Impact Cratering Mechanics and Morphologies PTYS 411/511 Geology and Geophysics of the Solar System Shane Byrne – shane@lpl.arizona.edu 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 2 PYTS 411/511 – Cratering Mechanics and Morphologies 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 3 PYTS 411/511 – Cratering Mechanics and Morphologies 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 4 PYTS 411/511 – Cratering Mechanics and Morphologies 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 5 Harris et al. PYTS 411/511 – Cratering Mechanics and Morphologies 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 6 PYTS 411/511 – Cratering Mechanics and Morphologies 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 7 PYTS 411/511 – Cratering Mechanics and Morphologies 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 8 PYTS 411/511 – Cratering Mechanics and Morphologies 9 PYTS 411/511 – Cratering Mechanics and Morphologies 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 10 PYTS 411/511 – Cratering Mechanics and Morphologies Strength Regime Cratering law Gravity Regime 11 PYTS 411/511 – Cratering Mechanics and Morphologies 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) 12 PYTS 411/511 – Cratering Mechanics and Morphologies Cratering in metals Regression gives n=0.4, m=0.5 Ref: Holsapple and Schmidt (1982) JGR, 87, 1849-1870. 13 PYTS 411/511 – Cratering Mechanics and Morphologies Regímenes de Impacto 14 PYTS 411/511 – Cratering Mechanics and Morphologies Regímenes de Impacto II 15 PYTS 411/511 – Cratering Mechanics and Morphologies 16 PYTS 411/511 – Cratering Mechanics and Morphologies 17 PYTS 411/511 – Cratering Mechanics and Morphologies Radius of transient crater depth d= Rfinal = 1.3 R d/Dfinal ~ 0.2 18 PYTS 411/511 – Cratering Mechanics and Morphologies In the gravity regime Diameter of transient crater Diameter of final rim Depth of transient crater Depth of final rim (Collins et al. 2005) 19 PYTS 411/511 – Cratering Mechanics and Morphologies 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 20 PYTS 411/511 – Cratering Mechanics and Morphologies 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 21 PYTS 411/511 – Cratering Mechanics and Morphologies 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 22 PYTS 411/511 – Cratering Mechanics and Morphologies 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 23 PYTS 411/511 – Cratering Mechanics and Morphologies 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 24 PYTS 411/511 – Cratering Mechanics and Morphologies 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 25 PYTS 411/511 – Cratering Mechanics and Morphologies 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 26 PYTS 411/511 – Cratering Mechanics and Morphologies 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 27 PYTS 411/511 – Cratering Mechanics and Morphologies 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 28 PYTS 411/511 – Cratering Mechanics and Morphologies 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 29 Impact Cratering Dating and the Planetary Record PTYS 411/511 Geology and Geophysics of the Solar System Shane Byrne – shane@lpl.arizona.edu 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 31 PYTS 411/511 – Cratering Mechanics and Morphologies 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 32 PYTS 411/511 – Cratering Mechanics and Morphologies 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 33 PYTS 411/511 – Cratering Mechanics and Morphologies Plotting styles compared for Phobos craters Hartmann and Neukum, 2001 Differential Cumulative R-plot 34 PYTS 411/511 – Cratering Mechanics and Morphologies 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 35 PYTS 411/511 – Cratering Mechanics and Morphologies When a surface is saturated no more age information is added Number of craters stops increasing 36 PYTS 411/511 – Cratering Mechanics and Morphologies Typical size-frequency curve Steep-branch for sizes <1-2 km Saturation equilibrium for sizes <250m 37 PYTS 411/511 – Cratering Mechanics and Morphologies 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. 38 PYTS 411/511 – Cratering Mechanics and Morphologies 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’ 39 PYTS 411/511 – Cratering Mechanics and Morphologies 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 40 PYTS 411/511 – Cratering Mechanics and Morphologies 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 41 PYTS 411/511 – Cratering Mechanics and Morphologies 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 42 PYTS 411/511 – Cratering Mechanics and Morphologies 43 PYTS 411/511 – Cratering Mechanics and Morphologies The sounds Two sounds: •Sonic Boom sónico: minutes after fireball •Electrofonic noise: simultaneous with fireball 44 PYTS 411/511 – Cratering Mechanics and Morphologies Infrasound records Fireball of the European Network Fireball Park Forest 45 PYTS 411/511 – Cratering Mechanics and Morphologies Seismic records of the airblast 46 PYTS 411/511 – Cratering Mechanics and Morphologies Seismic detections of Carancas First seismic detection of an extraterrestrial impact on Earth 47 PYTS 411/511 – Cratering Mechanics and Morphologies 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 48 PYTS 411/511 – Cratering Mechanics and Morphologies 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 49 PYTS 411/511 – Cratering Mechanics and Morphologies Ejecta blanket 50 PYTS 411/511 – Cratering Mechanics and Morphologies Secondary craters 51 PYTS 411/511 – Cratering Mechanics and Morphologies Crater rays 52 PYTS 411/511 – Cratering Mechanics and Morphologies Rings and multirings 53 PYTS 411/511 – Cratering Mechanics and Morphologies Focusing in the antipoe 54