G 3. AN ELECTRONIC JOURNAL OF THE EARTH SCIENCES Published by AGU and the Geochemical Society. Ridge-crossing mantle plumes and gaps in tracks

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1 Geosystems G 3 AN ELECTRONIC JOURNAL OF THE EARTH SCIENCES Published by AGU and the Geochemical Society Ridge-crossing mantle plumes and gaps in tracks Norman H. Sleep Department of, Stanford University, Stanford, California 94305, USA (norm@pangea.stanford.edu) Article Volume 3, Number 12 5 December , doi: /2001gc ISSN: Correction published 25 February 2003 [1] Hot spot tracks approach, cross, and leave ridge axes. The complications of this process make it difficult to determine the track followed by a plume and the evolution of its vigor. When a plume is sufficiently near the ridge axis, buoyant plume material flows along the base of the lithosphere toward the axis, forming an on-axis hot spot. The track of the on-axis hot spot is a symmetric V on both plates and an unreliable indication of the path followed by the plume. Aseismic ridges form more or less along flowlines from a plume to a ridge axis when channels form at the base of the lithosphere. A dynamic effect is that off-axis hot spots appear to shut off at the time that an on-axis hot spot becomes active along an axisapproaching track. This produces a gap in the obvious track and a jump of the hot spot to the ridge axis. The gap results from the effects of ponded plume material on intraplate (membrane) stress. Membrane tension lets dikes ascend efficiently to produce obvious tracks of edifices. An off-axis hot spot shuts down when the plume is sufficiently near the ridge axis that plume material flows there, putting the nearby lithosphere above the plume into compression, preventing dikes. In addition, the off-axis thickness of plume material, which produces membrane tension, decreases as the slope of the base of the lithosphere increases beneath young lithosphere. Slow spreading rates favor gaps produced in this way. Gaps are observed near both fast and slow ridges. Components: 14,807 words, 21 figures. Keywords: Mantle plumes; South Atlantic; mid-ocean ridges; hot spots; aseismic ridges; intraplate stress. Index Terms: 8121 Tectonophysics: Dynamics, convection currents and mantle plumes; 8150 Tectonophysics: Plate boundary general (3040); 8164 Tectonophysics: Stresses crust and lithosphere; 9360 Information Related to Geographic Region: South America. Received 6 December 2001; Revised 29 April 2002; Accepted 27 August 2002; Published 5 December Sleep, N. H., Ridge-crossing mantle plumes and gaps in tracks, Geochem. Geophys. Geosyst., 3(12), 8505, doi: /2001gc000290, Theme: Plume-Ridge Interaction Guest Editor: David Graham 1. Introduction [2] Hot spots include regions of midplate volcanism, like Hawaii, and regions of exceptionally voluminous on-ridge volcanism, like Iceland. Following Morgan [1972], Earth scientists commonly attribute both types of hotpots to mantle plumes, cylindrical conduits of hot low-viscosity material, which upwell from the deep mantle. The evolution of one type of hot spot into the other indicates that both result from the same process. During this evolution, by definition, primary hot spots occur above the plume orifice and secondary hot spots occur above plume material that has flowed laterally Copyright 2002 by the American Geophysical Union 1 of 33

2 Figure 1. Sea-surface satellite gravity map of the North Atlantic after Sandwell and Smith [1997]. The New England track crosses North America (red line) and extends through the New England seamounts. A gap exists between it and the on-axis Corner Seamounts. The hot spot is current near Great Meteor seamount on the African Plate. The Bermuda track also crosses North America. Gaps exist between the continent and Bermuda and between Bermuda and an ill-defined axial hot spot. The on-axis Bahama track began with a starting plume head centered in northern Florida (red circle). The hot spot is now in the Cape Verde islands. along the base of the lithosphere [Morgan, 1978]. The purpose of this paper is to discuss the kinematics and dynamics of ridge-crossing hot spots. [3] Several examples of ridge-crossing, ridge-leaving, and ridge-approaching hot spots permit tentative phenomenology. One feature is that a gap in the volcanic edifices often occurs between the off-axis ridge-approaching track and the on-axis track. Globally, seamount volcanism is relatively rare in this near-axis regions where gaps form [McNutt, 1990]. [4] The New England Great Meteor chain is the clearest track with a gap (Figure 1) [Tucholke, 1990; Sleep, 1992]. It can be traced from the continental volcanism in the Monteregian Hills, through New England, along the midplate New England seamounts, to the near- and on-axis Corner seamounts, and to the off-axis Great Meteor seamounts on the African plate. A gap exists in the track between the off-axis New England and the Corner Seamounts (Figure 1). Tucholke [1990] give a track rate of 112 mm yr-1 across the gap compared with 47 mm yr 1 before the gap based on geochronology. However, on-axis activity began while off-axis edifices were still forming. That is, the track basically jumped across the gap to the ridge axis. [5] Other gaps are less prominent. The off-axis Austral track approached the East Pacific rise, forming the near-axis Foundation Seamounts (Figure 2) [O Connor et al., 1998, 2001; Maia et al., 2001]. A gap exists between the between these two seamount groups. The Louisville track has approached the East Pacific rise (Figures 2 and 3) [e.g., Small, 1995]. Near and on-axis hot spot activity is now occurring mainly on the Pacific plate and a gap exists between this ridge and the off-axis chain. The Bermuda track is a less clear example of a ridge-approaching hot spot with an unclear on-axis hot spot between 20 N and 28 N (Figure 1). That is, activity has ceased near off-axis Bermuda (as with the other gaps) but has not yet clearly commenced near the axis. 2of33

3 Figure 2. Sea-surface satellite gravity map of the South Pacific after Sandwell and Smith [1997]. A gap exists between the off-axis Austral chain and the near-axis Foundation seamounts. A gap also exists west of the Austral seamounts where the track crossed older lithosphere. The Louisville track is evident in the southwest part of the map. [6] Other tracks began as near-axis hot spots and then moved off-axis. The Tristan track began with the massive Parana and Etendeka flood basalts in South America and Africa (Figure 4) [e.g., O Connor and Duncan, 1990]. It produced the on-axis Rio Grande Rise and Walvis Ridge before becoming a poorly defined off-axis hot spot on the Africa plate. That is, the ill-defined axis-leaving track of the Tristan hot spot is a complicated example of a gap. [7] Three possible mechanisms for producing gaps in ridge-approaching hot spots come to mind: (1) Deep interaction of the ascending plume tail with the material passively ascending toward the ridge axis deflects the plume tail. (2) The amount of melting within the ascending plume material decreases as the plume approaches the ridge axis. (3) Horizontally compressive stresses within the lithosphere keep melt from reaching the surface in the region of the gap. The former mechanism could well be applicable. Study of it, however, requires consideration of the three-dimensional flow pattern at great depth, which I do not attempt to model in this paper. The second mechanism is unlikely as the amount of pressure-release melting should increase as the plume conduit impinges on progressively thinner lithosphere as it approaches a ridge axis. [8] The third mechanism is qualitatively attractive. Plumes are sources of hot material, not candle-like point sources of heat. Material leaves the orifice on the top of a cylindrical tail conduit and flows along the base of the lithosphere. The relief on the base of the lithosphere acts as an upside-down drainage pattern for this material where plume material flows toward the ridge axis. On-ridge hot spot volcanism begins once the plume is close enough that a significant volume of material can reach the ridge axis. As discussed in section 3, ponded plume at the axis material puts the off-axis lithosphere into horizontal compression, retarding off-axis hot spot volcanism. [9] This hypothesis requires that plume material flows laterally over large distances from the plume conduit to the ridge axis. There are phenomeno- 3of33

4 Figure 3. Sea-surface satellite gravity map of the part of South Pacific after Sandwell and Smith [1997]. A gap exists between the off-axis Louisville chain and a near-axis hot spot associated with channels toward the ridge axis. logical and physical inferences that such flow in fact occurs, up to a few thousand kilometers from its source. Albers and Christensen [2001] modeled the Reykjanes ridge. Plume tail material flows 1000 km along the axis. Sophisticated numerical models do not exist for other examples. Plume material now flows from Salas y Gomez on the Nazca plate over 1000 km antiparallel to the spreading direction to the west rift of the Easter microplate [Kingsley et al., 2002; Simons et al., 2002]. Starting plume material from a hot spot centered in northern Florida flowed northward to Nova Scotia at 200 Ma [Sleep, 1996]. Karoo-Ferrar starting plume material flowed from southern Africa to New Zealand [Encarnación et al., 1996]. Iceland starting plume material flowed beneath the Irish Sea [Sleep, 1996]. East African starting and tail plume material flowed into the Afar and Cameroon regions [Ebinger and Sleep, 1998]. [10] A second feature related to lateral flow by Morgan [1978] is elongate aseismic ridges, which appear to overlie plume material channeled along the base of the lithosphere from off-ridge hot spots to coexisting on-ridge hot spots. Such features occur near the Reunion and Kerguelen hot spots, which began with flood basalts and produced nearaxis tracks on the Indian plate. Reunion is now on the African plate. Morgan [1978] attributed the Rodrigues hot spot to the flow of plume material toward the ridge axis from Reunion. Kerguelen is on the Antarctic plate. Plume material flows from it toward the ridge axis [Small, 1995]. Other channel hot spots discussed by Small [1995] include one from the Louisville track to the East Pacific Rise (Figure 3) and one between Discovery and the Mid-Atlantic Ridge (Figure 4). [11] These hypotheses require that pressure-release melting occurs within the plume material beneath secondary hot spots. The condition is likely to be met as local buoyancy drives lateral flow, implying that flow has an upward vertical component. I do not investigate this important topic in detail because I model the plume material as a single viscous fluid. That is, I do not attempt to explicitly model temperature, melting history, or heterogeneity within the plume material. [12] My plan is to first consider the kinematics of ridge-crossing hot spot tracks assuming that gaps, in fact, generally occur. I then consider intraplate stress as a mechanism that may produce gaps 4of33

5 Figure 4. Sea-surface satellite gravity map of the South Atlantic after Sandwell and Smith [1997]. Red circles show plausible present plume locations near Gough, Discovery, and Meteor rise. One, two or three plumes may actually exist. The ridge crossing at 80 Ma fixes the position of the Tristan plume at the time. Hypothesized tracks of the plume south of the Walvis spur end at the three suggested plume locations. The solid red lines show plausible parallel plume tracks that end near Discovery and near Meteor rise. where they are observed, that is, between an axisapproaching track and an on-axis track. I identify the thickness of plume material beneath the offaxis hot spot and the thickness of plume material ponded at the ridge axis as key parameters. I then examine the dynamics of plume material ponded at the base of the lithosphere to constrain these features. I need to consider channels between the near-axis plumes and the ridge for this task. 2. Kinematics of Ridge-Crossing Hot Spots [13] From the maps in Figures 1 4, it appears that gaps exist between off-axis and on-ridge parts of tracks. Both the gaps and the on-axis part of tracks complicate the determination of absolute velocities and the fixity or lack of fixity of hot spots, which is of interest to geodynamics [Richards, 1991; Steinberger, 2000]. The gaps also obscure any real variations of the flux of the plume. [14] Following Small [1995], I use the South Atlantic as a primary kinematic example as it shows the complicated geology of ridge-leaving hot spots. The gaps in the ridge-approaching tracks are kinematically simple. I include them in my generic example based on the South Atlantic. This lets me compare the kinematic history with real features in Figures 1, 2, 3, and 4. [15] I qualitatively introduce some physical concepts at this stage so that they can be discussed quantitatively in section 3. As noted in the introduction, plume material ponds at the base of the lithosphere and then flows toward regions of thin lithosphere. The lithospheric plate drags material in the direction of its movement. Pressure-release 5of33

6 Figure 5. The velocity of a plume relative to the overlying plate resolved into toward-ridge and ridge-parallel components. The half spreading rate of the ridge is U R. melting occurs as buoyancy-driven flow moves plume material to shallower depths Kinematics of Near-Ridge Hot Spots [16] With the simplified dynamics in mind, I define a coordinate system for a near-ridge hot spot. The velocity of the hot spot relative to the U P plate resolves into components parallel U S and perpendicular U D to the strike of the ridge (Figure 5). The hot spot approaches the ridge axis U D when is greater than the (half) spreading rate U R. The dip of the base of the lithosphere depends inversely on the square root of the half spreading rate. [17] The geometry of ridge-crossing hot spot tracks is visualized with velocity triangles (Figure 6, top). In the case of the South Atlantic, the hot spot moved from the South American to the African plate. For convenience in discussion, I project a schematic diagram about the pole of plate rotation and let the ridge strike north south and spread east west in this frame. [18] I obtain the kinematics of a hot spot starting with the well-known kinematics of ridges and transform faults. The E W line connecting the South American and African velocities represents the locus of velocity points that stay on a transform fault between the two plates. The locus of points that stay on a ridge axis is the N S perpendicular bisector of this line. The hot spot velocity lies to the southeast of the intersection of the ridge and transform lines implying that the hot spot moves in that direction relative to ridge transform intersections. The Tristan hot spot approached the ridge axis when it was on the South American plate and moved away when it was on the African plate. The track directions are given, respectively, by the lines (SAM-HOT) and (AFR-HOT). 6of33

7 Figure 6. The velocity triangle for the South American plate (SAM), the African plate (AFR), and a hot spot (HOT) (top). The velocity of the on-axis hot spot (ON) lies on the line for the ridge, which is the perpendicular bisector of the transform fault line along the spreading direction between the two plates velocities. Obliquely spreading ridges result in asymmetrical V-shaped patterns on the two plate given by the velocities (ONL) and (ONR) (bottom). A hot spot on the African plate approaches the northwest-striking oblique ridge. [19] It is likely that material flows laterally toward the ridge axis from the plume. This produces an on-axis hot spot whenever the plume is sufficiently near the ridge axis. The velocity of an on-axis hot spot produced in this way is constrained to lie on the ridge velocity line. The on-ridge hot spot (ON) forms a symmetric V of tracks on the plates. [20] The actual Mid-Atlantic Ridge is offset by numerous transform faults (Figure 4). Viewed broadly enough to ignore individual faults, the strike of the ridge is oblique to the spreading direction (Figure 6, bottom). Asymmetrical V s are produced by on-ridge hot spots in these cases. 7of33

8 Figure 7. Schematic diagram of ridge-leaving hot spots. The map in panel a (top, left) shows a track that is perpendicular to the ridge axis. It simply represents the modern region between Salas y Gomez and the ridge axis. Modern volcanism (pink circles) occurs between the ridge axis and somewhat east of the plume. This results from flow of material from the plume along the track shown in cross-section in panel b (right) [after Kingsley et al., 2002]. The current axial hot spot and the plume hot spot are most evident and have track velocities proportional to the vector between them and the point where the plume crossed the ridge axis and both tracks coincide (open blue square). The axial hot spot leaves paired tracks parallel to the plume track. A diffuse swath of volcanism occurs between an oblique track plume track and the axis (panel c, bottom left). The plume track, the paired axial tracks, and a track produced by volcanism within the axial track near the plume may be evident. The latter track results from the flow of plume material into the channel formed by the already hot and thin lithosphere of the axial track. The velocities of these tracks are proportional to the vector between their current positions and the ridge crossing point. The near track has the same direction but a lower velocity relative to the plate than the axial track. O Connor and Duncan [1990] implicitly used the near track on the Walvis ridge in their reconstructions. [21] An interesting geometrical situation arises if the regional strike of the ridge is sufficiently west of north. A hot spot on the Africa plate then approaches the ridge axis. In the actual South Atlantic, the ridge axis strikes mostly due north at the latitude where the plume first crossed onto the Africa plate (32 S), but strikes west of north further south where a plume may now be. A hot spot on the African plate to the north would move away from the ridge axis but one to the south would approach the axis. [22] I emphasize that volcanism currently occurs on the oceanic crust between plumes and their onaxis hot spot. I expect this feature because plume material flows continuously over this interval causing pressure-release melting. For example, young basalts occur from well east of Salas y Gomez to the west rift of the Easter Microplate [Kingsley et al., 2002; Simons et al., 2002]. [No oblique V exists here because the track is essentially along the spreading direction (Figure 7).] Young basalts erupted along the Wolf-Darwin chain near the Galapagos hot spot [Sinton et al., 1996]. [23] I concentrate on the on-axis hot spot in my diagrams because it indicates that plume material encroached on the ridge axis. It forms paired chains on the zero-age crust of the two plates with good age progression (Figure 7). In contrast, the off-axis volcanism between the plume and the ridge does not define on age progression at currently active hot spots. Drilling or dredging on old hot spot tracks, 8of33

9 Figure 8. Schematic map of a plume track at time 0 (panel a left) and time 1 (panel bright). The position of the plume is a filled circle, the ridge axis is a thick line, and isochrons are thin lines. The velocity triangle is from Figure 6. The plume material flows toward the ridge axis from the area of the plume. The off-track stops before time zero and hot spot activity jumps to the axis producing a gap. At time 1, formation of a symmetric V-shaped axial track is underway. This time applies to the gap between the New England and Corner seamounts in Figure 1. like the Walvis ridge, is likely to sample the time of the last massive volcanism when the edifice was near the plume, like modern Salas y Gomez. They may, however, sample less voluminous late volcanism as is now occurring east of Salas y Gomez [Kingsley et al., 2002; Simons et al., 2002] or even early volcanism that did not get buried (Figure 7) Generic Kinematic History [24] I illustrate the kinematics of a ridge-crossing plume using the South Atlantic. For simplicity, I begin with a straight ridge axis except for a small marker transform fault north of the region of interest (Figure 8). I use a constant hot spot velocity on a planar surface in the schematic diagrams. I start the generic hot spot (at time zero) away from this ridge axis and away from any continents so that I can show the kinematics of a ridge-approaching hot spot on the same diagram as a ridge-leaving hot spot. [25] The actual Tristan track began with the Etendeka flood basalts in Africa and the associated Parana basalts in South America (Figure 9). This event has all the features typically ascribed to the impingement of a starting plume head-on the lithosphere. A brief period of intense volcanic activity occurred between 133 and 131 Ma. I follow O Connor and Duncan [1990] and center the plume and the initial position of the plume tail beneath South America (Figure 9). The relative timing of the start of rifting and the plume head is unclear [O Connor and Duncan, 1990]. A rift may have begun to propagate from the south before the arrival of the plume head as magnetic anomaly M11 (133 Ma) is recognized at the latitude of Cape Town [Cande et al., 1988]. At the latitude where the Rio Grande and Walvis tracks meet the coast, seafloor spreading began after the plume head arrived. Coast-parallel dikes intruded at 126 Ma [e.g., Marzoli et al., 1999] and magnetic anomaly M4 occurs along the coast [Cande et al., 1988]. The exact position of the initial plume tail beneath South America is not evident; I make no attempt to refine it. 9of33

10 Figure 9. Isochrons and the positions of the Rio Grande Rise and Walvis Ridge after O Connor and Duncan [1990]. Red circle indicates the center of the starting plume head beneath South America. Paired aseismic ridges formed near the ridge axis extend from the coasts to anomaly 13. Tracked red line south of the Rio Grande Rise is an abandoned ridge axis, which jumped to green-filled circles. The Walvis Ridged bifurcated just before the time of the ridge jump. [26] Returning to the generic hot spot at time 0 (Figure 8), the plume is just close enough to the axis that the slope of the base of the lithosphere causes the flow of buoyant plume material to the ridge axis. Melting of this material creates an on-ridge hot spot. The center of the on-ridge hot spot need not be directly east of the plume. In Figure 8, the on-ridge hot spot is slightly north of east from the plume (on the grounds that material that exited the plume conduit upstream some time before time 0 has had longer to flow to toward the ridge axes than more recently vented material). The on-ridge Corner Seamounts have this inside-v relationship to the midplate England Seamounts (Figure 1). The offaxis track above the plume orifice becomes less evident at this time creating a gap between the offaxis track and the on-axis hot spot. [27] At time 1, the plume is close enough to the axis that Figure 9 applies to the Tristan plume. The plume has approached the ridge axis and a symmetric V-shaped track has formed. There is no tail track on the South American plate distinct from onaxis the Rio Grande Rise. [28] The plume approaches the ridge axis at time 2 and is on it at time 3 (Figure 10). The plume and on-axis hot spot tracks then intersect. At time 4, the hot spot is on the African plate (Figure 11). I associate this ridge-crossing event with features on the African and South American plates. An eastward ridge jump occurred between anomaly C32 (73 Ma) and C30 (68 Ma) times [Cande et al., 1988; O Connor and Duncan, 1990], indicating that the plume was already east of the ridge (Figure 9). The ridge jump corresponds with a geomorphic change in the Walvis ridge (Figure 4). In the region affected by the ridge jump, the northeast part of the Walvis ridge bifurcates into a southwest branch and a nearly north south striking spur. Samples just east of the spur are Ma [O Connor and Duncan, 1990]. On the South America plate, the Rio Grande rise became less developed southeast of the transition as would be expected if the plume was beneath the African plate. I suggest that the spur is the plume track and the southwest Walvis ridge is the on-axis hot spot track. [29] At time 6, the hot spot is well onto the African plate (Figure 12). This represents 70 Ma when the Walvis ridge began to take on some off-axis features like the ratio of topography to geoid and when the ridge jump occurred [O Connor and Duncan, 10 of 33

11 Figure 10. Schematic map at time 2 (left) and time 3 (right) as in Figure 8. The plume crosses the axis at time 3. This event occurred at 80 Ma for the Tristan plume. 1990]. Müller et al. [1993] give this the time of ridge crossing, rather than the time that ridge crossing is first evident from geological observations. Some hot spot activity still continued the South American plate, producing a paired track (Figure 9). At time 8, a weak near-ridge hot spot and an offaxis track directly above the plume exist on the Africa plate (Figure 13). These events are evident on Figure 9. The paired tracks end at anomaly 13 (35 Ma) and volcanism continues to the presentday on the African plate toward Tristan. [30] O Connor and Duncan [1990] implicitly recognized these issues in their track reconstruction by avoiding the paired tracks and allowing the plume hot spot the cross the ridge axis. They used basalt ages which were typically much younger than the underlying oceanic crust to define a track toward Tristan along the southwest Walvis ridge. As I noted near the start of section 2.1, such ages are like to detect voluminous volcanism near the plume and thus indicate its location to some extent (Figure 7). The data, as expected, show scatter including a sample from the northeast Walvis ridge (which formed while the plume was beneath the South American plate) that is 20 m.y. younger than the best fitting track. [31] There are two classes of ways of tracking the plume that involve the spur, rather than the southwest Walvis ridge as a plume track. Both involve a gap defined by a lack of large volcanic edifices in this region (Figure 4). One possible track follows a group of seamounts southwest ending at present near or southeast of Gough Island. Other options explain hot spot ridge axes further to the south. They require that the plume track went south from the spur, crossing a region where there are no prominent seamounts. Ridge segments with morphological and chemical indications of hot spot activity provide hints to the location of plumes beneath the African plate and the present end of the track. They include the segment immediately south of the Agulhas fracture zone (which appears to be fed along an aseismic ridge from the Discovery group), the Shona region of the Mid-Atlantic Ridge, and the Bouvet region of the Southwest Indian Ridge [Small, 1995; Douglass et al., 1999]. [32] Left-stepping transform faults, which offset the southern Mid-Atlantic Ridge, complicate the kinematics (Figure 4). Figure 13 shows two offsets at time 8. [WMW3] A near axis hot spot occurs on each ridge segment. Additional hot spots occur on the young side of fracture zones where plume material cascades from thick to thin lithosphere. This diagram applies if the Tristan plume or other independent Discovery and/or Meteor plumes impinge on this region. 11 of 33

12 Figure 11. Schematic map as in Figure 8 at time 4. The plume is just onto the African plate. The axial tracks continue to form. The plume is still too close to the ridge to form a distinct track. This corresponds to 70 Ma for the Tristan plume. [33] If only a single South Atlantic plume exists, its present location within the Meteor Group is preferable to one within the Discovery group. A plume now near Discovery would provide material for the former hot spot, but not for the two more southern ones. A strong Meteor plume is in a position to feed both the Shona and Bouvet Segments, which are longer and more elevated than the Agulhas segment. The aseismic ridges west of Discovery, Gough Island, and Tristan Island could be attributed to flow of plume material from beneath the plume-track swell toward the ridge axis. Alternatively, two (Tristan-Discovery and Meteor) or three (Tristan-Gough, Discovery, and Meteor) plumes may exist. [34] A plume track toward the Meteor group provides an explanation for the ridge jump south of the Agulhas fracture zone 59 Ma. Before this time, the active spreading center south of the Agulhas fracture zone was located south of the present position of Cape Rise ( Dead ridge axis in Figure 4). The active ridge axis north of the fracture zone was somewhat west of the Discovery group. Starting at 65 Ma, seafloor spreading separated the Islas Orcas rise from the Meteor Rise [Raymond and LaBrecque, 1988; Raymond et al., 1991]. The plate reorganization was complete by 59 Ma and the Agulhas fracture zone east of Meteor Rise and the ridge axis south of Cape Rise became inactive [Shipboard Scientific Party, 1988]. 12 of 33

13 Figure 12. Schematic map as in Figure 8 at time 6. The axial hot spot is somewhat north of the plume. The V- shaped tracks form a greater angle with the axis. The Walvis spur is the off-axis track in the South Atlantic. [35] I attribute the Islas Orcas Rise and the Meteor Rise to flow of plume material into a slowly spreading ridge axis between 65 and 59 Ma and voluminous pressure-release melting. Meteor Rise is south of the point where zero age offset existed of the Agulhas fracture zone [Raymond and LaBrecque, 1988]. This is the place where the lithospheric dam formed by the fracture zone was thinnest. The Agulhas ridge between the Meteor Rise and Cape Rise is attributed to melting of plume material ridge that cascaded from the old side to the young side of the transform fault. [36] Limited sampling indicates that Meteor Rise and Islas Orcas Rise formed just before the ridge jump. Islas Orcas ceased to be volcanically active, while volcanism continued after the reorganization on the Meteor Rise [Raymond et al., 1991]. The pronounced gravity anomalies of Meteor Rise are evidence that significant edifices formed when this region was old oceanic crust. The igneous age of the (fracture zone) Agulhas ridge is not known. [37] Cape Rise and the Discovery Group are less clearly explained by this hypothesis, which might imply the presence of two or three plumes in this region. A single-hot spot possibility is that Cape Rise and the Discovery group were short-lived ridge axes where thin lithosphere collected plume material. Unfortunately, the igneous ages of these features are unknown. [38] To reiterate, the kinematics of a ridge-crossing hot spot make it difficult to track the path followed 13 of 33

14 Figure 13. Schematic map as in Figure 8 at time 8. The plume is far enough onto the African plate that an off-axis track has started. The on-axis track on the South American plate ended at anomaly 13 time and a weak near axis hot spot persists on the African plate. by a plume. A ridge-approaching midplate track is likely to be evident if the hot spot begins far from the ridge axis as with the New England track (Figure 1). The initial encounter of plume material with the ridge axis (Figure 8) is likely to occur along a limited length of the ridge axis and produce a well defined start of a near-axis hot spot initially (Figure 1) on the North America plate (for New England). As the plume approaches and underlies the ridge axis (Figure 11), a well developed on-axis hot spot forms along a significant length of ridge axis. This makes is difficult to pick the center of the axial track, especially if the actual distribution of plume material is influenced by transform faults acting as dams for the along-axis flow of plume material (Figure 14). The along-strike component of motion may cause the most active on-ridge hot spot to jump from one ridge segment to another (here) to the south. As the plume moves off axis (Figure 12), a significant length of the ridge axis north of the plume continues to receive plume material. The most active on-ridge hot spot lies somewhat north of the plume. When the plume is well into the Africa plate (Figure 14), near-ridge activity occurs well north of the plume. The start-up position of the midplate plume track on the African plate and the end of the axial tracks on both plates may be ill defined. Left-stepping transform faults produce multiple near-axis tracks (Figure 14). 14 of 33

15 Figure 14. Alternative schematic map as in Figure 8 at time 8. Left-stepping transform offsets schematically represent the present geography in the South Atlantic. Multiple near-ridge and fracture-zone hot spots exist west and south of the plume. These include the Agulhas, Shona, and Bouvet hot spots. It is unclear whether the Tristan plume or other plumes on the African plate now impinge on this region. [39] I have shown that tracks produced by axial hot spots give unreliable estimates of the motion of the underlying plume. Unfortunately these are often the most recognizable tracks used in inversions for absolute plate motions. The ridge-crossing position at time 3 (Figure 10) presents a partial solution to this difficulty in that the on-axis and plume tracks on both plates intersect at this time. I recognized the Tristan crossing point by a ridge jump, which are expected to be toward the plume and by a change in the morphology of the Walvis ridge (Figures 4 and 9). 3. Intraplate Stress and Track Gaps [40] The concept of hot spots arose because of their off-axis volcanism and voluminous on-axis volcanism. Morgan [1978] then associated primary hot spots with underlying mantle plumes and secondary hot spots with lateral flow of material supplied by these plumes. In section 2, I discussed phenomenological evidence that plume material flows laterally and partially melts to cause secondary hot spots. I defer modeling the dynamics of lateral flow until section 4. In this section, I address a necessary condition for off-axis volcanism that magmas need to ascend through the lithosphere as dikes. For this to happen, the state of stress in the lithosphere must be conducive to vertical crack formation. Earth scientists have not thoroughly addressed this issue in this context, rather that cracks in the lithosphere are an alternative mechanism to plumes for producing midplate hot spots [e.g., Anderson, 2000]. I note that the hypothesis that variations over time and space in intraplate stress along hot spot tracks may create gaps when the stresses are unfavorable has been made. For example, O Connor et al. [1998] associated the gap between the Austral and Foundation Seamounts with the lack of stresses related to changes 15 of 33

16 in plate motions at the time of the gap. They obtain the direction of stress from the alignment of en echelon volcanic ridges. [41] Rubin [1995] reviews the physics of dike intrusion. The relationship of dikes to lithospheric stress is not fully understood. Yet, it is evident that dikes intrude and erupt in areas where the crust is extending and hence in horizontal tension. In both the laboratory and the field, dikes and hydrofractures intrude perpendicular to the least compressive stress. That is, vertical dikes, rather than horizontal sills, form when the axis of maximum tension is horizontal. From this, ascent of magma to the surface should be favored in regions where the lithosphere is in horizontal deviatoric tension and hindered in regions where it is in compression. [42] I present a semiquantitative approach that yields the sense of the effects of ponded plume material beneath the ridge axis and beneath midplate plate regions on intraplate stress. I consider stresses associated with lithospheric isostasy, which are easy to quantify and exist everywhere within the rigid lithosphere. I consider the ridge as a twodimensional feature. The nonzero components of membrane stress are then perpendicular and parallel to the ridge axis. I define these membrane stresses to be s xx s zz, where x is the horizontal coordinate perpendicular to the ridge axis and z is depth, and s yy s zz, where y is parallel to the ridge axis, respectively. I represent the plume material with three parameters, the thickness of ponded plume material beneath off-axis hot spot (S 0 ), the on-axis thickness of ponded plume material (S R ), and nearaxis thickness in the regions where gaps may form (S 1 ). I derive and compile scalings for these quantities in section 4. It suffices for now to know that the near-axis thickness is less than the midplate thickness and that the axial thickness increases as the plume approaches the ridge axis Two-Dimensional Intraplate Stress [43] The state of stress within isostatically compensated lithosphere provides a semiquantitative formulation, that is, the easily predictable part of the process. The integral of stress through the lithosphere (a stress resultant) is then constrained by the horizontal mass balance. I consider only the simplest case: the x component of the stress resultant is relevant to ridge jumps as it is opens cracks parallel to the ridge axis. The y component is more complicated (but analogous) as a simple boundary condition does not exist at the ridge axis and because the rheology of the lithosphere needs to be included [Dahlen, 1982; Sleep and Phillips, 1985]. [44] Intraplate stress in the ocean basins is potentially measurable, leading to testable hypotheses. Studies of intraplate earthquakes indicate that along-axis membrane tension exists within young lithosphere [Bergman and Solomon, 1984; Wiens and Stein, 1984]. However, intraplate earthquakes occur in limited regions rather than being a pervasive feature at least over the last 50 years for which data exist. A well-defined transition age between tensile and compressive events does not exist and thermoelastic stresses may be important. [45] I continue with stresses within a two-dimensional cross-section through a ridge axis. The cross-axis (membrane) stress resultant is Z x Z ½s xx s zz Šdz ¼ ðr ref r Þgz dz; ð1þ where integrals extend down to a depth that the upper mantle is essentially adiabatic, only firstorder terms are retained, drag at the base of the plate is ignored, tension is positive, s is the stress tensor, z is depth, x is distance from the ridge axis, r is density, and r ref is a reference density function of depth where x is zero [Turcotte and Schubert, 1982, p. 288]. [46] Only the integral of stress is constrained by the force balance in (1). The density differences from plume material extend down beneath the lithosphere. Significant deviatoric stresses s xx 6¼ s zz, however, are confined within the essentially rigid part of the lithosphere. The sign of the predicted stress resultant still provides an indication as to whether cracks can penetrate the lithosphere. Dikes (including those feeding observable volcanism) freeze and act as permanent dislocations within the lithosphere. In a local midplate region of intrusion, the frozen dikes reduce the horizontal tensional stress [Rubin, 1993]. This limits the 16 of 33

17 number of intrusion events and hence the duration and vigor of volcanism, proportionately to the initial amount of membrane tension. [47] I consider oceanic lithosphere where density is mainly a function of temperature because I am interested in gaps within oceanic hot spot tracks. Then (1) becomes Z x ¼ ðt ref TÞr 0 agz dz; ð2þ where T ref is a reference geotherm, T is the geotherm, r 0 is a constant representing typical upper mantle density, and a is the volume thermal expansion coefficient. [48] Equation (2) yields the familiar ridge push force at normal ridge axes. The ridge axis is weak in extension so that x is essentially zero there. That is, the reference geotherm may be taken as the nearly adiabatic geotherm at the ridge axis. In the absence of plumes (T T ref ), the plate away from the ridge axis is in horizontal membrane compression. To the first order, x ¼ r 0 agkt L T L ; where t L is lithospheric age and T L is the temperature difference between the mantle adiabat and the surface (and here the reference temperature in (2)) [Turcotte and Schubert, 1982, p. 288]. [49] Ponded plume material makes part of the integrand in (2) negative as T > T L. For simplicity, I let a layer of plume material with an excess temperature of DT P and a thickness S pond beneath normal lithosphere starting at a depth of Z L. (S scales with S 0 for a midplate hot spot and S 1 for a near-axis hot spot.) The stress resultant is then x ¼ r 0 ag 1 h ðz L þ SÞ 2 ZL 2 2 i DT P kt L T L ð3þ : ð4aþ p ffiffiffiffiffiffi The lithospheric thickness is a L kt L, implying that pffiffiffiffiffiffi S SDT x ¼ r 0 ag a L kt L þ 2 Þ P kt L T L : ð4bþ For a given thickness of plume material, the stress resultant is positive and the lithosphere is in tension for lithosphere younger than a critical age. Figure 15 shows the critical age as a function of thickness of ponded material. [50] I assumed that no plume material is at the ridge axis in deriving (4b). Alternatively, plume material may underlie a significant length of ridge axis, creating another two-dimensional geometry. Then the reference geotherm is approximately that of the plume dominated axis. Representing the axial plume material as a layer extending to the surface of thickness S R, (4b) becomes pffiffiffiffiffiffi S x ¼ r 0 ag a L kt L þ 2 SDT P kt L T L S2 R DT P 2 The maximum age of intraplate tension is shown for S R = 50 in Figure 15. There are no real solutions to (5) for small values of s, implying that the entire off-axis region is in membrane compression Qualitative Track History [51] Figure 15 shows the qualitative behavior [WMW4] of a hot spot track the hot spot moves closer to a ridge axis from (4b) and (5). At time A, the hot spot is beneath old lithosphere and the thickness of plume material is the midplate value S 0. The plate is in membrane compression and no significant volcanism is associated with the track. Later at time B, the thickness of the plume material is still S 0. The hot spot has moved to younger crust, letting the plume put the plate into membrane tension. Significant volcanism then vents through dikes. At time C, the plume is close enough to the axis that plume material flows there and ponds. This tends to put the midplate region into membrane compression. The slope on the base of the lithosphere becomes significant causing the thickness of plume material to decrease from S 0 to S 1 as discussed in section 4. This decreases the membrane tension from the ponded (midplate) plume material and lets the plate come into membrane compression. The combined effects of these processes tend to shut off dikes feeding the off-axis tail hot spot at about the time that a secondary on-axis hot spot becomes active. [52] This evolution is evident in some examples discussed in the introduction. First as a hot spot moves toward younger lithosphere, membrane stress becomes tensional and volcanism becomes vigorous (from time A to time B in Figure 15). That is, the hot spot track appears to turn on. The Bermuda track, which was active while crossing the southern United ð5þ 17 of 33

18 Figure 15. Solid line divides fields of intraplate compression from intraplate compression as function of plate age and thickness of material beneath the midplate swell. The dashed curve applies when 50 km of plume material ponds at the ridge axis. Times A, B, and C schematically apply to ridge-approaching hot spot. At time A, the midplate plume is beneath old oceanic crust and under compression. A surface hot spot is not active. At time B, the midplate plume is beneath younger lithosphere. A hot spot is active because the lithosphere is in tension. At time C, the plume has neared the ridge. Plume material becomes thinner as the slope of the base of the lithosphere aids flow toward the axis. The plume material ponded at the axis causes compression making the dashed curve apply. The midplate compression shuts off the off-axis hot spot, creating a gap in the track. States but inactive while crossing the older part of the Atlantic ocean, is a possible example of this effect. The off-axis Austral track turned on at 34 Ma (Figure 2) [O Connor et al., 1998]. [53] The gaps where the hot spot jumps to the ridge axis and the off-axis hot spot dies (time B to time C in Figure 15) are also evident. The obvious tracks of the Louisville hot spot west of the east Pacific Rise (Figures 2 and 3) [Small, 1995; cf. Géli et al., 1999] and between midplate New England and the near axis Corner Seamounts hot spot (Figure 1) [Tucholke, 1990; Sleep, 1992] are reasonable examples. A gap exists between the off-axis Austral and the near-axis Foundation Seamounts (Figure 2) [O Connor et al., 1998; Maia et al., 2001]. 4. Dynamics of Ridge-Crossing Hot Spots [54] Mantle plumes produce hot spots directly above the orifice of the tail and secondarily as plume material spreads laterally along the base of the lithosphere. I quantify the dynamics of ridgecrossing hot spots by considering plume material that has ponded beneath the lithosphere. I do not consider the dynamics of the plume orifice in any detail. I compile and find scaling relationships for the thickness of ponded plume material beneath the ridge axis and beneath near-axis and off-axis swells with the intent of applying these relationships to intraplate stresses and the dynamics of gaps in hot spot tracks as discussed in section 3. [55] I obtain scaling relationships for ridge plume interaction starting with the dynamics of flow away from a plume beneath a flat plate following Ribe and Christensen [1994, 1999], Ribe et al. [1995], Sleep [1996], Ribe [1996], Ribe and Delattre, [1998], and Albers and Christensen [2001]. My derivation follows that given in these papers with the modification that the plume velocity may be oblique to the spreading direction. I model the 18 of 33

19 plume material as a thin layer of constant properties, which flows laterally, beneath the lithosphere. I ignore the details of flow with a significant vertical component at the plume orifice and at the edges of the plume material. [56] That is, I assume that the plume material is sufficiently less viscous than normal mantle that it acts as flow channelized between the lithosphere and the underlying mantle. Viscous forces within the plume material resist its lateral flow. I apply dimensional analysis to lubrication theory, assuming that the plume material is thin compared with its extent. I represent the plume material as a single fluid layer with a viscosity and a density contrast relative to normal mantle. Numerical modeling by Albers and Christensen [2001] indicates that these approximations are justified in the complicated case of ridge plume interaction. There are alternative limiting cases, which I do not consider. One is that the model plume material is a fluid with such a low viscosity that flow is resisted mainly by the normal mantle [Griffiths and Campbell, 1991]. Another is that a wide plume is only modestly hotter and less viscous than normal mantle [Ito et al., 1997] Dynamics of Midplate Swells [57] I begin with the well-known dynamics of midplate swells. I compile relationships between the thickness of the plume material and its lateral extent. These quantities determine the easily observed elevation and (map) extent of a hot spot swell. I use these relationships to obtain the analogous relationships for near-axis hot spots in sections 4.2 and 4.4 and on-axis hot spots in section 4.3. [58] In my dimensional treatment of lubrication theory, the thickness of material above the plume S 0 provides a scaling for thickness and the distance from the plume to the nose of the hot spot swell L 0 provides a scaling for its lateral extent (Figure 16). The flux of material ignoring drag from the plate is dimensionally. F P ¼ DrgS4 0 L 0 h ; where Dr is the density contrast between normal mantle and plume material, g is the acceleration of gravity, and h is the viscosity of the plume ð6þ material. This flux 2pF P L 0 around a radius of L 0 from the plume is supplied by a volume flux Q. This material balance yields that S 0 ¼ hq 1=4 : ð7þ Drg [Ribe and Christensen, 1994, equation (23)]. The buoyancy flux of the plume is B DrQ. The length scale L 0 is obtained by noting that, at the nose of the swell, the flux from drag from the overlying plate is dimensionally F D ¼ U PS 0 2 : ð8þ At the stagnation point, the drag flux is equal (and opposite) to the flux from the plume in (6). This yields that the distance to the nose of the swell is L 0 ¼ 1=4 Q3 Drg hup 4 : ð9þ [Ribe and Christensen, 1994, equation (13)]. This dynamic stagnation distance scales inversely with plate velocity. [59] The parameters S 0 and L 0 define the vertical and horizontal scales for the swell. The base of the lithosphere is flat in the derivation, which ignores the dependence of lithospheric thickness on plate age. A crude near-axis criterion for significant interaction is evident: the plume is closer than L 0 to the ridge axis (Figure 16). I obtain more sophisticated criteria involving the slope of the base of the lithosphere in section 4.2. I discuss along-axis channeling of plume material in section 4.3 and toward-axis channeling in section Criteria for Significant Ridge Plume Interaction [60] I begin with the slope of the base of the lithosphere, which until now I have assumed to be flat, to see when its relief matters. The slope at the base of the plume material, which scales as S 0 /L 0, was assumed to drive flow (Figure 16). From (7) and (9), this ratio scales linearly with the plate velocity, P S 0 h 1=2 ¼ U P : ð10þ L 0 QDrg The relief at the base of the lithosphere has a significant effect when it is comparable or greater 19 of 33