J. D. O'Keefe

Shock melting and vaporization of lunar rocks and minerals.

The entropy associated with the thermodynamic states produced by hypervelocity meteoroid impacts at various velocities are calculated for a series of lunar rocks and minerals and compared with the entropy values required for melting and vaporization.Taking into account shock-induced phase changes in the silicates, we calculate that iron meteorites impacting at speeds varying from 4 to 6 km/s will produce shock melting in quartz, plagioclase, olivine, and pyroxene. Although calculated with less certainty, impact speeds required for incipient vaporization vary from ~ 7 to 11 km/s for the range of minerals going from quartz to periclase for aluminum (silicate-like) projectiles. The impact velocities which are required to induce melting in a soil, are calculated to be in the range of 3 to 4 km/s, provided thermal equilibrium is achieved in the shock state.

Planetary cratering mechanics

The objective of this study was to obtain a quantitative understanding of the cratering process over a broad range of conditions. Our approach was to numerically compute the evolution of impact induced flow fields and calculate the time histories of the key measures of crater geometry (e.g. depth, diameter, lip height) for variations in planetary gravity (0 to 10^9 cm/s^2), material strength (0 to 2400 kbar), and impactor radius (0.05 to 5000 km). These results were used to establish the values of the open parameters in the scaling laws of Holsapple and Schmidt (1987). We describe the impact process in terms of four regimes: (1) penetration, (2) inertial, (3) terminal and (4) relaxation. During the penetration regime, the depth of impactor penetration grows linearly for dimensionless times τ = (Ut/a) 5.1, the crater grows at a slower rate until it is arrested by either strength or gravitational forces. In this regime, the increase of crater depth, d, and diameter, D, normalized by projectile radius is given by d/a = 1.3 (Ut/a)^(0.36) and D/a = 2.0(Ut/a)^(0.36). For strength-dominated craters, growth stops at the end of the inertial regime, which occurs at τ = 0.33 (Y_(eff)/ρU^2)^(−0.78), where Y_(eff) is the effective planetary crustal strength. The effective strength can be reduced from the ambient strength by fracturing and shear band melting (e.g. formation of pseudo-tachylites). In gravity-dominated craters, growth stops when the gravitational forces dominate over the inertial forces, which occurs at τ = 0.92 (ga/U^2)^(−0.61). In the strength and gravity regimes, the maximum depth of penetration is d_p/a = 0.84 (Y/ρ U^2)^(−0.28) and d_p/a = 1.2 (ga/U^2)^(−0.22), respectively. The transition from simple bowl-shaped craters to complex-shaped craters occurs when gravity starts to dominate over strength in the cratering process. The diameter for this transition to occur is given by D_t = 9.0 Y/ρg, and thus scales as g^(−1) for planetary surfaces when strength is not strain-rate dependent. This scaling result agrees with crater-shape data for the terrestrial planets [Chapman and McKinnon, 1986]. We have related some of the calculable, but nonobservable parameters which are of interest (e.g. maximum depth of penetration, depth of excavation, and maximum crater lip height) to the crater diameter. For example, the maximum depth of penetration relative to the maximum crater diameter is 0.6, for strength dominated craters, and 0.28 for gravity dominated craters. These values imply that impactors associated with the large basin impacts penetrated relatively deeply into the planets surface. This significantly contrasts to earlier hypotheses in which it had been erroneously inferred from structural data that the relative transient crater depth of penetration decreased with increasing diameter. Similarly, the ratio of the maximum depth of excavation relative to the final crater diameter is a constant ≃0.05, for gravity dominated craters, and ≃ 0.09 for strength dominated craters. This result implies that for impact velocities less than 25 km/s, where significant vaporization begins to take place, the excavated material comes from a maximum depth which is less than 0.1 times the crater diameter. In the gravity dominated regime, we find that the apparent final crater diameter is approximately twice the transient crater diameter and that the inner ring diameter is less than the transient crater diameter.

Complex craters: Relationship of stratigraphy and rings to impact conditions

One of the key issues associated with the understanding of large scale impacts is how the observable complex crater structural features (e.g., central peaks and pits, flat floors, ring shaped ridges and depressions, stratigraphic modifications, and faults) relate to the impactors parameters (e.g., radius, velocity, and density) and the nonobservable transient crater measures (e.g., depth of penetration and diameter at maximum penetration). We have numerically modeled large-scale impacts on planets for a range of impactor parameters, gravity and planetary material strengths. From these we found that the collapse of the transient cavity results in the development of a tall, transient central peak that oscillates and drives surface waves that are arrested by the balance between gravitational forces and planetary strength to produce a wide range of the observed surface features. In addition, we found that the underlying stratigraphy is inverted outside of the transient cavity diameter (overturned flap region), but not inside. This change in stratigraphy is observable by remote sensing, drilling, seismic imaging and gravity mapping techniques. We used the above results to develop scaling laws and to make estimates of the impact parameters for the Chicxulub impact and also compared the calculated stratigraphic profile with the internal structure model developed by Hildebrand et. al. [1998], using gravity, seismic and other field data. For a stratigraphy rotation diameter of 90 km, the maximum depth of penetration is ∼43 km. The impactor diameter was also calculated. From the scaling relationships we get for a 2.7 g/cm^3 asteroid impacting at 20 km/s, or a 1.0 g/cm^3 comet impacting at 40 km/s, an impactor diameter of ∼13 km, and for a comet impacting at 60 km/s, an impactor diameter of ∼10 km.

Impact on the earth, ocean and atmosphere

Several hundred impact craters produced historically and at times as early as 1.9 × 109 years ago with diameters in the range 10−2 to 102 km are observed on the surface of the earth. Earth-based and spacecraft observations of the surfaces of all the terrestrial planets and their satellites, as well as many of the icy satellites of the outer planets, indicated that impact cratering was a dominant process on planetary surfaces during the early history of the solar system. Moreover, the recent observation of a circumstellar disk around the nearby star, β-Pictoris, appears to be similar to our own hypothesized protosolar disk. A disk of material around our sun has been hypothesized to have been the source of the solid planetesimals from which the earth and the other planets accreted by infall and capture. Thus it appears that the earth and the other terrestrial planets formed as a result of infall and impact of planetesimals. Although the present planets grew rapidly via accretion to their present size (in∼ 107 years), meteorite impacts continue to occur on the earth and other planets. Until recently meteorite impact has been considered to be a process that was important on the earth and the other planets only early in the history of the solar system. This is no longer true. The Alvarez hypothesis suggests that the extinction of some 90% of all species, including 17 classes of dinosaurs, is associated with the 1 to 150 cm thick layer of noble-element rich dust which is found all over the earth exactly at the Cretaceous-Tertiary boundary. The enrichment of noble elements in this dust is in meteorite-like proportions. This dust is thought to represent the fine impact ejecta from a ∼ 10km diameter asteroid interacting with the solid earth. The Alvarez hypothesis associates the extinction with the physics of a giant impact on the earth. Using finite-difference techniques, cratering flow calculations are used to obtain the spatial attenuation of shock pressure with radius, r, along the impact axis for the impact of silicate rock and iron impactors on a silicate half-space at speeds of 5 to 45 km/sec. Stress wave attenuation is found to be represented by two regimes, if the peak pressure, P, is fitted to expressions of the form P oc r2. At distances from 2.2 to 5.6 projectile radii into a silicate target, the constant, a, is on the order of −0.2. This low-attenuation rate impedance matching regime extends further into the target at the slower impact velocities. This occurs because of the slightly divergent flow associated with the penetration of a spherical projectile. For the near-field impact regime, an impact at 5 km/sec of an iron object with silicate surface will induce complete melting for silicate; the iron will remain solid. At 15 km/sec, partial vaporization occurs for both silicate and iron whereas at 45 km/sec, complete vaporization occurs in both materials. Similar calculations were conducted for a silicate meteoroid striking a silicate surface at velocities ranging from 5 to 45 km/sec. At greater radii in the far-field regime, the exponent, a, varies systematically from −1.45 to −2.15 for impacts of silicate onsilicate as the impact velocity is increased from 5 to 45 km/sec. For an iron projectile impacting at speeds of 5 to 45 km/sec, the exponent, a, varies from −1.67 to −2.95. Upon impact of a 10 to 30 km diameter silicate or water object onto a 5 km deep ocean overlying a silicate half-space planet at 30 km/sec, we find that from 12 to 15% of the incident energy is coupled into the water. In the gravity field of the earth, some 10 to 30 times the impactor mass of water is launched on trajectories which can achieve stratospheric heights. The amount of ejecta launched to stratospheric altitudes is similar to the 101 to 102 projectile masses which result from impact of objects on an ocean-free silicate half-space (land). In the case of impact directly onto a silicate-half-space, only ejecta launched on trajectories which would carry it to stratospheric heights, has an impactor to target mass ratio which matches the fraction (10−2 to 10−1) of extraterrestral material found in the platinum-metal-rich Cretaceous-Tertiary boundary layer. Oceanic impact results in impulsive-like giant tsunamis initially having amplitudes of ∼ 4km, representing the solitary waterwave stability limit in the deep ocean, and containing 10−2 to 10−1 of the energy of the impact. Calculation of the interaction of a ∼ 10km bolide with the atmosphere indicates that only some 8% of the energy is imparted to the air during initial passage through the atmosphere. However, upon impact with the earth ∼ 101to102 times the bolide mass of water or rock is ejected into the stratosphere, although, only ∼0.1 bolide masses are in <1μm particles. The vaporized, melted, and (<1mm) solid ejecta transfer up to ∼40% of their energy to the atmosphere. Using the results of a similarity solution for the flow of gas as a result of an explosion in exponential atmosphere it is found that the atmosphere above such a large energy source is entirely ejected at speeds exceeding the escape velocity of the earth. Using the similarity solution we have calculated the mass of atmosphere lost due to impacts of 1 to 5 km radius projectiles. No atmosphere is lost for surface sources with energies less than 1027 ergs. Impact of objects in the energy range 1027 to 1030 ergs causes gas losses of 1011 to 1014 kg or 10−8 to 10−5 of the total present atmospheric mass. Impact energies of greater than 1030 ergs cause little increase in atmospheric loss.

Oblique Impact: A Process for Obtaining Meteorite Samples from Other Planets

Cratering flow calculations for a series of oblique to normal (10� to 90�) impacts of silicate projectiles onto a silicate halfspace were carried out to determine whether or not the gas produced upon shock-vaporizing both projectile and target material would form a downstream jet that could entrain and propel SNC meteorites from the Martian surface. The difficult constraints that the impact origin hypothesis for SNC meteorites has to satisfy are that these meteorites are lightly to moderately shocked and yet have been accelerated to speeds in excess of the Martian escape velocity (more than 5 kilometers per second). Two-dimensional finite difference calculations were performed that show that at highly probable impact velocities (7.5 kilometers per second), vapor plume jets are produced at oblique impact angles of 25� to 60� and have speeds as great as 20 kilometers per second. These plumes flow nearly parallel to the planetary surface. It is shown that upon impact of projectiles having radii of 0.1 to 1 kilometer, the resulting vapor jets have densities of 0.1 to 1 gram per cubic centimeter. These jets can entrain Martian surface rocks and accelerate them to velocities greater than 5 kilometers per second. This mechanism may launch SNC meteorites to earth.

Impact and explosion crater ejecta, fragment size, and velocity

Abstract A model was developed for the mass distribution of fragments that are ejected at a given velocity for impact and explosion craters. The model is semiempirical in nature and is derived from (1) numerical calculations of cratering and the resultant mass versus ejection velocity, (2) observed ejecta blanket particle size distributions, (3) an empirical relationships between maximum ejecta fragment size and crater diameter, (4) measurements of maximum ejecta size versus ejecta velocity, and (5) an assumption on the functional form for the distribution of fragments ejected at a given velocity. This model implies that for planetary impacts into competent rock, the distribution of fragments ejected at a given velocity is broad; e.g., 68% of the mass of the ejecta at a given velocity contains fragments having a mass less than 0.1 times a mass of the largest fragment moving at that velocity. Using this model, we have calculated the largest fragment that can be ejected from asteroids, the Moon, Mars, and Earth as a function of crater diameter. The model is unfortunately dependent on the size-dependent ejection velocity limit for which only limited data are presently available from photography of high explosive-induced rock ejecta. Upon formation of a 50-km-diameter crater on an atmosphereless planet having the planetary gravity and radius of the Moon, Mars, and Earth, fragments having a maximum mean diameter of ≈30, 22, and 17 m could be launched to escape velocity in the ejecta cloud. In addition, we have calculated the internal energy of ejecta versus ejecta velocity. The internal energy of fragments having velocities exceeding the escape velocity of the moon (∼2.4 km/sec) will exceed the energy required for incipient melting for solid silicates and thus, the fragments ejected from Mars and the Earth would be melted.

Impact of comet Shoemaker‐Levy 9 on Jupiter

Three-dimensional numerical simulations of the impact of Comet Shoemaker-Levy 9 on Jupiter and the resulting vapor plume expansion were conducted using the Smoothed Particle Hydrodynamics (SPH) method. An icy body with a diameter of 2 km can penetrate to an altitude of -350 km (0 km = 1 bar) and most of the incident kinetic energy is transferred to the atmosphere between -100 km to -250 km. This energy is converted to potential energy of the resulting gas plume. The unconfined plume expands vertically and has a peak radiative power approximately equal to the total radiation from Jupiters disc. The plume rises a few tens of atmospheric scale heights in ∼10² seconds. The rising plume reaches the altitude of ∼3000 km, but no atmospheric gas is accelerated to the escape velocity (∼60 km/s).

Damage and rock-volatile mixture effects on impact crater formation

We explored simple geologic strength and material response models to determine which have the capability to simulate impact-induced faulting, complicated ejecta patterns and complex crater shapes. This led us to develop models for material damage, dilatancy, and inhomogeneous materials (mixtures). We found that a strength degradation (damage) model was necessary to produce faulting in homogeneous materials. Both normal and thrust ring faults may occur and extend relatively deeply into the planet during the transient cavity radial expansion. The maximum depth of fault development is about the depth of maximum penetration by the projectile. Dilatancy in geologic materials may reduce the final bulk density compared to the pristine state because of irreversible fracturing. When we include the effects of dilatancy, the radial position of faulting is displaced because of greater upward motions. In addition, the late time crater profile is shallower and the expression of features such as central peaks and rings may be more pronounced. Both damage and rock-ice mixtures effect the distribution of ejecta. The excavation flow field within the heavily damaged region is similar to flow fields in Mohr-Coulomb materials with no zero-pressure strength. In the outer, less damaged zone within the excavation cavity, the material trajectories collapse back into the crater. This effect creates a zone of reduced ejecta emplacement near the edge of the final crater. In the case of rock-ice mixtures, energy is preferentially deposited in the more compressible volatile component and the ejecta pattern is dependent upon the location of shock-induced phase changes in the volatile material.

Impact flows and crater scaling on the moon

The axisymmetric distribution of stress, internal energy and particle velocity resulting from the impact of an iron meteoroid with a gabbroic anorthosite lunar crust has been calculated for the regime in which shock-induced melting and vaporization takes place. Comparison of impact flow fields, with phase changes in silicates taken into account, with earlier results demonstrate that in the phase change case when the 15-km/s projectile has penetrated some two projectile radii into the moon, the peak stress in the flow is ∼0.66 Mbar at a depth of 66 km, and the stress has decayed to ∼66 kbar at a depth of 47 km. Rapid attenuation occurs because of the high rarefaction velocity of the high-pressure phases associated with a 35% (zero-pressure) density increase. This feature of the phase-change flow tends to strongly concentrate the maximum shock pressures along the meteoroid trajectory (axis) and makes the conical zone along which high internal energy deposition occurs, both shallow and narrow. Examination of the gravitational energies required to excavate larger craters on the moon indicates the importance of gravity forces acting during the excavation of craters having radii in the range greater than ∼2 – ∼140 km. It is observed that the “hydrodynamic” energy vs. crater radius relation approaches those for various “gravitational” energy vs. radius relations at the radii values corresponding to the larger mare basins. Cratering energy values in the range of (1.0 – 9.4) • 10^(32) erg are inferred on this basis for the Imbrium crater. Using these values and the criteria that all rocks exposed to ∼100 kbar or greater shock pressures are included in the ejecta (some of which falls back) implies that the maximum depth of sampling expected to be represented within the Apollo collection lies in the range 148–328 km.

The size distributions of fragments ejected at a given velocity from impact craters

Abstract The mass distribution of fragments that are ejected at a given velocity for impact craters is modeled to allow extrapolation of laboratory, field, and numerical results to large-scale planetary events. The model is semi-empirical in nature and is derived from (1) numerical calculations of cratering and the resultant mass versus ejection velocity, (2) observed ejecta blanket particle size distributions, (3) an empirical relationship between maximum ejecta fragment size and crater diameter, (4) measurements and theory of maximum ejecta size versus ejecta velocity, and (5) an assumption on the functional form for the distribution of fragments ejected at a given velocity. This model implies that for planetary impacts into competent rock, the distribution of fragments ejected at a given velocity is broad, e.g. 68% of the mass of the ejecta at a given velocity contains fragments having a mass less than 0.1 times a mass of the largest fragment moving at that velocity. The broad distribution suggests that in the impact process, additional comminution occurs after the initial shock has passed. This additional comminution produces the broader size distribution in impact ejecta as compared to that obtained in simple brittle failure experiments.