PowerPoint PresentationSlide 2Slide 3Slide 4Slide 5Slide 6Slide 7Slide 8Slide 9Slide 10Slide 11Slide 12Slide 13Slide 14Slide 15Slide 16Slide 17Slide 18Slide 19Slide 20Slide 21Slide 22Slide 23Slide 24Slide 25Slide 26Slide 27Slide 28Slide 29PTYS 554Evolution of Planetary SurfacesImpact Cratering IIImpact Cratering IIPYTS 554 – Impact Cratering II2Impact Cratering ISize-morphology progressionPropagation of shocksHugoniotEjecta blankets - Maxwell Z-modelFloor rebound, wall collapseImpact Cratering IIThe population of impacting bodiesRescaling the lunar cratering rateCrater age datingSurface saturationEquilibrium crater populationsImpact Cratering IIIStrength vs. gravity regimeScaling of impactsEffects of material strengthImpact experiments in the labHow hydrocodes workPYTS 554 – Impact Cratering II3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 equilibriumi.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 calibrationMercury – Young and OldPYTS 554 – Impact Cratering II4Crater population is countedNeed some sensible criteriae.g. geologic unit, lava flow etc…Tabulate craters in diameter binsBin size limits are some ratio e.g. 2½Size-frequency plot generatedIn log-log spaceFrequency is normalized to some areaPiecewise linear relationship: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 N(D, 2D) =kD- bAn ideal case… Do£ D £ 2DoPYTS 554 – Impact Cratering II5IncrementalCumulativeDifferentialRelativeThere are at least 4 ways to represent crater count dataBin spacing should be geometric, √2 is most commonPlots from craterstats (Michael & Neukum, EPSL, 2010)Definitions from the “CRATER ANALYSIS TECHNIQUES WORKING GROUP” (Icarus, 37, 1979)PYTS 554 – Impact Cratering II6Cumulative plots Tends to mask deviations from the idealNot binnedIncremental plotsThe ‘standard’ plot…NincD, 2D( )=k D- bNincD, 2D( )=Ncum(³ D) - Ncum(³ 2D)\ k=c 1- 2- b( ) Ncum(³ D) =cD- bIncrementalCumulativePYTS 554 – Impact Cratering II7Incremental plots with √2 diameter bin spacing is favored by HartmannIsochrons have become relatively standardized for MarsHartmann, 2005PYTS 554 – Impact Cratering II8Cumulative plots Differential plotsNdiffD, 2D( )=qD- b-1NdiffD, 2D( )=- Ncum(³ D) - Ncum(³ 2D)éëùûD- 2Déëùû\ q=c 1- 2- b( )2 - 1( ) Ncum(³ D) =cD- bCumulativeDifferentialPYTS 554 – Impact Cratering II9R-plotsSize-frequency plot with slope removed - Highlights differences from the idealArea of craters:Rarely usedR(D) = NdiffD, 2D( )éëùû2-34D- 3éëêùûúR(D) =r D- b+2where r =c2341- 2- b( )2 - 1( )A D ® 2D( )=p214D2æèççöø÷÷2Ncum³ D( )- Ncum³ 2D( )éëùûA D ® 2D( )=cp2142æèççöø÷÷21- 2- b( )D- b+2=0.27 R D( )Relative (R-Plot)CumulativePYTS 554 – Impact Cratering II10R-plots reveal different populations of cratering bodiesYoung surfaces are flatclose to a -2 slope in log(N) vs. log(D)Older surfaces show a different impacting populationMore on this laterStrom et al., 2005PYTS 554 – Impact Cratering II11When a surface is saturated no more age information is addedNumber of craters stops increasingThe whole premise of crater dating is that c (or k) increases linearly with timePYTS 554 – Impact Cratering II12Geometric saturationHexagonal packing allows craters to fill 90.5% of available area (Pf)A mix of crater diameters allows Ns = 1.54 D-2Crater arrays separated by a factor of two in diameter NSATArea( )=Pf4pD2=1.15D- 2or log NSAT/ Area( )=- 2log D( )+logPf4pæ è ç ö ø ÷ For equal sized cratersLog (D)Log (N)PYTS 554 – Impact Cratering II13Equilibrium saturation:No surface ever reaches the geometrically saturated 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This saturation diameter increases with time Deqµ t1b- 2PYTS 554 – Impact Cratering II14Summary of a classic crater size-frequency distributionTypical size-frequency curveSteep-branch for sizes <1-2 kmSaturation equilibrium for sizes <250mSample of Mare OrientaleMultiple slope breaksPYTS 554 – Impact Cratering II15In general, it’s hardly ever as neat and tidy as the lunar mare.Craters can get removed as fast as they arrive – an equilibrium populationproduction x lifetime = populationproduction & population knownCan find the crater lifetime…Usually crater lifetime is a power-law of diameter: a DxIf x=0, then the crater lifetime is the surface age i.e. all craters are preservedIf x=1, then crater lifetime is proportional to depth… e.g. constant infill ratePYTS 554 – Impact Cratering II16Viscous relaxation of icy topography can make craters undetectableMaxwell timeStress causes elastic deformation and creepTime after which creep strain equals elastic straintM = εel / (Δεcreep/t) = η/μμ is the shear modulus (rigidity), η is the viscosityOn EarthtM for rock >109 yearstM for ice ~ 100s secGanymede ice is intermediatePathare and Paige, 2005PYTS 554 – Impact Cratering II17Viscous relaxation on the icy Galilean satellitesImages by Paul Schenk Lunar and Planetary InstituteRelaxed craters Penepalimpset → PalimpsetPYTS 554 – Impact Cratering II18Secondary craters confuse the pictureSteep-branch of lunar production function caused controversyAre these true secondaries or collisional fragments generated in spaceAsteroid GaspraAlso has steep-branchDefinitely lacks true secondariesCase closed? Not really…PYTS 554 – Impact Cratering II19Analysis of Zunil by McEwen et al. Modeling suggests this one crater can account