Mathematics – Logic
Scientific paper
Jan 1999
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1999nvm..conf...23h&link_type=abstract
Workshop on New Views of the Moon 2: Understanding the Moon Through the Integration of Diverse Datasets, p. 23
Mathematics
Logic
Lava, Magma, Moon, Rock Intrusions, Lunar Craters, Lunar Maria, Rheology, Lunar Topography, Volcanoes, Viscosity, Yield Strength
Scientific paper
The lunar steep-sided Gruithuisen and Mairan domes are morphologically and spectrally distinctive structures that appear similar to terrestrial features characterized by viscous magma. We use the basic morphologic and morphometric characteristics of the domes to estimate their yield strength (about 105 Pa), plastic viscosity (about 109 Pa s), and effusion rates (about 50 cubic m/s). These values are similar to terrestrial rhyolites, dacites, and basaltic andesites and support the hypothesis that these domes are an unusual variation of typical highlands and mare compositions. Typical dike geometries are predicted to have widths about 50 m and lengths about 15 km. The magma rise speed implied by this geometry is very low, about 7 x 10-5 m/s, and the Reynolds number of the motion is about 2 x 10-8, implying a completely laminar flow regime. Introduction: The Gruithuisen and Mairan domes represent examples of topographically, morphologically, and spectrally distinctive structures on the Moon that appear to be candidates for very viscous magma. In this analysis, we use the basic morphologic and morphometric characteristics of the domes as a bases for estimating their yield strength, plastic viscosity, eruption rates, and dike feeder geometry (e.g., dike width and length). We begin by assuming that each dome is a single structure emplaced on a flat plain and use Blake's treatment of domes modeled as Bingham plastics to establish the order of magnitude of the yield strength, (t), and plastic viscosity (h). Inferred values of t are about 3 x 105 Pa for the Gruithuisen domes and 1.0 x 105 Pa for Mairan features. Next we use an empirical formula given by Moore and Ackerman to relate the plastic viscosity, to the yield strength. The most likely value of h for the Gruithuisen domes is about 1 x 1010 Pa s and for the Mairan domes is perhaps within a factor of two of 5 x 108 Pa s. As a specific example, we treat the Gruithuisen Gamma dome as an underlying symmetric dome of radius = 10 km and unknown thickness on which are superimposed three flow lobes; we assume that these merge toward the summit, where they have a common thickness. The values (t = 7.7 x 104 Pa; h = 3.2 x 108 Pa s) are, as expected, significantly less than the first approximations, which ignored the detailed morphology of the dome. Given the resolution of the images used and the consequent difficulties in mapping and measuring features, it might be argued that measurements for t and h represent a single Bingham plastic magma for which t = (10 +/- 3) x 104 Pa and h = (6+/- 4) x 108 Pa s. Alternatively, we could separate the two groups of domes and characterize the Gruithuisen dome magma by t = (12+/-3) x 104 Pa, h = (l0 +/- 5) x 108 Pa s and the Mairan dome magma by the slightly smaller values t = (8 +/- 4) x 104 Pa, h=(5 +/- 4) x 10)(exp8) Pa s. We now turn to the estimation of the eruption rates of the magmas forming the various dome units. To do this we assume that the advance of the flow front of each flow unit or dome-forming episode was limited by cooling. Pinkerton and Wilson show that a variety of types of lava flow cease to move when the Gratz number, a dimensionless measure of the depth of penetration into the flow of the cooled boundary layer, has decreased from its initially very high value to a critical value of -300. Blake's model of Bingham plastic domes shows the way in which the radius of the dome grows as a function of time. The assumption that flow lobes are cooling-limited always leads to effusion-rate estimates of lower bounds. This is because any flow unit assumed to be cooling limited may in fact have been volume-limited (i.e., ceased to flow simply because the magma supply was exhausted), implying that it had the potential to travel further than the observed distance and therefore had a higher effusion rate than that deduced. For each of the Gruithuisen domes we have either a second smaller dome or a flow lobe superimposed on a larger, earlier dome. It is very tempting to assume that the second unit in each case is a breakout at the vent caused by the magma supply continuing after the first unit has reached its cooling-limited length. This automatically implies that the effusion rates deduced from the large dome geometries (about 48,24, and 119 cubic M/S for Gruithuisen Delta, Northwest, and Gamma, respectively) are the realistic estimates and that the rates found from the smaller units are underestimates. For the Mairan domes we are not able to resolve multiple lobe structures and must regard the effusion rates of about 50 m/s as lower limits on the true rates. (Additional information is contained in the original)
Head James W.
Wilson Leslie
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