Asthenospheric flow and asymmetry of the East Pacific Rise, MELT area

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1 JOURNAL OF GEOPHYSICAL RESEARCH, VOL. 107, NO. B12, 2344, doi: /2001jb000807, 2002 Asthenospheric flow and asymmetry of the East Pacific Rise, MELT area James A. Conder, 1 Donald W. Forsyth, and E. M. Parmentier Department of Geological Sciences, Brown University, Providence, Rhode Island, USA Received 24 July 2001; revised 12 April 2002; accepted 6 September 2002; published 13 December [1] Although the Pacific and Nazca plates share the East Pacific Rise (EPR) as a boundary, they exhibit many differing characteristics. The Pacific plate subsides more slowly and has more seamounts than the Nazca plate. Both the seismic and magnetotelluric components of the Mantle ELectromagnetic and Tomography Experiment (MELT) found pronounced asymmetry in mantle structure across the spreading axis near 17 S. The Pacific (west) side has lower S-wave velocities, exhibits greater shear wave splitting, and is more electrically conductive than the Nazca (east) side. These results suggest asymmetric mantle flow and melt distribution beneath the EPR. To better understand the causes for these asymmetric properties, we construct numerical models of melting and mantle flow beneath a midocean ridge migrating to the west over a fixed mantle. Although the ridge is migrating to the west, the migration has little effect on the upwelling rates, requiring a separate mechanism to create the asymmetry. Models that produce asymmetric melting with a temperature anomaly require large (>100 C) excess temperatures and may not be consistent with the observed subsidence and crustal thickness. A possible mechanism for creating asymmetry without a temperature anomaly is across-axis asthenospheric flow, possibly driven by pressures created by upwelling beneath the Pacific Superswell to the west. Pressure-driven asthenospheric flow follows the base of the lithosphere, extending the upwelling region to the west as it follows the thinning lithosphere toward the axis, and shutting off melting as it crosses the axis and encounters an increasingly thick lithosphere to the east. INDEX TERMS: 8120 Tectonophysics: Dynamics of lithosphere and mantle general; 8121 Tectonophysics: Dynamics, convection currents and mantle plumes; 8150 Tectonophysics: Evolution of the Earth: Plate boundary general (3040); 8162 Tectonophysics: Evolution of the Earth: Rheology mantle; 9355 Information Related to Geographic Region: Pacific Ocean Citation: Conder, J. A., D. W. Forsyth, and E. M. Parmentier, Asthenospheric flow and the asymmetry of the East Pacific Rise, MELT area, J. Geophys. Res., 107(B12), 2344, doi: /2001jb000807, Introduction [2] Although considerable study has been devoted to understanding midocean ridges and their central role in plate tectonics, much is still not known about dynamic processes within the oceanic mantle beneath midocean ridges. The Mantle ELectromagnetic and Tomography Experiment (MELT) [Forsyth and Chave, 1994] was designed to image the melting structure beneath the fast spreading (145 mm/yr) East Pacific Rise (EPR) near 17 S (Figure 1). The main objective was to distinguish between models of broad and narrow zones of upwelling and melting at midocean ridges. There were two primary components of the experiment, a passive-source seismic deployment utilizing 52 ocean bottom seismometers (OBSs) distributed across the axis in two linear arrays [MELT Seismic Team, 1 Now at Department of Earth and Planetary Sciences, Washington University, St. Louis, Missouri, USA. Copyright 2002 by the American Geophysical Union /02/2001JB000807$ ] and a magnetotelluric experiment utilizing 47 seafloor instruments, also deployed across the axis in two linear arrays [Evans et al., 1999]. The results of the experiment are consistent with a broad zone of melting [MELT Seismic Team, 1998; Forsyth et al., 1998; Hung et al., 2000], but one of the most robust and pervasive observations in both the seismic and magnetotelluric data is a pronounced asymmetry about the rise axis (Figure 2). The experiment was successful in answering many questions about mantle structure beneath midocean ridges, but the unexpected degree of asymmetry raises many new questions about midocean ridge and oceanic mantle structure. [3] Asymmetry is manifest in nearly every geophysical observation in the MELT region. For instance, the west (Pacific) side subsides significantly slower than the east (Nazca) side. Slower subsidence may be an isostatic response to hotter mantle to the west [Cochran, 1986] or could be dynamically supported by pressures within the mantle [Phipps Morgan and Smith, 1992; Phipps Morgan et al., 1995]. The Pacific side has more seamounts than the Nazca side [Scheirer et al., 1996, 1998], suggesting that ETG 8-1

2 ETG 8-2 CONDER ET AL.: ASTHENOSPHERIC FLOW AND ASYMMETRY OF THE EPR Figure 1. Bathymetry of the MELT area of the East Pacific Rise (EPR). Triangles and squares show the geometry of the MELT experiment. Triangles are seismometer locations and squares are magnetotelluric instrument locations. Although the crustal accretion rate is nearly symmetric (black arrows), absolute plate motion is asymmetric (white arrows), with the Pacific plate moving 101 mm/yr and the Nazca plate moving 44 mm/yr. RRS denotes the Rano Rahi seamount field, and PPR with associated arrow shows direction of the Pukapuka ridges. more melt is present beneath the Pacific plate or that melt more easily penetrates the overlying lithosphere. Along the west side of the axial high is a flanking low, possibly caused by an asymmetry in crustal and mantle viscosity [Eberle and Forsyth, 1998]. Shear wave splitting delays from OBSs on the Pacific side are nearly twice those from OBSs on the Nazca side [Wolfe and Solomon, 1998]. Larger shear wave splitting values indicate a stronger lattice-preferred orientation (LPO) of anisotropic mantle minerals (e.g., olivine, enstatite), and/or a thicker layer of those anisotropically aligned mantle minerals. Both the anisotropic layer thickness and the degree of strain-induced LPO are expected to depend on the mantle flow field. The asymmetry in shear wave splitting suggests that mantle flow beneath the EPR is not the symmetric corner flow usually assumed in midocean ridge models [e.g., Phipps Morgan, 1987]. Rayleigh wave phase velocities are lower [Forsyth et al., 1998] and P and S wave arrivals are significantly later [Toomey et al., 1998] to the west of the EPR. These results strongly suggest that more melt is present beneath the Pacific plate than the Nazca plate. In addition, the electrical conductivity has an abrupt transition near the rise axis [Evans et al., 1999] with relatively conductive mantle to the west, possibly indicating the presence of melt, and highly resistive mantle to the east, suggesting dry, depleted mantle containing very little interconnected melt beneath the Nazca plate. [4] Possible mechanisms for creating the observed asymmetry about the EPR include ridge migration to the west, hot mantle material fed to the axis from the west, and across-axis, pressure-driven asthenospheric flow [Toomey et al., 2002]. Crustal accretion in the MELT area is fairly symmetric (Pacific 69, Nazca 76 mm/yr), but absolute plate motions are asymmetric (Pacific 101 mm/yr, Nazca 44 mm/yr), requiring 32 mm/yr of westward ridge migration [Scheirer et al., 1998]. The asymmetric motion may be directly responsible for the asymmetry in shear wave splitting [Wolfe and Solomon, 1998]. Potentially, as the ridge migrates to the west, the less depleted material beneath the leading (Pacific) plate could be preferentially melted compared to material beneath the trailing (Nazca) plate, which may already be somewhat depleted. Hotter mantle beneath the Pacific plate has been suggested to explain the asymmetric subsidence. The hotter material, possibly fed from the Pacific Superswell 1500 km to the west of the axis [McNutt, 1998], would also generate a greater amount of melting beneath the Pacific plate than beneath the Nazca plate. In this paper, we demonstrate that across-axis asthenospheric flow can create an asymmetry in the melt produced on either side of the axis by enhancing the upwelling on the upwind side and inhibiting upwelling on the downwind side. A pressure gradient strong enough to drive across-axis flow may be created by the superswell. We use numerical models to investigate these possible mechanisms and the conditions required to create a strong asymmetry about the EPR. In particular, we make the case that pressure-driven asthenospheric flow is likely an important factor in creating asymmetric melting and subsequent asymmetric geophysical anomalies. 2. Numerical Models [5] To investigate the possible causes of asymmetry in the melting region, we construct 2-D finite element-method numerical models of mantle flow beneath a midocean ridge. We solve the equations for viscous flow using a standard penalty function method [Reddy, 1993] with rectangular elements. Solutions are calculated on an node mesh with nonuniform rectangular elements (Figure 3). The mesh is centered about the ridge axis, and extends 300 km to each side and to 600 km depth. Node spacing decreases toward the ridge axis and with decreasing depth, providing the best resolution near the spreading center. For models including a temperature anomaly advected into the area from the west, 10 columns of grid cells are added to either side of the mesh, extending the box dimensions to ±1000 km from the Figure 2. Cross-section of S-wave velocities beneath the EPR in the MELT area [from Forsyth et al., 2000]. The region of velocities lower than 4.1 km/s, probably indicating the presence of melt, extends hundreds of kilometers to the west, but only several tens of kilometers to the east of the axis. Cross-section location is midway between the two main seismic lines shown in Figure 1. See color version of this figure at back of this issue.

3 CONDER ET AL.: ASTHENOSPHERIC FLOW AND ASYMMETRY OF THE EPR ETG 8-3 Figure 3. Mesh and boundary conditions used for numerical flow models. The models are in the ridgefixed reference frame. To account for ridge migration to the west, nodes along the bottom are assigned an eastward velocity corresponding to the ridge migration rate. To investigate the influence of a pressure gradient, different pressures (P 1 and P 2 ) are assigned along the left and right edges. For models investigating a pressure gradient only, the smaller (81 41 node) mesh outlined by the dashed line is used. For models including a thermal anomaly introduced on the left edge, the larger ( node) mesh is used. axis. Resolution near the edges is not critical, but the introduced temperature anomaly needs to begin far enough away that edge effects are not important. The model methods and governing equations for conservation of mass, conservation of energy, and mechanical equilibrium with variable viscosity are given by Braun et al. [2000] and Jha et al. [1994]. In addition to the temperature and the 2-D velocity field, calculated variables are viscosity, melt production, and mantle depletion from melting. Advection of temperature and depletion is calculated by an upwind finite differencing method with higher order corrections to reduce artificial diffusion [Smolarkiewicz, 1983]. [6] Boundary conditions along the top edge are velocity conditions. The models are in the ridge-fixed reference frame. Along the top, nodes left of the axis move to the left at 72 mm/yr and those right of the axis move to the right at 72 mm/yr, corresponding to the average half-spreading rate [Scheirer et al., 1998]. To account for ridge migration in the ridge-fixed reference frame, we apply a horizontal velocity along the bottom boundary of 30 mm/yr to the right, equivalent to the ridge migration rate to the left in the hot spot coordinate frame. We ignore the minor asymmetric spreading from rapid propagation of small-offset propagating rifts [Cormier and Macdonald, 1994] that adds to the net migration rate. In most of our models, no flow is allowed across the bottom boundary. The right and left edges have shear stresses set to zero and are assigned normal stresses to create the desired pressure gradient. Temperatures along the bottom are set to 1350 C (plus the adiabatic gradient, 0.3 C/km), while those across the top are set to 0 C. Temperature anomalies introduced from the side are applied as step functions, with material entering the box along the left edge above a certain-depth assigned a temperature in excess of 1350 C. [7] We do not explicitly include buoyancy forces. We approximate the effects of a far-off-axis, buoyant plume with a pressure gradient driving flow away from the hot spots toward the ridge axis. Buoyancy could lead to smallscale convection that would tend to homogenize temperatures within the low-viscosity asthenosphere and thin the lithosphere, but with our 2-D model geometry, Richter rolls [Richter and Parsons, 1975] are not allowed to develop even if buoyancy terms are included. Any off-axis convective component with a symmetry axis parallel to the spreading center would tend to be suppressed by shear in the asthenosphere. Buoyancy could create a narrow zone of upwelling at the ridge axis [Buck and Su, 1989], but the MELT found no indication of the predicted narrowing beneath the EPR [Hung et al., 2000]. Thus, we believe that the dominant effects for the purposes of this study can be represented with a passive, plate-driven flow model with the addition of pressure gradients driving flow in the asthenosphere. The absence of buoyancy forces does require that we use a no flow (vertical velocity = 0) boundary condition along the bottom to balance the pressures in pressure-driven flow (or flow exits through the bottom), and to permit passive temperature anomalies to advect to the spreading center (or a temperature anomaly introduced from the side is almost immediately caught in the corner flow and carried back outside the box). [8] Melting in the models occurs when the upwelling mantle exceeds the solidus temperature at a given pressure. We include solidi for both wet and dry melting. The wet and dry solidi are defined as and T wet ¼ 900 C þ r m gzðdt=dpþ wet ð1þ T dry ¼ 1100 C þ r m gzðdt=dpþ dry ð2þ where r m is density of the mantle, z is depth, g is acceleration due to gravity, and dt/dp is the slope of the solidus with pressure. The total amount of melt generated in the wet melting regime is expected to be small [Hirth and Kohlstedt, 1996], so we only allow 2% wet melting

4 ETG 8-4 CONDER ET AL.: ASTHENOSPHERIC FLOW AND ASYMMETRY OF THE EPR (F wet = 0.02), after which no more melting occurs until the dry solidus is exceeded. We allow up to 20% total melting, assuming the exhaustion of clinopyroxene at this value [Hirschmann et al., 1998]. Melt production for a given amount of decompression is given by and F ¼ F wet ðt T wet Þ= T dry T wet ð3þ F ¼ ð@f=@tþpt T dry þ Fwet ð4þ in the wet and dry melting regimes respectively. The amount of melt produced is adjusted by the isobaric melt productivity, (@F/@T) P, that takes into account the amount of depletion each parcel of mantle has already undergone. The melt production rate, q m, as a function of depth is q m ¼ u z ðdf=dzþ ð5þ where u z is the upwelling rate and df/dz is the amount of melt produced per unit depth. [9] Depletion, d p (total amount of melting a particle has experienced), boundary conditions for material entering the box below the solidus are set to zero (no prior melting). Material advected out of the box simply retains its prior depletion value (dd p /dxj edge = 0). Material that enters the box above the solidus is assigned a value greater than zero, depending on its depth and temperature, to reflect prior melting it must have undergone. This latter condition is only important with pressure-driven flow. Passive-flow cases mostly tend to draw material into the box from below the solidus. [10] The asymmetry produced in the flow models depends on the viscosity structure. Dislocation and diffusion creep are the two primary deformation mechanisms in the upper mantle [e.g., Karato and Wu, 1993]. The effective viscosity, h, for each creep mechanism is described by h ¼ As ð n 1 Þ exp½ðe* þ Pv* Þ=RTŠ ð6þ where E* is the activation energy, P is the pressure, v*isthe activation volume, R is the gas constant, T is the temperature, s is differential stress, n is the stress exponent (n = 1 for diffusion creep, n 3 for dislocation creep), and A is a preexponential constant. The activation and preexponential values for the different mechanisms are not necessarily the same. The uppermost part of the mantle that we are most interested in is expected to be dominated by dislocation creep, which we adopt for the entire region. The temperature dependence of mantle viscosity is reasonably well known, as E* for olivine undergoing dislocation creep is well constrained by laboratory experiments (515 ± 25 kj/mol [Hirth and Kohlstedt, 1996]), but the activation volume (pressure dependence) is not as well constrained. Possible values range from 10 to m 3 /mol [Karato and Wu, 1993; Hirth and Kohlstedt, 1996]. To remove the nonlinear dependence on stress for dislocation creep, we use a linear approximation for viscosity by reducing the activation values by a factor of two (E* = 250 kj/mol, v* = m 3 /mol) and setting the stress exponent equal to 1 [Christensen, 1984]. This approximation greatly simplifies the flow calculations, and because activation values for diffusion creep are roughly half those of dislocation creep [Karato and Wu, 1993], no significant change to the viscosity in the model is required deeper in the mantle where the transition to diffusion creep is likely to occur. Activation values hereafter described in this paper are those we are trying to approximate, i.e., before dividing by two and changing the stress exponent, and thus can be directly comparable to laboratory constraints. We evaluate A by assigning the viscosity at the base of the model to Pas. Different values within the possible range of v* can lead to different degrees of asymmetry. The larger the value of v*, the more pressure-dependent the viscosity, and the more plate- or pressure-driven flow will be confined within a shallow, low-viscosity layer, which can more directly affect the region of melting beneath the axis. 3. Model Results [11] To provide a quantitative description of the degree of asymmetry about the axis for a given model, we determine a value y given by y ¼ q mwest =q mtot where q mtot is the integrated melt production rate over the entire box and y is the fraction of the total west of the axis. This measure is nonunique in that it does not weight melt production values further from the axis relative to values near the axis, but in practice it works well for relating models to each other in all but a few cases. Visual examination of maps of calculated melt production shows that an unambiguous asymmetry exists when two-thirds or more of the melt production occurs to the west of the axis. Therefore we choose y 0.66 as a threshold for significant asymmetry Ridge Migration [12] Rapid ridge migration is caused by the more rapid motion of the Pacific plate in the hot spot reference frame [Scheirer et al., 1998]. The rapid migration of the ridge (32 mm/yr) has been widely cited as a possible cause of melting asymmetry [e.g., MELT, 1998; Scheirer et al., 1998; Buck, 1999; Evans et al., 1999]. As the ridge migrates, it may tap less depleted material beneath the leading (Pacific) side, preferentially creating more melt to that side [e.g., Davis and Karsten, 1986]. Calculations for this case show that ridge migration by itself does not create any significant asymmetry in the melting region (Figure 4). The deep mantle (>200 km) moves from west to east, but the shallow mantle (<100 km), where melting occurs, has a predominantly symmetric upwelling structure. To a first approximation, the flow is a superposition of that driven by plate separation, which generates upwelling, and simple shear driven by migration of the entire system relative to the deeper mantle. Because the latter involves no upwelling except that caused by changes in plate thickness, it has little effect on the upwelling rates and subsequent melt production. [13] The symmetric upwelling structure creates a symmetric layer of depleted mantle about the axis. Because flow into the melt production region comes from below the ð7þ

5 CONDER ET AL.: ASTHENOSPHERIC FLOW AND ASYMMETRY OF THE EPR ETG 8-5 Figure 4. Depletion from melting, streamlines, and melt production for ridge migration only case. Melt production contours used throughout the manuscript. Although mantle flow deeper than 200 km is dominantly west to east, flow in the upper 150 km is dominated by symmetric corner flow, resulting in symmetric depletion (grayshades) and melt production (contours) about the axis. Units are dimensionless, so only relative magnitudes are important. Melting within the wet region is far less than that in the dry melting region and does not show up at these contour levels. our models, the incoming temperature anomaly must be at least 100 C (Figure 5) and extend over the depth range in which flow lines turn back westward for the anomaly to reach the axis, but no deeper, or hot material is fed to the east side of the axis as well (Figure 6). This depth range depends somewhat on v*, which controls the depth distribution of the return flow. If the anomaly extends more than km deep (base of return flow) the model advects high temperature material to both sides of the ridge, reducing the asymmetry by increasing melting on both sides of the axis (Figure 6c). If the extent of the anomaly is much shallower than the base of the return corner flow (<150 km), depleted layer (Figure 4), the geometry of melting is not affected by influx or recycling of mantle that has been previously partially melted at the ridge. A greater pressure dependence on viscosity (larger v*) confines the return flow to a narrower shallow channel, potentially increasing the incorporation of previously melted material into the axial melting region. Because the depleted layer tends to be symmetric, however, even with the highest experimental estimate of v*, no asymmetry develops in the melting region with ridge migration alone. Faster ridge migration may also increase asymmetry, but even a migration rate equal to the full spreading rate does not produce significant melting asymmetry. With reasonable parameters, ridge migration in our models never produces y > 0.53, well below the threshold of any detectable asymmetry. Melting of enriched heterogeneities, as envisioned by Davis and Karsten [1986], does not necessarily produce asymmetry of the correct sense because all mantle material entering the melting region comes from below. If heterogeneities are randomly distributed with depth, just as much excess melting would occur on the east side as the west side, because the material on both sides of the axis in the melting region has come from the west, below the recently depleted mantle (Figure 4) Temperature Anomaly [14] The explanation of hotter mantle temperatures to the west will produce more melt beneath the Pacific plate. A temperature gradient in the mantle was proposed by Cochran [1986] to explain the slow subsidence of the Pacific plate. In his model, a linear gradient was superimposed on a cooling half-space model, but the mechanism for maintaining this gradient was not discussed. The MELT Seismic Team [1998] and Toomey et al. [2002] suggest that hot asthenospheric material is fed to the ridge from the Pacific Superswell, 1500 km to the west. The explanation of incoming hotter material from the west as a cause for asymmetric melting about the axis is more complicated than it may initially seem. To exceed the 0.66 threshold for y in Figure 5. Dependence of asymmetry (y = 0.5, symmetric, 1, completely asymmetric) on viscosity structure (v*), temperature anomaly magnitude (Ta), and anomaly depth extent (z ta ). Higher v* corresponds to more pressure dependent viscosity. Weaker pressure dependence creates deeper corner flow, requiring a deeper anomaly to affect melting at the axis. The dotted contour is y = 0.66, where significant asymmetry begins to develop. All models require a temperature anomaly 100 C to create significant asymmetry. Temperature anomaly dimensions <150 km and >250 km deep do not create much asymmetry for any of the allowable viscosity structures.

6 ETG 8-6 CONDER ET AL.: ASTHENOSPHERIC FLOW AND ASYMMETRY OF THE EPR to the west and constricts the melting region to the east is consistent with the observed asymmetry about the EPR. [16] A global convection model, based on density variations inferred from seismic tomography, predicts pressures in the Pacific Superswell region strong enough to create 2 km of dynamic topography [Forte and Perry, 2000]. Dynamic pressures of this magnitude could create a pressure gradient in the mantle as large as a few 10s of kpa/km, large enough to create significant across-axis flow for reasonable mantle viscosities. Application of a pressure gradient of a few kpa/ km in the models induces significant across-axis asthenospheric flow, which is necessarily faster than simple platedriven flow. The resultant structure of the velocity field depends mainly on the relative viscosity structure, while the magnitude of the velocities depends on the absolute viscosity structure. A strong pressure dependence on viscosity (large v*) confines pressure-driven flow to a shallow asthenospheric channel. Because a shallower high velocity channel more directly affects the melting region beneath a spreading center, higher values of v* require smaller horizontal velocities within the asthenosphere to produce the same degree of asymmetry. A midrange v* value of m 3 /mol and a pressure gradient of 1500 Pa/km (assuming a normalization viscosity of Pas) creates highly asymmetric melting (y 0.75), extending 100s of km to the west and 10s of km to the east (Figure 7a), and implies a peak horizontal asthenospheric velocity of 300 mm/yr near Figure 6. Temperature (T), streamlines, and melt production for models with a 100 C thermal anomaly (Ta) introduced from the west at (a) 150 km, (b) 200 km, and (c) 250 km depth. Asymmetry values for each are 0.58, 0.66, and 0.62, respectively. Melt production asymmetry in these models comes from a larger increase the amount of melt on the west side than on the east side. If the anomaly is confined above the 150 km deep streamline, there is little effect on the melting region. If the anomaly extends down to the 250 km or deeper streamlines, the anomaly increases melt production on both sides of the axis. See color version of this figure at back of this issue. the excess temperatures will not reach the axis and no excess melting will occur, producing y values comparable to ridge migration alone (Figure 6a) Pressure-Driven Flow [15] Pressure-driven asthenospheric flow may be an important factor in creating asymmetry about the EPR. Pressure-driven flow tends to follow the base of the overlying lid (lithosphere). Since the lithosphere thins toward the axis, flow from the west has more upwelling on the western ( upwind ) side, enhancing the melt production. In contrast, flow across the axis to the east encounters an increasingly thick lithosphere, forcing a downward component to the flow, restricting the amount of upwelling and melt production on the eastern ( downwind ) side of the axis. Flow that simultaneously expands the melting region Figure 7. Melt production in models including a pressure gradient. The degree of asymmetry increases with an increasing pressure gradient and with increasing pressure dependence on viscosity. (a) With intermediate pressure dependence of viscosity and a modest pressure gradient, asthenospheric flow rates reach 300 mm/yr and produce asymmetry, y, equal to 0.75 close to that suggested by seismic results of the MELT experiment (see text). (b) with a slightly larger pressure gradient and stronger pressure dependence on viscosity, asthenospheric flow reaches rates near 1 m/yr and produces y equal to 0.93, close to that suggested by the electrical conductivity results of the MELT experiment.

7 CONDER ET AL.: ASTHENOSPHERIC FLOW AND ASYMMETRY OF THE EPR ETG 8-7 Figure 8. Dependence of asymmetry, y, on viscosity structure (v*) and asthenospheric flow velocities (u x )for pressure-driven flow. Asymmetry increases with faster asthenospheric flow and increasing v*. The dotted contour is y = 0.66, where notable asymmetry begins to develop (same as Figure 5), and the dashed is y = 0.75, a value consistent with the seismic results from the melt experiment. The white line corresponds to asthenospheric velocity of 300 mm/yr, consistent with the Pukapuka ridge propagation rate towards the EPR from the superswell. Our preferred model is found where the white line and dashed contour intersect. 100 km depth. Stronger pressure gradients and larger activation volumes for a given pressure gradient increase both the degree of asymmetry and the horizontal velocities within the asthenosphere. A pressure gradient of 5000 Pa/km and v* = m 3 /mol creates an extremely asymmetric melting region (y 0.93) (Figure 7b), but also implies a peak asthenospheric velocity near 1 m/yr. [17] To explore the range of possible states of the mantle, assuming the known asymmetries are caused by a pressure gradient, we ran a suite of models over a range of pressure gradients and possible v* values. Velocities in the asthenosphere depend on both the magnitude of the pressure gradient and the absolute mantle viscosity. Because mantle pressure gradients and viscosity are constrained only by order of magnitude estimates, we report our results here in terms of peak asthenospheric velocity (u x ) rather than absolute pressure gradient magnitudes. Peak asthenospheric velocity as reported in this paper is the maximum horizontal velocity within the mantle column 300 km west of the axis. The dependence of the asymmetry, y, onu x and v* are shown in Figure 8. y increases with increasing u x and with increasing v*. Upper values of v* ( m 3 /mol) begin to exhibit significant asymmetry (y 0.66) with asthenospheric velocities 200 mm/yr. The same degree of asymmetry at lower values of v* requires asthenospheric velocities near 400 mm/yr. 4. Discussion 4.1. Degree of Asymmetry [18] Figures 5 and 8 show the model parameters required for various degrees of melt production asymmetry. The degree of asymmetry required to match the observations is less clear. None of the observations are directly sensitive to the melt production rate. Densities, seismic velocities, and electrical properties all depend on the amount of melt actually present and how it is distributed, rather than the rate it is produced. We do not know the pathways and efficiency of melt extraction from the mantle, but we note that none of the observations reported to date require that more than 1 2% melt be present [Forsyth et al., 1998; MELT Seismic Team, 1998; Toomey et al., 1998; Webb and Forsyth, 1998; Evans et al., 1999]. Consequently, we assume that some small melt fraction is retained wherever melt is produced and that melt above that fraction is efficiently extracted. In the exploration of models presented in this paper, we do not attempt to match the observations precisely. Instead, we compare our models to qualitative indications of the presence of melt inferred from the seismic and electromagnetic components of the MELT. The Rayleigh wave tomography (Figure 2) shows that low velocities at km depth in the primary melt production range extend km off-axis to the west, but only tens of km to the east. Resistivities [Evans et al., 1999] within km of the axis to the east give no indication of the presence of melt or water, while a more conductive structure to the west indicates the possible presence of 1 2% interconnected melt. The horizontal extent of the more conductive region to the west is not well constrained. [19] There are several possible explanations for the apparent difference in the abruptness of the change in structure at the axis. At first glance, the electrical conductivity suggests essentially no melt production east of the axis, or y 1 (e.g., Figure 7b). The Rayleigh wave data seems compatible with lower degrees of asymmetry, closer to y 0.75 (e.g., Figure 7a). One possibility is just differences in horizontal resolution. The Rayleigh wave tomography, for example, involves horizontal averaging over scales on the order of 100 km [Forsyth et al., 1998]. There also may be geological reasons for the discrepancy. For instance, the difference could be in the connectivity of the melt present. The velocity structure is sensitive to melt fraction and the shape of the melt pockets, whereas conductivity depends critically on whether the melt pockets are interconnected [Schmeling, 1986]. Thus, if some small melt fraction is retained outside the melt production region and is no longer being extracted through interconnected channels, it could have both low conductivity and low seismic velocities. Another possible explanation is an anisotropic distribution of melt pockets or crystalline fabric. The Te and Tm modes of the electrical conductivity measurements are sensitive to conductivity in the horizontal directions, but relatively insensitive to conductivity in the vertical direction [Evans and Everett, 1992]. If water is present in olivine, it most strongly lowers resistivity along the a-axis of the crystals [Mackwell and Kohlstedt, 1990]. If the a-axes were oriented upward in a vertically upwelling region, the apparent resistivity in a magnetotelluric experiment would resemble that of dry olivine. Similarly, if melt on the east side of the axis is aligned in vertical channels, it may give slow seismic velocities and a resistive conductivity structure. Why melt would align differently on one side of the axis than the other is speculative, but it may occur if melt is focused to the axis through a fractal tree of melt channels, as some geo-

8 ETG 8-8 CONDER ET AL.: ASTHENOSPHERIC FLOW AND ASYMMETRY OF THE EPR chemical and field mapping studies suggest [Hart, 1993; Kelemen et al., 1995]. A fractal tree that drains a region with a strong asymmetry in melt production may comprise more horizontal branches to the west, and more vertical branches to the east. Given the uncertainties in the interpretation of the electrical conductivity measurements, we prefer a model with a y value Temperature Anomaly [20] As noted above, melting asymmetry 0.66 is created by an incoming temperature anomaly from the west only if the anomaly is >100 C and extends from the shallowest mantle to 200 km depth (Figure 8). The anomaly required to match the observed asymmetry (y ) must be 150 C 200 C. Even 100 C is much larger than the 40 C temperature anomaly beneath the superswell inferred from the seismic structure [McNutt and Fischer, 1987]. A 100 C anomaly extending to 200 km depth also overpredicts the asymmetric seafloor subsidence. The appropriate depth of compensation for calculating seafloor topography depends on the viscosity structure, as a shallow, low viscosity layer isolates deeper structure from creating a topographic response [Robinson et al., 1988]. Depending on the viscosity contrasts in the mantle, density anomalies can have different contributions to seafloor topography. For a large contrast between a low-viscosity asthenosphere and a higher-viscosity mesosphere, density anomalies within the asthenosphere have a decreasing effect on seafloor topography with increasing depth, becoming effectively zero for anomalies at the base of the asthenosphere. For smaller viscosity contrasts, the seafloor has a greater response to deep density anomalies, particularly at longer wavelengths [Robinson et al., 1987]. [21] To calculate the seafloor topography for a given model we assume a 20 km thick, high-viscosity lithosphere, which contributes fully to seafloor topography, overlying a 200 km thick asthenosphere that has a linearly decreasing contribution with depth, above a semiinfinite mesosphere that does not contribute to seafloor topography. By assuming that the viscosity contrast is large between the asthenosphere and the mesosphere so that the seafloor response goes to zero at the base of the asthenosphere, we obtain a minimum estimate of the subsidence asymmetry created by different thermal anomalies within the asthenosphere. If the viscosity contrast is not large, any additional response from deep anomalies will only increase subsidence asymmetry. Assuming this response kernel, a 200 km deep, 100 C anomaly makes the subsidence too asymmetric by shallowing the western side of the axis by meters relative to the eastern side (Figure 9). Another observation inconsistent with the temperature anomaly model is that the crustal thickness in the MELT area ( km) is near or possibly thinner than the global average [Canales et al., 1998]. Higher temperatures should result in more melting and generate thicker crust unless the melt does not make it to the axis or the east side is anomalously cold. A final caveat to the incoming temperature anomaly model is that introducing anomalously warm material to one side of the axis can increase the melt production on that side, but cannot decrease the amount of melting on the other side, as many of the observations suggest (delay times, velocity structure, electrical conductivity, etc.). A small incoming Figure 9. EPR bathymetry (solid line) with predicted subsidence from models creating significant melting asymmetry solely with a thermal anomaly axis from the west. The dashed line is the predicted subsidence with 200 km deep, 100 C anomaly (Figure 6b). The model overpredicts the asymmetric subsidence by more than 100 meters. If a viscosity increase with depletion from melting is assumed, a 100 C anomaly 300 km deep (Figure 13) is required to create significant melting asymmetry, producing an even poorer fit to the subsidence (dotted line). temperature anomaly may likely be present but is not sufficient to explain the observed asymmetry, with the simple, passive flow models considered here Subsidence [22] The southern EPR exhibits the largest subsidence asymmetry of any oceanic spreading center, subsiding at rates of m/myr 1/2 to the west and m/ Myr 1/2 to the east [Cochran, 1986]. The asymmetry has usually been attributed to thermal variations within the mantle [Rea, 1978; Cochran, 1986; Marty and Cazenave, 1989; Lago et al., 1990; Perrot et al., 1998]. As an alternative to thermal models, the asymmetry could be caused by dynamic topography from a pressure gradient superimposed on a symmetrically subsiding lithosphere. We note that there is no identifiable long-wavelength trend in the free-air gravity anomaly to suggest dynamically supported topography. Therefore, dynamic topography must either be small or compensated by a downward deflection of a deeper density contrast, such as the 410 or 660 mantle discontinuities or even an asthenosphere-mesosphere boundary [Phipps Morgan et al., 1995]. To investigate the different mechanisms for subsidence asymmetry, we extracted from the predicted topography of Smith and Sandwell [1997] a profile normal to the EPR spreading axis to compare with various models (Figures 9, 10, and 11). The profile location was chosen to avoid seamounts; it is centered on W, 17.1 S, and extends 1000 km to each side of the axis. [23] Cochran [1986] proposed a horizontal, linear temperature gradient of C/km within the asthenosphere beneath a symmetrically subsiding plate that could explain the subsidence of the EPR. Because thermal anomalies rapidly advect through the near-ridge region of melting, homogenizing mantle temperatures, such a gradient must either be a transient feature approximating the current temperature structure, or be maintained by vigorous,

9 CONDER ET AL.: ASTHENOSPHERIC FLOW AND ASYMMETRY OF THE EPR ETG 8-9 [25] With the addition of a linear gradient, the subsidence is described by d ¼ d 0 þ C 1 t 1=2 þ mx ð9þ Figure 10. Subsidence for models with imposed temperature gradients of 0.1 C/km (dashed) and 0.2 C/km (dotted) applied across the bottom. The bottom boundary must be open to flow so the gradient can be advected upward without being smeared out. The 0.1 C/km model fits the topography well, but does not exhibit much asymmetric melting (y = 0.59), as the total temperature difference across the melting region is only on the order of 20 C. A gradient of 0.2 C/km produces more melting asymmetry (y = 0.64), but has a noticeably worse fit to the topography (dotted line). small-scale convective mixing, tapping a larger mantle reservoir. A gradient as high as 0.1 C/km fits the topography (Figure 10), but is not large enough to produce major asymmetry in melting (y = 0.59). Larger gradients yield more easily detectable asymmetry in melting, but poorer fits to the topography (Figure 10). Thus, in addition to requiring an unknown mechanism to create the thermal gradient, no linear temperature gradient alone adequately matches both the asymmetric subsidence and the asymmetric seismic and conductivity structure. [24] More complex, time-dependent, thermal models for subsidence have also been proposed. For example, Lago et al. [1990] proposed a model for asymmetric subsidence in which the temperatures beneath the ridge axis are different than asthenospheric temperatures, but still could not find a reasonable fit to subsidence in the MELT area. Perrot et al. [1998] suggest that the initial ridge depth (d 0 ) and seafloor subsidence parameter of each side of the axis (C 1,2 ), given by where x is distance from the axis (positive to the east). The best fitting ridge depth and subsidence parameter for this model are 2790 m and 319 m/myr 1/2, respectively. The linear gradient has a slope (m) of 0.17 m/km, which can be explained by a pressure gradient of 7800 Pa/km, assuming a compensating deflection on a deeper boundary (twice the gradient required for topography alone, since half the excess pressure is required to deflect a deeper density interface to satisfy the gravity constraint). The twelve parameter model of Perrot et al. [1998] for four age zones fits slightly better (Figure 11) than this simpler model, but if the subsidence parameters are not allowed to be less than 100 m/myr 1/2 in any age interval, then an F test demonstrates that the fit with twelve parameters is not significantly better than our fit with three Pressure-Driven Mantle Flow [26] Pressure-driven mantle flow from the Pacific superswell can create asymmetry in the melting region that matches the observations. An important effect of pressuredriven flow is that a low-viscosity asthenosphere can flow significantly faster than plate-driven flow. The velocity at which the asthenosphere flows is unknown. Vogt [1971] suggested that asthenosphere flows from Iceland along the Reykjanes Ridge at a rate of 200 mm/yr. Modeling results have suggested asthenospheric velocities in the Indian mantle as high as 1 m/yr [Yale and Phipps Morgan, 1998]. For the highest acceptable activation volume ( m 3 /mol), melt production asymmetry in our models closely matching S-wave velocity asym- d ¼ d 0 þ C 1;2 t 1=2 ð8þ where d is the seafloor depth and t is age, are dependent on the thermal structure of the ridge at the time of crustal production, which can vary with time. To explain the asymmetry in subsidence, they appeal to the same asthenospheric temperature mechanism invoked by Cochran, because variations in axial conditions alone predict no asymmetry. Their calculations suggest an increase in asymmetry with increasing age of the seafloor. We believe that the asymmetry and the apparent increase in asymmetry when modeled as subsidence proportional to the square root of age are better explained by the superposition of a linear, west-to-east, topographic gradient on a symmetric subsidence profile. Figure 11. Thermal and dynamic models of asymmetric subsidence in the MELT area. Solid line is across-axis bathymetry. Vertical, dotted lines show four separate time intervals used to find best-fitting parameters (following Perrot et al. [1998]). Data is fit fairly well (thick dashes) if unrealistically slow (<100 m/myr 1/2 ) subsidence parameters are allowed. Thin solid line shows the same data fit with a linear topographic gradient (0.174 m/km) superimposed on symmetric subsidence. If the 12 parameter model is required to use subsidence parameters >100 m/myr 1/2, the resulting fit is not statistically better than the three parameter model.

10 ETG 8-10 CONDER ET AL.: ASTHENOSPHERIC FLOW AND ASYMMETRY OF THE EPR metry (y 0.75) develops with an asthenospheric velocity near 170 mm/yr (Figure 8). In a preferred model with a less extreme activation volume ( m 3 / mol), but exhibiting the same asymmetry (y 0.75), the asthenospheric flow rates are near 300 mm/yr (Figure 7a). Although these flow rates seem high, independent evidence may support this rate of transport toward the ridge axis in this area. The Pukapuka intraplate volcanic ridge propagated from French Polynesia to near the EPR at about 17 S at a rate of about 300 mm/yr [Sandwell et al., 1995]. The lavas carry a distinct isotopic signature and are derived from shallow melting of an enriched source [Janney et al., 2000]. Transport of a compositional heterogeneity toward the EPR in the asthenosphere from the superswell could have triggered melting and local small-scale convection that may have been responsible for ridge formation. Assuming the pressure gradient determined by the asymmetric subsidence, this flow rate suggests that the asthenospheric viscosity in this area near the EPR reaches a minimum of about Pas, consistent with the Pas asthenospheric viscosity inferred at Iceland from glacial rebound studies [Sigmundsson, 1991]. [27] Seismic results from an experiment across the Lau back arc spreading center [Wiens et al., 1995] also suggest the possibility of melting asymmetry created by across-axis flow. P wave tomography exhibits a markedly asymmetric slow region beneath the axis, extending 200 km to the west and <50 km to the east [Zhao et al., 1997]. Attenuation tomography from the same data exhibits a fairly symmetric low Q region just beneath the axis [Roth et al., 1999]. Seismic velocities and attenuation are both sensitive to temperature and melt present, but velocities are more sensitive to melt while attenuation is more sensitive to temperature [Forsyth, 1992]. Back arc mantle dynamics are likely dominated by corner flow induced from the subduction zone [Davies and Stevenson, 1992]. Imposing corner flow over a back arc region with a spreading center may induce more upwelling on one side of the axis than the other, but would have little direct affect on the temperatures near the axis, accounting for both the asymmetric velocity structure and the symmetric attenuation structure. More investigation is required to confirm this model, but qualitatively it matches the observations well Dehydration Effect [28] Some laboratory experiments suggest that the presence of water reduces the viscosity of olivine by a factor of [Hirth and Kohlstedt, 1996]. Since water is incompatible during melting, melting extracts water and may consequently increase mantle viscosity. Several midocean ridge modeling studies have incorporated this effect [e.g., Phipps Morgan, 1997; Ito et al., 1999; Braun et al., 2000]. These studies assume seafloor spreading is a symmetric process, using symmetry boundary conditions beneath the axis. Following Braun et al. [2000], we use a parameter, h dry, to examine the effects of a possible large increase in viscosity with dehydration. Mantle that has been depleted by more than 2% is assumed to be dry, so its viscosity from equation (6) is multiplied by h dry. Viscosity increases for mantle with depletion values less than 2% are assumed to be linearly proportional to h dry. Figure 12. (a) Viscosity profile directly beneath the axis assuming a 100 viscosity increase with depletion from melting (solid line). The dotted line is a profile from an identical model without a viscosity increase with depletion. (b) Melt production in a model including both the pressure gradient used in Figure 7a and a 100 viscosity increase with depletion. The shallowest mantle where melting has occurred is coupled to lithospheric plate spreading, driving symmetric upwelling beneath the spreading center (y = 0.53). (c) Temperature, streamlines, and melt production for a model with the temperature anomaly (100 C) required to make asymmetric melting (y = 0.66) when an increase in mantle viscosity with depletion is assumed. Because the uppermost mantle couples to the lithosphere with an increase in viscosity, spreading is symmetric to greater depths. A temperature anomaly originating far from the axis, must be 300 km deep to reach the axis. The subsidence predicted by this model is a poorer fit to the data than a model with no viscosity increase (Figure 9). See color version of this figure at back of this issue. Figure 12 shows a viscosity profile and the melting regime for the same model shown in Figure 7a but with h dry equal to 100. The increase in viscosity in the shallow mantle couples the shallow mantle flow with the lithospheric plate spreading, driving symmetric upwelling in the melting regime. A viscosity increase with dehydration implies that the lowest viscosity mantle will always be beneath the melting zone. Because the lowest viscosities are deeper than the melting region, shear between the plates and deep mantle is accommodated below the upwelling and melting zone. Figure 13 shows the asymmetry dependence on u x and v* forh dry = 10 and 100. For asymmetric melting to develop with pressure-driven flow, asthenospheric velocities must be roughly doubled even for a modest viscosity increase of one order of magnitude with depletion. A viscosity increase by a factor of 100 requires asthenospheric velocities on the order of meters per year even for large v* values. A viscosity increase in the shallow mantle