Numerical modeling of trace element transportation in subduction zones: implications for geofluid processes
© Ikemoto and Iwamori; licensee Springer. 2014
Received: 29 November 2013
Accepted: 24 March 2014
Published: 30 April 2014
This study presents the first numerical model for trace element transportation associated with dehydration and fluid migration from the subducting slab and aims to incorporate both fluid dynamical processes (e.g., flow mode and mass fluxes) in subduction zones and associated geochemical evidence (e.g., chemical compositions of arc lavas). The model includes temperature and flow structures associated with slab subduction and mantle-fluid two-phase flow, as well as phase relations of hydrous phases (e.g., dehydration-hydration reactions and melting) and trace element partitioning among the phases (solid, aqueous fluid, and melt). The model calculations show that if instantaneous chemical equilibrium is achieved associated with porous flow of slab-derived fluid, the elements expelled with the ascending fluid (e.g., Pb) are absorbed into the down-going hydrated mantle layer developed above the slab. As a result, these elements are considerably depleted in the resultant magma generated by fluid-flux melting in the core part of the mantle wedge, and it therefore fails to reproduce the geochemical characteristics of arc lavas. In contrast, if disequilibrium element transport (e.g., associated with channel flow) is assumed when the hydrated mantle layer liberates the fluid, then the key elements are delivered to the melting region to reproduce certain arc lava signatures. These results suggest that disequilibrium fluid transport in the wedge mantle, such as through channels, plays an important role in element cycling in subduction zones.
Subduction zones are one of the most tectonically active sites on Earth and are associated with remarkable amounts of material and energy transport. For example, it is believed that arc volcanism is derived from a combination of solid flow in the mantle wedge and fluid flow originating from the subducting slab. The slab-derived fluid (hereafter referred to as slab-fluid) migrates upwards in relation to buoyancy due to the density contrast and significantly reduces the melting temperature of the overlying mantle wedge by several hundred degrees with an input of some thousands parts per million H2O (e.g., Green 1973; Iwamori 1998). Slab-fluid can also have chemical impact and is believed to metasomatize and enrich the wedge in incompatible elements. This process may explain the characteristic composition of arc magma, as well as the continental crust (e.g., relative Nb depletion and Pb positive spike in spidergram; Tatsumi and Eggins 1995). In addition, recent studies have indicated that slab dehydration and mantle metasomatism in subduction zones could lead to global mantle isotopic heterogeneity through fractionation between parent-daughter elements, e.g., Rb-Sr, Sm-Nd, and U-Th-Pb (Iwamori and Albarède 2008).
In order to quantify the potential importance of such element transport in subduction zones, the trace element and isotopic composition of subducted materials, slab-fluids, mantle wedge, and arc volcanic rocks have been extensively studied, involving elemental partitioning during dehydration and melting (e.g., Ishikawa and Nakamura 1992; Ayers 1998; Plank and Langmuir 1998; Pearce et al. 2005; Nakamura et al. 2008; Kimura et al. 2009). Such studies assume a simple configuration for the fluid and element transport and use a box model for the subducted slab material, mantle wedge, and volcanic rocks, with prescribed elemental fluxes among the ‘boxes.’
Fluid dynamical approaches can be complementary to the geochemical approaches mentioned above and have been constructed to quantitatively examine the fluid generation-migration and resultant melting in the mantle wedge (e.g., Iwamori 19982007; Arcay et al. 2005; Cagnioncle et al. 2007; Hebert et al. 2009). Such numerical models provide constraints on the fluid fraction, migration velocity, and degree of melting that have been compared with the seismic velocity structures (Iwamori and Zhao 2000; Nakajima et al. 2005; Tonegawa et al. 2008). However, elemental transport has not been incorporated into those fluid dynamical models, and consequently, the actual mechanism for elemental transport has not been addressed.
In this study therefore, we combine geochemical and fluid dynamical approaches. The pioneering works of Spiegelman and McKenzie (1987) and McKenzie and O´Nions (1991) gave an analytical expression of the elemental fluxes associated with fluid flow interacting with the convecting solid in the mantle wedge, providing an idealized two-phase flow system that assumes a constant fluid fraction and partition coefficient. However, the study presented here includes a more realistic model setup, which allows a variable fluid fraction and partition coefficient based on a numerical two-phase flow model (Iwamori 1998) and recent knowledge of trace element partitioning between solid, melt, and aqueous fluid (e.g., Green et al. 2000; Kessel et al. 2005; Kimura et al. 2009). In addition, it is also the first numerical model to integrate a thermal flow structure, H2O-bearing phase relations (including dehydration and melting reactions), and the transport of trace elements associated with fluid flow in subduction zones. Through this model, we aim to understand the elemental cycling and solid-fluid flow beneath arcs based on acquired geochemical data.
In order to examine the chemical processes in subduction zones, we developed a numerical model for fluid processes based on Iwamori (1998). In this model, the phases present (aqueous fluid, melt, and solid) and the amount of H2O in each phase are calculated based on parameterized phase relationships and H2O solubility (Iwamori 19982007).
The constant velocity and angle of a subducting slab are assumed to drive the circulation of solids in the mantle wedge by the process of dragging; for simplicity, mantle rheology is assumed to be isoviscous. Due to the density contrast and the solid flow, aqueous fluid is assumed to migrate as porous flow along the solid grain boundaries according to the pressure gradient, and if the water content is higher than the maximum water content, excess water is allocated to aqueous fluid. Melt is assumed to migrate with solid, and if the melt fraction exceeds 2 wt.%, the excess melt is assumed to be instantaneously extracted from the mantle (Iwamori and Zhao 2000; Nakajima et al. 2005; Zhu et al. 2013). In this model, the melt fraction depends on the water fraction, temperature, and pressure, but not on the degree of mantle depletion (i.e., major element composition) due to melt extraction, and this assumption is likely to result in an overestimate for the amount of produced melt; the validity of this will therefore be examined later. Water partitioning between solid and melt is assumed to reach equilibrium instantaneously, with a constant partition coefficient of 0.01 (Aubaud et al. 2008; Kohn and Grant 2006). The energy transported by the aqueous fluid and energy for phase transformation related to hydration and dehydration are neglected.
For phase i (m = melt, s = solid, a = aqueous fluid), ρ i is density, ϕ i is the volume fraction, v i is the velocity vector, is the concentration of H2O, and t is time. In Equation 1 for the local bulk system (b = m + s + a), ρ b is the average density and is the average concentration of H2O. Although the aqueous fluid dissolves a significant amount of silicate components in the pressure and temperature range of interest (Nakamura and Kushiro 1974; Fujii et al. 1997), (aqueous fluid) is assumed to be unity. In Equations 2 and 3 for the solid flow, Ψ is the stream function. In Equation 4 for the flow of aqueous fluid (McKenzie 1984), is the permeability, η a is the viscosity, Δρ a is ρ s − ρ a , g is the acceleration due to gravity, R is the radius of the solid grain, and n and B are the constants (n = 3 and B = 103 are assumed after McKenzie (1984)). Although this formulation neglects viscous force in relation to compaction of the solid matrix and its associated nonlinear behavior (e.g., solitary porosity wave), it gives a reasonable estimate for the fluid velocity when the compaction length is small, which is considered likely to be the case with mantle melting (McKenzie 1984; Scott and Stevenson 1984). is the partition coefficient of water between solid and melt. C p i is the heat capacity at constant pressure, α i is the thermal expansion coefficient, ΔS is the entropy change associated with melting, and K is the thermal conductivity. For these constants, we set ρ s = ρ m = ρ b = 3.5 × 103kg m− 3, ρ a = 1.0 × 103kg m− 3, Δρ a = 2.3 × 103kg m− 3, Δη a = 10− 3Pa s, g = 9.8m s− 2, R = 1.0 × 10− 3m, α s = α m = 2.4 × 10− 5K− 1, ΔS = 3.5 × 102J kg− 1K− 1, K = 1.0 × 10− 6m2s− 1, C p s = C p m = 1.2 × 103J kg− 1K− 1 (Iwamori 1998).
where is the composition of element X in phase i, is the partition coefficient between solid and melt, and is the partition coefficient between solid and aqueous fluid. Since elemental diffusion has a significantly smaller effect than the representative velocity of advective transport (e.g., Iwamori 1998), it has been neglected here. We calculate a bulk partition coefficient using an individual mineral-fluid and mineral-melt partition coefficients and the modal composition of minerals (Ayers and Watson 1993; Ayers et al. 1997; Kogiso et al. 1997; Green et al. 2000; Green and Adam 2003; Feineman et al. 2007; Usui et al. 2007; Kimura et al. 2009), together with their temperature dependence for garnet, clinopyroxene, orthopyroxene, chlorite, and amphibole (Garrido et al. 2005; Kessel et al. 2005; Moyen and Stevens 2006; Kimura et al. 20092010). We then calculate the modal compositions of minerals for the mantle based on Kimura et al. (20092010), as a function of pressure and temperature.
The thermal boundary conditions used in this study are as follows: At the vertical boundaries of the model box, the temperature depth profile is fixed in terms of time. In order to simulate subduction of the Pacific Plate beneath northeast (NE) Japan, a geotherm for the plate age of 130 million years (Myr) is applied to the oceanic side boundary, based on the one-dimensional cooling model of semi-infinite half-space (Turcotte and Shubert 1982) with an initial potential temperature of 1,350°C (Parsons and Sclater 1977). Similarly, in order to reproduce the thermal condition beneath the Japan Sea, the geotherm for an oceanic plate of 7.5 Myr is used for the vertical boundary of the back-arc side, based on geothermometer with mantle-crust xenoliths Takahashi (1978). No heat conduction is assumed at the bottom boundary, whereas the surface is fixed at 0°C.
The boundary conditions concerning water are as follows: The top and left side of the box are permeable for fluid flow. For the subducting slab, the upper boundary allows permeable flow from the dehydrating slab and the water content on the oceanic side boundary is fixed, serving as a water source into the calculated system. The H2O content of the subducting oceanic crust is assumed to be 3 wt.% (Rüpke et al. 2004) but is assumed to be zero under the oceanic crust, i.e., a dry peridotite for the subducting lithosphere (Iidaka and Suetsugu 1992; Kawakatsu and Yoshioka 2011).
We set a constant trace element composition on the oceanic side boundary (as with water), which consists of oceanic crust composed of altered oceanic crust (Kelley et al. 2003) and a depleted MORB mantle (DMM) (Workman and Hart 2005). The mantle composition flowing into the wedge is also assumed to have a DMM composition, while we neglect the composition of the arc crust because chemical reactions within the arc crust are not considered in this model. Other boundaries are permeable in terms of the elemental fluxes associated with both solid and fluid flows.
Results and discussion
Water transport and melting
When the melt is generated, H2O is preferentially partitioned into it, up to 25 wt.% under PT conditions in the mantle wedge (Iwamori 1998). If melt extraction occurs, the H2O contained in the melt is also extracted from a rock packet, which increases the solidus temperature and suppresses subsequent melting of the rock packet. This suppression is seen in Figure 2d (the melting region (A) in Figure 2d), where melt is extracted along the nearly horizontal streamline (from left to right along the dotted lines in Figure 2d) consisting of an initially dry solid. No subsequent melting occurs along the streamline towards the wedge corner. Exceptionally, the rock packet melts when it is significantly hydrated within an aqueous fluid column with an H2O content of 0.2 wt.% (melting region (B) in Figure 2d). As will be shown later, the melt compositions in (A) and (B) of Figure 2d are distinct, reflecting the difference in the melting conditions: (A) exhibits a higher temperature, lower water content, and lower melting degree; and (B) has a lower temperature, higher water content, and higher melting degree. It is noted that the melting degree, which is not shown, differs from the information presented in Figure 2d, which shows melt fraction present in each rock packet. Considering the geometry of the streamlines (dotted lines in Figure 2d), (B) in Figure 2d corresponds to the remelting of the residue from the melting in (A) of Figure 2d, which results in the higher melting degree in (B).
In the additional file, we present an additional calculation in which we incorporate the effects of mantle depletion in the major elements, by integrating the melt extraction and by calculating the subsequent melting according to the degree of depletion. Additional file 1: Figure S1 shows that the overall melting structure remains essentially the same, even when the effects of mantle depletion in major elements are taken into account (cf. Figure 2c). The following discussions will therefore be based on the model results, without incorporating the ‘major element depletion effects’ as in Figure 2.
Trace element composition of magma
The other pattern is not smooth and consists of generally low abundances (orange lines in Figure 3), in particular the relative depletion of Nb and Ta and the relative enrichment of Rb, which reflects the higher degree of melting of a source that has been affected by both prior melt extraction and concurrent fluid addition in region (B) (Figure 2b). These melt compositions, as well as the direct inspection of fluid compositions in the numerical results, show that the aqueous fluids added to regions (A) and (B) are very diluted in terms of trace element abundances (except for the relative enrichment of Rb that affects the source region (B) where the overall trace element abundances in the solid have already been lowered by prior melt extraction). The reason for the extreme dilution of the aqueous fluids generated at point <3> of Figure 1 is investigated in detail below.
The thickness of the material boundary layer that absorbs a specific element depends on the concentration and the partition coefficient of the specific element. For example, Rb requires a thicker layer of 30 km in order to be absorbed, compared with that of Sr which requires a layer of 15 km in thickness. These material boundary layers absorb the fluid-mobile elements, resulting in no relative enrichment of elements, which characterizes the arc magmas, for the model melt (Figure 3). This leads us to consider that if fluid migration occurs in a chemical disequilibrium with the surrounding solid mantle, these elements could reach a melting region that fertilizes the resultant melt. Iwamori and Nakakuki (2013) demonstrate that the seismic velocity structures beneath the NE Japan arc, in terms of variability within the ΔVp-ΔVs relationship, correspond to the existence of a fracture system in the mantle wedge, and it is known that fluids in such a fracture system have a reduced contact area with the surrounding mantle, possibly resulting in chemical disequilibrium due to slow elemental diffusion in the solid (Iwamori 1993).
Although the model melts also show an abundance of heavy REEs (i.e., Y to Lu in Figure 5), these are lower than those of the observed range. The low abundances reflect the dominant involvement of garnet upon melting, because heavy REEs are preferentially absorbed into garnet (Green et al. 2000). In this model, the instantaneous melt extraction has been assumed (i.e., the chemical reactions between the melt and the solid during melt ascent have been ignored). If the melt that originated in the garnet stability field ascends with a continuous re-equilibration with the spinel peridotite at shallower depths, it is likely that the heavy REE depletion may be relaxed to some extent.
These similarities and differences in chemical compositions between the model melt and the actual lavas provide new insights as follows: The element transport in subduction zones sensitively reflects the PT condition (which controls the partition coefficients) and in order to explain the observed positive spikes of several key elements including Pb, the fluid liberated from the slab must deliver those elements to the melting regions without being significantly absorbed in the down-going mantle materials. We therefore suggest that a disequilibrium fluid transport system through channels exists, such as a fracture system in the wedge mantle. By improving the model assumption and our knowledge on the partition coefficients between fluid, melt, and solid phases, we strive to better understand the elemental cycling in subduction zones.
We are very grateful to Hitomi Nakamura, Jun-Ichi Kimura, Shyunsuke Horiuchi, and Morihisa Hamada for their considerable help in constructing the numerical model. We also thank Kenta Ueki and Masaoki Uno for their critical discussion.
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