Other
Scientific paper
Sep 2008
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2008epsc.conf..467w&link_type=abstract
European Planetary Science Congress 2008, Proceedings of the conference held 21-25 September, 2008 in Münster, Germany. Online a
Other
Scientific paper
Introduction. We have documented the range of eruption styles on the Moon and linked there to processes of magma generation, ascent and eruption [1]. With the availability of high-resolution images of the Moon from new missions, we have been revisiting the range of eruption conditions implied by these surface volcanic features. Here we focus estimating eruption conditions of lunar mare lavas, especially volume eruption rates, V. The youngest and bestpreserved flow units in Mare Imbrium have lengths, X, in the range 300 to 1200 km, widths, w, of order 20 km and thicknesses, d, of ~20 m [2]. Two assumptions can be made about eruption conditions of the flows: they may have been either cooling-limited (stopped due to excessive cooling) or volume-limited (stopped because of exhausted magma supply at the source). We explore the implications of these assumptions and derive estimates of likely eruption conditions, melt volumes, and feeder dike geometries. Cooling-limited flows. If flows were cooling limited they would have stopped when the Gratz number, Gz, defined by Gz = [(16 d2)/(k t)], decreased from an initially large value to the critical limiting value, Gzc, equal to ~300 [3]. Here k = 7 × 10-7 m2 s-1 is the thermal diffusivity of silicate lava and t is the time when lava motion ceased. Assuming a constant flow speed S, X = (S t) where X is the length of the flow. We do not know S and so we eliminate this by noting that V = (S w d) so that we can write 300 = (16 V d)/(k X w) or V = (18.75 k X w)/d. Thus the volume flux can be written in terms of the measurable quantities X, w and d. With X = 300 km, w = 20 km and d = 20 m, we find V = ~4000 m3 s-1, which implies a flow speed S = V/(w d) = ~1 cm s-1 and a time of flow emplacement of t = ~12 months. For the longest flow units with X = 1200 km and the same values of w and d, V = ~16000 m3 s-1, S = 4 cm s-1 and the emplacement time is the same as before, t = 12 months. Volume-limited flows. The other extreme is to assume that flows were volume-limited. They must have flowed at a speed determined by their thickness d, density r, viscosity h, the ambient topic slope a, and the acceleration due to gravity, g. In laminar flow Jeffreys' equation holds: S = (r g d2 sin a)/(3 h). Using r = 3000 kg m-3, h = 10 Pa s, g = 1.63 m s-2, d = 20 m and sin a = 1 × 10-3, we find S = 65 m s-1. But when we evaluate the Reynolds number Re = (4 d S r)/h we find Re = 1.56 × 106, totally inconsistent with the flow being laminar, which requires Re < ~500. Using the turbulent flow equivalent of Jeffreys' equation, S = [(2 r g d sin a)/(10-2 r)]1/2, where the constant 10-2 is an empirical friction factor [4], we find S = 2.55 m s-1 and Re = 6.1 × 104, fully consistent with turbulent flow (Re > ~2000). The corresponding volume flux is V = (S w d) = 1.04 × 106 m3 s-1, and the implied duration for a 300 km-long flow unit is ~33 hours. We see no explicit signs of flow deflation, but it is possible that the longest mare lava flows ponded and inflated, so we explore setting d smaller by a factor of three at 7 m; it is also possible that loading has caused subsidence of the centers of mare basins so that the slope was less at the time when the flows were emplaced, so we set sin a = 0.3 × 10-3, also a factor of three smaller than now. These changes still lead to the prediction of turbulent flow, now with S = 0.825 m s-1, Re = 6930 and V = 1.16 × 105, with a 300 km flow emplaced in ~100 hours. For the assumed magma viscosity, h = 10 Pa s, it is only if the flow thickness decreases below 2.3 m when sin a = 10-3 and below 3.4 m when sin a = 0.3 × 10-3 that the flow ceases to be turbulent. It is very hard to escape the conclusion that lava flows like those in Mare Imbrium were volume limited and were emplaced rapidly (1-3 m s-1) at high (105-106 m3 s-1) volume fluxes. We now explore the implications of this for the geometries of feeder dikes. Feeder dikes. Assume that a surface flow unit is fed by a fissure of horizontal length L. Then the volume flux V must be equal to (L W U) where W is the fissure width and U is the magma rise speed through the lithosphere. The sources of the Mare Imbrium flows are hard to identify but the proximal parts of flow units suggest that L is ~ 20 km. For our solution with V = 1.02 × 106 m3 s-1, V/L = W U = 51.0 m2 s-1. The rise speed, U, of magma in a dike is given by U = (W2 dP/dz)/(12 h) in laminar flow where dP/dz is the vertical pressure gradient driving magma rise, so we can put W U = (W3 dP/dz)/(12 h) = ~50 m2 s-1. If the driving pressure gradient were purely due to positive magma buoyancy of magma of density rm in host rocks of density rh then dP/dz = g (rh - rm) and if we considered only the magma-mantle density difference we would take dP/dz = ~800 Pa m-1, as did many early treatments. In fact lunar basalts were most often positively buoyant in the mantle but almost equally negatively buoyant in the crust, and we show below (Table 1) that dP/dz lies within a factor of 5 of 20 Pa m-1. This implies W = 6.7 m and U = 7.5 m s-1, with a factor of ~1.7 spread in values of W and U. The equivalent turbulent flow formula for U is U = [(W dP/dz)/(10-2 r)]1/2 so V/L = (W U) = [(W3 dP/dz)/(10-2 r)]1/2 implying W = 15.5 m and U = 3.2 m s-1, also with a factor of ~1.7 spread in the values. A check on Reynolds numbers shows that this latter, turbulent, solution is the correct one. The magma rise time from the ~200 km depth implied by the magma chemistry would have been t = ~17 hours. The distance a wave of cooling could penetrate in this time is ~[2.32 (k t)1/2] on each side of the dike [5], a total of almost exactly 1 m, << than the 15.5 m dike width, so the magma would have suffered negligible cooling during its ascent. The minimum volume of the dike is given by the product of its vertical extent, horizontal extent and width. With a vertical extent of, say, 200 km, a horizontal extent equal to the fissure vent outcrop length of 20 km and a width of 13-14 m, the volume is ~55 km3. More likely the dike was penny-shaped with a horizontal extent similar to the vertical length, making the volume estimate ~430 km3. With L = 20 km, the smaller volume flux found earlier, V = 1.16 × 105 m3 s-1, gives V/L = W U = 5.79 m2 s-1. The turbulent magma flow solution is again the relevant one and yields a dike width of 3.6 m and a magma flow speed of 1.6 m s-1 when the pressure gradient is 20 Pa m-1. Minimal and more likely dike volume estimates are close to 10 and 100 km3, respectively. The magma rise time from 200 km depth is t = ~35 hours and total cooling penetration would have been ~1.4 m, less, but not very much less, than the ~3.2 m dike width. Thus this magma would have suffered significant cooling in transit, and clearly magma cannot be erupted directly from depths of order 200 km if the volume flux is much less than 105 m3 s-1. To explore the properties of dikes in more detail we model a dike reaching the surface from a depth of 70 km below the base of a 70 km thick crust using equations in [6]. We take magma and mantle densities of 3000 and 3400 kg m-3, respectively, and vary the crustal density, rc. The range of crustal densities over which eruptions are possible is a strong function of the tectonic stress state of the crust. Table 1 shows typical results using a uniform compressive stress, C, of 15 MPa, a value relevant to the latter half of lunar history when global cooling had led to net crustal compression. The quantities in the Table are the excess pressure in a magma column just reaching the surface, Pe; the pressure at the base of the crust holding the dike open, Pd; the pressure gradient driving magma motion, dP/dz; the mean dike width, W; the mean magma rise speed, U; and the product (W U) = (V/L). For C = 15 MPa, only intrusions are possible unless rc lies between ~2600 and ~2700 kg m-3. Within this range allowing eruptions: (i) at low crustal densities, dikes are potentially wide but magma pressure gradient is small; (ii) at high crustal densities, magma pressure gradient is large but dike widths are small; (iii) at intermediate crustal densities h
Head James W. III
Wilson Leslie
No associations
LandOfFree
Lunar volcanic eruptions: Mare lava flow eruption rates and implications for mantle melt volumes and dike geometries. does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Lunar volcanic eruptions: Mare lava flow eruption rates and implications for mantle melt volumes and dike geometries., we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Lunar volcanic eruptions: Mare lava flow eruption rates and implications for mantle melt volumes and dike geometries. will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-1793782