G 3. AN ELECTRONIC JOURNAL OF THE EARTH SCIENCES Published by AGU and the Geochemical Society

Geosystems G 3 AN ELECTRONIC JOURNAL OF THE EARTH SCIENCES Published by AGU and the Geochemical Society From rift to drift: Mantle melting during continental breakup Thomas K. Nielsen Danish Lithosphere Center, Øster Voldgade 10 L, DK-1350 Copenhagen K, Denmark Now at Maersk Olie og Gas A/S, Esplanaden 50, DK-1263 Copenhagen K, Denmark (tkn@maerskoil.dk) John R. Hopper Danish Lithosphere Center, Øster Voldgade 10 L, DK-1350 Copenhagen K, Denmark Article Volume 5, Number 7 30 July 2004 Q07003, doi:10.1029/2003gc000662 ISSN: 1525-2027 Now at IFM-GEOMAR/Leibniz Institute for Marine Science, Wischhofstrasse 1-3, Geb. 8/D, D-24148 Kiel, Germany ( jhopper@ifm-geomar.de) [1] Volcanic rifted margins show a temporal evolution in igneous crustal thickness and thus provide additional insights into mantle dynamics compared to the steady state situation at mid-ocean ridges. Although details between different provinces vary, volcanic rifted margins generally show a short-lived pulse of extreme magmatism that quickly abates to a steady state mid-ocean ridge. The generation of thick igneous crust at volcanic rifted margins requires either melting of hot mantle material to higher degrees than observed at mid-ocean ridges or melting of larger amounts of mantle material than would be the case for plate-driven upwelling. To assess under what conditions buoyantly driven upwelling or small-scale convection at rifting plate boundaries is important, a fluid dynamical model with non-newtonian viscosity that includes the feedback from melting on the physical properties of the mantle is developed. To generate a pulse of high magmatic production requires a viscosity and density structure that also leads to excessive fluctuations in magmatic productivity or a sustained high productivity that continues long after breakup. A viscosity increase due to dehydration caused by melting effectively suppresses buoyant upwelling above the depth to the dry solidus, thereby restricting shallow flow to plate-driven upwelling. While this stabilizes the time dependence and forces the productivity to values consistent with mid-ocean ridge accretion, it does so at the expense of eliminating the breakup instability. Models that assume an abrupt change in prerift lithospheric thickness suffer from the same deficits. However, including a sublithospheric hot layer leads to a model that can predict the temporal evolution of igneous crustal thickness observed in refraction seismic data from the southeast Greenland volcanic rifted margin. Components: 12,940 words, 15 figures, 1 table. Keywords: edge convection; mantle convection; mantle melting; North Atlantic; volcanic margin. Index Terms: 8109 Tectonophysics: Continental tectonics extensional (0905); 8120 Tectonophysics: Dynamics of lithosphere and mantle general. Received 7 November 2003; Revised 26 March 2004; Accepted 3 May 2004; Published 30 July 2004. Nielsen, T. K., and J. R. Hopper (2004), From rift to drift: Mantle melting during continental breakup, Geochem. Geophys. Geosyst., 5, Q07003, doi:10.1029/2003gc000662. 1. Introduction [2] New igneous crust is formed from decompression melting of upwelling mantle material, which is caused by tectonic processes or by buoyancy of the upwelling material [White et al., 1992]. Models of passive plate-driven upwelling of presumably normal temperature mantle successfully predict the crustal thickness produced at mid-ocean ridges Copyright 2004 by the American Geophysical Union 1 of 24

[McKenzie and Bickle, 1988]. In passive upwelling models, variations in crustal thickness are produced by variations in asthenospheric temperature [e.g., White, 1997]. This relation between crustal thickness and mantle temperature has been used to infer that the thick basaltic crust generated at volcanic rifted margins results from melting of mantle with anomalously high temperatures [McKenzie and Bickle, 1988; White and McKenzie, 1989]. However, high magmatic productivity can also result from an enhanced flux of mantle material through the melting region so that the upwelling rate exceeds that produced by diverging plates. Recent models have shown that upwelling of a 1500 C mantle plume with velocities 10 times higher than expected for plate-driven flow near the base of the melting region is consistent with observations of crustal thickness and composition in central Iceland [Maclennan et al., 2001]. This result is also in agreement with upwelling rates in fluid dynamical models of a ridge-centered hot plume and viscosities that depend on the amount of water in olivine [Ito et al., 1996, 1999]. Thus there is an emerging consensus that deep buoyant upwelling as well as a modest increase in temperature is responsible for the melting anomaly associated with volcanism on Iceland, although chemical heterogeneities may also play a role [e.g., Korenaga and Kelemen, 2000]. [3] Many volcanic rifted margins have an igneous crustal thickness comparable to that of Iceland. It is tempting to view these margins as transient counterparts to the steady state plume upwelling scenario near Iceland and assume that the governing processes are the same. However, the large lateral extent of many of these margins and the existence of volcanic margins well away from any known hot spot have led many to propose alternatives where excess volcanism is intrinsic to the dynamics of the rifting process itself [e.g., Mutter et al., 1988; Hopper et al., 1992; Holbrook and Kelemen, 1993; King and Anderson, 1995]. In particular, Mutter et al. [1988] propose that buoyant active upwelling, or small-scale convection, could result from lateral temperature gradients associated with a narrow necking region during breakup. This would allow greater amounts of mantle to be fluxed through the melting region, generating significantly more melt than passive upwelling alone even without a mantle temperature anomaly. However, numerical models of small-scale convection during rifting and breakup have had only limited success in producing key aspects of volcanic rifted margins. Models of narrow necking regions [Keen and Boutilier, 1995] and of convection near steep lithospheric boundaries [King and Anderson, 1995, 1998] show high upwelling rates and small-scale convection. Although anomalous magmatic productivity has been inferred, these models do not include melting and it is not evident that the high upwelling rates reach shallow enough depths to produce volumetrically significant amounts of melt. In addition, it is not clear that the required timescales of transient high magmatic productivity at volcanic rifted margins can be simulated. More recent models that include estimates of melting show that high upwelling rates can produce melt anomalies, but this is at the expense of excessive temporal variations in crustal thickness produced after breakup [Boutilier and Keen, 1999]. A viscosity increase due to dehydration caused by melting was suggested as a mechanism that can stabilize the flow and reduce the fluctuations in upwelling velocity after the first pulse of magmatism [Boutilier and Keen, 1999]. The creation of such a compositional lithosphere is now generally accepted for mid-ocean ridge studies and has a fundamental effect on ridge dynamics by influencing both the buoyancy and viscosity structure of the mantle at the ridge axis [Hirth and Kohlstedt, 1996; Phipps Morgan, 1997; Braun et al., 2000]. However, in the continental rift models of Boutilier and Keen [1999], this effect could not be studied directly since the feedback of melting on the physical properties of the mantle was not included in a self-consistent way. [4] In this contribution, we use a fluid dynamical model with non-newtonian viscosity to explore how melting induced changes in the physical properties of the mantle affect flow of the solid mantle during continental breakup. This allows us to assess the conditions under which small-scale convection during continental breakup is important for the formation of volcanic rifted margins. A fundamental guiding principle is that a successful model should be consistent with what is known from mid-ocean ridge studies. To understand the dynamic processes operative during volcanic margin formation, a model that can produce a significant melt anomaly that naturally evolves into a plate-driven, passive mid-ocean ridge accretion system is required. Model predictions of magmatic productivity through time are compared with seismic data from the southeast Greenland volcanic rifted margin that constrain igneous crustal thickness as a function of time and distance from the Iceland plume track [Holbrook 2of24

Geosystems G 3 nielsen and hopper: mantle melting 10.1029/2003GC000662 et al., 2001; Korenaga et al., 2000; Hopper et al., 2003]. 2. Model Formulation 2.1. Governing Equations [5] The mantle is treated as an incompressible fluid with infinite Prandtl number and the Boussinesq approximation is used. The deviatoric stress tensor t is defined as t ¼ 2h_e pi; where I is the identity matrix, h is viscosity, p is pressure, and _e is the strain rate tensor. The viscosity function is described in detail later. The strain rate tensor depends on spatial derivatives of mantle flow rate u according to _e ij ¼ 1 @u i þ @u j : ð2þ 2 @x j @x i ð1þ Mantle convection is then governed by conservation of mass, momentum and energy: ru ¼ 0 ð3þ rt ¼ DrðT; X ; fþg~z ð4þ @T @t ¼ kr2 T u rt TDS _M; ð5þ c p where Dr is a density anomaly, g is gravity, T is temperature, k is thermal diffusivity, DS is entropy change due to melting, M is melt fraction, c p is specific heat, f is the mantle porosity, which can hold retained melt, and X is the concentration of a perfectly compatible element and parameterizes the amount of mantle depletion. Equation (3) satisfies the Boussinesq equation and neglects dilatational flow due to the mass transfer related to melting, since the effect on the solid mantle flow is assumed to be small. More complete formulations where the divergence is equated to the melting rate show that this assumption is justified to study first order effects [Cordery and Phipps Morgan, 1993; Turcotte and Phipps Morgan, 1992]. The density variation depends on temperature, depletion, and retained melt according to Dr ¼ r 0 ðat þ bf þ gfþ; ð6þ where r 0 is the mantle reference density, a is the coefficient of thermal expansion, F is the mantle depletion factor (F =1 1/X [see Scott, 1992]) and b and g are defined below. [6] Equations are nondimensionalized in the usual way: x ¼ dx 0 ; t ¼ d2 k t0 ; T ¼ T d T 0 ; h ¼ h 0 h 0 ; ð7þ where d is the height of the box, h 0 is the scaling viscosity, and T d is the super-adiabatic temperature drop from the base to the top of the box. Constant thermal diffusivity is assumed. Dropping the primes, equations (3) and (4) become rt ¼ r 0gd 3 kh 0 ru ¼ 0; The thermal Rayleigh number is ð8þ ðat d T þ bf þ gfþ: ð9þ Ra ¼ r 0gaT d d 3 kh 0 : ð10þ Additional buoyancy terms are parameterized by and b ¼ r 0 r Xref r 0 ðx ref 1Þ ð11þ g ¼ r 0 r m r 0 ; ð12þ where r Xref is the density of residual mantle that has been melted by a reference amount prescribed by X ref, and r m is the melt density. The nondimensional energy equation becomes @T @t ¼r2 T u rt þ G ð13þ where G is the change in nondimensional temperature from melting. 2.2. Viscosity [7] Olivine is the most abundant mineral in the upper mantle and it is therefore commonly assumed that mantle rheology is dominated by that of polycrystalline olivine [Karato and Wu, 1993]. Neglecting effects from variable grain size, the viscosity can be written as h ¼ c H2Oc m A exp E þ pv nrt A _e ð1 nþ=n ð Þ ð14þ 3of24

where c H2 O and c m are the viscosity changes due to dehydration and melting, A is a rheologic parameter, E and V are the activation energy and volume respectively, R is the gas constant, T A is the absolute temperature, and n is the stress exponent. At the beginning of each calculation, we specify a scaling viscosity, h 0, and set A according to a reference state given by T A = 1598 K and _e =1 10 15 s 1, and a depth of 100 km. This gives rheologic parameters consistent with Karato and Wu [1993] but allows us to easily vary a single parameter to test relatively stronger or weaker reference states. [8] Major rheological changes occur due to the extraction of water from olivine. Water has long been known to weaken olivine [Chopra and Paterson, 1984] and recently the effect has been quantified by Hirth and Kohlstedt [1996] and Mei and Kohlstedt [2000a, 2000b]. Experiments show that at 0.3 GPa the viscosity of a water saturated aggregate is reduced by a factor of 100 compared to dry olivine [Hirth and Kohlstedt, 1996]. The strong partitioning of water into melt implies that small amounts of deep melting below the dry solidus will dry out the solid mantle and increase the viscosity. Calculations show that nearly all the water is extracted with 2% melting, leading to the full viscosity increase [Hirth and Kohlstedt, 1996]. The effect is included through the function c H2 O that changes linearly from 1 to 10 as a function of hydrous melting below 2% of melting. After 2% of melting, mantle material is rapidly dehydrated and the viscosity is then increased by a total of two orders of magnitude (c H2 O = 100) [Hirth and Kohlstedt, 1996]. [9] The presence of melt counteracts this strengthening effect by enhancing creep and reducing the viscosity. Melt may also inhibit grain growth and thus the dynamically recrystallized grain size in the mantle may decrease with the onset of melting. The grain size effect, however, is not well constrained [Hirth and Kohlstedt, 1995a, 1995b; Kohlstedt and Zimmerman, 1996]. The meltinduced reduction in viscosity is modeled by the relationship c m ¼ expð afþ; ð15þ where a is an empirical constant between 30 and 50. Here, a = 45, which fits well with experimental data in both the dislocation and diffusion creep regime [Kelemen et al., 1997]. Assuming 2% melt, this yields c m = 0.4. This factor of 2 reduction in viscosity, while important, is thus small compared to the two order of magnitude increase due to dehydration at the same amount of melting. [10] Deformation in the shallow continental mantle lithosphere and crust is not included in the results shown. However, studies of models that simulate brittle failure in the crust and cold lithosphere by pseudo-plastic yielding [e.g., Christensen, 1992] have shown that the larger-scale mantle flow may be relatively insensitive to crustal deformation. To keep the first generation of models simple, this effect is ignored for now and the continental lithosphere is treated as a high-viscosity, buoyant lid. [11] The resulting viscosity profile for a typical steady state spreading condition assuming h 0 = 9 10 20 Pa s is shown in Figure 1. The viscosity below the wet solidus depends on temperature, pressure and strain rate. Between the wet and the dry solidus, the competing effects of dehydration strengthening and melt weakening are similar in magnitude with the strengthening effect dominant at the base of the melting column. After the dry solidus is reached, the total extraction of water causes a sudden increase in viscosity that is subsequently counteracted by the increasing amount of melt until the maximum depletion is reached. At this point melt productivity vanishes and the viscosity increases further due mainly to the rapidly decreasing temperature. 2.3. Melting [12] Melt productivity is computed at each time step and here we followed the method outlined by Scott [1992]. The approach is similar to that of Ito et al. [1996] and similar equations are derived by Phipps Morgan [2001] except that in these later studies, melting is parameterized with melt depletion factor F =1 1/X. The approaches are all equivalent, however. Melting constrains the temperature in the partially molten region to the solidus [e.g., Scott, 1992]: T RM ¼ T M0 þ @T M @z z þ X @T M @X ðx 1Þ; ð16þ where T RM is the solidus temperature, T M0 is the solidus temperature at the surface, and X is the concentration of a perfectly compatible trace element in the solid, i.e., X = 1 for unmelted mantle and X increases as melting progresses. This z 4of24

Figure 1. Vertical profiles of physical parameters computed for a typical model of steady state spreading, including melting effects on viscosity, which are included in models M8 M12, M15, and M16. Reference viscosity of 9 10 20 Pa s is used. (left) Wet and dry solidus (dotted lines) and the effect of melting on temperature and the resulting melt present (solid lines). (middle) Viscosity profile showing the competing effects of pressure, temperature, dehydration, and melt. (right) Melt productivity (dotted line) and depletion (solid line). is changed to potential temperature by correcting for the adiabatic temperature change @T ¼ gat R @z S c p @T M T M ¼ T M0 þ @T @z X @z S z þ @T M @X z ð17þ ðx 1Þ: ð18þ The @T M /@X term accounts for the change in solidus temperature as a function of the amount of depletion. Essentially, the more depleted the mantle, the more difficult it is to melt and the solidus temperature is modified accordingly. In each time step, changes in the variables due to advection and diffusion are first calculated. For super-solidus temperatures the amount of melting is Composition, or depletion, is found by @X @t ¼ urx þ X M; 1 f _ ð22þ where the melting rate, _M, is determined by the amount of melt produced at each time step. The first term on the right hand side simply tracks the solid mantle flow and the second term accounts for irreversible changes in composition due to extraction of melt. For unmelted mantle, the wet solidus is used initially. The change in solidus temperature with depletion is adjusted linearly so that the dry solidus is reached after 2% melting [e.g., Braun et al., 2000]. Following Ito et al. [1996], the average extent of melting is found by weighting the degree of melting in each model cell by its melting rate. Igneous crustal thickness h c can then be estimated by assuming that all melt in a plane perpendicular to the ridge is focused to and accretes at the axis: where and df ¼ T T M L þ @T M @f @T M @f ¼ X @T M 1 f @X ; ð19þ ð20þ L ¼ T M DS c p : ð21þ h c ¼ 2 Z Z r 0 u x r m _Mdxdz: ð23þ However, not all melt is necessarily focused and extracted at the ridge and thus the equation provides an upper limit of the crustal thickness. 2.4. Method and Boundary Conditions [13] The equations are solved with a multigrid finite element method [Moresi and Solomatov, 1995]. The code is a modified version of CITCOM, which is rigorously tested [e.g., Moresi et al., 5of24

1996] and is now in wide use. A key advantage to CITCOM is that is written with a modular approach and only a few modules were rewritten to address the problems studied here. The flow solver, advection, integration, matrix assembling, and interpolation routines were not changed. The viscosity, buoyancy, and melting routines were modified according the formulation outlined above. Viscosity is calculated at every velocity integration point within each element according the viscosity function described earlier. The new functions were validated by running tests where the parameters give a viscosity structure identical to the unmodified CITCOM code and verifying that the new version generated the same result. Similarly, modifications to the buoyancy functions were made and tested by comparison to the unmodified code. Tests of the melting functions were performed by running models with parameters appropriate for mid-ocean ridges and comparing the steady state flow field and melt productivity to previous studies to verify that we obtained a good match (described further below). [14] The model box represents the upper mantle and includes a rift that develops into a spreading center (Figure 2). The sides of the box are reflective boundaries and there is no lateral flow of heat or material across these boundaries. The base of the model box is a closed no-slip surface. The temperature is fixed at 0 C at the surface and T ref at the bottom and @T/@x = 0 at the sides of the box. In terms of realistic earth models, some of these boundary conditions are questionable, in particular the side boundaries away from the upwelling region. For this reason, the bottom boundary and the side boundary away from the rift are placed distant from the rift/ridge corner where melting occurs. Thus the behavior of the region of interest in this study is considered to be largely independent of assumptions about these boundary conditions. Table 1 shows a list of the basic variables and assumed values. [15] The box is 700 km deep, extends 2800 km laterally and is defined by 256 256 elements unless noted otherwise. We tested the resolution by repeating some calculations with different grid sizes. For the solid flow field without melting, models with only 128 128 elements were indistinguishable from the denser grid, but problems arose on the coarser grid when melting was included. Adequate resolution of the melting region is a major challenge, especially to begin to link convection codes to detailed geochemical observations and experiments. Here, only first order effects are considered, in particular estimates of the total volume of melt produced for comparison to volcanic margins. We tested some models by repeating experiments at 512 512 elements and in terms of the predicted crustal thicknesses produced, differences of only a few percent were noted. [16] Two basic types of models are considered (Figure 2). In the first type, convection is forced by driving the top boundary horizontally at a constant velocity. The velocity tapers to zero at the corners. Symmetry is assumed and only one side of the rift is considered. The lithosphere close to the rift is prethinned when the model is started, similar to the initial conditions of Boutilier and Keen [1999]. To test the sensitivity of the results and conclusions to the initial condition, model runs that begin with an initially flat lithosphere were also run. Compositional differences that exist in a continental crust and lithosphere are not fully considered, but to simulate continental rifting, the initial lithosphere is assumed to be depleted and thus compositionally buoyant and more viscous than ambient mantle at the same temperature. In the second type of model, free convection that develops in response to sharp changes in a lithospheric thermal boundary are considered, similar to the class of models studied by King and Anderson [1995]. This so-called edge-driven convection has never been tested with a model that includes melting. In a final set of tests, rifting at such a boundary is considered. 3. Model Results 3.1. Steady State Crustal Thickness [17] The numerical experiments are not designed to determine the oceanic crustal thickness at steady state but rather to investigate the temporal evolution in crustal thickness and magmatic productivity during breakup. However, to test that the mantle parameter space is reasonable, the steady state crustal thickness for various mantle temperatures and spreading rates were calculated (Figure 3). The crustal thickness increases rapidly as the spreading velocity is increased from a half-spreading rate of 5 mm/yr to 20 mm/yr. Crustal thickness increases more slowly from 20 mm/yr to 100 mm/yr. For constant spreading rate the thickness increases with temperature as expected. The results shown in Figure 3 compare well with results from mid-ocean ridge modeling studies for comparable mantle 6of24

Figure 2. Initial geometry of the solution space and boundary conditions. In the top two panels, symmetry is assumed, and only half the rift is modeled. The lithosphere is prethinned at the start by a factor of 2 over three horizontal elements (half-width of rift is 25 km). Representative starting (left) temperature profiles and (right) viscosity profiles are also shown. The dotted line is the temperature function at the center boundary, and the solid line is the function over the thick lithosphere. Most calculations use the geometry of the top panel, but we also include a hot sublithospheric layer in some models (middle panel). The bottom panel shows the last class of models considered and assumes an abrupt change in lithospheric thickness from either 62.5 km or 125 km on the right to 250 km at the left. viscosities [e.g., Cordery and Phipps Morgan, 1993; Su and Buck, 1993]. [18] The spreading velocity during continental rifting that proceeds to seafloor spreading is most likely not constant, but changes from slow initial deformation that accelerates and ultimately transitions into seafloor spreading [e.g., Steckler et al., 1988; Hopper and Buck, 1993]. For the particular case of the North Atlantic, early faster drifting was short-lived and quickly slowed to values similar to the present-day half rate of 10 mm/yr [Larsen and Saunders, 1998]. These time variations in spreading rate go beyond the study here. 7of24

Table 1. Model Parameters and Assumed Values Variable Meaning and Units Value c p specific heat, J kg 1 K 1 1200 d reference length, km 700 g acceleration of gravity, m s 2 9.8 E activation energy J mol 1 530 10 3 h c crustal thickness, km I identity matrix _M time derivative of melt fraction, wt% s 1 n stress exponent 3 p pressure, Pa R gas constant, J K 1 mol 1 8.314 DS entropy change on melting J kg 1 K 1 400 DT L temperature anomaly of sublithospheric layer, K 0 200 T 0 surface temperature, K 273 T A absolute real temperature, K T ref reference mantle temperature, K 1598 T d super-adiabatic temperature drop, K 1325 solidus real temperature, K T MS T M solidus potential temperature, K T M0 solidus surface temperature, K 1373 @T M /@z depth derivative of solidus, K m 1 3.4 10 3 @T M /@X depletion derivative of solidus, K 440 u mantle flow rate, m s 1 V activation volume, m 3 mol 1 5 10 6 V x horizontal plate velocity X concentration of perfectly compatible trace element a coefficient of thermal expansion, K 1 3.3 10 5 b coefficient of depletion density reduction 0.04 _e strain rate, s 1 g coefficient of melt density reduction 0.16 G nondimensional temperature change due to melting k thermal diffusivity, m 2 s 1 10 6 h viscosity, Pa s h 0 reference viscosity, Pa s f retained melt r 0 mantle reference density, kg m 3 3340 r m melt density, kg m 3 2800 r Xref density of residue at X ref =1.3,kgm 3 3295 t deviatoric stress, Pa c H2 O viscosity increase factor due to dehydration 0 100 c m viscosity reduction factor due to interstitial melt 0 10 For modeling, a constant half-spreading rate of 10 mm/yr was chosen as most appropriate for eventual comparison to N. Atlantic data sets. However, this choice also puts the models in the spreading rate regime where the thickness of igneous crust produced at mid-ocean ridges is more variable than for ridges faster than 20 mm/yr. Depending on the mantle viscosity, the model parameter space might also be close to a transition between a flow pattern that can be described adequately in 2D, as is likely to be the case for fast spreading ridges [e.g., Spiegelman and Reynolds, 1999], and a flow pattern that is inherently three-dimensional [e.g., Parmentier and Phipps Morgan, 1990; Choblet and Parmentier, 2001]. In addition, the assumed mantle potential temperature in the models is 1325 C, which is a few percent higher than generally considered reasonable for the upper mantle [e.g., McKenzie and Bickle, 1988; Turcotte and Phipps Morgan, 1992]. At 10 mm/yr spreading rate, this generates a crustal thickness of 7.4 km, close to the average oceanic crustal thickness of 7.1 km [White et al., 1992] and close to the 8 9 km thick crust produced by the Reykjanes Ridge [e.g., Bunch and Kennett, 1980; Smallwood and White, 1998]. [19] The spreading rate and temperature values chosen are open to debate since they are different from what is typically assumed for mid-ocean ridge studies. They reflect a bias toward producing 8of24

Figure 3. Steady state crustal thickness as a function of spreading rate for different mantle potential temperatures. Spreading rate varies from 5 to 100 mm/yr, and temperature varies from 1275 to 1375 C. These tests assume symmetry at the ridge, h 0 =9 10 20 Pa s, dehydration strengthening, and melt weakening and include buoyancy from the residue and interstitial melt. results consistent with observations from the North Atlantic region, where some of the best data sets are available for comparison to model results. In particular, the temperature is likely an upper bound on mantle potential temperature and predisposes the results toward allowing buoyant upwelling and small-scale convection. This point should be kept in mind when interpreting the results of the model runs. 3.2. Viscosity, Buoyancy, and Temperature Anomalies [20] In simple thermal convection problems, the behavior of the system is controlled by a single parameter, the thermal Rayleigh number, which quantifies the trade-off between buoyancy and viscosity [e.g., Turcotte and Schubert, 2002]. In highly nonlinear systems such as the one here, the same concepts apply [e.g., Ito et al., 1996], but the situation is more complicated (e.g., equations (8), (10), and (11)]. Thus, to better understand the physical system it useful to examine the effect of varying the scaling viscosity without melting effects and then to consider separately the effects from different sources of buoyancy. Then, the effect that melting has on the viscosity structure of the mantle is included in the same models. Last, the effect of including a thin, sublithospheric, hot layer is examined. 3.2.1. Viscosity [21] The first tests examine the effect of varying the scaling viscosity for models with no temperature anomaly at the base of the lithosphere and a viscosity that is unaffected by dehydration or melt weakening (i.e., c H2 O = c m = 1). All buoyancy sources are included. Figure 4 shows the temporal evolution of model M1, with a high scaling viscosity of 4.5 10 21 Pa s. Initially, the asthenosphere upwells to fill the void created by the surface plate divergence. Because mass is conserved, upwelling velocities are initially higher than the plate spreading velocity to compensate for the narrowness of the upwelling zone compared to the thickness of the lithosphere. The melting zone is also restricted due to the narrowness of the rift and lateral conductive cooling from the cold lithosphere. A consequence of the narrow melting region is that melt production is modest despite the high upwelling velocities. As time progresses, the upwelling velocities decrease and the melting region widens until steady state is reached after 20 m.y. [22] For a lower scaling viscosity of 4.5 10 20 Pa s, buoyant upwelling is dominant (Figure 5, model M3). The early evolution is very similar to that of the high scaling viscosity model, but after 6.6 m.y., buoyant upwelling has become important close to the ridge as can be seen from the high upwelling rates compared to the plate spreading rate. Significant buoyant upwelling continues since the viscosity is low relative to the available buoyancy forces from depletion and melting. Note that the viscosity is about an order of magnitude lower than in Figure 4 and that lateral viscosity variations in the sublithospheric, isothermal mantle are due to variations in strain rate. Although not immediately evident from the cross-section snap shots, a smallscale convection cell has developed in this example. This can be seen more clearly by plotting the upwelling rate relative to the plate spreading rate as a function of time (Figure 6). As before, initially high upwelling rates are a result of the initial condition which imposes a narrow upwelling region at the beginning. The ratio, however, increases with time until 7.5 m.y. and indicates small-scale convection. [23] Figure 6 also summarizes the crustal thickness generated, the average temperature of melting, and the maximum depth of melting. Curves for a number of assumed reference viscosities are shown in addition to the calculations shown in Figures 4 and 5. For the highest viscosity case (M1, h 0 =4.5 10 21 Pa s, Figure 4), the productivity slowly increases to a steady state value corresponding to an igneous crustal thickness of 7.5 km, consistent with average oceanic crustal thickness [e.g., White et al., 1992]. Decreasing the scaling viscosity to 9of24

Figure 4. Temporal evolution of temperature and viscosity for model M1. A subset of the model close to the ridge axis is shown. The left column shows temperature field; temperatures below 1050 C are shown with the same color. White arrows indicate solid mantle flow, and the imposed spreading velocity is 10 mm/yr for scale. The right column shows viscosity field with 2% and 10% melt contours in white. h 0 =4.5 10 21 Pa s, h(t, p, _e), and r(t, X, f). Times after model start in m.y. are given for each plot. 9 10 20 Pa s (M2) results in only a very modest peak of extra melt production that eventually decays to average crustal production over a timescale in excess of 20 m.y. A scaling viscosity of 4.5 10 20 Pa s (M3) marks a transition to sustained but stable buoyant upwelling that always enhances melt production and generates thicker than average crust. These models never decay to a passive spreading system where the upwelling rate is roughly equal to the plate spreading rate. Eventually, the system becomes unstable and for h 0 =9 10 19 Pa s (M4) highly time-dependent flow results in excessive variability in crustal production. 3.2.2. Buoyancy [24] Next, three different sources of buoyancy in the models are considered: buoyancy from thermal expansion, buoyancy from the less dense residue after melting, and buoyancy from interstitial melt 10 of 24

Figure 5. Temporal evolution of temperature and viscosity for model M3. The same as in Figure 4 except that h 0 = 4.5 10 20 Pa s. (equation (6)). A fixed scaling viscosity of 9 10 20 Pa s and a spreading rate of 10 mm/yr are assumed. The viscosity is a function of temperature, pressure and strain rate, but again is not directly affected by melting (c H2 O = c m = 1). Figure 7 shows a set of calculations that demonstrate the competing effects of different buoyancy sources. [25] For models with thermal buoyancy only, a prolonged period of enhanced upwelling is followed by reduced melt production, and steady state is reached after 65 m.y. (model M5, Figure 7). Peak magmatic productivity occurs 15 m.y. after the start of the calculation and is about 70% greater than eventual steady state productivity. Cold material is brought into the melting zone between 20 30 m.y. and causes a slightly lower productivity than at steady state. Thus the time for a small-scale convection cell to go through a single turnover cycle is quite long. Small-scale convection continues long after breakup at the continental edge but the effect on melting becomes progressively smaller as the distance to the ridge center increases. [26] Next, depletion buoyancy, which occurs because of a density decrease of the residual mantle 11 of 24

the effect. Melt buoyancy initially enhances the upwelling. Assuming that 90% of the produced melt is extracted, however, leaves the overall behavior virtually unchanged from the case with thermal and depletion buoyancy, with the main difference being a slightly larger peak in excess magmatism and a reduced decay time to steady state (model M2, Figures 6 and 7). Assuming less efficient melt extraction (50%) causes an increase in peak productivity and sustained buoyant upwelling that generates very thick crust. A steady state thickness of 11 km is reached after 100 m.y. of spreading. Figure 6. Temporal evolution of melting variables for models with no thermal anomaly, no dehydration strengthening, and decreasing scaling viscosity: M1, 4.5 10 21 ; M2, 9 10 20 ; M3, 4.5 10 20 ; and M4, 9 10 19 Pa s. The top panel is the ratio of the average upwelling velocity in the melting region relative to the plate spreading velocity; the second panel is the average temperature in the melting region; the third panel is the maximum depth of melting; and the bottom panel is the total crustal thickness produced. See text for discussion. 3.2.3. Melting Effect on Viscosity and Hot Layers [28] Last, the effect that melting has on the viscosity structure of the mantle is added and sublithospheric hot layers are considered. As previously outlined, melt can both strengthen the mantle through dehydration, and weaken the mantle by reducing the viscosity. For melting below 5%, the weakening effect is less than an order of magnitude whereas dehydration causes a two order of magnitude increase in viscosity after only 2% melting. Thus the dehydration effect is dominant. We specifically test the idea that the viscosity increase due to dehydra- after melting and melt extraction, is included (model M6, Figure 7). The most prominent effect of the density reduction of the residue is to stabilize the small-scale convection that developed in model M5. For small-scale convection to develop, a return flow is required away from the ridge axis. With only thermal buoyancy, cooling of the residual mantle material enables this return flow to occur. Depletion, however, is permanent and the buoyant residue resists small-scale convection even after cooling. Thus variations in crustal thickness are damped and decay to steady state is faster. The maximum crustal thickness produced in this case is only 35% greater than steady state crustal production. [27] Inclusion of buoyancy from retained melt, which has a lower density than the solid matrix, is investigated by running two models that assume 90% and 50% melt extraction efficiency. It is generally accepted that the residual mantle contains at most 2% unconnected porosity that can potentially contain melt. If 20% of the mantle melts, then 90% of the melt will be efficiently extracted. 50% is clearly unreasonable for the mantle, but is included as an extreme end-member case to demonstrate Figure 7. Temporal evolution of melting variables for models with different sources of buoyancy. M5, only thermal buoyancy included; M6, thermal buoyancy plus depleted residual buoyancy; M2, thermal buoyancy, depletion buoyancy, and buoyancy from retained melt assuming 90% efficiency of melt extraction; M7, same as M2 but with only 50% efficiency of melt extraction. See text for discussion. 12 of 24

tion can result in a system that is initially buoyancy driven to one that is essentially plate driven, as proposed by Boutilier and Keen [1999]. [29] Figure 8 shows the results of rerunning the models shown previously but with the melting effect included. There is essentially no difference between the evolution of these models. All models show a gradual increase in crustal production until steady state is reached. It is clear that the dehydration effect on mantle viscosity dominates in these model runs, even in the cases where there is significant excess buoyancy to drive small-scale convection. Model M10, for example, is equivalent to the 50% retained melt example shown previously (model M7). Thus, even with this unreasonable amount of excess buoyancy, an increase in melt productivity is not observed. The viscosity increase due to dehydration occurs deep in the melting region of the mantle, and well below the depth to the dry solidus. This effectively forces the shallow mantle upwelling to be a passive plate-driven system and buoyant upwelling is suppressed. Because most of the melt is produced in the shallow mantle and above the depth of the dry solidus, it is difficult to generate significant excess melt. The full viscosity increase and shallow transition to passive flow occurs after only small quantities of melt have been produced. [30] Finally, the possibility that a thin warm layer beneath the lithosphere can enhance initial productivity is considered. Figure 9 shows the results of calculations where a 50 km thick hot layer is placed beneath the lithosphere. In models M13 and M14, temperature anomalies of 100 C and 200 C above the assumed mantle potential temperature are assumed. In both cases, sharp peaks in crustal production are observed shortly after the calculation begins. In the case of 100 C layer, a single peak is seen that generates crust 3.5 times thicker than the steady state solution. Within 5 m.y. after peak melt production, the crustal thickness has been halved and is followed by a more gradual decay. For the 200 C layer, a double peak in productivity is seen and the decay to steady state is considerable longer. The productivity peaks result in crust that is 10 times and 4 times thicker than steady state. [31] Including the viscosity changes from melting, however, again has a dramatic effect on the results. The two models above were rerun with these effects and are shown in Figure 9 (models M15 and M16). In these cases, excess melt production is reduced, but not eliminated. In the 100 C case, Figure 8. Temporal evolution of melting variables for models with the same parameters as models M1 M4 and M6 but with melting-induced viscosity changes included. crust only 50% thicker than steady state is produced. In the 200 C case, the double peak is eliminated. Instead, a single pulse of 2.5 times steady state productivity is observed that linearly decays over 15 20 m.y. 3.3. Prerift Lithospheric Geometry [32] The basic model runs shown so far used prethinned lithosphere at the rift as an initial condition. The abrupt necking profile observed at some rifted margins suggest that such an initial condition is not entirely inappropriate. Nonetheless, it is a critical assumption that requires further testing. To test the sensitivity of the results to the initial condition, two additional starting geometries are considered. First, models where the prethinning is eliminated are shown and second, the possibility that steep, lateral changes in the boundary layer can drive additional convection that may enhance melt production is investigated. In these tests, the effect of melting on viscosity is again ignored. [33] Two models with the same parameters as M2 and M7 were run but with an initially flat bottom, i.e., no prethinning (Figure 10). Lithospheric stretching occurs and strain is localized in the corner because of the top velocity boundary condition. Again, the assumed 50% melt extraction efficiency of M7 is unreasonable, but permits testing a case where extreme buoyant upwelling is observed. 13 of 24

[34] In terms of melt productivity, no major difference is seen between the prethinned and flat lithosphere cases, except that the onset of volcanism is delayed relative to the models with prethinned lithosphere. In addition, the large component of initial active upwelling is not observed. Thus the high upwelling rates seen initially in many of the model runs are due primarily to the steep lithospheric boundary imposed at the start rather than anything intrinsic in the dynamics of the system. [35] A sharp change in lithospheric thickness over a short distance has been proposed as a mechanism to generate pronounced small-scale convection that might produce significant magmatism [e.g., King and Anderson, 1995, 1998]. To investigate this possibility, a series of experiments were run (models M19 M23) where the lithosphere thickness changes abruptly by either a factor of two from 250 km to 125 km, or a factor of four from 250 km to 62.5 km. The former case might be expected near a Proterozoic/Archean boundary. The latter case is probably more appropriate for oceanic lithosphere next to Archean lithosphere and thus is questionable as a starting condition for continental breakup, but allows for better comparison to the models presented by King and Anderson [1998]. [36] First, a calculation with a free slip top boundary, no imposed plate spreading, and a factor of four lithospheric thickness change is considered. Figure 11 shows that a convection cell develops next to the edge of the thick lithosphere (model M19). This convection cell is very similar to that shown by King and Anderson [1998] and the upwelling velocities are also roughly the same (10 mm/yr) despite differences in the assumed viscosity structure. The thick lid, however, prevents significant upwelling at shallow depths were significant melt production can occur. [37] To examine how such a convection cell may impact melt production during extension, spreading is imposed at the top surface. The imposed surface velocity ramps to zero at the location where the lithosphere thickness changes abruptly, forcing strain to localize at the boundary. The evolution is highly asymmetric as shown in Figure 12 (M20). Nevertheless, in terms of melt productivity, the calculation is virtually indistinguishable from the previous models with the same scaling viscosity and assumptions about buoyancy and melting. For h 0 =9 10 20 Pa s, modest extra productivity of 25% occurs before decaying toward steady state Figure 9. Temporal evolution of melting variables for a model like M2, but assuming a thin, sublithospheric hot layer at the start. M13 and M14 do not include meltinduced viscosity changes, but M15 and M16 do. M13 and M15, 100 C anomaly; M14 and M16, 200 C anomaly. (Figure 13, M20). Reducing the scaling viscosity (Models M21, h 0 =4.510 20 Pa s and M22, h 0 = 9 10 19 Pa s) is similar to the result shown in Figure 6, where excessive time dependence and sustained buoyant upwelling occurs long after breakup. [38] Last, the possibility of a 1% thermal perturbation in the mantle is considered for comparison to King and Anderson [1998]. The thermal perturbation adds sufficient extra thermal buoyancy to enhance melt production and facilitate small-scale convection (M23, Figure 13). Productivity peaks nearly double the steady state value occur. However, excessive time dependence is again observed, leading to multiple peaks and sustained excess productivity like in models M21. Interestingly, the differences between M21 and M23 are minor, suggesting that the model is insensitive to thermal perturbations of only a few percent. [39] It is clear from model M19 M23 that the model results are relatively insensitive to assumptions about the initial condition in terms of melt generation. In particular, edge-driven convection is only significant well below the melting region and appears to be a second order effect for understanding the time and length scales of crustal productivity. Although the viscosity effects from melting are not included here, the results of the previous 14 of 24

Figure 10. Temporal evolution of melting variables for models to test sensitivity to the initial condition. Model M17 is the same as M2, and M18 is the same as M6, but without a prethinned lithosphere. Apart from the time delay for models started without prethinning of the lithosphere, no major changes are seen. section leave little doubt that dehydration melting would effectively suppress the buoyant upwelling and small-scale convection observed in this set models as well. 4. Application of Model Results to the North Atlantic [40] Initial opening of the North Atlantic began during the Paleocene and was accompanied by the eruption of enormous quantities of volcanic products in a short period of time [e.g., White and McKenzie, 1989; Larsen and Saunders, 1998]. To date, most modeling efforts associated with the North Atlantic Igneous Province have focused on plume-ridge interaction to understand present-day Iceland and have ignored the early continental breakup phase of volcanism. While these studies have shown that active upwelling associated with a hypothesized plume plays an important role for understanding present-day volcanism, the mantle dynamics associated with continental breakup and the existence of anomalous margin volcanism up to 1200 km away from the presumed plume stem has received comparatively little attention. [41] To examine the volumes and rates of volcanic production during breakup in the North Atlantic, the SIGMA seismic survey was carried out in 1996 [Holbrook et al., 2001] (Figure 14). Close to and along the Greenland-Iceland ridge (GIR), which may mark a plume track [e.g., Lawver and Müller, 1994], igneous crust up to 30 km thick is observed [Holbrook et al., 2001; Korenaga et al., 2000]. Farther from the GIR, igneous crust produced at breakup is less, but is still in excess of 15 km [Holbrook et al., 2001]. Figure 15 shows SIGMA profile III, located 600 km south of the GIR [Hopper et al., 2003]. The profile is particularly important because the seismic transect is coincident with ODP drilling that sampled the breakup basalts [Saunders et al., 1998]. Argon dating combined with well-defined magnetic anomalies farther seaward, provide tight controls on the timing of events [Larsen and Saunders, 1998; Sinton and Duncan, 1998]. The combined data sets constrain both the spatial and temporal scales of margin formation. In addition, the profile is well away from the region near a hypothesized plume stem associated with Iceland [Holbrook et al., 2001]. Thus volcanism here is unlikely to have been directly affected by any plume upwelling. Nonetheless, all of the post-breakup basalts sampled have an Icelandic-type depleted mantle source [Fitton et al., 1998]. [42] The key result is that at 56 Ma., final continental breakup occurred and 18.3 km thick crust accreted to the margin. The profile ends in 9 10 km thick crust at magnetic anomaly C21N, or 47 Ma. using the timescale of Cande and Kent [1995]. There is little data available on younger crust, but seismic experiments along the Reykjanes Ridge to determine the crustal thickness variation associated with V-shaped gravity anomalies emanating from Iceland are consistent with 8 10 km thick crust not far from a flow line connecting SIGMA III to the spreading ridge [Smallwood and White, 1998]. Thus volcanic margin formation away from Iceland is accompanied by a single, transient pulse of magmatism that is reduced in half within 10 m.y. Subsequent seafloor spreading results in crust that varies with time, but this variation is only on the order of ±2 km and less [Lizarralde et al., 1998]. [43] The models show that if the changes in viscosity due to melting are ignored, some smallscale convection and buoyant driven upwelling is possible, generating excess crustal thickness. However, in the models that evolve into a platedriven steady state accretion, only modest peaks of excess melt are produced. Models that generate crust as thick as observed off SE Greenland, either 15 of 24

Figure 11. Small-scale convection at lithospheric thickness change (M19). Temporal evolution of temperature and viscosity for a model setup similar to Figure 1 of King and Anderson [1998] with a free-slip top boundary. 128 128 elements. Convection velocities of up to 8 mm/yr occur too deep to cause any melting. See text for discussion. result in sustained buoyant upwelling that generates too much crust long after breakup, or results in highly time dependent behavior that is not observed. Even so, the excess melt production seen in these models, is effectively suppressed by the viscosity increase caused by dehydration at the onset of melting. In either case, the models cannot reproduce the spatial and temporal scales of melt production observed along the SIGMA III profile. [44] Thus the breakup related excess productivity seems to require a thin anomalous layer in the mantle at the time of breakup. In the models here, a hot thermal layer serves to decrease the local viscosity, promoting small-scale convection which contributes to the excess melt generation, but because the anomaly is a thin layer, is quickly exhausted and the system rapidly evolves to steady state plate-driven flow. For the SIGMA III data and no dehydration effect on the viscosity, a D TL of 100 C is consistent with the crustal thickness observed, but the timescale of the decay is slightly too rapid. With a dehydration induced increase in viscosity, D TL can be as high as 200 C, but the 16 of 24

Figure 12. Small-scale convection for a model with lithospheric thickness change (M20) and imposed spreading. 512 512 elements. See Figure 13 for time evolution of melting variables. Note the large-scale asymmetry that develops. decay timescale is slightly too large. These results are consistent with Nielsen et al. [2002], who showed that the lack of along strike variation can be explained by a rapidly spreading low viscosity layer beneath the lithosphere. They demonstrated that a temperature anomaly on the order of 100 C 200 C is sufficient to lower the viscosity to the point where rapid lateral flow beneath the lithosphere can occur and reach the distances appropriate for the SE Greenland margin. [45] Alternatively, the anomalous layer could be a fertile chemical anomaly as suggested by Korenaga et al. [2002] and Korenaga [2004]. This is well beyond the scope of this model, but we note that the suggestion of an iron rich mantle source [Korenaga and Kelemen, 2000; Korenaga, 2004] presents an even greater difficulty. An iron rich source should yield a denser mantle than assumed here and would have the effect of reducing, not increasing the amount of active upwelling from buoyancy driven 17 of 24

In the following we examine the validity of certain assumptions: the effect of dehydration on viscosity, the influence of melt extraction efficiency on buoyancy and viscosity, lithospheric geometry, stability of the deep continental lithosphere. Figure 13. Melting variables generated for a starting model with a sudden change in lithospheric thickness and spreading. Model setup is similar to Figure 2 of King and Anderson [1998]. M21 has a low scaling viscosity and extreme time dependence. M22 has an intermediate scaling viscosity; M23 is the same as M22, but a 1% thermal perturbation has been added to the mantle. flow with breakup. However, chemical modeling and data are needed to investigate these possibilities further. 5. Discussion [46] To better understand the conditions under which volcanic passive margins form, we have investigated mantle dynamics during continental breakup that continues to seafloor spreading. The feedback from melting on the physical properties of the mantle is included and how this affects upwelling and magmatic productivity through time is examined. A number of factors that influence both the buoyancy and viscosity of the mantle are considered. In particular, density variations due to depletion and retained melt can increase the local buoyancy in a rift and developing spreading center. Significant viscosity changes can also occur. Melting leads to rapid dehydration of the mantle and can increase the viscosity of the residue by at least 2 orders of magnitude. On the other hand, the presence of small amounts of interstitial melt can facilitate grain boundary sliding and other creep mechanisms and reduce the effective viscosity. In addition, the extent to which the initial lithospheric geometry is an important factor has been assessed. 5.1. Buoyancy and Viscosity [47] At sufficiently low scaling viscosity, the models show that a large pulse in magmatic productivity during continental breakup is possible. However, the subsequent spreading system is highly unstable and shows extreme variability in crustal thickness, confirming the results of Boutilier and Keen [1999]. Keen and Boutilier [2000] suggested that an increase in viscosity due to dehydration caused by melting [Chopra and Paterson, 1984; Hirth and Kohlstedt, 1996; Mei and Kohlstedt, 2000a, 2000b] could have a stabilizing effect on the crustal productivity after breakup while at the same time allowing for an initial pulse of magmatism. This hypothesis is not viable if dehydration caused by melting happens rapidly compared to the timescale of margin formation, the latter of which is typically a few millions of years. The timescale of dehydration strengthening depends primarily on how fast melt is extracted from the mantle under a rift. The question of melt extraction and the amount of retained or interstitial melt also has direct importance for both viscosity and buoyancy. While few constraints exist in rift settings, the preservation of isotopic disequilibria in mid-ocean ridge basalt seems to require rapid ascent of melt, on the order of meters per year [e.g., Faul, 2001]. It is likely that similar timescales apply to melt extraction during margin formation. Thus dehydration appears to lack the required time delay that would allow this mechanism to work. In these models, the dehydration induced viscosity increase effectively limits small-scale convection and buoyant upwelling by immediately forcing the shallow mantle into a passive, plate-driven flow. For this mechanism to remain viable, a way to pool substantial quantities of melt beneath the lithosphere prior to breakup is required. In this regard, edge convection may still provide a mechanism to deliver melt beneath a continent prior to breakup. As shown earlier, however, most of this convection is deep and it is not clear that sufficient volumes of melt can be produced in the absence of active rifting. With active rifting, the models show that edge convection does not significantly enhance melt production. Additional problems with the possibility of high degrees of retained melt before breakup is discussed further below. 18 of 24

Figure 14. Summary map of the North Atlantic Igneous Province. Dark blue areas show outcrops of subaerially extruded basalts. Light blue areas show regions where subaerially extruded basalts have been subsequently submerged below sea level. Red lines show locations of major deep seismic programs. Those where wide-angle data were collected also show the maximum thickness of igneous crust accreted to the continental margin (numbers below lines). C&L, Chian and Louden [1994]; SIGMA I and SIGMA IV, Holbrook et al. [2001]; SIGMA II, Korenaga et al. [2000]; SIGMA III, Hopper et al. [2003]; ICE and BGR-77, Nielsen et al. [2002]. Open circles near SIGMA II and III are ODP drill sites. The SIGMA III profile is shown in Figure 15, and the dashed red line connects the end of SIGMA III to the Reykjanes Ridge along a flow line based on the poles of rotation of Srivastava and Tapscott [1986]. Note in particular that there is no correlation between the volume of crust produced at breakup and the location of the Archean boundaries. Yellow dots mark locations of major seismic programs on and near the Reykjanes Ridge. They provide evidence that crust generated within the last several million years varies from 8 to 10 km thick. A, Angenheister et al. [1980]; B, Smallwood and White [1998]; C, Bunch and Kennett [1980]. [48] Although it is clear that most of the melt is extracted rapidly, observations also indicate that the presence of 1 2% melt could be distributed on grain size scale over large regions [Turner et al., 2001; Spiegelman et al., 2001; Faul, 2001]. It is generally thought that this amount of interstitial melt will cause only a modest lowering of the viscosity because the melt is distributed in threeand four grain junctions and does not wet two-grain boundaries, which would otherwise provide short circuit paths for diffusion [Hirth and Kohlstedt, 1995a, 1995b; Mei and Kohlstedt, 2000a, 2000b]. However, a substantial additional decrease in viscosity might arise if the onset of melting promotes a decrease in the dynamically recrystallized grain size and a transition to grain boundary sliding [Hirth and Kohlstedt, 1996; Braun et al., 2000]. This effect has been included in models of mid-ocean ridges [Braun et al., 2000; Choblet and Parmentier, 2001]. It is potentially most important 19 of 24

Figure 15. Cross section along the SIGMA III profile based on results presented by Hopper et al. [2003]. Colors are seismic velocities derived from travel time modeling of wide-angle data. Ocean bottom seismometer and land seismometer stations are marked by black dots on the seafloor and topography. Triangles along the top are Ocean Drilling Program Legs 152 and 163 coring locations. Times labeled along the top are from 39 Ar- 40 Ar dating of basalts and from well-defined magnetic anomalies (not shown). The box above the cross section shows the total igneous crustal thickness accreted to the margin after breakup and the average seismic velocity of the igneous part of the crust. in the region of wet melting (i.e., deeper than the depth to the dry solidus), where the competing effects on viscosity from grain boundary sliding and dehydration are likely to be of similar magnitude. But if a volumetrically significant part of the melting took place below the dry solidus then it would cause a geochemical composition that is not supported by observations [Klein and Langmuir, 1987]. Above the depth to the dry solidus the viscosity increase due to dehydration is dominant. [49] The presence of 1 2% of melt also has a limited effect on buoyancy. However, this effect will persist after breakup. To explain the transition from a volcanic rifted margin to steady state oceanic accretion by melt buoyancy would require that high amounts of melt are retained initially and decrease to a steady state after breakup. However, increasing amounts of melt will lead to higher permeability which in turn will lower the amount of retained melt and thus may self-limit the volumes produced. Thus it seems unlikely that melt buoyancy is the mechanism that causes the transition from initially rapid buoyant upwelling to later plate-driven flow. Nonetheless, it cannot be excluded and requires further investigation. As noted above, this scenario may be a requirement for the mechanisms proposed by Boutilier and Keen [1999] and King and Anderson [1998]. [50] In summary, above the depth to the dry solidus, the viscosity increase due to dehydration is dominant and prohibits small-scale convection and active upwelling in the shallow mantle where the volumetrically significant amounts of melt are produced. Buoyant upwelling below the dry solidus is still likely and may be important for maintaining the close to average oceanic crustal thickness observed for slow spreading rates [Braun et al., 2000]. The models here suggest that smallscale convection and buoyant upwelling may be capable of producing second-order, smaller-scale effects. We speculate that buoyant upwelling in the wet melting region may still offer a viable explanation for smaller-scale melting anomalies, such as some volcanic island chains in the Pacific [e.g., Raddick et al., 2002] or more modest volcanic margins such as the Cuvier margin [Hopper et al., 1992]. Unfortunately, data sets that tightly constrain both the spatial and temporal scales of 20 of 24