On a geological time scale, science

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1 F RONTIERS OF S IMULATION TWO- AND THREE-DIMENSIONAL ASTEROID IMPACT SIMULATIONS Performing a series of simulations of asteroid impacts using the SAGE code, the authors attempt to estimate the effects of tsunamis and other important environmental events /04/$ IEEE Copublished by the IEEE CS and the AIP On a geological time scale, science must consider the impacts of asteroids and comets with Earth a relatively frequent occurrence, causing significant disturbances to biological communities and strongly perturbing evolution s course. 1 Most famous among known catastrophic impacts, of course, is the one that ended the Cretaceous period and the dominance of the dinosaurs what researchers now believe caused the shallow-water impact event at the Chicxulub site in Mexico s Yucatan Peninsula. (See the Chicxulub Site Impact sidebar for specifics on this event and its importance.) In preparation for a definitive simulation of a large event like Chicxulub, we developed a program for modeling smaller impacts, beginning with impacts in the deep ocean where the physics is somewhat simpler. Smaller impacts happen more frequently than dinosaur-killer events. 2,3 Besides seafloor cratering, these events give rise to GALEN R. GISLER, ROBERT P. WEAVER, AND CHARLES L. MADER Los Alamos National Laboratory MICHAEL L. GITTINGS Science Applications International tsunamis 4 that leave traces many kilometers inland from a coast facing the impact point. In this article, we report on a series of simulations of asteroid impacts we performed using the SAGE code from Los Alamos National Laboratory (LANL) and Science Applications International Corporation (SAIC), developed under the US Department of Energy s program in Accelerated Strategic Computing (ASCI). With our ocean-impact simulations, we estimate impactgenerated tsunami events as a function of the size and energy of the projectile, partly to aid further studies of potential threats from modestsized Earth-crossing asteroids. We also present a preliminary report on a simulation of the impact that created the Chicxulub crater in Mexico s Yucatan Peninsula. This is a rich test because of the stratigraphy s complexity at Chicxulub, involving rocks like calcite and anhydrite that are highly volatile at the pressures reached during impact. (The Chicxulub strata s volatility is what made this event so dangerous to the megafauna of the late Cretaceous.) To model this volatility s effects and to better understand what happened, we must use good equations of state and constitutive models for these materials. We report on progress in developing better constitutive models for the geological materials involved in this impact and in cratering processes in general. 46 COMPUTING IN SCIENCE & ENGINEERING

2 Chicxulub Site Impact Scientists now widely accept that the worldwide sequence of mass extinctions at the Cretaceous Tertiary (K/T) boundary 65 million years ago was directly caused by the collision of an asteroid or comet with Earth.1,2 Evidence for this includes the large (200-km diameter) buried impact structure at Chicxulub in Mexico s Yucatan Peninsula, the worldwide iridium-enriched layer at the K/T boundary, and the tsunamic deposits well inland in North America, all dated to the same epoch as the extinction event. Consensus is building that the K/T impactor was a bolide of diameter roughly 10 km; its impact was oblique (not vertical), either from the southeast at 30 degrees to the horizontal or from the southwest at 60 degrees; its encounter with layers of water, anhydrite, gypsum, and calcium carbonate (all highly volatile materials at the pressures of impact) lofted many hundreds of cubic kilometers of these materials into the stratosphere. These materials then resided there for many years and produced a global climate deterioration that was fatal to many large-animal species on Earth. All these points are still under discussion, however, and researchers still need to address several scientific questions: How is the energy of impact (in the realm of hundreds of teratons TNT equivalent) partitioned among the vaporization of volatiles, the lofting of other materials, the generation of tsunamis, and the cratering of the substrate? How is this partition of energy reflected in the observables detectable after 65 million years? What is the projectile s fate? What is the distribution of proximal and distal ejecta around the impact site? How do these questions depend on the problem s unknown parameters namely, bolide mass, diameter, velocity, and impact angle? References 1. J.V. Morgan et al., Peak-Ring Formation in Large Impact Craters: Geophysical Constraints from Chicxulub, Earth and Planetary Science Letters, vol. 183, 2000, pp E. Pierazzo, D.A. Kring, and H.J. Melosh, Hydrocode Simulation of the Chicxulub Impact Event and the Production of Climatically Active Gases, J. Geophysical Research, vol. 103, 1998, pp SAGE Code The SAGE hydrocode is a multimaterial adaptivegrid Eulerian code with a high-resolution Godunov scheme originally developed by Michael Gittings for SAIC and LANL. It uses continuous adaptive mesh refinement (CAMR), meaning that the decision to refine the grid is made cell by cell and cycle by cycle continuously throughout the problem run. Refinement occurs when gradients in physical properties (density, pressure, temperature, and material constitution) exceed user-defined limits, down to a minimum cell size the user specifies for each material in the problem. With the computing power concentrated on the regions of the problem that require higher resolution, we can simulate very large computational volumes and substantial differences in scale at low cost. We can run SAGE in several modes of geometry and dimensionality: explicitly 1D Cartesian and spherical, 2D Cartesian and cylindrical, and 3D Cartesian. The RAGE code is similar to SAGE but incorporates a separate module for implicit, gray, nonequilibrium radiation diffusion. Both codes are part of LANL s Crestone project, in turn part of the Department of Energy s ASCI program. Because scientists commonly do modern supercomputing on machines or machine clusters containing many identical processors, the code s parallel implementation is supremely important. For portability and scalability, SAGE uses the widely available message-passing interface (MPI). It accomplishes load leveling using an adaptive cell pointer list, in which newly created daughter cells are placed immediately after the mother cells. Cells are redistributed among processors at every time step, while keeping mothers and daughters together. If there are M cells and N processors, this technique gives nearly M/N cells per processor. As neighbor-cell variables are necessary, the MPI s gather and scatter routines copy those neighbor variables into local scratch. In a multimaterial code like SAGE, every cell in the computational volume can contain all the materials defined in the problem, each with its own equation of state (and strength model, as appropriate). A number of equations of state are available, analytical and tabular. In our impact prob- MAY/JUNE

3 Asteroid initial position 30-km altitude t = 0.5 seconds 1.0 seconds 1.5 seconds 2.0 seconds Atmosphere 47 km Ocean water 5 km 3.0 seconds Basalt crust 7 km Mantle 5 km 20 km/sec 37.0 seconds 5.0 seconds 10.0 seconds seconds Figure 1. Montage of 10 separate images from the 3D run of the impact of a 1-km-diameter iron bolide at an angle of 45 degrees with an ocean 5 km deep. These are density raster graphics in a 2D slice in the vertical plane containing the asteroid trajectory. Note the initial uprange downrange asymmetry and its disappearance in time. Maximum transient crater diameter of 25 km is achieved at about 35 seconds. The maximum crown height reaches 30 km, and the jet seen forming in the last frame eventually approaches 60 km. SAGE ast308 Pressure.01 mbar/cm Grid spacing: 10 km 5.00 seconds Figure 2. Perspective plot of an isosurface of the pressure gradient at a time five seconds after the beginning of a 3D run of the impact of a 1- km-diameter iron bolide at an angle of 30 degrees with an ocean 5 km deep. The pressure gradient isosurface is colored by the value of pressure, with a color palette chosen to highlight interfaces between mantle and basalt as well as basalt and water in the target. The isosurface shows both the atmospheric shock accompanying the incoming trajectory of the projectile (right) and the explosively driven downrange shock (left) that carries the horizontal component of the projectile s momentum. Also visible are seismic waves generated in the mantle and crust and the expanding transient crater in the water. Pressure (bar) lems, we use the LANL Sesame tables for air, basalt, calcite, granite, iron, and garnet (as a rather stiff analog to mantle material), and for water, we use a somewhat more sophisticated table (including a good treatment of the vapor dome) from SAIC. When we judged strength to be important, we used a simple elastic-plastic model with pressure hardening (with depth) for the crustal material (basalt for the water impacts, calcite, and granite for the K/T impact that is, the impact at the Cretaceous Tertiary [K/T] boundary). The boundary conditions we use in these calculations allow unhindered outflow of waves and material. We accomplish this by using freeze regions around the computational box s edges, which are updated normally during the hydrodynamic step, then quietly restored to their initial values of pressure, density, internal energy, and material properties before the next step. This technique has proven to be extremely effective at minimizing the deleterious effect of artificial reflections. By far the best technique for dealing with unwanted boundary effects is to put the boundaries far away from the regions of interest or to place the boundary beyond a material interface that truly exists in the problem and might be expected to interact with waves appropriately that is, through reflection, transmission, and absorption. In the ocean-impact simulations, the physical boundary that is most important is of course the seafloor, which partly reflects and partly transmits the waves that strike it. The crust mantle interface provides further impedance to waves that propagate toward the computational box s bottom boundary. For land (or continental shelf) impact simulations, the sediment crust and crust mantle interfaces play similar roles. With these material interfaces, and our freeze-region boundary conditions, reflections from the computational boundaries are insignificant. 3D Water-Impact Simulations We performed 3D simulations of a 1-km-diameter iron asteroid impacting the ocean at 45- and 30-degree angles at 20 km/s on the ASCI White machine at LLNL, using 1,200 processors for several weeks. We used up to 200 million computational cells, and the total computational time was 1,300,000 CPU hours. The computational volume was a rectangular box 200-km long in the direction of the asteroid trajectory, 100-km wide, and 60-km tall. We divided the vertical extent into 42 km of atmosphere, 5 km ocean water, 7 km basalt crust, and 6 km mantle material. Using bilateral symmetry, we simulated a half-space only, the boundary of the halfspace being the vertical plane containing the impact trajectory. 48 COMPUTING IN SCIENCE & ENGINEERING

4 SAGE ast304 The asteroid starts at a point 30 km above the water s surface (see Figure 1). The atmosphere we used in this simulation is a standard exponential atmosphere with a scale height of 10 km, so the medium surrounding the bolide is tenuous (with a density of approximately 1.5 percent of sea-level density) when the calculation begins. During the 2.1 seconds of the bolide s atmospheric passage at approximately Mach 60, a strong shock develops (see Figure 2), heating the air to temperatures upwards of 1 ev ( K). Less than 1 percent of the bolide s kinetic energy (roughly 200 gigatons high-explosive equivalent yield) is dissipated in the atmospheric passage. The water is much more effective at slowing the asteroid; essentially, all its kinetic energy is absorbed by the ocean and seafloor within 0.7 seconds. The water immediately surrounding the trajectory vaporizes, and the rapid expansion of the resulting vapor cloud excavates a cavity in the water that eventually expands to a diameter of 25 km. This initial cavity is asymmetric because of the asteroid s inclined trajectory, and the splash, or crown, is markedly higher on the downrange side (see Figures 1 and 3). The crown s maximum height is nearly 30 km at 70 seconds after impact. The collapse of the crown s bulk makes a rim wave or precursor tsunami that propagates outward, somewhat higher on the downrange side (see Figures 1 and 4). The crown s higher portion breaks up into fragments that fall back into the water, giving this precursor tsunami an uneven and asymmetric profile. The rapid conversion of the asteroid s kinetic energy into thermal energy produces a rapid expansion in the volume occupied by the newly vaporized water and bolide material. This is much like an explosion and acts to symmetrize the subsequent development. Shocks propagate outward from the cavity in the water, in the basalt crust and the mantle beneath (Figure 2). Subsequent shocks are generated as the cavity refills and by cavitation events that occur in the turbulence that accompanies the development of the large-amplitude waves. The shocks are partly reflected and partly transmitted by the material interfaces, and the interactions of these shocks with each other and with the waves make the dynamics complicated. The hot vapor from the initial cavity expands into the atmosphere, mainly in the downrange direction because of the horizontal component of the asteroid s momentum (Figure 2). When the vapor s pressure in the cavity has diminished sufficiently at about 35 seconds after the impact water begins to fill the cavity from the bottom, driven by gravity. This filling has a high degree of symmetry because of the uniform gravity responsible for the water pressure. An asymmetric fill could result from nonuniform seafloor topography, but we do not consider that here. The filling water converges on the cavity s center, and the implosion produces another series of shock waves and a jet that rises vertically in the atmosphere to a height in excess of 20 km at 150 seconds after impact. The collapse of this central vertical jet produces the principal tsunami Time: seconds p (gm/cm 3 ) p 0.50 (gm/cm 3 ) p 1.50 (gm/cm 3 ) LANL Figure 3. Perspective plot of three isosurfaces of the density from the 3D run of a 45-degree impact of a 1-km-diameter iron bolide into an ocean 5 km deep, 30 seconds after the beginning of the calculation (27.5 seconds after impact). We chose the isosurfaces to show the basalt underlayment, the ocean water s bulk, and the cells containing water spray (mixed air and water). The crown splash s asymmetry is evident, as is its instability to fragmentation. Cratering in the basalt is seen, to a depth of approximately 1 km. The transient cavity s diameter is at this time approximately 25 km. SAGE ast304 Time: seconds p (gm/cm 3 ) p 0.50 (gm/cm 3 ) p 1.50 (gm/cm 3 ) LANL Figure 4. Perspective plot of three isosurfaces of the density from the 3D run of a 45-degree impact of a 1-km-diameter iron bolide into an ocean 5 km deep, 115 seconds after impact. The transient cavity has collapsed under the surrounding water s pressure to form a central jet, and the crown splash has collapsed almost completely, pock-marking the water s surface and generating the first precursor wave. MAY/JUNE

5 SAGE ast304 Time: seconds p (gm/cm 3 ) p 0.50 (gm/cm 3 ) p 1.50 (gm/cm 3 ) LANL wave (see Figure 5). This wave has an initial height of 1.5 km and a propagation velocity of 170 meters/second (m/s). We follow this wave s evolution in three dimensions for 400 seconds after impact and find that the inclined impact eventually produces a tsunami that is nearly circularly symmetric at late times (see Figure 6). The tsunami declines to a height (defined as a positive vertical excursion above the initial water surface) of 100 meters at a distance of 40 km from the initial impact, and its propagation speed continues at roughly 170 m/s. Figure 5. Similar to Figure 4, but 150 seconds after impact. The central jet has now collapsed, and both the pock-marked precursor wave and the somewhat smoother principal wave are evident. The latter wave is ~1.5 km in initial amplitude, and moves with a speed of ~175 m/s. 6e e e e e e (a) 6e e e e e e e e e e e + 06 (b) 0 6e e e e e + 06 Height (cm) (p 0.9 gm/cm 3 ) Height 0.1 cm) LANL Figure 6. Overhead plots at a late time showing wave height as a function of distance along the trajectory (horizontal) and perpendicular to the trajectory (units of centimeters). The asteroid entered from the right. At 270 seconds, (a) the irregular precursor wave has declined to a few meters in height and strongly bears the asymmetry of the crown splash, while the much more regular principal wave, at an amplitude significantly greater than 100 meters, is much more symmetrical. The wavelength, measured as the crest-to-crest distance from precursor to principal wave, is 34 km. At 385 seconds, (b) the precursor wave has left the box, and the principal wave has a mild quadrupole asymmetry with the maximum wave height roughly 100 meters, at a distance of 40 km from the impact point. 2D Water-Impact Simulations Because of the high degree of symmetry achieved late in the 3D calculations, we can learn much about the physics of impact events by performing 2D simulations. These are, of course, much cheaper than full 3D calculations, so we can undertake parameter studies to isolate the phenomena s dependence on the impactor s properties. We have therefore performed a series of supporting calculations in two dimensions (cylindrical symmetry) for asteroids impacting the ocean vertically at 20 km/s, using the ASCI Blue Mountain machines at LANL. We took the asteroid s composition to be either dunite (3.32 grams per cubic centimeter [g/cc]) as a mockup for typical stony asteroids, or iron (7.81 g/cc) as a mockup for nickel-iron asteroids. For these projectiles, instead of the Sesame tables, we used the simpler analytical Mie-Grüneisen equation of state to avoid time-step difficulties during the atmospheric passage. The strength model used for the crust and asteroid are the same in all cases namely, an elastic-plastic model with shear moduli and yield stress similar to experimental values for aluminum. For the known increase of strength with depth, we use a linear pressurehardening relationship. We designed these simulations to follow an asteroid s passage through the atmosphere, its impact with the ocean, the cavity generation and subsequent recollapse, and the generation of tsunamis. The parameter study included six different asteroid masses. We used stony and iron bodies of diameters 250 meters, 500 meters, and 1,000 meters, all at speeds of 20 km/s. The impacts kinetic energies ranged from 1 gigaton to 200 gigatons (highexplosive equivalent yield). Table 1 gives a tabular summary of our parameter study and lists the bolide s input characteristics (composition, diameter, density, mass, velocity, and kinetic energy) and the impact s measured characteristics (maximum depth and di- 50 COMPUTING IN SCIENCE & ENGINEERING

6 Table 1. Summary of parameter-study runs. Asteroid material Dunite Iron Dunite Iron Dunite Iron Asteroid diameter 250 m 250 m 500 m 500 m 1,000 m 1,000 m Asteroid density 3.32 g/cc 7.81 g/cc 3.32 g/cc 7.81 g/cc 3.32 g/cc 7.81 g/cc Asteroid mass 2.72e13 g 6.39e13 g 2.17e14 g 5.11e14 g 1.74e15 g 4.09e15 g Asteroid velocity 20 km/s 20 km/s 20 km/s 20 km/s 20 km/s 20 km/s Kinetic energy 1.3 GT 3 GT 10 GT 24 GT 83 GT 195 GT Maximum cavity diameter 4.4 km 5.2 km 10.0 km 12.6 km 18.6 km 25.2 km Maximum cavity depth 2.9 km 4.3 km 4.5 km 5.7 km 6.6 km 9.7 km Observed displacement 4.41e16 g 9.13e16 g 3.53e17 g 7.11e17 g 1.79e18 g 4.84e18 g Time of maximum cavity 13.5 s 16.0 s 22.5 s 28.0 s 28.5 s 33.0 s Time of maximum jet 54.5 s 65.0 s 96.5 s 111 s s 142 s Time of rebound s s s 162 s s s Tsunami wavelength 9 km 12 km 17 km 20 km 23 km 27 km Tsunami velocity 120 m/s 140 m/s 150 m/s 160 m/s 170 m/s 175 m/s ameter of the transient cavity, quantity of water displaced, time of maximum cavity, maximum jet and jet rebound, tsunami wavelength, and tsunami velocity). The amount of water displaced during cavity formation is found to scale nearly linearly with the asteroid s kinetic energy, as Figure 7 illustrates. A fraction of this displaced mass (ranging from 5 percent for the smaller impacts to 7 percent for the largest ones) is vaporized during the encounter s explosive phase, while the rest is pushed aside by the vapor s pressure to form the transient cavity s crown and rim. Figure 7 indicates that the linear scaling with kinetic energy differs from the scaling predicted by Keith Holsapple. 5 Holsapple, using dimensional analysis informed by experimental results over many decades in scaled parameters, found that the ratio of the displaced mass to the projectile mass scales as the Froude number, u 2 /ga, to the two-thirds power, where u is the projectile velocity, g is acceleration due to gravity, and a is the projectile radius. The difference between the Holsapple scaling and our results is most likely due to the effect of vaporization, which the dimensional analysis does not include. We also note that our two projectile compositions differ from each other by a factor greater than two in density, and this is also omitted in the dimensional analysis. We have begun a new series of 27 runs to investigate the scaling issue further. These runs are similar to the six runs we report here, yet we also include bolides of ice and velocities of 10 and 15 km/s. We used Lagrangian tracer particles to measure the amplitude, velocity, and wavelength of the waves produced by these impacts. These measures are somewhat uncertain because the wave trains are highly complex and the motions are turbulent. There are multiple shock reflections and refractions at the water crust and water air interfaces, as well as cavitation events. For the larger impacts, the tracer particles execute highly complex motions, while for the smaller impacts, the motions are superpositions of approximately closed elliptical orbits. In all cases, we measure wave amplitudes by taking half the difference of adjacent maxima and minima in the vertical excursions executed by the tracer particles, and we measure wave speeds by plotting the radial positions of these maxima and minima as a function of time. With these warnings, we find the tsunami amplitude to evolve in a complex manner, eventually decaying faster than 1 r, where r is the distance of propagation from the impact point (see Figure Mass of water displaced (grams) 1.0E E E E E E E E + 28 Asteroid kinetic energy (ergs) Figure 7. The mass of water displaced in the initial cavity formation scales with the asteroid s kinetic energy. The squares are the results from the parameter-study simulations, as Table 1 tabulates, and the solid line illustrates direct proportionality. About 5 to 7 percent of this mass is vaporized in the initial encounter. The circles are predictions of the crater scaling formula from Keith Holsapple. 5 MAY/JUNE

7 Amplitude (m) 10,000 1, Dn 250 tr Dn 250 lsq Fe 250 tr Dn 250 lsq Dn 250 tr Dn 500 lsq Fe 500 tr Fe 500 lsq Dn 1k tr Dn 1k lsq Fe 1k tr Fe 1k lsq 1/r ,000 Distance from impact (km) Figure 8. The tsunami amplitude declines with propagation distance faster than 1/r. The legend identifies the points associated with individual runs, where the notation signifies the asteroid s composition (Dn for dunite and Fe for iron) and diameter in meters. We also show lines indicating least-squares power-law fits, with the power-law indices varying from 2.25 to 1.3. Wave crest position (km) Dn 250 m Fe 250m Dn 500m Dn 250 tr Dn 1kn Fe 1kn 150 m/s 221 m/s (Shallow-water theory) Time (sec) Figure 9. We plot the tsunami wave-crest positions as a function of time here for the six runs of the parameter study. The notation in the legend is similar to Figure 6, with the solid lines at constant velocity to illustrate that these waves are substantially slower than the shallow-water theory s prediction. There is an indication, however, that the waves may be accelerating toward the shallow-water limit at late times. 8). We found the steepest declines for the smaller projectiles (as expected from linear theory 4 ), and we have greater confidence in the amplitudes measured for these than in the amplitudes measured for the larger projectiles because of the more complex motions executed by the tracer particles in the large-projectile simulations. Geometrical effects account for a pure 1/r decline, and the remainder of the decline is due partly to wave dispersion and partly to dissipation via turbulence. Realistic seafloor topography will also influence the wave s development, of course. We also remark that our first measured amplitude points are well outside the transient cavity. Tracers from within the cavity execute much larger excursions (indeed, some of them join the jet), and we cannot measure reliable amplitudes from them. We expect that the tsunami waves will eventually evolve into classic shallow-water waves 6 because the wavelengths are long compared to the ocean depth. However, the initial wave train s complexity and the wave-breaking associated with the interaction of shocks reflected from the seafloor do not permit the simplifications associated with shallow-water theory. Much previous work on impact-generated tsunamis 7 has used shallow-water theory, which gives a particularly simple form for the wave velocity namely, v = ( gd), where g is the acceleration due to gravity and D is the water depth. For an ocean 5 km deep, the shallow-water velocity is 221 m/s. In Figure 9, we show the wave-crest positions as a function of time for the simulations in our parameter study, along with constant-velocity lines at 150 and 221 m/s. From this, we see that the wave velocities are substantially lower than the shallowwater limit, although there is some indication of an approach to that limit at late times. This asymptotic approach is only observed for the largest impactors because the waves from the smaller impactors die off too quickly for reliable measurement of the far-field limit in our simulations. To illustrate the complications we encountered in our large-projectile runs, we show in Figure 10 a close-up snapshot of density and pressure from the wave train produced by a 1-km iron projectile. This snapshot is taken 300 seconds after impact and about 35 km from the impact point. The wave moves to the right, and the impact point is to the left. The vertical excursion of the bulk water above the original surface is about 1 km at this point. The dense spray above the wave (up to 1 percent water density) extends 3.5 km up into the atmosphere, while the lighter spray goes up more than twice as far. Apparently, the surrender of wave energy to the atmosphere is a significant loss mechanism. The bottom frame shows pressure with a banded palette to highlight differences. Besides the turbulent pressure field in the atmosphere, two significant features are a decaying cavitation event just aft of the main peak/trough system, and a shock propagating backwards from that event and scraping the wa- 52 COMPUTING IN SCIENCE & ENGINEERING

8 ter crust interface. A new series of runs we are planning incorporates new diagnostics to better interpret the energy flows. Preliminary Study of a Major Terrestrial Impact When the projectile diameter is large compared to the depth of water in the target, the deceleration is accomplished almost entirely by the rock beneath. We therefore need to deal directly with the issues of the instantaneous fluidization of target rock and its subsequent evolution through regimes of visco-plastic flow through freeze-out. Because this is a rather new regime for our code, we decided to begin by examining a well-studied event. 8 In extending our impact study to larger diameters, we accordingly chose to focus on the shallow-water impact event at the Chicxulub site in Mexico s Yucatan Peninsula and anticipate that our early effort on this will not do very well with the final, strength-dependent, phases of the crater evolution. Scientists discovered the Chicxulub impact structure with Petroleos Mexicanos (Pemex), the Mexican national oil company. 9,10 This discovery established the suggestion that an impact was responsible for the mass extinction at the end of the Cretaceous period, as Luis and Walter Alvarez and their colleagues proposed, 11 on the basis of the anomaly in abundances of iridium and other platinum-group elements in the boundary bedding plane. Paleogeographic data suggests that the crater site, which presently straddles the Yucatan coastline, was submerged at the end of the Cretaceous on the continental shelf. The substrate consisted of fossilized coral reefs over continental crust. In our simulation, we therefore constructed a multilayered target consisting of 300 meters of water, 3 km of calcite, 30 km of granite, and 18 km of mantle material. It is likely that the Chicxulub target contained multiple layers of anhydrites and other evaporites as well as calcite, but for simplicity (and because of access to good equations of state), we simplified the structure to calcite above granite. Above this target, we included a standard atmosphere up to 106 km altitude and started the asteroid s plunge at 45 km altitude. We performed 3D simulations with impact angles of 30, 40, and 60 degrees to the horizontal as well as a 2D vertical-impact simulation. In the horizontal plane, our computational domain extended 256 km by 128 km because we elected to simulate a half-space. We ran these simulations on the new ASCI Q Figure 10. A snapshot in density (top) and pressure (bottom) for a small part of the simulation of the 1-km-diameter iron projectile vertical impact. This snapshot is taken 300 seconds after impact and illustrates the principal wave train 35 km out from the impact point, which is to the left. This frame s horizontal dimension is 28 km, and the vertical dimension is 15 km. The wave is traveling to the right. In the top frame, the height of the principal wave above the original water surface is 1.2 km, the maximum extent of the dense spray (about 1 percent water density) is 3.5 km above the original water surface, and the light spray extends almost to the tropopause at 10 km altitude. The bottom frame uses a banded palette to highlight pressure differences. A cavitation event is seen just aft of the principal wave, and a decaying shock produced by this event is seen propagating backward (toward the impact point to the left) and scraping the ocean bottom. computer at Los Alamos, a cluster of ES45-alpha boxes from HP/Compaq. Generally, we ran on 1,024 processors at a time and used about 1 million CPU hours over the course of these runs. Our adaptive mesh included up to a third of a billion computational cells. The simulation illustrates three prominent features for a 45-degree impact. First, the impact produced a rooster tail that carries much of the horizontal component of the asteroid s momentum in MAY/JUNE

9 Figure 11. Seven seconds after a 10-km-diameter granite asteroid strikes Earth, billions of tons of hot material are lofted into the atmosphere. This material consists of asteroid fragments, mixed with vaporized water, calcite, and granite from Earth. Much of this debris is directed downrange (to the right and back of this image) carrying the horizontal momentum of the asteroid in this 45-degree impact. This image is a perspective rendering of a density isosurface colored by material temperature (0.5 ev = 5,800 K). We chose the isosurface, at density g/cm 3, to show everything denser than air. This picture s scale is set by the back boundary, which is 256-km long. The maximum height of the rooster tail at this time is 50 km Temperature (ev) will ignite vegetation many hundreds of kilometers away from the impact site. Second is the highly turbulent and energetic plume of ejecta directed predominantly upward (see Figure 12). Ballistic trajectories carry some of this material back to Earth in the conical debris curtain that gradually moves away from the crater lip and deposits a blanket of ejecta around the forming crater (see Figure 13). Some material is projected into orbits that have ground termini far outside the computational volume, even extending to the antipodal point and beyond. We found the blanket of ejecta to be strongly asymmetrical around the crater, with the uprange portion much thinner than the rest. This owes partly to the coupling of the horizontal component of the asteroid s momentum to the debris, and partly to the ionized and shocked atmosphere in the asteroid s wake producing a zone of avoidance for the entrained debris. The ejecta blanket s lobate structure seen in Figure 13 is a second-order effect, due to the break-up of the unstable flow in the debris curtain. The hot structure seen within the crater in Figure 13 is the incipient formation of a central peak. We are conducting further analysis of the simulation results from these runs, with the aim of determining material and energy partitions among the resultant features as functions of the impact s parameters. Figure 12. Forty-two seconds after impact, the rooster tail has left the simulation volume and gone far downrange. The dissipation of the asteroid s kinetic energy, some 300 teratons TNT equivalent, produces a stupendous explosion that melts, vaporizes, and ejects a substantial volume of calcite, granite, and water. The dominant feature in this picture is the curtain of the debris that has been ejected and is now falling back to Earth. The ejecta follows ballistic trajectories, with its leading edge forming a conical surface that moves outward from the crater as the debris falls to form the ejecta blanket. The turbulent material interior to the debris curtain is still being accelerated upward by the explosion produced during the crater s excavation. the downrange direction (see Figure 11). This material, consisting of vaporized fragments of the projectile mixed with the target, is extremely hot, and We are continuing the study we outline here, with an aim toward including better physics for the later stages of the crater s development. For this, it is important we include a proper characterization of the material strength of the geological strata in which the impact occurs and the dependence of those strength properties with depth, temperature, strain, and strain rate. The data for these studies is still not readily available for many of the geological materials of interest, and some controversy exists over the best way to implement strength breakdown in hydrocodes. Our intention is to use a few choices for strength degradation (for example, acoustic fluidization and damage mechanics) in our code and include visco-elastic models as well as the elastic-plastic models we have already used. Applying our code to other geologic scenarios that involve rock mobilization (for example, volcanic eruptions and landslides) will guide us in appropriately implementing and validating these models. 54 COMPUTING IN SCIENCE & ENGINEERING

10 Acknowledgments We thank Bob Greene for assistance with the visualization of the 3D runs and Lori Pritchett for help with executing the simulations. We had helpful conversations with Eileen Ryan, Jay Melosh, Betty Pierazzo, Frank Kyte, Erik Asphaug, Steve Ward, and Tom Ahrens on the impact problem in general. We also thank the anonymous reviewers for comments that helped improve this article. References 1. E. Pierazzo and H.J. Melosh, Understanding Oblique Impacts from Experiments, Observations, and Modeling, Ann. Rev. Earth and Planetary Sciences, vol. 28, 2000, pp F.T. Kyte, Iridium Concentrations and Abundances of Meteoritic Ejecta from the Eltanin Impact in Sediment Cores from Polarstern Expedition ANT XII/4, Deep Sea Research II, vol. 49, 2002, pp S.A. Stewart and P.J. Allen, A 20-km-Diameter Multi-Ringed Impact Structure in the North Sea, Nature, vol. 418, 2002, pp S.N. Ward and E. Asphaug, Impact Tsunami Eltanin, Deep Sea Research II, vol. 49, 2002, pp K.A. Holsapple, The Scaling of Impact Processes in Planetary Sciences, Ann. Rev. Earth and Planetary Sciences, vol. 21, 1993, pp C.L. Mader, Numerical Modeling of Water Waves, Univ. of Calif. Press, D.A. Crawford and C.L. Mader, Modeling Asteroid Impact and Tsunami, Science of Tsunami Hazards, vol. 16, 1998, pp E. Pierazzo, D.A. Kring, and H.J. Melosh, Hydrocode Simulation of the Chicxulub Impact Event and the Production of Climatically Active Gases, J. Geophysical Research, vol. 103, 1998, pp A.R. Hildebrand et al., Chicxulub Crater: A Possible Cretaceous/Tertiary Boundary Impact Crater on the Yucatan Peninsula, Mexico, Geology, vol. 19, 1991, pp V.L. Sharpton et al., New Links Between the Chicxulub Impact Structure and the Cretaceous/Tertiary Boundary, Nature, vol. 359, 1992, pp L. Alvarez et al., Extraterrestrial Cause for the Cretaceous/Tertiary Extinction, Science, vol. 208, 1980, pp Galen R. Gisler is an astrophysicist at the Los Alamos National Laboratory. He has many years of experience in modeling and understanding complex phenomena in Earth, space, and astrophysical contexts. His research interests include energetic phenomena in geosciences and using the SAGE and RAGE codes of the Los Alamos Crestone Project. He has a BS in physics and astronomy from Yale University and a PhD in astrophysics from Cambridge University. Contact him at grg@lanl.gov. Robert P. Weaver is an astrophysicist at Los Alamos and leader of the Crestone Project, part of the Department of Energy s Advanced Simulation and Computing Initiative. This project develops and uses sophisticated 1D, 2D, and 3D radiation-hydrodynamics codes for challenging problems of interest to the DOE. He has a BS in astrophysics and mathematics from Colgate Figure 13. Two minutes after impact, the debris curtain has separated from the rim of the still-forming crater as material in the curtain falls to Earth. The debris from the curtain is deposited in a blanket of ejecta that is asymmetric around the crater with more in the downrange than in the uprange direction. The distribution of material in the ejecta blanket can be used as a diagnostic to determine the direction and angle of the asteroid s impact. University, an MS in physics from the University of Colorado, and a PhD in astrophysics from the University of Colorado. Michael L. Gittings is an assistant vice president and chief scientist at Science Applications International. He works full time on a multiyear contract with the Los Alamos National Laboratory to support and improve the SAGE and RAGE codes that he began developing in He has a BS in mechanical engineering and mathematics from New Mexico State University. Charles L. Mader is a fellow emeritus of the Los Alamos National Laboratory, president of Mader Consulting, fellow of the American Institute of Chemists, and editor of the Science of Tsunami Hazards journal. He also has authored Numerical Modeling of Water Waves, Second Edition (CRC Press, 2004) and Numerical Modeling of Explosives and Propellants (CRC Press, 1998). He has a BS and MS in chemistry from Oklahoma State University and a PhD in chemistry from Pacific Western University. Renew your IEEE Computer Society membership today! MAY/JUNE