On lateral mixing efficiency of lunar regolith

Abstract

[1] To reexamine the potential for lateral mixing over large distances (>100 km) by impact craters, a mathematical model utilizing the stable probability distribution is proposed for estimating lateral mixing efficiency on the Moon. The proposed model divides material mixing into shallow slope and steep slope regimes. Mixing in the shallow slope regime conforms to the condition that the exponent of the power law describing lunar crater size frequency is larger than the exponent of the power law describing the rim thickness plus 2; otherwise the mixing is called the steep slope regime. The model suggests that in the shallow slope regime, lateral mixing on the Moon is efficient enough to deliver 20-30% exotic components over distances greater than 100 km (e.g., highland material to the mare). The model indicates that lateral mixing conforming to the steep slope regime is not efficient if linear addition of ejecta deposits is assumed because in this regime, impact cratering is driven by small craters reworking lunar surface, and the addition of crater ejecta is an invalid assumption. If the result of the proposed model for the shallow slope regime is applied to regolith layers below the reworked zone, a significant number of ''exotic'' components is predicted.

Heterogeneous impact transport on the Moon

“…For example, the Apollo 15 lunar module site was in the secondary field (South Cluster) of rays of either Autolycus or Aristarchus Crater [ Swann et al , ]. Li and Mustard [] suggest that distal ejecta from distances of >100 km away could explain an elevated amount of nonlocal material in a sampling location, though, again, they did not consider the heterogeneous nature of this distal ejecta.…”

“…Li and Mustard [] suggested that large craters >100 km away from contacts may explain the elevated nonmare abundance of >20% in most mare soil samples. To test this large crater hypothesis, we performed a global run to account for the effect of larger craters at large distances from the mare/highland contact.…”

“…If locally derived materials dominate on the lunar surface, and distal ejecta is insignificant, then the mixing process across mare/highland contacts can be modeled by only considering deposition of the proximal continuous ejecta. Li et al [1997] modeled the material exchange between mare and highland plains as a classical diffusion process, which describes the movement of a particle as random walk, with each step of motion spanning a finite distance. The finite step that a crater generates is limited to the extent of the continuous ejecta blanket.…”

“…One way to evaluate the relative importance of proximal ejecta and distal ejecta is to examine how the basalt/anorthosite material mixing ratio changes as a function of distance from a mare/highland boundary [Schonfeld and Meyer, 1972;Rhodes et al, 1974;Rhodes, 1977;Li et al, 1997;Li and Mustard, 2000]. The material mixing process across mare/highland contacts is driven by impacts, and the area where this mixing occurs is called the mixing zone.…”

Evidence for explosive silicic volcanism on the Moon from the extended distribution of thorium near the Compton‐Belkovich Volcanic Complex

“…The formalism does not, however, give a value of the ejecta thickness at a particular point—only the characteristic function of the probability density function (pdf) of the total ejecta thickness, φ ρ ( u ): where Γ is the Gamma function, , and sgn( u ) is 1 if u > 0 and −1 if u < 0. Obtaining the pdf from this characteristic function requires the use of a numerical integrator, and we follow Li and Mustard [] in using the STABLE code [ Nolan , ].…”