Subduction and volatile recycling in Earth's mantle(Abstract Only)

Subduction and volatile recycling in earth’s mantleScott D. King and Joel J. Ita

Citation: AIP Conference Proceedings 341, 33 (1995); doi: 10.1063/1.48748 View online: http://dx.doi.org/10.1063/1.48748 View Table of Contents:

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Subduction and Volatile Recycling in Earth's Mantle

Scott D. King* and Joel J. Ita t

*Department of Earth and Atmospheric Sciences, 1397 CIVIL Purdue University, West Lafayette, IN ~7907-1397

t Seismological Laboratory, MS 252-21, California Institute of Technology 1 Pasadena, CA 91125

The subduction of water and other volatiles into the mantle fTom oceanic sediments and altered oceanic crust is the major source of volatile recycling in the mantle. Until now, the geotherms that have been used to estimate the amount of volatiles that are recycled at subduction zones have been produced using the hypothesis that the slab is rigid and undergoes no internal deformation after subduction. We consider the effects of the strength of the slab using two-dimensional calculations of a slab-like thermal downwelling with an endothermic phase change. Because the rheology and composition of subducting slabs are uncertain, we consider a range of Clapeyron slopes which bound current laboratory estimates of the spinel to perovskite plus magnesiowiistite phase transition and simple temperature-dependent rheologies based on an Arrhenius law diffusion mechanism. Phase tran- sitions can have two pronounced effects on subducting slab deformation and the resulting geotherms. First, an endothermic phase transformation can inhibit the vertical descent of the slab. If the slab is weak, this can lead to large deformation, even in the upper 200 km of the slab. Second, the phase transformation can slow the subduction velocity (and plate velocity) of the entire slab, a more pronounced effect than the slab deformation. Because the initial thermal structure of the descending lithosphere, the volatile content, and subduction velocity all affect the viscosity of the slab, it is likely that subduction zones may behave differently-some with more pronounced pile-up and avalanche periods and some where the subduction velocity is more uniform with time. These mechanisms create a highly uneven distribution of recycled components in the mantle within relatively short periods of time in Earth's history.

I N T R O D U C T I O N

The thermal s ta te of descending oceanic lithosphere plays a major role in the recycling of volatiles in the Ear th ' s mantle. Early thermal models of subduction zones sought to explain arc volcanism by producing enough heat to

1Presently at: Department of Earth and Atmospheric Sciences, Purdue University

�9 1995 A m e r i c a n I n s t i t u t e of Phys ic s 33



34 Subduc t i on a n d Volat i le Recyc l ing in E a r t h ' s M a n t l e

melt the crust at the top of the slab (e.g., (1)). It is now accepted that the temperatures at 100-150 km depth at the top of the slab are not sufficient to melt oceanic crust. However, the volatiles, mostly water driven out of hydrated minerals in the oceanic crust, interact with the hot mantle wedge to form the source melts for arc volcanism. These models use analytic or finite-difference solutions to model the thermal structure of the descending oceanic lithosphere at a uniform velocity. They generally make the assumption that heat is transferred down-dip only by advection and perpendicular to slab dip by pure conduction. Simple advection-conduction models, like those mentioned above, are still used in conjunction with dehydration reactions to understand the fate of water and other volatile components in the downgoing slab (e.g., (2,3)). While these models provide some guidance in our under- standing of the thermal state in and around subduction zones, there are two important limitations that must be considered when applying them.

First, the slab is forced to descend along a specific geometry by an imposed, external, uniform, velocity field and is not dynamically consistent with the density contrast between the cold slab and surrounding mantle. Because the velocity fields used in these models are often steady-state fields, these models may miss significant effects associated with the initiation of subduction or the time-dependence of plate motions. One dynamical mechanism that may produce strongly time-dependent plate velocities is the interaction of the subducting material and the phase transformations at 410 and 660 kilometers depth on the downgoing slab. The endothermic phase transformation of spinel to perovskite and magnesiowiistite inhibits the downward descent of the downgoing limb can can lead to a style of convection with periods of slow, uniform plate velocities as the subduction material collects above the phase transformation boundary. This quiet phase is interrupted by short periods with high plate velocities when the pool of cold, dense material becomes unstable and flushes into the lower mantle (e.g., (4,5)). As we will show, this has important consequences for the P-T path in a subduction zone.

The second limitation of the advection-conduction models is that they do not account for deformation within the downgoing slab. In previous models, the geometry of the flow is simple and the slab is assumed to behave rigidly. These models assume either a uniform velocity distribution or a corner flow solution, and these are assumed constant both in space and time. Folding, bending, thickening and thinning of the slab, all of which can alter its thermal structure, are not considered in the advection-conduction models. The rigid slab assumption is the opposite end-member of most constant viscosity mantle convection calculations (e.g., (4,5)). In constant viscosity convection calculations the slab has no greater, or lesser, strength than the surrounding mantle and, thus, as it subducts the slab deforms substantially. The Earth lies somewhere in between these two end-member views.

In this paper, we will explore the effect of temperature-dependent viscosity on the dynamics of convection in the presence of an endothermic phase change. While this topic has been studied in detail in several recent papers (6), we will focus our attention on the thermal structure of the downgoing limb in



S. D. King and J. J. Ita 35

an attempt to understand the slab geotherm (i.e., the pressure-temperature- time paths of subducting material). To understand the first-order effects of temperature-dependent viscosity on the dynamics of convection in the presence of an endothermic phase transition, we consider a model with one phase transition (to represent the 660 km discontinuity) at one-half the depth of the box. The effect of the exothermic reaction of olivine to spinel at 410 km depth appears to weaken the effect of the 660 km phase transformation (e.g., (5)). Thus, including only one phase transformation we can capture the first-order effects of the phase transformations on subduction. Because we focus on the geotherm in the upper 300 km of the slab, the complexities of the transition zone probably have little influence, to first-order, on our results. While ig- noring many of the complexities in a subduction zone environment, such as thrust faults, viscous heating, and dehydration reactions, our model allows us to concentrate on the effect of slab rheology in a model that is driven by the density contrast between the slab and the mantle in a self-consistent manner. We will calculate geotherms through the subduction zone from these calculations to address the impact of mantle layering on subduction geotherms, something that the advection-conduction models with an imposed flow have not addressed.

EQUATIONS A N D METHOD

We use a modified version of the two-dimensional, Cartesian, finite element convection code ConMan, described in Ref. (7). We incorporate spinel- perovskite phase transformation using a method similar to that in Ref. (8) which includes the effect of latent heat released from the major endothermic phase transformation. We do not include the effect of the latent heat of the metamorphic dehydration reactions. Ref. (2) demonstrates that these have an almost negligible effect on the temperature of the slab. Further details on this formulation can be found in Ref. (9).

The phase transformation occurs, on average, at a normalized depth of 0.5. If our results are scaled such that the phase transition is half completed at 660 km depth, the phase transition would occur over a 70-km depth range. This was done to minimize the computational expense and to allow the highest possible resolution, without a highly irregular grid, around the phase transformation. The Clapeyron slope and density change associated with the phase transition are incorporated through the nondimensional phase buoyancy parameter, P, such that

p = TAp ~v~gh' (1)

where 7 is the Clapeyron slope, Ap is the density change across the transition, po is the reference density, a is the thermal expansivity, g is the force of gravity, and h is the depth of the box. In the following calculations, Ap is fixed at 0.35 Mg/m 3. This value is consistent with seismically inferred mantle density models (10). Thus, P will measure the change in the Clapeyron slope.



36 Subduction and Volatile Recycling in Earth's Mantle

0.0

0.2

0.4

~0.6 /

0 . 8 ~ /

1.O V 10 o

V I I llllll I I I l t l l l l I I I I I I I I I

101 10 2 10 3

Rela t ive Viscos i ty FIG. 1. Viscosity laws used in this study from Equation 2; solid line - uniform viscosity, long dash - weakly temperature-dependent (E* = 1.0), medium dash - moderately temperature-dependent (E* = 2.0), short dash - strongly tempera~ ture-dependent (E* = 3.0)

We use an Arrhenius form for the temperature-dependent part of our viscosity law:

7(0) = 7" exp O + To 1.0+ To (2)

where 7" is the normalized pre-exponential viscosity, y(e) is the effective viscosity, e is the dimensionless temperature, E* is the activation energy divided by RAT, where AT is the temperature scaling factor (for reference E* ~ 6 for olivine if AT ~ 3000~ To is the temperature offset; a temperature offset is needed because when ~ = 0, the first term becomes singular. The second term in the exponential scales ~?(O) such that 7(1.0) = 7*. The viscosity pro- files used in this investigation resulting from this functional form are shown in Figure 1.

The calculations are performed in a 4 by 1 box with free-slip bottom and reflecting boundary conditions on the sides. On the top, the majority of the surface is free-slip, but several nodes are pinned at the far right-hand side of the box to keep the boundary layer on the right side of the trench immobile. This helps to create an asymmetry in the downwelling at the trench. For all the problems we consider here, the grid size is 384 by 96 uniformly spaced elements. Temperature boundary conditions along the top and bottom are

= 0.0 and 0 = 1.0, respectively. Internal heating is incorporated in the model with approximately 50% of the heat flux at the surface coming from the bottom of the box. All calculations used the same initial condition, a 4 by 1 box with a downwelling in the center and no phase transition. Because




TABLE I. Physical Properties

Symbol f Name Value po density 3.5 x 10 a kg/m ~ h depth 1340 km go magnitude of gravity 10 m/s 2 AT temp. drop across h 1600 ~ ~o thermal diffusivity 1 x 10 -s m2/s C~o thermal expansivity 3 x 10-S~ -1 yo viscosity 1022 Pa-s

tSubscript o refers to the value of the variable at the upper surface.

we use several temperature-dependent viscosity laws, it is difficult to specify an exact Rayleigh number. We attempted to keep the logarithmic volume averaged Rayleigh number as close as possible in all of our calculations. The volume averaged Rayleigh number for each calculation is within the range 2 • 105 - 4 • 105 based on the reference values shown in Table 1.

To create plate-like surface velocities, we impose weak zones at the trench and ridge (11). This is accomplished by reducing the pre-exponential term, ~* in equation (2) in a specific geometric zone of the computational domain to a value denoted by the variable Y~z. In these calculations, the weak zones are located at the upper left hand corner of the box, the model spreading center, and at the top center of the box, the model trench. In the upper left hand corner, the weak zone is 3 by 3 elements. The weak zone at the top center of the box is 9 by 20 elements. In the constant viscosity models, we used a two element thick high viscosity layer across the top between the weak zones to enforce the piecewise uniform velocity.

R E S U L T S

In uniform viscosity convection models, subducted material collects above the phase transformation boundary until the pool of cold, dense material becomes gravitationally unstable and sinks into the lower mantle. This style of convective motion has been observed in both 2-D and 3-D calculations in spherical and Cartesian geometries (e.g., (4)). Figure 2 illustrates the effect on the downgoing limb of increasing the Clapeyron slope of the phase change (increasing the phase buoyancy parameter). From the contours of temperature, it is clear that for the weakest phase change (P = -0.19 or q = -3 .0 MPa/~ the downgoing limb penetrates the phase change with little or no deformation, while for the stronger phase changes, (P = -0.29 or 7 = -4 .5 MPa/~ and P = -0.39 or 7 = -6 .0 MPa/~ the downgoing limb is strongly deflected along the phase transformation boundary. The surface velocities also decrease systematically with the increasing magnitude of the Clapeyron slope. As the slope varies from -3 .0 MPa/~ to -4 .5 MPa/~ to -6 .0 MPa/~ the surface velocity decreases from approximately 450 mm/yr to 325 mm/yr to 150 mm/yr respectively (see Figure 2).




F I G . 2. Temperature contours and surface velocities from three constant viscos- i ty plate models with varying phase buoyancy parameters (Clapeyron slope); a) P = -0 .19 or 7 = 3.0 MPa /~ b) P -- -0 .29 or 7 = - 4 . 5 MPa/~ c) P -- -0 .39 or 7 -- - 6 . 0 MPa /~ Pla te velocities are in ram/yr .



S. D. K i n g a n d J. J. I ta 39

300

i !

250 /

200 /

~ 150 / / /

100 "- / " ' " / /

0 / " ~ i I I I i J i 0 200 400 600 800

T e m p e r a t u r e

FIG. 3. Slab geotherms from the from the temperature fields shown in Figure 2; solid line - P -- -0.19 or 7 = 3.0 MPa/~ short dash - P = -0.29 or 7 = -4.5 MPa/~ long dash - P = -0.39 or 7 = -6.0 MPa/~

From the calculations in Figure 2, we can construct 'slab' geotherms. Be- cause these are incompressible calculations, there is no adiabatic temperature gradient. We compensate for this by adding a 0.3 ~ gradient to the temperature fields from these calculations. Because the subduction is one- sided (from the velocities in Figures 2a-2c the right hand side of the box has a zero surface velocity), to a first approximation the top of the slab will co- incide with the coldest temperature. This is not exactly correct because, as the cold top of the slab comes in contact with warm mantle, the top of the slab will heat up by diffusion and the coldest part of the slab will migrate inwards as a function of depth (time). Because the time interval of these calculations is short compared to the diffusion time, the coldest part of the slab will be within 10 km of top of the slab. This is smaller than the grid resolution of our calculations. Figure 3 illustrates the "slab" geotherm for the three temperature fields shown in Figure 2. From Figure 3 it is clear that in addition to its effect on the deep structure of the slab (i.e., whether or not the slab penetrates the phase transformation), the phase boundary influences the shallow temperature structure of the slab. For this particular choice of parameters, the temperature at 150 km depth increases by 250 ~ when the Clapeyron slope varies from -3.0 MPa/~ to -6.0 MPa/~ We also note the negative correlation between surface or "plate" velocity and slab geotherm; as the velocity increases, the slab geotherm decreases. This agrees with previous work (2,3).




FIG. 4. Temperature contours and surface velocities from three temperature-dependent plate models with P = -0.39 or 7 - -6.0 MPa/~ a) constant viscosity b) weakly temperature-dependent viscosity c) strongly temperature-dependent viscosity. Plate velocities are in ram/yr.




300 -

250

200

150 q~

100

50

/ ,,'/ / , ' /

/ ,,,,'/ / / , , , / /

~ I I I I I i 0 I

0 200 400 600 800 T e m p e r a t u r e

FIG. 5. S l~ ~otherms #ore the #ore the t empe ra t e fields shown in Fig~e 4; solid line - we~ slab, short d~h - i n t e r m e ~ e sl~, long d~h - ~rong sl~.

Choosing one phase buoyancy parameter (P = -0.39 or 7 = -6.0 MPa/~ we now investigate the influence of viscosity on the structure of the downgoing limb in the presense of a phase transformation. These calculations are shown in Figures 4a-4c. It is important to note that the thickness of the downgoing limb in the center of the box near the surface is noticeably different for each calculation (Figure 4). In Figure 4a, the downgoing limb is thinner than the thermal boundary layer on the upper left-hand side prior to subduction. In contrast, the downwelling in Figure 4c is about the same thickness as the plate. This is because as the strength of the temperature- dependent viscosity increases, the maximum depth of the stiff portion of the slab increases. For the constant rheology case shown in Figure 4a, the viscosity of the slab and the surrounding fluid are almost identical. In the weakly temperature-dependent case (Figure 4b), again, the deeper part of the slab is still approximately the same viscosity as the surrounding fluid. In the strong viscosity case, (Figure 4c), the viscosity of the slab is ten to thirty times the background viscosity. In this case, a noticeable contrast between the slab and the background fluid persists over the entire depth extent of the slab. Thus, while the viscosity law acts over the entire fluid, the major effect of changing the viscosity law is to change the strength of the deep slab.

We can again construct slab geotherms from these temperature fields. We follow the same procedure we used in constructing the geotherms in Figure 3; adding a 0.3 ~ gradient to the temperature field and using the coldest temperature of the slab as the approximation for the top of the slab. The slab geotherms for the fixed phase buoyancy parameter and varying viscosity



42 S u b d u c t i o n a n d Volati le Recyc l ing in E a r t h ' s M a n t l e

structure are shown in Figure 5. The effect of theology on the slab geotherms is as strong as the effect of the Clapeyron slope illustrated in Figure 3. There is approximately a 250 ~ temperature difference between these three models at 150 km depth. The strong slab is thicker and the interior of that slab is colder than the weak and constant viscosity slabs which appear to thin significantly while subducting.

When we consider the surface velocity, we find that it decreases by a factor of two when the viscosity model varies from constant or weakly temperature- dependent to strongly temperature-dependent. This means that the slab geotherm decreases with decreasing plate velocity. Thus, for this value of the Clapeyron slope, variations in rheology lead to a positive correlation between plate velocity and slab geotherm; as the plate velocity increases, so does the slab geotherm. Note that this is the inverse of the relationship we found in models in which the theology was held Constant and the Clapeyron slope varied. This arises from the fact that increases in velocity brought on by variations in rheology are accompanied by increases in internal deformation of the slab. Not surprisingly, this is not observed in the simple advection-conduction models because they proscribe the style of slab deformation a priori.

The difference in slab geotherm between the different theologies is most pronounced in the cases where the magnitude of the Clapeyron slope is large enough to effectively stop the cold, downgoing slab from penetrating the phase transformation. In cases where the Clapeyron slope is smaller, the results from the four theologies look much more similar, so the case in Figure 4 should be considered as an end-member case. In Figure 4a and to a lesser extent in Figure 4b, the layering of the phase change sets up a small scale convection cell near the slab (notice the thinning of the isotherms just to the left of the slab). This small scale circulation enhances the larger plate scale circulation and is responsible for thinning of the slab.

If we had created a subduction zone using a narrow fault, rather than a broad weak zone, it is possible that the deformation would have been less dramatic in the weak and constant viscosity cases; however, a recent study suggests that the effect of viscou s dissipation in temperature-dependent fluids may be significant enough to increase the temperature of the slab by as much as several hundred degrees (12). Because the region of greatest deformation coincides with the weak zone in our models, the weak zone provides the effect of viscous dissipation on the rheology (but not the temperatures). The importance of the slab rheology and parameterization of the plate on mass transport across the phase transformation are discussed in greater detail in (6).

CONCLUSIONS

While simple analytical models of can provide limited insight into the thermal structure of subduction zones, these simple models do not account for the effect of the 410 and 660 km phase transformations on subducting slabs. If the 660 km discontinuity does act as a barrier to convection, and subducted



S. D. King and J. J. I t a 43

slabs are slowed and deformed in the upper mantle, then these simple models could underestimate the temperatures of the shallow slab by up to several hundred degrees. However, it is important to note that the range of slab geotherms we have presented are all within the range of geotherms presented from the advection-conduction models with various plate velocities. This is not surprising in light of the fact that in a fully dynamic calculation with temperature-dependent rheology and an endothermic phase transformation, the slab geotherm is highly correlated with the plate (and thus slab) velocity. However, the nature of this correlation is dependent upon the choice of parameters selected as we demonstrate above. Thus it is not clear that the variation in geotherm with plate velocity seen in the kinematic models is representative of that in the Earth.

The time-dependent nature of plate motions also has an important effect on slab geotherms. While we don't have the space to discuss it in detail, we can make the following observation: during the pile-up period, the slab geotherm is characteristic of geotherms produced by steady-state slab models with slow plate velocities; however, during the avalanche period, when the material that has been stored above the phase change begins to flush into the lower mantle, the subducting slab geotherm approaches the geotherms from steady- state models with fast velocities. The difference between the subducting slab velocities of the two periods (the pile-up period and the avalanche period) decreases with increasing viscosity of the slab.

We also draw attention to the fact that the temperature-pressure curves presented in this paper should be treated with great caution. Because these calculations are incompressible and are performed at a grid resolution of 10's of kilometers, they should not be used to evaluate subduction zone chemistry in detail. What they do illustrate is that the effects of slab rheology and the 660 km phase transformation can significantly alter the P-T path of the shallow slab, but this seems to be primarily in the case where the Clapeyron slope is large enough to strongly layer the flow. Neither rheology or phase transformations are accounted for in the simple models currently used to make inferences on dehydration reactions in slabs; however, the isotherms from the strong temperature-dependent viscosity slab look much more like the advection-conduction models than the weak viscosity models do. Thus, our results are in agreement with the general characterists of the advection- conduction models except for weak viscosity slabs with strong phase changes. If slabs are truly weak and the phase change strongly layers the flow, then the advection-conduction models may underestimate the deformation in the slab and underestimate the temperature in the slab.

This directly impacts the amount of volatiles being recycled back into the mantle. Weak slabs and/or strongly layered flows will lead to high slab geotherms and a shallow devolatilization of the subducting lithosphere. Whereas, strong slabs and/or weakly layered flows will lead to lower slab geotherms and and a deeper emplacement of volatile materials. It is very probable that the characteristics of subduction zones are spatially and tem- porally dependent and the resulting concentration of volatiles within the Earth




will not lend itself to a simple analysis.

ACKNOWLEDGMENTS

We gratefully acknowledge support from NSF grants EARo9218621 and EAR-9206036. JI also acknowledges support from NSF grant EAR-9218390. Reviews by S. Peacock and an anonymous reviewer noticeably improved the manuscript.

REFERENCES

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2. S. Peacock, Tectonics 9, 1197 (1990). 3. H. Standigel and S. D. King, Earth Planet. Sci. Lett. 109, 517 (1992). 4. S. Honda, S. Balachandar, D. A. Yuen, and D. Reuteler, Science 259, 1308

(1993); P. J. Tackley, D. J. Stevenson, G. A. Glatzmaier, and G. Schubert, Nature 3{il, 699 (1993).

5. P. J. Tackley, D. J. Stevenson, G. A. Glatzmaier, and G. Schubert, J. Geophys. Res. 99, 15877 (1994).

6. S. Zhong, and M. Gurnis, J. Geophys. Res. 99, 15903 (1994); S. D. King and J. J. Ita, J. Geophys. Res. Submitted, (1995).

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8. F. M. Richter, Rev. Geophys. Space Phys. 11, 223 (1973). 9. J. J. Ita and S. D. King, J. Geophys. Res. 99, 15919 (1994).

10. A. M. Dziewonski and D. L. Anderson, Phys. Earth Planet. Int. 25, 297 (1981). 11. M. Gurnis and B. H. Hager, Nature 335, 317 (1988); G. F. Davies, Geophys. J.

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Subduction and volatile recycling in Earth's mantle(Abstract Only)

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