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England and Katz, 2010 LETTER doi:10.1038/nature09417 Melting above the anhydrous solidus controls the location of volcanic arcs Philip C. England1 & Richard F. Katz1 Segregation of magma from the mantle in subduction zones is one (,120 6 40 km; refs 1, 3 and 5). The sharpness of the volcanic fronts of the principal mechanisms for chemical differentiation of the implies that a key process in the generation or transport of magma is Earth. Fundamental aspects of this system, in particular the pro- similarly focused beneath the arcs, but there is no consensus as to what cesses by which melt forms and travels to the Earth’s surface, remain that process may be. A wide range of metamorphic and melting re- obscure. Systematics in the location of volcanic arcs, the surface actions, either in the slab or in the mantle wedge, have been proposed expression of this melting, are widely considered to be a clue to as candidate processes. Some authors suggest that the arcs lie above processes taking place at depth, but many mutually incompatible places where the degree of melting in the mantle wedge becomes high interpretations of this clue exist (for example, see refs 1–6). We enough for the melt to segregate from the solid2,4. Others suggest that discriminate between those interpretations by the use of a simple the locations of arcs are determined by the release of fluid near the top scaling argument derived from a realistic mathematical model of of the slab in reactions that are either strongly pressure-dependent1,3,5 heat transfer in subduction zones. The locations of the arcs cannot or strongly temperature-dependent6,9. None of these suggestions has, be explained by the release of fluids in reactions taking place near however, produced a successful quantitative prediction of the location the top of the slab. Instead, the sharpness of the volcanic fronts, of volcanic arcs. Here we take a different approach: starting with the together with the systematics of their locations, requires that arcs observed correlation between the descent speed of the slab and its must be located above the place where the boundary defined by the depth beneath the volcanic arcs8, we use a simple mathematical model anhydrous solidus makes its closest approach to the trench. We to fit the data and reveal the petrological processes responsible for the show that heat carried by magma rising from this region is sufficient locations of the arcs. to modify the thermal structure of the wedge and determine the Although calculations of the full temperature field in subduction pathway through which both wet and dry melts reach the surface. zones require numerical models10, their results can be encapsulated in Volcanic arcs are characterized by sharp fronts whose locations may simple scaling relations that show11 that temperatures within the mantle be described, with misfits of no more than a few kilometres, by small wedge and at the top of the slab depend upon a single parameter, Vrd2/ circles on the Earth’s surface (Fig. 1 and refs 7 and 8); furthermore, the k. Here V is the convergence rate across the plate boundary, d is the dip depth of the top of the slab beneath these fronts falls in a narrow range of the slab, r isthe radial distance from the wedgecorner (Fig. 1), and k is a b Trench Arc front δ δ z 100 Overriding plate w D 500 D R 1,000 T Region enlarged in b Wedge 500 Subducting slab 1,1,000 000 V Zero-stress boundary Zero-stress Figure 1 | Idealized cross-sections of a subduction zone, drawn wedge is at a depth zw. b, Enlargement of temperature structure of the rectangle perpendicular to the trench and the island arc. a, Two plates converge at a in a: Isotherms are shown at intervals of 100 uC. A schematic isotherm, labelled speed V, with the slab of oceanic lithosphere being subducted at an angle d T, has its closest approach to the wedge corner (its ‘nose’) immediately beneath beneath the overriding plate. The arc front is a zone a few kilometres wide, the volcanic front, at a distance R from the corner (black circle). An open circle across which volcanic activity begins as one moves away from the trench; it lies marks the top of the slab directly below the corner of this isotherm, at a depth D at a distance D above the top of the slab. The relative motion between slab and below the surface. The distance R cannot be determined by observation, but is overriding plate generates a creeping flow in the wedge of mantle between similar to RD 5 (D 2 zw)/sind, the radial distance of the top of the slab (open them, which follows stream lines, shown as curved lines. The corner of the circle) from the wedge corner. 1Department of Earth Sciences, South Parks Road, Oxford, OX1 3AN, UK. 700|NATURE|VOL467|7OCTOBER2010 ©2010 Macmillan Publishers Limited. All rights reserved LETTER RESEARCH a b c 1,400 800 0 1,300 700 50 1,200 600 T 1,100 500 Moho 100 40 mm yr–1 1,000 (°C) 400 (°C) r s T –1 T 60 mm yr 150 900 300 Depth (km) 80 mm yr–1 800 200 100 mm yr–1 200 700 100 600 0 250 0 25 50 75 100 125 0 25 50 75 100 125 0 50 100 150 200 250 (Vrδ2)/κ (Vrδ2)/κ Horizontal distance (km) Figure 2 | Scaling relations for temperatures in the core of the mantle the top of the slab) for convergence rates V of 40–100 mm yr21 and a slab dip of wedge, and at the top of the slab. a, Maximum temperature in the wedge, Tr,as 40u. c, The temperature structure near the wedge corner for a calculation with a a function of dimensionless distance from the wedge corner, Vrd2/k, where V is convergence speed V of 80 mm yr21 and a slab dip of 40u. The location of the convergence speed, d is dip of the slab, and k is thermal diffusivity. Dots with 500 uC isotherm is shown by green lines and the 1,225 uC and 1,275 uC error bars indicate the averages and standard deviations of Tr, determined from isotherms are shown by red lines. Green arrowheads show the horizontal extent calculations in which V varies from 10 mm yr21 to 100 mm yr21, in steps of over which some part of the oceanic crust is at a temperature of 500 uC. Red 10 mm yr21, while d varies from 20u to 70u in steps of 10u. The red line arrowheads show the range over which the maximum temperature in the corresponds to the theoretical expression for Tr (equation (1)), with mantle wedge lies between 1,225 uC and 1,275 uC (a typical range of T0 5 1,420 uC, B 5 3.3 and b 520.8. b, As for a, but for temperatures within temperature represented by the error bars in Fig. 3b). Uncertainties in the the slab. The thick blue line corresponds to the theoretical expression for Ts,the temperatures arising from idealizations in the model are discussed in section B2 temperature on the top of the slab (equation (2)), with C 5 1.4 and c 520.06. of the Supplementary Information. Thin blue lines indicate the temperatures at the base of the crust (7 km below the thermal diffusivity of the mantle. In this scaling, the maximum variation rules out the hypothesis that the arcs are located above the temperature in the mantle wedge Tr is given by: place where the top of the slab reaches a critical pressure correspond- "# 1,3,5 b ing to a single dehydration reaction . We may also rule out the Vrd2 T <T exp {B ð1Þ hypothesis that the release of fluids by temperature-dependent re- r 0 k actions near the top of the slab determines the location of arcs (see, for example, ref. 6). The top of the slab lies within a thermal boundary while the temperature Ts at the top of the slab is: layer a few tens of kilometres thick, across which there is a temperature , ÀÁTr difference of 1,000 uC. Because isotherms within this boundary layer Ts< c ð2Þ 1zCVrd2 k are almost parallel to the slab, any given temperature will be found over a large range of pressure (Fig. 2b, c). Therefore, temperature-dependent where T0 is a scale temperature, and B, C, b and c are constants, the processes taking place near the top of the slab cannot be sharply loca- values of which depend on the details of the flow near the top of the lized, but must occur over a broad range of down-dip distances14. slab. This scaling was initially derived for a model of subduction zones In contrast, the steep lateral thermal gradients in the core of the that treated the mantle as a constant-viscosity fluid11; we show here that mantle wedge provide a setting in which localization of temperature- these relations also hold for the case in which the viscosity has a dependent processes is likely2,4. The maximum temperature in the dependence on temperature that is appropriate for the upper mantle mantle wedge depends on the dimensionless distance from the wedge (Fig. 2 and Supplementary Information). corner Vrd2/k (equation (1) and Fig. 2a). Accordingly, we should Precise earthquake hypocentral locations12 reveal that the depth D expect that if a temperature-dependent process is localized beneath to the top of the slab beneath the fronts of volcanic arcs is constant, to the arc, the relevant isotherm will reach its closest approach to the within a few kilometres, along individual segments of arc, but varies wedge corner (which we refer to below as its ‘nose’) at a distance R that from 80 km to 160 km between different segments8,13 (Fig.
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