Earth and Planetary Science Letters 270 (2008) 231–240
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Earth and Planetary Science Letters j o u r n a l h o m e p a g e : w w w. e l s e v i e r. c o m / l o c a t e / e p s l
Mantle flow and melting beneath oceanic ridge–ridge–ridge triple junctions Jennifer E. Georgen ⁎ Department of Geological Sciences, Florida State University, 311A Carraway, Tallahassee, FL 32306, USA
A R T I C L E
I N F O
Article history: Received 12 March 2008 Accepted 13 March 2008 Available online 9 April 2008 Editor: R.D. van der Hilst Keywords: mid-ocean ridge numerical model Rodrigues Triple Junction Azores Triple Junction Southwest Indian Ridge Terceira Rift
A B S T R A C T Plate boundary geometry likely has an important influence on crustal production at mid-ocean ridges. Many studies have explored the effects of geometrical features such as transform offsets and oblique ridge segments on mantle flow and melting. This study investigates how triple junction (TJ) geometry may influence mantle dynamics. An earlier study [Georgen, J.E., Lin, J., 2002. Three-dimensional passive flow and temperature structure beneath oceanic ridge-ridge-ridge triple junctions. Earth Planet. Sci. Lett. 204, 115–132.] suggested that the effects of a ridge–ridge–ridge configuration are most pronounced under the branch with the slowest spreading rate. Thus, we create a three-dimensional, finite element, variable viscosity model that focuses on the slowest-diverging ridge of a triple junction with geometry similar to the Rodrigues TJ. This spreading axis may be considered to be analogous to the Southwest Indian Ridge. Within 100 km of the TJ, temperatures at depths within the partial melting zone and crustal thickness are predicted to increase by ~ 40 °C and 1 km, respectively. We also investigate the effects of differential motion of the TJ with respect to the underlying mantle, by imposing bottom model boundary conditions replicating (a) absolute plate motion and (b) a threedimensional solution for plate-driven and density-driven asthenospheric flow in the African region. Neither of these basal boundary conditions significantly affects the model solutions, suggesting that the system is dominated by the divergence of the surface places. Finally, we explore how varying spreading rate magnitudes affects TJ geodynamics. When ridge divergence rates are all relatively slow (i.e., with plate kinematics similar to the Azores TJ), significant along-axis increases in mantle temperature and crustal thickness are calculated. At depths within the partial melting zone, temperatures are predicted to increase by ~ 150 °C, similar to the excess temperatures associated with mantle plumes. Likewise, crustal thickness is calculated to increase by approximately 6 km over the 200 km of ridge closest to the TJ. These results could imply that some component of the excess volcanism observed in geologic settings such as the Terceira Rift may be attributed to the effects of TJ geometry, although the important influence of features like nearby hotspots (e.g., the Azores hotspot) cannot be evaluated without additional numerical modeling. © 2008 Elsevier B.V. All rights reserved.
1. Introduction The geometry of plate boundaries may play a significant role in the style of magmatic production along mid-ocean ridges. For example, studies have focused on the importance of transform offsets in suppressing melting (Phipps Morgan and Forsyth, 1988; Shen and Forsyth, 1992) and the effects of obliquity on ridge tectonics and crustal accretion (Dauteuil and Brun, 1993; Okino et al., 2002; Dick et al., 2003). This study uses three-dimensional numerical modeling to investigate mantle processes at another distinct type of plate boundary geometry, the triple junction. Triple junctions, defined as locations where three plate boundaries meet at a single point, are likely to mark regions of unusual mantle geodynamics. This study examines the particular case where all three boundaries of a triple junction are divergent ridges. Such ridge–ridge– ridge (RRR) triple junctions are observed in a number of locations, ⁎ Tel.: +1 850 645 4987; fax: +1 850 644-4214. E-mail address:
[email protected]. 0012-821X/$ – see front matter © 2008 Elsevier B.V. All rights reserved. doi:10.1016/j.epsl.2008.03.040
including the Rodrigues Triple Junction (RTJ) in the Indian Ocean (Tapscott et al., 1980; Sclater et al., 1981; Mitchell and Parson, 1993; Patriat et al., 1997), the Azores Triple Junction (ATJ) in the north Atlantic Ocean (Krause and Watkins, 1970; Searle, 1980), the Bouvet Triple Junction in the south Atlantic Ocean (Sclater et al., 1976; Ligi et al., 1999), and the Galapagos Triple Junction (GTJ) in the Pacific Ocean (Searle and Francheteau, 1986; Lonsdale, 1988). Neglecting factors such as segment-scale melt focusing, the flow fields and thermal patterns along single ridges are predicted to be principally two-dimensional, with upwelling underneath the ridge axis transitioning to dominantly horizontal plate-driven flow away from the spreading center (e.g., Reid and Jackson, 1981; Spiegelman and McKenzie, 1987; Phipps Morgan and Forsyth, 1988). However, near a triple junction, the flow fields of three ridges are likely to interact, producing a complex, three-dimensional pattern of mantle motion and gradients of crustal thickness along ridge axes. An earlier study (Georgen and Lin, 2002) presented a simplified model of mantle geodynamics for the three ridges of an RRR triple junction with geometry similar to the RTJ. Their investigation used a model in which
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upwelling of an isoviscous mantle was driven by divergence of three surface plates away from a fixed triple junction point. In this way, the calculations of Georgen and Lin (2002) represent a passive, relative plate motion model. Georgen and Lin (2002) predicted strong along-axis flow, as well as significant gradients in mantle temperature and upwelling velocity, along the slowest-spreading of the three ridges. In contrast, the geodynamics of the two faster-spreading ridges differed little from the single-ridge case. Therefore, in this investigation we will focus on calculating mantle velocity, mantle temperature, and crustal thickness for the slowest-spreading ridge, the branch predicted to be most affected by the triple junction geometry. We will incorporate factors not considered in Georgen and Lin (2002), such as variable viscosity, thermal buoyancy, and differential motion of the triple junction with respect to the underlying mantle. We will also compare model predictions to bathymetry, gravity, and geochemical data collected along spreading centers most analogous to the modeled systems, the Southwest Indian Ridge (SWIR) and Terceira Rift, to draw inferences about mantle processes in these two settings. 2. Geometry of RRR triple junctions More than twenty triple junctions currently exist, and considerably more have operated throughout Earth's history. Many of these present and paleo triple junctions have been the subject of studies focusing on their plate kinematics and seafloor morphology. For example, Searle (1980) used bathymetric and GLORIA sidescan data to investigate seafloor fabric and rift propagation at the ATJ. The GTJ has been the focus of extensive
surveys and plate motion studies, including Searle and Francheteau (1986), Lonsdale (1988), and Klein et al. (2005). Larson et al. (2002) and Pockalny et al. (2002) explored the now-extinct Tongareva triple junction in the western Pacific, and Sager et al. (1999) examined the creation and evolution of the Pacific–Izanagi–Farallon triple junction. 2.1. Rodrigues Triple Junction This study focuses primarily on a plate kinematic configuration similar to that of the RTJ (also known as the Indian Ocean Triple Junction) (Fig. 1). This triple junction is comprised of the ultra-slow-spreading SWIR (half-rate ~0.7–0.8 cm/yr), and the intermediate-spreading Central (CIR) and Southeast Indian (SEIR) ridges, with half-rates of ~2.3 cm/yr and ~2.8 cm/yr, respectively. The RTJ is a good candidate for numerical modeling because of its relatively simple geometry. For example, the kinematics of the RTJ are not complicated by the presence of a microplate. Additionally, upwelling patterns at the RTJ are not expected to be influenced by features such as mantle plumes, as the nearest hotspot to the triple junction, Reunion, is presently located more than 1000 km away. Moreover, the RTJ is a relatively stable feature. Plate kinematic and seafloor morphology studies suggest that the triple junction has been stable for perhaps as long as 40 Myr (Tapscott et al., 1980; Sclater et al., 1981). For the last ~80 Myr, the triple junction has been migrating eastward in the hotspot reference frame, accommodated by lengthening of the CIR and the SEIR by 1.3 and 2.7 cm/yr, respectively (Tapscott et al., 1980). Thus, because of its long-term stability, large distance from hotspot influence, and relatively simple plate boundary
Fig. 1. Location maps for the (a) Rodrigues, (b) Azores, and (c) Galapagos triple junctions. Black lines indicate plate boundaries, and yellow stars mark the locations of the nearest hotspot to each triple junction. SWIR = Southwest Indian Ridge, SEIR = Southeast Indian Ridge, CIR = Central Indian Ridge, N. MAR = Mid-Atlantic Ridge north of the Azores Triple Junction, S. MAR = Mid-Atlantic Ridge south of the Azores Triple Junction, Ter. R. = Terceira Rift, N. EPR = East Pacific Rise north of the Galapagos Triple Junction, S. EPR = East Pacific Rise south of the Galapagos Triple Junction, and GSC = Galapagos Spreading Center. Free-air gravity data are from Sandwell and Smith (1997), and ridge coordinates are from Mueller et al. (1997). (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)
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configuration, the RTJ is selected to be the type example for the numerical modeling experiments in this investigation. In an earlier numerical modeling study also focusing on the RTJ, Georgen and Lin (2002) predicted that for the slowest-spreading (SWIR-like) ridge, a strong component of along-axis flow advected material away from the triple junction point. Likewise, they calculated that upwelling velocity along the slowest-spreading ridge increases more than threefold within 200 km of the triple junction, and that mantle temperatures within the melting zone increase by approximately 75 °C over roughly the same distance. In contrast, the upwelling velocity and temperature for the fastest-spreading ridge was not predicted to differ significantly from the single-ridge case. Thus, this investigation constructs a numerical model specifically designed to examine the geodynamics of the boundary predicted to be most affected by the triple junction configuration, the slowestspreading (or SWIR-like) ridge. For modeling simplicity, the two faster-spreading ridges are oriented perpendicular to the slowestspreading ridge. Although strictly speaking such a triple junction configuration would not be stable in nature (McKenzie and Morgan, 1969), we find that this model reproduces to within b5% the velocity and temperature fields predicted for the corresponding model setup of Georgen and Lin (2002), where the ridges are aligned in a nonperpendicular, unconditionally stable configuration. Therefore, this more convenient model configuration is likely to represent well the first-order patterns of triple junction mantle flow. 2.2. Azores and Galapagos triple junctions Another purpose of this investigation is to explore the effect of varying spreading rates on patterns of mantle flow and temperature. Thus, we also use model boundary conditions with characteristics similar to the GTJ and the ATJ, which have overall spreading rates faster and slower, respectively, compared to the RTJ. There is evidence that the ATJ (Fig. 1) has existed since approximately 45 Ma (Krause and Watkins, 1970; Searle, 1980). Two branches of the ATJ
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are the Mid-Atlantic Ridge (half-rate 1.1–1.2 cm/yr). The third branch is the Terceira Rift. The Terceira Rift has been variously explained as a zone of distributed deformation or as an extensional strike-slip boundary (Miranda et al.,1988; Lourenco et al., 1998; Luis et al.,1998), but we follow researchers such as Vogt and Jung (2004) in describing the Terceira Rift as an ultra-slow diverging ridge with a half-rate of ~0.3 cm/yr. The Terceira Rift is a relatively recent feature; divergence likely began only in the last 5 Myr (Luis et al., 1998; Vogt and Jung, 2004). Crustal accretion processes at the ATJ are significantly affected by the nearby Azores hotspot. Although the nature and source of excess volcanism in the Azores region is debated (e.g., Bonatti, 1990), several lines of evidence point to the hotspot as a plume-like structure. For example, the hotspot is associated with mantle seismic anomalies (Zhang and Tanimoto, 1992; Montelli et al., 2004; Yang et al., 2006), plume noble gas signatures (Moreira and Allegre, 2002; Madureira et al., 2005), and bathymetry and gravity anomalies (Goslin and Triatnord Scientific Party, 1999; Cannat et al., 1999a; Escartin et al., 2001). The location of the plume conduit is likely to be ~100–300 km to the east of the Mid-Atlantic Ridge (Zhang and Tanimoto, 1992; Yang et al., 2006). The GTJ (Fig. 1) is comprised of a northern branch of the East Pacific Rise, a southern branch of the East Pacific Rise, and the Galapagos Spreading Center, with half-rates of 6.9, 6.8, and 2.1 cm/yr, respectively. The tectonics of the GTJ appear to be quite complex, with a complicated pattern of microplates, incipient rifts, and failed rifts (Lonsdale, 1988; Lonsdale et al., 1992; Klein et al., 2005). However, it is unlikely that the upwelling patterns at the GTJ are influenced by the Galapagos hotspot, which is located more than 1000 km away from the junction point. 3. Numerical method We use a three-dimensional, finite element numerical model to solve for steady-state patterns of incompressible mantle flow. As discussed previously, the numerical box (Fig. 2) is designed to focus on geodynamical processes along a single branch of the triple junction,
Fig. 2. Schematic representation of the computational domain. The triple junction is represented by the intersection of two collinear spreading branches with a slower-spreading ridge. Mantle flow is driven by the surface divergence of two plates at the top of the model domain, indicated by thick gray arrows. Surface divergence vectors are taken from earlier studies of triple junction kinematics (e.g., Tapscott et al., 1980 for the RTJ-like case). Spreading vectors for the faster ridges and slower ridge (ufaster and uslower, respectively) are the component of the plate motion vectors perpendicular to the spreading boundaries, and are shown with thin black arrows. Boundary conditions for the top, bottom, and vertical side boundaries underneath the faster ridges are indicated on the figure. All other boundaries are assigned neutral velocity conditions and zero horizontal temperature gradient.
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here chosen to be the slowest-spreading ridge. The top surface of the model box is divided into two plates, separated by an intervening linear ridge of length 600 km. Two faster-spreading ridges orthogonally intersect the slowest-spreading ridge. Flow is driven by the motion of the surface plates. The component of the plate velocity vector perpendicular to each ridge is equal to the ridge's halfspreading rate (e.g., for the RTJ-like case, 0.7 cm/yr for the slowerspreading ridge). We emphasize that in the numerical models, elements of the seafloor geological complexity have been simplified considerably to make the models numerically tractable. For example, the GTJ-like case does not include microplates, which are likely to alter the dynamics of mantle upwelling near the triple junction point. Rather than exactly modeling a specific geological system, the purpose of these numerical experiments is to investigate how characteristics of the mantle flow are affected by changing some of the important variables that control marine geodynamical processes, such as plate spreading rate. We use the finite element software package COMSOL to solve the coupled equations for conservation of mass ju¼0
ð1Þ
momentum jp þ qg ¼ j ½gju
ð2Þ
and energy jj2 T ¼ u jT
ð3Þ
where u is velocity vector, ρ is mantle density, p is fluid pressure, g is the magnitude of gravitational acceleration, T is temperature, and κ is thermal diffusivity. Values for scalar parameters are provided in Table 1. For the variable-viscosity calculations, mantle density ρ is temperature-dependent, such that q ¼ qo ð1 aT Þ:
ð4Þ
where ρo is the reference mantle density. Viscosity is calculated as a function of temperature and pressure g ¼ go exp½ðE þ pV Þ=ðRT Þ
ð5Þ
where ηo is reference viscosity, E is activation energy, p is depthdependent pressure, V is activation volume, and R is the ideal gas constant. For numerical simplicity, we approximate the mantle as a Newtonian fluid by using appropriately-scaled values for activation energy and volume (Christensen, 1984; Shen and Forsyth, 1992). We allow viscosity to vary over three orders of magnitude (from 1019 to 1022 Pa s), which is sufficient for the formation of a lithospheric layer at the top of the model box.
Table 1 Model parameters Variable
Meaning
Value
Units
E V ηo ρo g R κ α x y z u T p
Activation energy Activation volume Minimum viscosity Reference mantle density Gravitational acceleration Universal gas constant Thermal diffusivity Coefficient of thermal expansion Along-axis distance Axis-perpendicular distance Depth below model surface Velocity vector Temperature Pressure
260 4 × 10 6 1019 3300 9.8 8.3144 1 3 × 10− 5
kJ/mol m3/mol Pa s kg/m3 m/s2 J/mol K mm2/s K− 1 km km km cm/yr °C Pa
Melting is calculated in a manner similar to Sparks and Parmentier (1993) and Shen and Forsyth (1992), following McKenzie and Bickle (1988). The solidus is defined as Tsolidus ¼ 1160- þ 3:25z
ð6Þ
where z is depth in km. Melt fraction F is F ¼ ðT Tsolidus Þ=400 -C
ð7Þ
and melt production rate Γ is C ¼ jF u:
ð8Þ
Crustal thickness is then determined by integrating melt production rate over an axis-perpendicular plane, dividing by the spreading rate, and assuming that all melt produced is delivered to the ridge axis. In a future study (Georgen et al., in prep.), melting will be treated in a more rigorous manner, to predict geochemical trends along the slowest-spreading ridge axis. That is, melting will be coupled in with the conservation equations. In this way, there will be additional feedbacks that modulate the temperature field. For example, the inclusion of a latent heat term would be expected to reduce the calculated temperatures somewhat. However, because high gradients in temperature and velocity near the triple junction point make numerical stability difficult to achieve, such calculations are beyond the scope of the current paper, and we instead provide the results of very simplified crustal thickness predictions merely to illustrate primarily-qualitative first-order trends in melting along the ridge axis. At the top and bottom of the model box, temperature is set to be Ts = 0 °C and Tm = 1350 °C, respectively. For all boundaries except the top surface and the vertical plane defining the axes of the fastspreading ridges, velocity boundary conditions are set to neutral — e.g. p2I þ g ju þ ðjuÞT n ¼ 0: ð9Þ For all boundaries except the top, bottom, and vertical plane defining the axes of the fast-spreading ridges, temperature boundary conditions are set to have zero horizontal gradient. For the vertical plane under the fast-spreading ridge axes, temperature is assigned to be 1350 °C, and velocity is set to the upwelling velocity for a ridge diverging with the half-rate of the SEIR (Reid and Jackson, 1981). The model box is 600 km along the axis of the slowest-spreading ridge, 300 km in the axis-perpendicular direction, and 200 km in depth. Horizontal resolution ranges from 6 km (near the triple junction point) to 21 km (near the side of the model farthest from the triple junction). Vertical resolution ranges from 5 km at the surface to 20 km at depth. A selection of 200 km for the depth of the model box (rather than a greater depth coincident with, for example, the 410 km discontinuity) allows increased resolution near the surface of the model, where large gradients in temperature and velocity are expected. However, the neutral velocity boundary conditions assigned to the bottom of the model make the calculated patterns of temperature and flow generally insensitive to the depth of the boundary. To quantitatively verify this, a flow solution for an isoviscous case with the bottom boundary at 400 km was calculated. Predicted temperatures and velocities in the top 200 km of the model space differed by b5% for the smaller and larger model boxes. 4. Results 4.1. RTJ-like temperature and velocity fields For the numerical solutions with pressure- and temperaturedependent viscosity, both upwelling velocity and mantle temperatures are predicted to increase toward the triple junction. However, the magnitudes and wavelengths of the predicted increases are significantly different from the isoviscous case. At a depth of 45 km
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(i.e., within the partial melting zone), pronounced increases in isoviscous upwelling velocity begin approximately 150–200 km away from the triple junction (Fig. 3). At distances farther from the triple junction point, upwelling velocity is only ~ 0.5 cm/yr. In contrast, for the variable-viscosity solutions, upwelling velocity remains relatively constant to within ~100 km of the triple junction, where it begins increasing from ~1 cm/yr to N2 cm/yr (Fig. 3). The overall faster upwelling rate for the variable-viscosity case is consistent with earlier modeling work that suggests that use of temperature- and pressuredependent mantle rheology results in increased subaxial upwelling speeds (e.g., Shen and Forsyth, 1992). Like the isoviscous calculations presented in Georgen and Lin (2002), the variable-viscosity numerical models also predict a significant component of along-axis flow directed away from the triple junction, with the magnitude of along-axis velocity approximately equal to that of the upwelling velocity. However, it is important to note that the geometry of the numerical model box, which essentially imposes the CIR-like and SEIR-like branches as a boundary condition, does not permit quantification of sub-ridge material transfer across the triple junction. Similar to upwelling velocity, the use of variable viscosity also localizes axial thermal increases closer to the triple junction point (Fig. 4). For the isoviscous case, long-wavelength gradients in temperature at depths within the partial melting zone (30 km) were predicted, increasing by approximately 75–100 °C over a length of
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500 km. However, when variable viscosity is employed, the mantle remains relatively isothermal (at a given depth) to within ~150 km of the triple junction point. At depths within the partial melting zone and distances within ~150 km from the triple junction, the temperature of mantle with pressure- and temperature-dependent viscosity is calculated to be only ~40 °C higher because of the triple junction configuration. 4.2. Effects of triple junction motion with respect to the mantle Although geometrically stable, RRR triple junctions generally migrate with respect to the underlying mantle. To assess how this additional component of motion may affect predicted velocity and thermal fields, we performed two numerical experiments where basal velocity boundary conditions were added to the RTJ-like model shown in Fig. 2. In the first case, called “base flow model 1” (Fig. 5), a threedimensional asthenospheric flow pattern is assigned to the bottom boundary of the model space according to the flow predictions of Behn et al. (2004). Behn et al. (2004) calculated upper mantle flow for the African superplume area resulting from plate-driven and density-driven forces. In the second base, called “base flow model 2,” lower boundary conditions replicate absolute plate motion (Gripp and Gordon, 2002). Application of these bottom velocity boundary conditions only subtly changes axial temperature (Fig. 5) and velocity patterns, suggesting that
Fig. 3. a) Calculated solution for upwelling velocity at a depth of 45 km below the top surface of the model domain, for the case where the half-rate of the slowest-spreading ridge is 0.7 cm/yr (similar to the Rodrigues Triple Junction). In this figure as well as in Figs. 4–9, results are not plotted for the ~ 15 km closet to the triple junction so as not to visually portray the fixed boundary conditions assigned to the faster-spreading ridges. Curve labeled “isoviscous” indicates the solution calculated using constant mantle viscosity, while curve labeled “variable viscosity” was determined using pressure- and temperature-dependent viscosity. Gray rectangle shows the upwelling velocity predicted for two plates separating at a half-rate of 0.7 cm/yr over an isoviscous mantle. For the isoviscous case, significant along-axis increases in upwelling velocity are predicted to begin within ~ 150–200 km of the triple junction, whereas when variable viscosity is used, these increases are confined to approximately 100 km of triple junction-proximal ridge. b) Predicted upwelling velocity for a triple junction with Rodrigues-like spreading rates, plotted for the vertical plane defining the slowest-spreading ridge axis as well as for a vertical plane parallel to and 25 km away from the faster-spreading ridges. Light blue arrows indicate divergence of the slowest-spreading ridge. Note the significant increase in upwelling velocity at all depths within the model within ~ 150 km of the triple junction along the slowest-spreading ridge. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)
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Fig. 4. a) Calculated solution for temperature at a depth of 30 km below the top surface of the model domain, for the case where the half-rate of the slowest-spreading ridge is 0.7 cm/yr (similar to the Rodrigues Triple Junction). Curve labeled “isoviscous” indicates the solution calculated using constant mantle viscosity, while curve labeled “variable viscosity” was determined using pressure- and temperature-dependent viscosity. Note that along-axis increases in temperature are significantly less for the variable-viscosity solution (~ 40 °C) than for the isoviscous solution (~ 80 °C). b) Predicted temperature structure for a triple junction with spreading rates similar to the Rodrigues Triple Junction. Temperature is plotted for the vertical plane defining the slowest-spreading ridge axis, as well as for five vertical planes parallel to the faster-spreading ridges. Note the increase in shallow mantle temperature along the slowest-spreading ridge as the triple junction is approached. (For colour version of this figure, the reader is referred to the web article.)
the dynamics of the modeled system are dominated by surface plate divergence. Therefore, we do not incorporate bottom velocity boundary conditions in the additional models described below.
Fig. 5. Along-axis profile of predicted temperature at a depth of 30 km, for each of the three bottom velocity boundary conditions. For the “no base flow” model runs (red line), the bottom velocity boundary condition was neutral. For “base flow model 1” (green line), a 3D asthenospheric flow pattern was assigned to the bottom boundary, consistent with the flow predictions of Behn et al. (2004). For “base flow model 2” (blue line), basal boundary conditions replicate motion of the triple junction in the absolute plate motion reference frame (Gripp and Gordon, 2002). Note that differences between these isoviscous model runs are relatively insignificant, indicating the importance of surface plate divergence in determining mantle temperature. Although not shown, calculated velocities are also similar for each of the three basal boundary conditions. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)
4.3. GTJ-like and ATJ-like temperature and velocity fields We next explore the effects of different surface plate divergence rates on predicted flow and thermal fields by using the model geometry in Fig. 2, and scaling the magnitude of the plate motion vectors by a factor of either co or 1/co, where co = 2.4. Coincidentally, as noted in Georgen and Lin (2002), such scaling roughly approximates the kinematic conditions of the GTJ and ATJ, respectively. Thus, in addition to allowing us to explore the spreading-rate-dependence of model results, this exercise also affords qualitative insight into the geodynamics of these two triple junctions. As is the case for the RTJ-like models, triple junction geometry is predicted to affect both upwelling velocity (Fig. 6) and temperature (Fig. 7) for the GTJ-like and ATJ-like cases, albeit to different extents. With the scaling factor of co (GTJ-like case), little increase in along-axis temperature is predicted for either the isoviscous or variable-viscosity models, consistent with Georgen and Lin (2002). This may suggest that the geodynamical effects of the triple junction configuration are less pronounced when the opening rate of the slowest-spreading ridge is intermediate or greater. In contrast, dramatic along-axis temperature increases are predicted when the scaling factor is 1/co. Over a distance of 500 km and at depths within the partial melting zone, axial temperatures for the variable-viscosity ATJ-like case are predicted to increase from ~1150 °C to 1350 °C at the triple junction. Roughly half (~100 °C) of this increase is accommodated within 100 km of the triple junction point. These axial thermal increases are substantially decreased from those predicted for the isoviscous case, but still represent significant lateral thermal gradients within the sub-ridge mantle.
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Fig. 6. Upwelling velocity at a depth of 45 km, calculated for co = 1 (black lines), co = 2.4 (blue lines), and co = 1/2.4 (red lines). Solid lines indicate isoviscous model calculations, while dashed lines show solutions obtained with pressure- and temperaturedependent viscosity. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)
4.4. Crustal thickness predictions To investigate how these patterns of mantle flow and temperature affect crustal accretion processes around a triple junction, we calculate mantle melting as a function of temperature above the solidus, and integrate melt production in axis-perpendicular planes. As noted above, while this method of determining crustal thickness is very simplified, it provides some insight into how trends in melt production vary for the different mantle rheologies and surface plate divergence rates considered in this investigation. The numerical values of predicted crustal thicknesses discussed below are the result of using methods similar to those of Reid and Jackson (1981), but we also employed the anhydrous melting parameterizations of Katz et al. (2003) and obtained similar qualitative trends. Also, because the effects of triple junction geometry appear to exert little control on mantle flow patterns along the slowest-spreading ridge of a GTJ-like configuration, we focus here on just the RTJ-like and ATJ-like cases. For calibration purposes, we first calculate crustal thickness for a simple two-plate divergence case, where the additional two ridges are not present. A crustal thickness of b0.5 km is predicted for isoviscous corner flow driven by two plates spreading at 0.7 cm/yr half-rate. With pressure- and temperature-dependent viscosity, crustal thickness is predicted to increase to ~ 5.2 km (Fig. 8), consistent with seismic estimations of SWIR crustal thickness at distances of several hundred kilometers away from the RTJ (Muller et al., 1999). Next we consider crustal thickness predictions for models with RTJ-like surface plate divergence vectors (Fig. 8). With constant
Fig. 7. As in Fig. 8, but for predicted temperature at a depth of 30 km. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)
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Fig. 8. Crustal thickness calculated for corner flow in a two-plate configuration (green line), RTJ-like spreading rates (black lines), and ATJ-like spreading rates (red lines). For triple junction solutions, solid lines show crustal thicknesses calculated for isoviscous model runs, while dashed lines indicate solutions obtained using pressure- and temperature-dependent viscosity. Note the relatively small increase in crustal thickness towards the triple junction for the variable-viscosity RTJ-like case, as compared to the isoviscous solution. Note also the significant along-axis increase in crustal thickness predicted for the slowest-spreading branch in an Azores-like configuration. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)
mantle viscosity, crustal thickness is calculated to increase from b1 km far from the triple junction point to more than 8 km as the triple junction is approached. Such increases in melt production are unlikely to be realistic. With the addition of variable viscosity and thermal buoyancy, crustal thicknesses greater than ~ 150 km away from the triple junction point are the same as those predicted for the simple corner flow configuration (~5.2 km). However, within 150 km of the triple junction, crustal thickness is calculated to increase to ~7 km. Significantly more dramatic increases are predicted for the ATJ-like case, where the modeled ridge has an ultra-slow or “hyper-slow” (Vogt and Jung, 2004) spreading rate (Fig. 8). For models with pressure- and temperature-dependent viscosity, crustal thickness remains 0 km at distances greater than 300 km from the triple junction. Such low magmatic production is not unexpected, as a thin or non-existent crust appears to be characteristic of sections of ultraslow ridges such the western SWIR (Dick et al., 2003). However, a pronounced increase in crustal thickness, from ~ 2 km to ~ 6 km, occurs within 100 km of the triple junction point. We emphasize that this significant increase is due just to plate boundary geometry effects. 5. Discussion 5.1. Comparison to trends in observational data along the SWIR In the last decade or so, shipboard surveys and dredge sampling of the SWIR have significantly increased observational constraints on geological processes operating along the ridge. In general, the eastern SWIR (east of the Melville FZ at ~61°E) is inferred to be a domain of low melt productivity, characterized by deep axial bathymetry and thinner than average crustal thickness (Rommevaux-Jestin et al., 1997; Muller et al., 1999). However, the numerical modeling predicts that melting processes within roughly 100 km of the RTJ are more robust than those at greater axial distances. Trends in axial bathymetry and mantle Bouguer anomaly (MBA) along the SWIR are consistent with the numerical predictions. Axial depth shallows by approximately 1 km within 150 km of the RTJ, and MBA decreases by approximately 40 mGal over the same distance (e.g., Rommevaux-Jestin et al., 1997; Cannat et al., 1999b; Georgen et al., 2001). Additionally, predictions of the variable-viscosity numerical model are consistent with seismic studies around the RTJ, which may suggest a transition in mantle processes within ~100–200 km of the triple junction. Inversion of Love and Rayleigh wave seismogram data shows
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a low-velocity anomaly extending along a significant portion of the SEIR and CIR, and overlapping several hundred kilometers of the eastern SWIR at upper mantle depths (Debayle and Leveque, 1997). A study of P-wave travel time residuals using 18 OBSs arrayed around the RTJ also revealed a similar qualitative trend (Sato et al., 1996). Four OBSs were located along the SWIR axis, within approximately 75 km of the triple junction. The two stations closest to the RTJ yielded delayed arrivals, on average, whereas the two stations at distances greater than 50 km from the triple junctions had faster mean arrival times. Geochemical evidence may likewise suggest a transition in crustal accretionary processes near the RTJ, at a location that is consistent with the trends predicted by the variable-viscosity model. Meyzen et al. (2005) analyzed a suite of basalts dredged between 35°E and 69°E along the SWIR. As also noted earlier by Mahoney et al. (1989), Meyzen et al. point out that the closest samples to the RTJ, located 78 km from the triple junction, are isotopically distinct from those dredged near the junction point. Additionally, in an analysis of abyssal peridotites from the SWIR between 52° and 68°E, Seyler et al. (2003) find that there might be some indication of slightly greater melting in the extreme eastern portion of their study area. Thus, these studies might suggest different conditions of mantle melting along the SWIR in the immediate vicinity of the RTJ, as opposed to more distant sections of the ridge axis. However, given the present sample spacing, further interpretation of geochemical trends would be speculative. Clearly, significant additional dredging along the easternmost ~ 100 km of the SWIR axis is required to clarify possible gradients in mantle melting and isotope geochemistry. 5.2. Additional factors to be considered in future triple junction models Although the current study incorporates both pressure- and temperature-dependent viscosity as well as thermal buoyancy, an improvement over previous isoviscous triple junction models (e.g., Georgen and Lin, 2002), additional factors may also be integrated into future calculations. For example, as discussed previously, fully coupling melting into the governing equations would be expected to affect temperature fields (through cooling due to latent heat extraction). Additionally, once melting is incorporated, both melt retention and melt depletion terms may be added to the determination of buoyancy. Other parameterizations of viscosity are also possible. Studies like those by Braun et al. (2000) and Behn et al. (2007) demonstrate that incorporation of factors such as the presence of melt, cooling during melting, mantle dehydration, and more complex deformation rheologies can affect calculated viscosity structure. More specifically, while the effects of both cooling during melting and the presence of melt are expected to be minimal (less than an order of magnitude), addition of either dehydration or more complex deformation rheologies can change viscosity–depth profiles by as much as two orders of magnitude. It is important to note, however, that these additional factors somewhat counteract one another, acting in opposite ways to either increase or decrease viscosity. 5.3. Interaction between a hotspot and a triple junction: Implications for the ATJ Interaction between a triple junction and a mantle plume may result in the formation of a large igneous province (LIP) or oceanic plateau. In this scenario, LIP formation begins as plate motions bring a triple junction into the vicinity of a mantle plume. As the plume “captures” the triple junction, it preferentially delivers to it anomalously warm asthenospheric material, resulting in excess volcanism. This process may be analogous to plume–ridge interactions along a single ridge. Laboratory and numerical modeling studies (e.g., Kincaid et al., 1995; Ribe, 1996; Ito et al., 1997) predict that flow from a near-
ridge plume can be directed along the base of the sloping lithosphere to the spreading axis, resulting in voluminous magmatic activity and anomalous geochemical and geophysical signatures. For the case of a plume interacting with a single ridge, excess volcanism results from the superposition of the essentially 2D flow field of the ridge with the 3D dispersion pattern of the mantle plume. However, for the case of a plume interacting with a triple junction, both the ridge and the plume flow fields are expected to be 3D, resulting in a more complex pattern of plume distribution. This process could give rise to the creation of a spatially-extensive LIP. Evidence indicating the coincidence of a triple junction and mantle plume exists for several LIPs. For example, tectonic reconstructions of the Shatsky Rise in the Pacific Ocean suggest interaction between the Pacific–Izanagi–Farallon Triple Junction and a hotspot (Sager et al., 1999; Nakanishi et al., 1999). Similarly, the Manihiki Plateau in the western Pacific is associated with the Pacific–Phoeniz–Farallon/ Tongareva Triple Junction (Larson et al., 2002; Viso et al., 2005). Finally, the Bouvet plume has been linked to the formation of the Agulhas Plateau in the southwest Indian Ocean (Martin, 1987). We note, however, that not all evidence in these examples unequivocally points to plume/triple junction interaction. For example, recent geochemical investigations addressing the origin of Shatsky Rise may discount plume involvement, as isotopic data from drilled basalts yield a normal MORB signature (Mahoney et al., 2005). Use of these numerical models may yield some insight into the possible role that the triple junction configuration itself might play in excess crustal production. To first‐order, flow and thermal fields from adjacent ridges must be continuous in the sub-ridge mantle. Thus, the juxta position of the upwelling patterns of the faster-spreading branches against those of the slowest-spreading branch should result in a section of the slow-spreading ridge with hotter mantle temperatures and faster upwelling than the divergence rate would imply. For triple junctions where all three ridges spread at intermediate rates or higher (e.g., the GTJ-like case), this effect is predicted to be minimal at most. For triple junctions where all three ridges spread at somewhat lower rates (e.g., the RTJ-like case), both the distance over which excess magmatism occurs, as well as the magnitude of crustal thickening, are calculated to be slightly more significant (~ 100 km and ~1 km, respectively). However, where overall spreading rates are even lower (e.g., the ATJ-like case), the geodynamical effects of triple junction geometry may play a pronounced role in crustal accretion processes along the slowestspreading ridge. In fact, at depths within the melting zone, mantle temperatures are predicted to increase ~ 150 °C within ~200 km of the triple junction. These elevated mantle temperatures fall within the range of the excess temperatures suggested for mantle plumes (e.g., Schilling, 1991; Wolfe et al., 1997; Ito et al., 1999; Li et al., 2000; Albers and Christensen, 2001). It is important to note that we do not interpret the numerical modeling results to rule out the potential importance of the Azores hotspot. Many different lines of evidence suggest the existence of the hotspot, including noble gas ratios (Moreira and Allegre, 2002; Madureira et al., 2005), finite frequency seismic tomography (Montelli et al., 2004; Yang et al., 2006) and V-shaped ridges in bathymetry and gravity data along the MAR south of the ATJ, similar to those observed near Iceland (Cannat et al., 1999a). Calculation of model-predicted thermal, or isostatic, topography can be used to assess the relative importance of plate boundary geometry versus hotspot influence on magnetic processes along the Terceira Rift. The topographic variation Δh can be calculated as: Dh ¼
R
aqm ½ðT To Þ=ðqc qw Þdz;
ð10Þ
where the coefficient of thermal expansion α=3×10− 5 °C− 1, reference mantle density ρm =3300 kg/m3, reference crustal density ρc =2700 kg/m3, water density ρw =1030 kg/m3, T is mantle temperature, and reference
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mantle temperature To =1350 °C at depth z=200 km. We assume that vertical columns of mantle are in isostatic equilibrium at depth z=200 km. Consistent with studies of MBA along the GSC (Ito and Lin, 1995) as well as along the Reykjanes Ridge near Iceland (Ito et al., 1996), we assume that mantle thermal variations contribute approximately ~30% to the observed topography, with the remainder due to crustal sources. Comparison of model-predicted thermal topography to observed trends along the Terceira Rift (Fig. 9) shows that the contribution of triple junction geometry to seafloor bathymetry is most pronounced within ~150 km of the triple junction point. In contrast, the peak in measured topography is approximately 200 km from the triple junction, roughly in the location of the island complex of Graciosa, Terceira, Sao Jorge, Faial, and Pico. The difference between the model-predicted and observed bathymetric profiles may be used as a quantitative measure of the strength of the Azores hotspot, and may be used to constrain future models that focus on the physics of plume/triple junction interaction for the ATJ. This future modeling can also be constructed to address the trends in bathymetry, gravity, and geochemistry along the Mid-Atlantic Ridge that suggest Azores hotspot influence (e.g., Schilling, 1991; Detrick
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et al., 1995; Goslin et al., 1998; Cannat et al., 1999a; Escartin et al., 2001), and could incorporate time-dependent evolution of the relatively young Terceira Rift. 6. Conclusions This numerical investigation of mantle dynamics at oceanic ridge– ridge–ridge triple junctions yields the following main conclusions: (1) In models incorporating variable viscosity and focusing on the slowest-spreading ridge of a Rodrigues-like triple junction, the along-axis length over which pronounced increases in upwelling velocity, temperature, and crustal thickness occur is approximately 100 km. Within this length of ridge, increases in crustal thickness and mantle temperature at partial melting depths are predicted to be approximately 1 km and 40 °C, respectively. (2) Models were also calculated to examine the effects of spreading rate magnitude on mantle temperature, upwelling velocity, and crustal production. For numerical experiments with overall faster spreading rates (i.e., Galapagos Triple Junction-like case), the presence of the faster-spreading ridges is predicted to have little or no effect on the thermal conditions of the slowerspreading ridge. In contrast, for numerical experiments with overall slower spreading rates (i.e., Azores Triple Junction-like case), significant increases in axial temperature and crustal thickness are calculated. At depths within the partial melting zone, temperatures are predicted to increase by ~ 150 °C within 200 km of the triple junction, and crust is calculated to thicken by approximately 6 km over the same region. Such results may imply that some component of the observed magmatic activity along the Terceira Rift may be attributed to the effects of triple junction geometry. Acknowledgments This work was supported by NSF grant OCE-0550250. J. Lin is thanked for earlier collaborations on triple junction geodynamics. The helpful comments of an Editor and an anonymous reviewer are appreciated. References
Fig. 9. a) Lowpass-filtered seafloor depths around the ATJ. Data are from Smith and Sandwell (1997). Contours indicate 1.6 km and 2.5 km depth. Coordinates for the Terceira Rift are from Vogt and Jung (2004). b) Along-axis profiles of filtered seafloor bathymetry (solid line) and model-predicted thermal (or isostatic) topography (dashed line) for the Terceira Rift. Gap in seafloor bathymetry profile corresponds to transformlike offset across Sao Miguel Island inferred by Vogt and Jung (2004). The level at which the isostatic topography curve is plotted is somewhat arbitrary, so the depth far (~ 500 km) from the triple junction was fixed to correspond with the bathymetry along the easternmost portion of the Azores island chain, farthest from hotspot or triple junction influence. Predicted isostatic topography was not plotted in the immediate vicinity of the triple junction point so as not to display the depth that was calculated for the faster-spreading ridges, which serve as a boundary condition for the numerical model.
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