1. Modeling Complex Crater Collapse Gareth Collins and Zibi Turtle Lunar and Planetary Laboratory, University of Arizona, Tucson, AZ 85721, USA

2. Motivation To summarize the current state of numerical modeling of complex crater formation. To highlight the major avenues for further research, both observational and in modeling.

3. Overview Why model impact crater collapse? The fundamentals of modeling collapse Dynamic rock strength during an impact Major results from modeling collapse Where to go from here?

4. Why model crater collapse? No direct observation of crater collapse. Laboratory and nuclear test experiments of limited use to study of crater collapse. Means of studying dynamics of large crater collapse. Best instrumented experiment.

5. Fundamentals of Modeling Importance of the initial conditions Late stage impact cratering is a very different process to the contact-early excavation stage – sensible to model separately. Z-model with static starting conditions is an approximation: not appropriate in all cases. Late stages controlled by gravity and strength – need to model strength differences. Final crater-transient crater scaling laws not always appropriate either.

6. Fundamentals of Modeling Importance of the Constitutive Model Crater collapse is controlled by the competition between gravity and the strength of the target. The constitutive model describes the response of a material to deformation. It combines the concepts of: –Elasticity (strain proportional to stress) –Plasticity (elastic until yield stress) –Fluid flow (strain rate a function of stress)

7. Constitutive Model Used in Impact Simulations Target Rheology The most commonly used constitutive model for rock material is elastic-plastic. Yield strength is a function of pressure: Damage: and internal energy (temperature):

8. Coulomb-Von Mises model Target Rheology Pressure Yield strength Cohesion D = 0 D = 1

9. Current strength models do not allow sufficient collapse Target Rheology For standard strength models of rock materials, the transient crater is stable in a gravity field. First determined using analytical modeling by Dent (1973), then by Melosh (1977) and McKinnon (1978). All numerical modeling work echos this result.

10. Standard Strength Model Target Rheology Movie courtesy of Boris Ivanov

11. Target Weakening Facilitates Crater Collapse Target Rheology Movie courtesy of Boris Ivanov

12. Something is missing from current strength models Target Rheology Some form of temporary target weakening is required to facilitate collapse. Candidates include: –Fragmentation (during shock release or deformation) –Heat (shock or friction melting, thermal softening) –Pressure vibrations (remnant from passing shock) –Dynamic weakening (bulking, strain localization)

13. Modeling has constrained the required weakening effects Target Rheology The target’s strength must be reduced by an order of magnitude or more. A volume of material at least equivalent to the transient crater volume must be weakened. The weakened material must be mobile enough to overshoot the target surface (<10 9 Pa-sec, for largest terrestrial crater).

14. Modeling has constrained the required weakening effects Target Rheology For external ring formation in multi-ring basins there is an additional constraint. There must be a weak, mobile layer at depth (Melosh and McKinnon, 1978). Supported by numerical modeling (Turtle, 1998) and analogue modeling (Allemand and Thomas, 1999).

15. Major recent results Results Melosh and Ivanov, 1999 O'Keefe et al., 2001 Collins et al., 2002 Ivanov and Artemieva, 2002 Shuvalov et al., 2002 Turtle, 1998 Allemand and Thomas, 1999

16. Model for Peak-Ring Formation Results

17. Model for Peak-Ring Formation Results

18. Model for Peak-Ring Formation Results

19. Model for Peak-Ring Formation Results

20. Model for Peak-Ring Formation Results

21. Model for Peak-Ring Formation Results

22. Peak-Ring Formation Model Supported by Seismic Data Comparison with observations Peak ring identified as a topographic high at ~40km radius, reaching a max. height ~500m. slump blocks Weak reflector Weak, shallow-dipping reflector beneath peak-ring Peak ring overlies the base of the slump blocks Peak ring

23. Peak-Ring Formation Model Supported by Seismic Data Comparison with observations Peak-ring formation due to the collision between the two regimes: Inward collapse of transient crater Outward collapse of central uplift Inwardly collapsing crater rim Outwardly collapsing central uplift.

24. Subsurface Structure Model for Generic Peak Ring Crater Results

25. Fate of the Melt? Results Simulations by Boris Ivanov

26. Fate of the Melt? Results

27. Chicxulub Formation Model (Courtesy of Dugan O’Keefe) Results

28. Chicxulub Formation Model Results

29. Chicxulub Formation Model Results

32. Summary Results

33. Key Results Collapse requires temporary weakening: –Order of magnitude reduction in strength. –Volume of weakened material > V tc –Material mobile enough to overshoot surface. –External rings also require mobile sub-surface layer Significant central structural uplift ~ 0.1D Modeling suggests “over-thrusting” model for peak-ring formation. Majority of melt lies within the peak ring.

34. Further Work What is the weakening mechanism? Current state of modeling cannot distinguish between weakening mechanisms. How can one distinguish between these mechanisms in the field? More experimental work needs to be done to understand dynamic rock strength!

35. How can we test the models? Further Work Best test is still morphometry. Need to test peak-ring and structural-uplift models with geological, geophysical and drill core data. Test predictions of damaged region dimensions. Test predictions of melt volume and distribution.

36. How can we test the models? Further Work Need for code benchmarking. Test problem comparison for early-stage calculations. Compare strength models in late-stage codes.