| Summary: | We present a mathematical model for the evolution of the (226Ra / 230Th) activity ratio during simultaneous fractional crystallization and ageing of magma. The model is applied to published data for four volcanic suites that are independently known to have evolved by fractional crystallization. These are tholeiitic basalt from Ardoukoba, Djibouti, MORB from the East Pacific Rise, alkali basalt to mugearite from Vestmannaeyjar, Iceland, and basaltic andesites from Miyakejima, Izu–Bonin arc. In all cases (226Ra / 230Th) correlates with indices of fractional crystallization, such as Th, and the data fall close to model curves of constant fractional crystallization rate. The best fit rates vary from 2 to 6 × 10− 4 yr− 1. Consequently, the time required to generate moderately evolved magmas (F ≤ 0.7) is of the order of 500 to 1500 yrs and closed magma chambers will have lifetimes of 1700 to 5000 yrs. These rates and timescales are argued to depend principally on the specific power output (i.e., power output per unit volume) of the magma chambers that are the sites of fractional crystallization. Equating the heat flux at the EPR to the heat flux from the sub-axial magma chamber that evolves at a rate of ca. 3 × 10− 4 yr− 1 implies that the magma body is a sill of ca. 100 m thickness, a value which coincides with independent estimates from seismology. The similarity of the four inferred differentiation rates suggests that the specific power output of shallow magma chambers in a range of tectonic settings covers a similarly narrow range of ca. 10 to 50 MW km− 3. Their differentiation rates are some two orders of magnitude slower than that of the basaltic Makaopuhi lava lake, Hawaii, that cooled to the atmosphere. This is consistent with the two orders of magnitude difference in heat flux between Makaopuhi and the East Pacific Rise. (226Ra / 230Th) data for magma suites related by fractional crystallization allow the magma differentiation rate to be estimated and, from this, the thermal budget of the magma chamber ...
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