Mathematics – Logic
Scientific paper
Jul 1993
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1993metic..28q.455w&link_type=abstract
Meteoritics, vol. 28, no. 3, volume 28, page 455
Mathematics
Logic
Exposure Ages, Impact Craters, Lunar Meteorites, Mare Basalts, Meteorites, Snc Meteorites
Scientific paper
Lunar meteorites (LMs) tend to be launched from shallow depths. Of the unpaired LMs for which unambiguous isotopic-CRE constraints have been derived, 5 out of 8 (and 5 out of 6 that are polymict breccias) were launched from depths of <= 3.2 m. For comparison, the average depth of excavation from a crater with diameter D = 3.6 km, the size estimated by Melosh [1] to be a minimum for origin of ALHA81005 (31 g, vs. 724 g for the largest LM), is roughly 150 m. These statistics support Melosh's basic concept that proximity to the lunar surface plays a key role in launching rocks at velocities greater than the lunar nu(sub)esc (2.20-2.44 km/s). The proportion of discrete launch events represented among LMs is another key observation. If LM "yield" scales in proportion to crater volume, or especially if it scales to volume of the launch-triggering projectile [1], then conventional wisdom regarding the recent cratering rate (N = variation of D^-b where for D of the order 10 km b is between 2 and 3), implies that more LM mass should be arriving from large craters than from small ones, which should result in frequent launch-crater pairing. The highest-velocity ejecta is always derived from within a few impactor radii of the crater center: nu(sub)ej scales as (x/r)^y, where x is distance, r is impactor radius, and y ~3 [2]. For lunar craters with D = 1-30 km and nu(sub)i large enough to conceivably launch a LM, r is only 0.01-0.04 x D. Thus, geochemical diversity among LMs can be compared to the diversity expected within a region of crust less than about 3 km across, and for more plausible nu(sub)i and D, <1 km across. Six of the nine LMs for which meaningful isotopic-CRE constraints exist are polymict breccias (five are grossly polymict regolith breccias), and of the other four, one has a uniquely high launch age, while two (the two YA mare basalts) share another distinctive launch age. Apollo data indicate that even at sites chosen to straddle geologic terrain boundaries, regolith breccias collected within a 0.5-km radius are almost uniform in composition. By combining the CRE-isotopic constraints with probability arguments based on serendipitously extreme contrasts in KREEP content and/or mg ratio among the polymict samples, I infer that very probably >=5 different launch craters were involved in supplying the nine LMs. This result favors a high value for the modern b (cf. [3]). However, shallow provenance of most LMs suggests that yields from LM launch events may scale roughly with the cross-sectional area of the projectile (or crater), instead of with its volume; i.e., with r^2 instead of r^3. In Melosh's [1] theory of stress-wave interference in LM launch, he assumes a constant velocity c(sub)L for the shock and rarefaction waves. For the shock wave, c(sub)L is equivalent to seismic V(sub)p. But the outer few hundred meters of the Moon is a region in which V(sub)p grades, probably in a tiered fashion, from the rocklike value (5-6 km/s) assumed by Melosh [1] at depth, to ~0.1 km/sec in the outer 10 m (regolith). For reasonable choices of D, nu(sub)i, and c(sub)L, the interference zone thickness z(sub)P is directly proportional to c(sub)L, and in a region with c(sub)L increasing with depth rarefactions may not begin fast enough to interfere with compressive waves except within the outermost few (~10) meters of the Moon. Even a crude modification of Melosh's [1984] model to have c(sub)L = 1.0 km/s implies that for points <= 4r from the point of impact, with nu(sub)i >= 6 km/s and crater D <= 10 km, z(sub)P is limited to <65 m; for D <= 3 km, z(sub)P is limited to <15 m. Note that the shallow provenance of the LMs, like their diverse CRE ages and bulk compositions, suggest relatively small source craters. Implications for SNC meteorites will also be discussed. References: [1] Melosh H. J. (1984) Icarus, 59, 234-260. [2] Housen K. R. et al. (1983) JGR, 88, 2485-2499. [3] Strom R. G. et al. (1992) in Mars (H. H. Kieffer et al., eds.), 383-423.
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