohesive strength
Isostatic adjustment after a large impact removing crust and uplift mantle