PTYS 554 Evolution of Planetary Surfaces Impact Cratering

PTYS 554 Evolution of Planetary Surfaces Impact Cratering III

PYTS 554 – Impact Cratering III l Impact Cratering I n n n l Impact Cratering II n n n l Size-morphology progression Propagation of shocks Hugoniot Ejecta blankets - Maxwell Z-model Floor rebound, wall collapse The population of impacting bodies Rescaling the lunar cratering rate Crater age dating Surface saturation Equilibrium crater populations Impact Cratering III n n n Strength vs. gravity regime Scaling of impacts Effects of material strength Impact experiments in the lab How hydrocodes work 2

PYTS 554 – Impact Cratering III l Scaling from experiments and weapons tests to planetary impacts 3

PYTS 554 – Impact Cratering III l Morphology progression with size… l Transient diameters smaller than final diameters n n Simple ~20% Complex ~30 -70% Simple 4 Moltke – 1 km Complex Peak-ring Euler – 28 km Schrödinger – 320 km Orientale – 970 km

PYTS 554 – Impact Cratering III l Scaling laws apply to the transient crater l Apparent diameter (Dat), diameter at original surface, is most often used l Target properties n l Density, strength, porosity, gravity Projectile properties n Size, density, velocity, angle 5

PYTS 554 – Impact Cratering III l Lampson’s law n n n Length scales divided by cube-root of energy are constant Crater size affected by burial depth as well Very large craters (nuclear tests) show exponent closer to 1/3. 4 6

PYTS 554 – Impact Cratering III l Hydrodynamic similarity (Lab results vs. Nature) Mass, Momentum and energy conservation for compressible fluid flow n Conservation of mass, momentum & energy (Mostly) invariant when distance and time are rescaled x→αx and t →αt i. e. n Lab experiments at small scales and fast times = large-scale impacts over longer times n n w 1 cm lab projectile can be scaled up to 10 km projectile (α = 106) w Events that take 0. 2 ms in the lab take 200 seconds for the 10 km projectile w Velocities (u), Shock pressures (P) & energy densities(E) are equivalent at the same scaled distances and times l …but gravity is rescaled as g→g/α n n l Lab experiments at 1 g correspond to bodies with very low g In the above example… the results would be accurate on a body with g~10 -5 ms-2 Workaround… increase g n n Centrifuges in lab can generate ~3000 gmoon So α up to 3000 can be investigated… w A 30 cm lab crater can be scaled to a 1 km lunar crater 7

PYTS 554 – Impact Cratering III l If g is fixed… (one crater vs another crater) l If x→αx then D→αD and E ~ ½mv 2 → α 3 E (mass proportional to x 3) 8 n So D/Do= α and (E/Eo)⅓ = α Lampson’s scaling law: n In the gravity regime (large craters) energy is proportional to n Experiments show that strength-less targets (impacts into liquid) have scaling exponents of 1/3. 83 n exponent closer to 1/3. 4 in ‘real life’ (nuclear explosions)

PYTS 554 – Impact Cratering III l PI group scaling n n n Buckingham, 1914 Dimensional analysis technique Crater size Dat function of projectile parameters {L, vi, ρi}, and target parameters {g, Y, ρt} Seven parameters with three dimensions (length, mass and time) So there are relationships between four dimensionless quantities w PI groups l Cratering efficiency: n n n n Mass of material displaced from the crater relative to projectile mass Popular with experimentalists as volume is measured An alternative measure Popular with studies of planetary surfaces as diameter is measured Close to the ratio of crater and projectile sizes Crater volume (parabolic) is ~ If Hat/Dat is constant then 9

PYTS 554 – Impact Cratering III l Other PI groups are numbered n l Ratio of the lithostatic to inertial forces n n l A measure of the importance of gravity Inverse of the Froude number Ratio of the material strength to inertial forces n l πD = F(π2, π3, π4) A measure of the effect of target strength Density ratio n Usually taken to be 1 and ignored 10

PYTS 554 – Impact Cratering III l 11 When is gravity important? n n ρg. L > Y gravity regime ρg. L < Y strength regime Gravity is increasingly important for larger craters If Y~2 MPa (for breccia) w Transition scales as 1/g w At D~70 m on the Earth, 400 m on the Moon n l Gravity regime n l Strength/gravity transition ≠ simple/complex crater transition π3 can be neglected, also let π4 → 1 so πD = F(π2) Strength regime n π2 can be neglected, also let π4 → 1 so πD = F(π3) Holsapple 1993

PYTS 554 – Impact Cratering III l In the gravity regime strength is small n so π3 can be neglected, also let π4 → 1 so πD = F’(π2) Experiments show: If H/D is a constant… seems to be the case So: l In the strength regime gravity is small n so π2 can be neglected, also let π4 → 1 so πD = F’(π3) Experiments show: 12

PYTS 554 – Impact Cratering III l Combining results for gravity regime… (competent rock) l Crater size scales as: l Combining results for strength regime… (competent rock) 13

PYTS 554 – Impact Cratering III l Pi scaling continued n n How does projectile size affect crater size If velocity is constant, ratio of πD’s will give diameter scaling for projectile size: Gravity regime For competent rock β~0. 22 so D/Do= (E/Eo)1/3. 84 n (verified experimentally) n Pi scaling can be used for lots of crater properties w Crater formation time w Ejecta scaling Strength regime 14

PYTS 554 – Impact Cratering III l 15 More recent formulations just combine these two regimes into one scaling law Holsapple 1993 l Simplify with: l Into:

PYTS 554 – Impact Cratering III l Mass of melt and vapor (relative to projectile mass) n Increases as velocity squared n Melt-mass/displaced-mass α (g. Dat)0. 83 vi 0. 33 Very large craters dominated by melt n Earth, 35 km s-1 16

PYTS 554 – Impact Cratering III Crater-less impacts? l l l Impacting bodies can explode or be slowed in the atmosphere Significant drag when the projectile encounters its own mass in atmospheric gas: n Where Ps is the surface gas pressure, g is gravity and ρi is projectile density n If impact speed is reduced below elastic wave speed then there’s no shockwave – projectile survives Ram pressure from atmospheric shock n n n If Pram exceeds the yield strength then projectile fragments If fragments drift apart enough then they develop their own shockfronts – fragments separate explosively Weak bodies at high velocities (comets) are susceptible Tunguska event on Earth Crater-less ‘powder burns’ on venus Crater clusters on Mars 17

PYTS 554 – Impact Cratering III l ‘Powder burns’ on Venus l Crater clusters on Mars n 18 Atmospheric breakup allows clusters to form here w Screened out on Earth and Venus w No breakup on Moon or Mercury Mars Venus

PYTS 554 – Impact Cratering III l Impact Cratering I n n n l Impact Cratering II n n n l Size-morphology progression Propagation of shocks Hugoniot Ejecta blankets - Maxwell Z-model Floor rebound, wall collapse The population of impacting bodies Rescaling the lunar cratering rate Crater age dating Surface saturation Equilibrium crater populations Impact Cratering III n n n Strength vs. gravity regime Scaling of impacts Effects of material strength Impact experiments in the lab How hydrocodes work 19

PYTS 554 – Impact Cratering III l Courtesy of Betty Pierazzo Hydrocode simulations n n 20 Commonly used simulate impacts Computationally expensive Oslo University, Physics Dept. Total number of timesteps in a simulation, M, depends on: 1) the duration of the simulation, T 2) the size of the timestep, Smallest timestep: Dt Dt Δx/cs (Stability Rule) (Δx is the shortest dimension) Overall: and M = T/ Dt N run time = Nr M Nr+1

PYTS 554 – Impact Cratering III 21 Courtesy of Betty Pierazzo Example: problem with N=1000 10 double-precision numbers are stored for each cell (i. e. , 80 Bytes/cell) For 1 D Storage: 80 k. Bytes (trivial!) Runtime: 1 million operations (secs) For 2 D Storage: 80 MBytes (a laptop can do it easily!) Runtime: 1 billion operations (hrs) For 3 D Storage: 80 GBytes (large computers) Runtime: 1 trillion operations (days) (and N=1000 isn’t very much)

PYTS 554 – Impact Cratering III 22 Courtesy of Betty Pierazzo l Problem… n n Some results depend on resolution Need several model cells per projectile radius Ironically small impacts take more computational power to simulate than longer ones Adaptive Mesh Refinement (AMR) used (somewhat) to get around this Crawford & Barnouin-Jha, 2002

PYTS 554 – Impact Cratering III There are two basic types of hydrocode simulation 23 Courtesy of Betty Pierazzo Lagrangian and Eulerian Cells follow the material -the mesh itself moves Cell volume changes (material compression or expansion) Cell mass is constant R Free surfaces and interfaces are well defined Q Mesh distortion can end the simulation very early

PYTS 554 – Impact Cratering III There are two basic types of hydrocode simulations 24 Courtesy of Betty Pierazzo Lagrangian and Eulerian Material flows through a static mesh Cell volume is constant Cell mass changes with time ö Cells contain mixtures of material Q Material interfaces are blurred R Time evolution limited only by total mesh size

PYTS 554 – Impact Cratering III 25 Courtesy of Betty Pierazzo Artificial Viscosity Artificial term used to ‘smooth’ shock discontinuities over more than one cell to stabilize the numerical description of the shock (avoiding unwanted oscillations at shock discontinuities) Equations of State account for compressibility effects and irreversible thermodynamic processes (e. g. , shock heating) Change of volume COMPRESSIBILITY Deviatoric Models relate stress to strain and strain rate, internal energy and damage in the material Change of shape STRENGTH

PYTS 554 – Impact Cratering III 26 Courtesy of Betty Pierazzo l Given all that… models differences should be expected n Compare results from impact into water