Proc. Lunar Planet. Sci. Conj. !Ith (1980), p. 2347-2378. Printed in the United States of America 1980LPSC...11.2347C Cratering flow fields: Implications for the excavation and transient expansion stages of crater formation Steven Kent Croft Lunar and Planetary Institute, 3303 NASA Road I, Houston, Texas 77058 Abstract-A Maxwell Z-model cratering flow field originating at non-zero depths-of-burst has been used to calculate theoretical depths and volumes of excavation, hinge radii, ejection angles, and transient structural rim uplifts for comparison with experimental and field data from impact and explosion craters. The model flow fields match the observed data well for values of Z between 2.5 and 3.0 for both explosion and impact craters, and effective depths-of-burst near one projectile di- ameter for impacts. The model flow field is therefore inferred to be a reasonable first-order quantitative approximation for several important crater structures, and to embody the important qualitative fea- tures of impact and explosion cratering flows. Formation of a hinge about which the coherent ejecta flap rotates at the rim of the transient crater divides material in the flow field into ejected and down- ward and outward-driven portions. Ejected material originates from an excavation cavity which has a geometry distinct from the transient crater. The excavation cavity and transient crater have the same diameter, D1c, but the depth of the excavation cavity is -0. I D1c, or about one-third of the transient crater depth, and, in the case of simple bowl-shaped craters, about one-half the depth of the final apparent crater. Down-driven material, including a central "cone" of shallow, highly-shocked material, moves downward and outward to form the walls of the transient crater and displaces an equivalent volume above the original ground surface to form the structural rim uplift. The shallow depths of excavation both observed in impact and explosion craters and predicted by the Z-model flow fields imply that thickness estimates of lunar geologic units, such as the maria basalts, determined by assuming that excavation depths are similar to final or transient crater depths must be reduced by factors of two to three, respectively. In the Z-model flow field, streamline shapes are gravity independent and geometrically similar (except very near the center of flow). This implies that excavation cavities, whose shapes depend on hinge streamline geometry, are geometrically similar in craters of all sizes. Consequently, lunar basin excavation cavities are inferred to exhibit propor- tional growth and to have maximum depths of excavation near 0.1 the diameter of the basin transient crater. Thus, basin transient craters may attain diameters -IOX the local crustal thickness before ejecting mantle material. The observed paucity of lunar mantle materals on the lunar surface around the Imbrium basin is compatible with the proportional growth of the excavation cavity if the diameter of the excavation cavity was ~700 km, or near one of the innermost rings. INTRODUCTION Grieve (1979) has recently re-emphasized the necessity of a coherent model for the excavation stage of impact craters. Such a model is necessary to obtain structural information about the lunar crust from the lunar sample collection, and to interpret the geology of terrestrial impact structures and the petrography of their associated melt and ejecta deposits. Considerable effort has gone into the 2347 © Lunar and Planetary Institute • Provided by the NASA Astrophysics Data System 2348 S. K. Croft numerical simulation of impact and explosion crater formation based on the phys- ical properties of shock waves, target and projectile materials (e.g., Bjork et al., 1967; O'Keefe and Ahrens, 1978a; Orphal, 1977; Bryan et al., 1978; Thomsen 1980LPSC...11.2347C et al., 1979; Roddy et al., 1980; Orphal et al., 1980; Austin et al., 1980). Cra- tering calculations are extremely complex, but often limited to the earliest stages of crater formation so that there are few points of contact between phenomena indicated in the calculations and the crater examined by the geologist in the field. A few calculations carried to later stages of crater formation (e.g., Austin et al., 1980; Orphal et al., 1980) have yielded systematics in particle movements during the excavation stage that may help bridge the gap between the physics of cratering and geology of craters. A simplified analytical description of systematic particle movements during cratering, i.e., the cratering flow field, has been described by Maxwell (1977) for explosion craters. In the following discussions, the general properties of cratering flow fields are first described. Second, a modified form of Maxwell's (1977). flow field model is derived that is proposed to describe both impact and explosion cratering flow fields. Third, specific predictions derivable from the modified flow field are compared with field observations to evaluate the applicability of the modified flow field model to actual craters. Last, implications of features of crater formation predicted by the flow field model for the depth of origin of lunar samples is discussed. Cratering flow fields Crater formation in explosions or impacts may be divided into three stages: a short high-pressure phase, a longer cratering flow phase, and a modification stage. The first two stages have been modeled numerically and are described in detail by Bjork et al. (1967) and Kreyenhagen and Schuster (1977), among others. Briefly, the high pressure phase is characterized by an expanding region of ex- tremely high pressure behind the primary shock created by the explosion or impact. Rarefactions propagating from free surfaces quickly reduce pressures behind the primary shock to low levels, "detaching" the primary shock from the zone immediately around the explosion or impact. Virtually all material ultimately ejected from the crater is "shock processed" during the high-pressure phase, but comparatively little material movement or ejection occurs during this phase due to its short duration. In contrast, the cratering flow phase is characterized by a low-pressure, large-deformation inertial flow of target material fractured and heated by the passage of the primary shock. The preponderance of particle motion in crater formation occurs under the low-pressure conditions of the relatively lengthy cratering flow stage. The modification stage is characterized by (possibly) complex particle motions occurring very late in the cratering process in very large craters, or craters in weak materials. The cratering flow field may be thought of as the aggregate of paths followed by particles set in motion by an impact or explosion that ultimately produces a © Lunar and Planetary Institute • Provided by the NASA Astrophysics Data System Cratering flow fields 2349 crater. Consequently, the properties of the flow field determine how individual particles in the projectile and the cratered surface move with respect to each other and where they will be found in relation to the final crater. Therefore, if 1980LPSC...11.2347C the nature of cratering flow fields can be deduced from theory or observation, a coherent model of crater formation can be constructed. A qualitative description of individual particle paths during impact cratering was given by Gault et al. (1968) on the basis of observations of the development and final structures of hypervelocity impact craters in sand in the laboratory. They found that during the cratering flow stage, which they called the excavation stage, particles traveled in concave-upward arcuate paths in response to rarefactions propagating down- ward from the free surface. A quantitative description of particle motion during the cratering flow stage of near-surface explosions, the so called Z-model, was developed and described by Maxwell and others (Maxwell, 1973, 1977; Maxwell and Seifert, 1974; Orphal, 1977). The Z-model is derived from three assumptions: 1. Flow below the ground plane is incompressible. 2. The radial velocity, R, of particles below the ground plane is given by R = a/R2 , where R is the radial distance from the effective origin of flow, a is a measure of the strength of the flow field, and Z determines the change of velocity with increasing radial distance. 3. Particles follow independent ballistic trajectories after spallation at or near the ground plane. The assumption of incompressibility and the expression for R lead to particle paths that are stationary streamlines similar to the empirical paths described by Gault et al. (1968). Values of Z for realistic computed flow fields for near-surface explosions vary from Z = 2 near the vertical downward axis to Z = 4 near the ground surface, with an average for the whole flow below the ground plane of Z = 3. If a and Z are assumed to be constant, the flow field at all times can be explicitly evaluated, and quantitative descriptions of several features of near-surface explosion crater formation are obtained, including early hemispheric growth of the transient cavity (Orphal, 1977), angle of ejection, and development and deposition of an inverted ejecta flap (Maxwell, 1977). The as- sumption of constant a and Z is not consistent with the conservation of energy (Maxwell, 1977), but provides a good first order approximation to a real flow field (Orphal, 1977). The Z-model, however, was generalized from numerical simulations of near- surface explosions, thus the application of the Z-model to impact craters was problematical, despite its great utility. Thomsen et al. (1979) investigated the ability of a constant a, constant Z-model to represent the impact cratering flow field of a 6 km/sec impact of aluminum on clay, and found that the Z-model was applicable at very early times provided: 1) the origin of the flow field is at some depth below the ground surface, and 2) the model is applied late enough in time that the projectile's momentum has dissipated. The depth of the effective center of Z-model flow ( EDOZ) found by Thomsen et al.