Spreading ridge migration enabled by plume-ridge de-anchoring

Domain: earth_science
Published: 2024-10-16
Editorial outcome: minor_revision

Abstract
It has long been recognised that spreading ridges are kept in place by competing subduction forces that drive plate motions. Asymmetric strain rates pull spreading ridges in the direction of the strongest slab pull force, which partially explains why spreading ridges can migrate vast distances. However, the interaction between mantle plumes and spreading ridges plays a relatively unknown role on the evolution of plate boundaries. Using a numerical model of mantle convection, we show that plumes with high buoyancy flux (>3000 kg/s) can capture spreading ridges within a 1000 km radius and anchor them in place. Exceptionally high buoyancy fluxes may fragment the overriding plate into smaller plates to accommodate more efficient plate motion. If the plume buoyancy flux wanes below 1000 kg/s the ridge may be de-anchored, leading to rapid ridge migration rates when combined with asymmetric plate boundary forces. Our results show that plume-ridge de-anchoring may have contributed to the rapid migration of the SE Indian Ridge from 43 million years ago (Ma) due to waning buoyancy flux from the Kerguelen plume, supported by magma flux estimates and radiogenic isotope geochemistry of eruption products. The plume-ridge de-anchoring mechanism we have identified has global implications for the evolution of plate boundaries near mantle plumes.

Introduction
Plate tectonic motions are primarily driven by slab pull at subduction zones and, to a lesser extent, plume push at spreading ridges. The migration of spreading ridges is thought to be driven by asymmetric plate motions on either ridge flank transmitted from far-field slab pull forces. Within this canonical model of plate motion, the geometry and location of spreading ridges are independent of lower mantle dynamics. However, this fails to explain observed interactions between spreading ridges and mantle plumes, such as observed instances of ridge capture and successive ridge jumps towards a plume, how the proximity of ridges to plumes may be accommodated by extensive transform faults, and why ridge migration rates are perturbed in the vicinity of mantle plumes. Moreover, while numerical models predict that mantle plumes and spreading centres should preferentially align, the dynamics and temporal evolution of plume–ridge interaction and its influence on the geometry and migration of spreading ridges is not fully understood.

In nature, plume–ridge interactions are commonly preserved as conjugate large igneous provinces (LIPs), which form on each flank of a spreading ridge as new crust is created. In most cases, the de-anchoring of plumes and spreading ridges is demarcated by a switch from conjugate LIP formation or ridge formation, via a plume head beneath a spreading ridge, to trails of intraplate hotspot volcanoes on one plate signifying the plume and spreading ridge have separated. For example, the Kerguelen plume and SE Indian Ridge record three stages of interaction: (i) conjugate LIP formation while seafloor spreading was slow (>80 Ma), (ii) the SE Indian Ridge remained coupled to the Kerguelen Plume as India rapidly migrated northward, due to strong slab pull forces and/or ridge-push from the Reunion plume, forming the Ninety-East Ridge on the Indian plate (80–43 Ma), and (iii) de-anchoring at 43 Ma as the SE Indian Ridge migrated northwards to accommodate the rapid motion of the Australian plate, which resulted in a switch to low-volume intraplate volcanism on the Kerguelen Plateau. De-anchoring has been preserved in the geometry of the SE Indian Ridge by spreading segments that are offset by transform faults towards the Kerguelen plume beneath the Antarctic Plate and the magma-poor William’s Ridge–Broken Ridge rifted margins. In conjunction with insights into plume–ridge interactions from a numerical model of whole-mantle convection, we analyse the geochemistry and magma flux along the Ninety-East Ridge as a key example from nature to understand the drivers of plume–ridge de-anchoring and its feedback with the geometry of plate boundaries and ridge migration rates.

Results
Ridge capture
To understand the processes responsible for ridge de-anchoring and ridge migration rates, it is first necessary to understand the dynamics of ridge capture by mantle plumes. We adopt a 3D spherical numerical model of mantle convection at Earth-like vigour. The model produces self-consistent plate-like behaviour and dynamic mantle plumes that reproduce plume excess temperatures, and buoyancy fluxes statistically comparable to Earth observations. From the long model timespan of 323 Myr, we track the evolution of multiple mantle plumes and spreading ridges through time. Plume and spreading ridge dynamics are not prescribed but naturally emerge from solving these set of equations, which enables us to study feedbacks in constantly evolving plume–ridge interactions.

The model resolves 40 instances of plume–ridge interactions where ~50% of all model plumes come within 1000 km of a ridge during the 323 Myr timespan. Of those plumes that approach ridges, 13 out of 40 exhibit plume–ridge capture and de-anchoring dynamics. Box plots of the plume buoyancy flux (see “Methods” section), calculated across these 13 instances, show that high flux generally corresponds to ridge capture and low flux corresponds to ridge de-anchoring (Fig. 1). We have analysed the dynamics of all 13 plume–ridge coupled systems and present one representative example of plume–ridge interaction where the ~1000 km proximity of a relatively stationary plume conduit to a spreading ridge causes the ridge to be captured (Fig. 2a–c and Supplementary Movie 1). Ridges appear in the model where the tensile forces are stronger than the strength of the lithosphere, which causes the viscosity to drop and localises deformation. Here, the plume is located ~1000 km from the ridge for nearly 30 Myr in the lead up to the ridge capture. Plume–ridge attraction is evidenced by extensive transform-like boundaries, which displace ridge segments progressively closer to the plume and a 10° tilting of the plume towards the ridge (Fig. 2a). The tilting of the plume in concert with the offset of ridge segments closer to the plume demonstrates the attraction is mutual, which is an advance on previous numerical simulations of plume–ridge interactions, particularly 2D simulations where transform-like offsets are, by definition, impossible.

In the 30 Myr lead up to ridge capture, the mean plume buoyancy flux, averaged from the core-mantle boundary to the surface, increases from 4500 kg/s to 6000 kg/s and thermally weakens the overriding plate (Fig. 3a). By thinning this boundary layer, the plume makes the boundary weaker and helps to localise a ridge segment if the configuration of forces is favourable for plate fragmentation. This is manifested in a new proto-ridge extending from above the plume to the original spreading ridge (Fig. 2b). The previous spreading ridge develops into a triple junction directly on top of the plume as spreading along the proto-ridge establishes a new plate boundary (Fig. 2c). Following the ridge capture, the triple junction is anchored to the reference frame of the plume and the spreading rate increases from 5.5 to 8.5±1.5 cm/yr (measured by the velocity of the plates relative to the plume, Fig. 3c).

We find that plumes of higher buoyancy flux locally increase the spreading rate along ridge segments (Fig. 4a), which is largely because the plume is strong enough to break the plate into smaller pieces (like a triple junction) to accommodate more efficient plate motion. Now anchored to the triple junction, the high plume buoyancy flux maintains a weak zone in the boundary layer, which remains while the configuration of plate boundary forces is consistent. In this example, the plume and triple junction stay coupled for the remaining 60 Myr of the time series while the plume flux remains high, and the plume conduit straightens sub-vertically in the upper mantle.

2D dynamic models have shown that an increased rate of magmatic heating, associated with higher plume buoyancy flux, is required to initiate a ridge jump under faster spreading. In agreement with the 2D models, the increased buoyancy flux in our 3D spherical simulation, combined with the absence of any significant variation in seafloor spreading rates in the first 30 Myr of the simulation, causes the ridge to jump 1000 km on top of the plume conduit (Fig. 3b) where the plume has thermally weakened the overriding plate (Supplementary Fig. 2b). The timescale of the ridge jump occurs within 1 Myr, consistent with the 10^5–10^6 year time frame seen in 2D models. At the time of the ridge jump, the plume buoyancy flux reaches 6700 kg/s at its peak (Fig. 3a) which is within the range of the present-day Hawaiian plume (2800–8700 kg/s). Spreading ridges approaching within 1000 km of mantle plumes that do not result in a ridge jump have low buoyancy fluxes (<2000 kg/s), a similar magnitude to the present-day Galapagos plume (1000–1800 kg/s), suggesting that weak plumes are unable to sufficiently weaken the overriding plate to reshape spreading centres.

Ridge de-anchoring
If high plume buoyancy flux is a significant factor controlling how spreading ridges are captured and held by plumes, then we can test the hypothesis that low buoyancy flux is associated with plume–ridge de-anchoring. From the 13 instances of plume–ridge interaction we interrogated from the numerical model, the mean plume buoyancy flux was ~25–35% lower on average during ridge de-anchoring than ridge capture (Fig. 1), indicating that reduced buoyancy flux prior to de-anchoring is consistent across all model plumes. The tight range in plume buoyancy flux across 13 instances of plume–ridge de-anchoring suggests there is a critical threshold of below ~2000 kg/s where de-anchoring is likely to occur. Only when the plume buoyancy flux wanes below this critical threshold do high convergence rates attached to one of the plates succeed in de-anchoring the spreading ridge from the mantle plume.

As before, we analysed the dynamics of all 13 plume–ridge coupled systems and present one representative example where a spreading ridge decouples from a mantle plume (Fig. 2d–f and Supplementary Movie 2). For the first 80 Myr of the time series, the plume and the ridge are coupled as the mean plume buoyancy flux gradually decreases from 2600 to 400 kg/s (Fig. 3e). This is primarily accommodated by a 50–100 °C decrease in excess temperature across the entire depth of the plume (Fig. 5e) and a reduction in the plume upwelling velocity from ~30 to 3 cm/yr in the upper mantle (Fig. 5g). As a result, thermal weakening of the overriding plate by the plume decreases, as evidenced by a 500 °C temperature drop at 30 km depth in the overriding plate (Supplementary Fig. 2d).

At 75 Myr, the plume has waned below 1000 kg/s of buoyancy flux and decouples from the spreading ridge (Fig. 3e), which rapidly migrates 60 km away from the plume over 10 Myr, with a maximum rate of 12 cm/yr (Fig. 3f). The seafloor spreading rate increases from 2 to 8 cm/yr (Fig. 3g) to accommodate rapid ridge migration following a change in plate boundary forces associated with established far-field subduction zones (Supplementary Fig. 2f). As the ridge rapidly migrates away from the plume, the conduit strongly tilts toward the ridge by up to 15° measured in the upper mantle (Fig. 3h). Transitory tilted plume conduits have been proposed to generate dual hotspot tracks, which could have important implications for the distribution of intraplate volcanism following plume–ridge de-anchoring.

We propose the coupling of a mantle plume with a spreading ridge acts as an anchor, thereby impeding ridge migration. De-anchoring caused by asymmetric plate velocities mechanically rips spreading ridges away from mantle plumes but is tempered by the plume buoyancy flux. The rate of ridge migration during de-anchoring is inversely proportional to the buoyancy flux (Fig. 4b), indicating that stronger plumes impede ridge migration. A stronger buoyancy flux equates to a greater upwelling velocity and higher temperature. The former means the plume penetrates to a greater extent in the overriding lithosphere, and the latter results in lower viscosity. Both are weakening agents which maintain the localisation of deformation in the overriding plate which, when reduced, facilitates ridge migration.

We contend that a reduction in plume buoyancy flux facilitates ridge migration contrary to the counter argument that the migration of a spreading ridge results in a reduction in plume buoyancy flux because (1) ridge migration occurs only after the plume buoyancy flux has substantially decreased, and (2) the plume buoyancy flux is reduced from the core-mantle boundary to the surface at the time of de-anchoring. A local decrease in buoyancy flux within the upper mantle would be anticipated following plume–ridge de-anchoring, but this would not significantly reduce the plume buoyancy flux across the entire plume conduit. We observe a wholesale reduction in the mean buoyancy flux in the lead up to ridge migration (Figs. 1 and 5h), which suggests that waning plumes facilitate plume–ridge de-anchoring.

Reconstructing plume flux
One such example of plume–ridge coupling and de-anchoring in nature is observed between the Kerguelen plume and the SE Indian Ridge (Fig. 6). Fragmentation of the Indian, Australian, and Antarctic plates was likely driven by the initially high buoyancy flux of the Kerguelen plume which broke the Indian and Australian plates to accommodate the rapid northward trajectory of the Indian Plate propelled by double subduction and/or plume push from the Reunion plume (Fig. 6a). Tectonic reconstructions predict a triple junction close to the present-day location of the Kerguelen plume, and the eruption of multiple LIPs associated with the Kerguelen plume suggests a buoyancy flux at least as high as the triple junction-forming plumes observed in our numerical model (Fig. 2c).

The coupling of the Kerguelen plume with the SE Indian Ridge produced the Ninety-East Ridge on the Indian Plate from >80 to 43 Ma (Fig. 6b). The Ninety-East Ridge records ~37 Myr of plume products embedded within the Indian plate from the coupled Kerguelen plume, up until plume–ridge de-anchoring at 43 Ma. We relate variations in plume flux from the Kerguelen plume to magma production along the Ninety-East Ridge by measuring the fluctuations in seafloor bathymetry at multiple cross-sections (Fig. 7a–d). This involves subtracting the height of the Ninety-East Ridge from the height of adjacent seafloor away from plume–ridge influence and integrating the area (Supplementary Fig. 3, see “Methods” section). The resulting magma production (in km^2) is the excess area (over regional bathymetry) that includes all plume material incorporated into the Indian Plate from the Kerguelen plume, such as erupted volcanics, sill injection, and magma underplating. This excludes any plume products on the slower-moving Antarctic or Australian plates.

From our calculations, the magma production increased from 220 km^2 at 6° N (78 Ma) and reached its peak of ~440 km^2 at 15° S (55 Ma) implying the buoyancy flux for the Kerguelen plume reached its zenith during its coupling with the SE Indian Ridge (Fig. 7b–d). Since then, the magma production has decreased to a minimum point of 160 km^2 at 27° S (45 Ma) after which the SE Indian Ridge decoupled from the Kerguelen plume (43 Ma). Superimposing box plots of radiogenic isotopes on top of Fig. 7b–d show a strong association with the estimated magma production for a given latitude. In general, the variations in magma production with Sr, Nd, and Pb isotopic compositions corroborate a trend from moderately low plume flux at 78 Ma to high plume flux at 55 Ma and low plume flux at 45 Ma. This implies that the plume buoyancy flux diminished significantly prior to the de-anchoring of the Kerguelen plume from the SE Indian Ridge at 43 Ma.

Isotope ratios help to discern the mantle source of melting for eruption products. Geochemical variations in mantle domains between mid-ocean ridge basalts (MORB) and ocean island basalts (OIB) have long been attributed to heterogeneity and mixing between upper and lower mantle reservoirs. For a trail of volcanic products linked to the same plume–ridge system, the compositional spread between MORB and enriched plume end members likely reflects changes in the melt fraction delivered by the plume from more deeply sourced upwelled mantle. It follows then that the plume buoyancy flux should play a first-order control on the mixing between these two end members. Additional variations in enrichment may occur due to the entrainment of upper mantle into the upwelling plume or variations in plume source composition with time. Using the end-member compositions of enriched plume compositions defined by 24–25 Ma basalts and picrites of the Kerguelen Plateau and normal mid-ocean ridge basalts (N-MORB) from the SE Indian Ridge, we compare the relative proportions of plume and asthenospheric mantle along the Ninety-East Ridge to changes in plume buoyancy flux (Fig. 8).

Lower 87Sr/86Sr and higher 143Nd/144Nd characterise the youngest samples along the Ninety-East Ridge (Fig. 8a, d) reflecting greater proportions of upper mantle melting. Pb isotopes exhibit a weaker age correlation (Fig. 8c). In general, the variations in Sr, Nd, and Pb isotopic enrichment illustrate a trend from higher plume proportions at 55 Ma to higher N-MORB proportions at 45 Ma, reflecting a diminished buoyancy flux of the Kerguelen plume immediately prior to plume–ridge de-anchoring at 43 Ma. This coincides with the onset of rapid northward migration of the SE Indian Ridge from the Kerguelen plume driven by the fast motion of the Australian Plate (Fig. 7e).

De-anchoring, a driver of ridge migration?
The decrease in magma production and higher upper mantle proportions in melts at the youngest part of the Ninety-East Ridge support our hypothesis that the waning Kerguelen plume culminated in the de-anchoring of the SE Indian Ridge at 43 Ma. We propose that thermal weakening of the overriding plate likely decreased as the plume buoyancy flux waned, thus the localisation of deformation could not be sustained while strong asymmetric plate velocities associated with the rapid migration of the Australian plate mechanically ripped the SE Indian Ridge away from the Kerguelen plume. As a result, the SE Indian Ridge has migrated away from the present-day location of the Kerguelen plume at 2.7 cm/yr (Fig. 7e), translating to 5.4 cm/yr northward migration of the Australian plate, and a transition to intraplate volcanism on the Kerguelen Plateau. We speculate that if the buoyancy flux of the Kerguelen plume were greater at 43 Ma, then progressive ridge jumps closer to the Kerguelen plume would be observed.

Following de-anchoring, the volcanic products should switch from MORB to OIB systematics as intraplate volcanism is established. Since its separation from the SE Indian Ridge, the Kerguelen plume has produced the intraplate Kerguelen Archipelago on the northern Kerguelen Plateau with a range of flood basalts aged between 29 and 24 Ma. Lower eruption volumes for these islands indicate a waning plume buoyancy flux (827 kg/s) with volcanism occurring over a diffuse area. Present-day estimates of buoyancy flux for the Kerguelen plume is between 200 and 500 kg/s, which is well below the 1000 kg/s threshold for our predictions of plume–ridge de-anchoring to take place and suggests that the Kerguelen plume has continually waned from 60 Ma to the present day.

Our numerical model predicts that following de-anchoring, the waning plume can tilt 15° within the upper mantle toward the migrating ridge. If the stem of the Kerguelen plume is currently beneath Heard/McDonald Island, then both the Kerguelen Archipelago and Amsterdam–St Paul Islands could be diapirs rising from the plume conduit tilting northward toward the SE Indian Ridge. This would explain why the isotopic compositions of Amsterdam–St. Paul Islands are strongly N-MORB (from the SE Indian Ridge) mixed with a small enriched plume component.

If the buoyancy flux of mantle plumes is a significant factor controlling ridge capture and de-anchoring, then this mechanism may be used to help explain the evolution of plume–ridge interactions and asymmetric accretion of oceanic crust globally. We find the attraction between mantle plumes and spreading ridges is strongest for plumes of high buoyancy flux. For example, up to 300 km displacement away from the expected age-progressive seamount chains has been attributed to the attraction of the Hawaiian plume (present-day buoyancy flux of 7400 kg/s) towards the ridge separating Kula and Pacific plates. High plume buoyancy flux may also be a key driver of triple junction formation, since a faster upwelling velocity and excess temperature will fragment the overriding plate into smaller plates to accommodate more efficient plate motion.

For waning mantle plumes close to the critical 1000 kg/s buoyancy flux threshold, spreading ridges may abandon the plume. The balance of forces on each plate pair (or triple) controls the rate of ridge migration. Strong asymmetries in plate boundary forces are a prerequisite to drive rapid ridge migration enabled by plume–ridge de-anchoring. For the Kerguelen plume, strong slab pull on the Australian plate married with little to no plate boundary forces on the Antarctic plate translated to the rapid northward migration of the SE Indian Ridge during de-anchoring.

If the balance of forces on each plate pair is similar to each other, then the spreading ridge would migrate much more slowly following plume–ridge de-anchoring than if the plate force balance was highly asymmetric. The Atlantic Ocean is not bounded by subduction zones which indicate the balance of plate boundary forces along the Atlantic Ridge is relatively similar to each other. Therefore, it is unlikely that plume–ridge de-anchoring would translate to fast ridge migration rates. For example, the transition from the Walvis Ridge to the intraplate Tristan-Gough seamount chains reflect the de-anchoring of the mid-Atlantic spreading ridge from the Tristan plume due to decreased plume buoyancy flux at around 70 Ma (Supplementary Fig. 4), which did not coincide with rapid ridge migration. Instead, de-anchoring is merely manifested by a gradual separation between plume and ridge.

Similarly, the force balance between the Nazca and western Pacific plates is mostly comparable (convergence rates between 9 and 11 cm/yr, along the Andes and Tonga-Kermadec Trench), which explains why the East Pacific Rise has not migrated rapidly away from the Easter plume following plume–ridge de-anchoring. The seamounts of the Easter hotspot chain have become progressively less enriched westwards toward the present-day location of the Easter plume, suggesting its buoyancy flux has continually waned below that of the Galapagos plume.

Our work demonstrates that the interactions between plumes and ridges are modulated by plume buoyancy flux which can anchor plate boundaries in place. This outcome provides new insights into the forces that govern plate tectonics and plume dynamics, which has significant implications for the evolution of plate boundaries, the distribution of plume-related volcanism, and the reconstruction of ocean basins.

Methods
Setup of a whole-mantle convection model
We used the StagYY code to model incompressible whole-mantle convection using the Boussinesq approximation for an incompressible fluid in 3D spherical geometry. We set the reference Rayleigh number to 10^7, which favours the self-generation of Earth-like amplitudes of surface topography (~20 km peak-to-peak), heat flow (~50 TW), and plate velocities (~3 cm/yr). Viscosity varies with both temperature and depth through an Arrhenius law, producing 7 orders of viscosity variations throughout the mantle. To model lower convective vigour in the lowermost mantle, thermal expansivity decreases by a factor of 3 throughout the mantle domain, consistent with mineral physics experiments at high pressure and temperature, and we impose a 30-fold increase of viscosity at the transition zone, as suggested by the study of Earth’s geoid. Self-consistent plates are generated at the surface through pseudo-plasticity, by using a surface yield stress of ~50 MPa and a depth-dependent yield stress coefficient of ~1000 Pa/m. Once the yield stress is reached, viscosity drops by several orders of magnitude, focussing deformation into narrow regions and thus mimicking plate-boundaries formation, distribution, and evolution self-consistently with mantle convection. We model continents as less dense, more viscous, and stronger rafts than oceanic lithosphere in order to ensure their positive buoyancy and stability throughout the model evolution. Their initial geometry and location correspond to a reconstruction of Earth’s continents at 80 million years ago, reflecting their dispersed geographical distribution at that time. Continental material is tracked by tracers, which are allowed to advect after an equilibration phase (not considered for the here-described model analysis) during which convection reaches a quasi-statistic equilibrium, corresponding to statistically stable average mantle temperature and boundary heat fluxes.

The model used here corresponds to Model 2 of ref. 16, where all quantitative details can be found about its setup, the general behaviour of mantle plumes, and the method used to track absolute plume motions.

Calculation of plume buoyancy flux
The buoyancy flux of mantle plumes is calculated from the following relation,

B_p = \rho_m \alpha \Delta T A_p v_p

where \rho_m is the mantle reference density, \alpha is the reference thermal expansivity, \Delta T is the mantle plume excess temperature, A_p is the cross-sectional area of the mantle plume conduit, and v_p is the buoyant rising speed. Plumes are identified from the numerical model by isolating where the temperature is greater than one standard deviation from the mean temperature for each depth interval from the core-mantle boundary to the surface of the model. The excess temperature is then calculated across this temperature where the plume can be resolved (e.g. some plumes terminate below the surface of the Earth). The cross-sectional area is calculated from the area of the convex hull of points that encircles the plume for each depth interval, and the upwelling velocity is extracted from the radial component of the velocity field in spherical coordinates within this convex hull. The plume buoyancy flux is calculated using the above relation and averaged across the depth range of the plume. Plume tilting is calculated from the difference between the location of the centroid of the cross-sectional area at each depth interval and the mean plume centroid averaged across the entire depth range of the plume. In the main text, the tilting is calculated in the upper mantle (from 660 km depth to the surface, where tilting is generally greatest) and expressed in degrees by summing the distance away from the mean plume centroid and calculating its arctangent with 660 km to the surface. The plume buoyancy flux within the numerical simulations of whole-mantle convection ranges from 10 to 20,000 kg/s and is 5000 kg/s on average. A plume tracking algorithm was implemented to track the migration of plumes (relative to the geographic grid) and the changes in buoyancy flux across multiple timesteps. If a plume is spaced <400 km between timesteps (measured at the surface), they are considered to be the same plume. Plumes move little compared to tectonic plates between model timesteps, which means the distance tolerance of 400 km relative to the geographic grid is sufficiently large to identify separate plumes yet small enough to avoid duplicate plumes. If multiple plumes are detected within 400 km radius of each other (and have different plume fluxes) then these are tracked as separate plumes.

Calculation of ridge spreading rates and distances to plumes
Spreading ridges are identified in the numerical model from the surface temperature and velocity fields. We identify sharp discontinuities in the surface velocity field combined with a white top-hat transform of the surface temperature (a peak-finding algorithm) to identify continuous ridge segments for each timestep. (Using just the velocity incorrectly identifies triple junctions, and using only the temperature incorrectly identifies plumes as spreading ridges.) We calculate the spreading rate by seeding two points orthogonal to the strike of the ridge and sampling the velocity field at those locations. The distance to the nearest plume is calculated using the Haversine distance, which accounts for the curvature of the sphere.

Calculation of convergence rates and distances to plumes
Subduction zones are identified in the numerical model from the density field at 125 km depth and the surface velocity field. We identify sharp discontinuities in the surface velocity field combined with a white top-hat transform of the density field to identify continuous trench segments for each timestep. We calculate the convergence rate by seeding two points orthogonal to the strike of the trench and sampling the velocity field at those locations. The distance to the nearest plume is calculated using the Haversine distance, which accounts for the curvature of the sphere.

Estimates of magma flux for the Kerguelen plume
Latitudinal cross sections of ETOPO1 elevation were taken at 0.3° increments along the Ninety-East Ridge from 6° N to 27° S. Each cross section is 3° in length along the longitudinal plane. Sediment thickness is subtracted from the topography to remove the influence of continental sediments on the calculation of magma flux. The area of the topographic bulge is calculated by selecting a basal seafloor height for each cross section, which we define as the 5th percentile of the elevation across the cross section. The area is calculated by integrating the elevation above the seafloor basal height (Supplementary Fig. 3). Choosing a different seafloor basal height changes the magnitude of the area calculation but does not perceptibly alter the relative differences in area across multiple cross-sections. We interpret these variations in area between cross sections as caused by changes in plume magmatic flux. This encompasses all excess material emplaced in oceanic seafloor from the mantle plume, including erupted volcanics, sill injection, and magma underplating. Here we assume eruption material was incorporated instantaneously in oceanic seafloor (i.e. no overlap of eruption ages between cross sections), and the age of eruption material is identical to the age of the seafloor (which is reasonable during periods of plume–ridge coupling because the formation of the Ninety-East ridge occurs at the spreading ridge). More advanced methods to calculate the absolute magma flux for a given cross section would account for isostatic loading of the lithosphere to estimate the magma flux below the surface of the seafloor, however, this is not critical for our study because we are interested in long-wavelength trends and not the absolute values of magma flux.

Peer review rounds
[{"round": 1, "reviewer_comments": {"reviewer_1": "This manuscript addresses a topic that has been in need of attention for quite some time. Considerable research has considered plume-ridge interaction from geochemical, geophysical, and geodynamics perspectives, but those studies have not directly addressed the specific mechanism of how plumes interact with ridges and affect their migration via anchoring/de-anchoring. The multidisciplinary approach taken by the authors that combines geodynamic modeling with geochemistry to “ground truth” the modeling is an effective one, for the most part, but not as clearly conveyed or applied as it could be in the manuscript, something easily addressed. The idea that plume flux into a ridge system is a controlling factor in terms of how effectively a ridge can be anchored to a plume is an important concept to have identified in a systematic way. In short, I anticipate that this paper will be appreciated and referenced by many researchers working on near-ridge plumes and near-plume ridges in the future.\nSome comments as I go through the manuscript:\n1. I am not a modeler, so I cannot assess the model details or methodology. That said, it would help readers like me who are not modelers to clarify a bit of the Results section. For instance, why was a 323 Myr timespan chosen? At the most basic level, is this modeling a generic spherical planet with Earth-like mantle convection or one that has some of Earth’s characteristics (plates, plumes, etc.)? Stating this unequivocally up front would eliminate some questions to those who are not in the modeling realm, and would help make this more friendly to the non-modeler.\n2. Figure 1 could use a bit more explanation in the caption of how the flux was modeled; just recapping it in a sentence in the caption would help make this a more understandable figure.\n3. Figure 2 would benefit from some explanation in the caption to indicate that it’s effectively showing 3 dimensions; at first it is confusing b/c it looks like it’s a bird’s eye (2D) view, but I think (?) that it’s meant to show the tilt in the plume conduit? If this is incorrect, then it supports my point that it’s a bit hard to know how to understand this figure clearly. Same applies to the two animation clips.\n4. In Results (and in the model), is the plume flux changing in response to the interactions with the ridge, or is it changing b/c it’s a generic plume lifetime that includes increasing in intensity then waning flux as it goes extinct? What I’m trying to ask is whether plume flux is tied to ridge motion in some way, because around line 94, the paper reads as though the flux is being documented, not pre-determined. I am sure I’ve missed something here, but stating clearly (even if it's obvious to modelers) that you are or are not modeling the plume flux behavior would help. This section is written as though the plume flux is a response to the model parameters, but I’m unclear if that’s the case in reality. Again, if I missed something, apologies. NOTE: I think I sorted this out, see point 21…if that’s correct, some of these comments may not be as relevant; if that’s NOT correct, then definitely things need to be clarified.\n5. Line 96: Is this meant to be Figure 2a or 3a? Seems confusing to be jumping to Figure 3 when the paper is mostly focused on Figure 2 here.\n6. Why does the spreading rate increase again (Figure 3g) once the plume has been disconnected from the ridge? This seems counter-intuitive from a physical perspective and definitely needs to be discussed.\n7. The Results section would be easier to follow if it were split into shorter, single-focus paragraphs, each dealing with one figure/phenomenon at a time.\n8. Line 113-114 how old is “older” seafloor? How much older can it be in a near-ridge plume system?\n9. Line 118: Within 1 Myr of what?\n10. Line 121: Need a “within” in front of 1000 km, and the “which” should be a “that”\n11. Caption of Figure 4: Isn’t it kind of a given that “plumes that are active over a longer timespan within the numerical model tend to have a larger buoyancy flux” or is that not the case? Would be good to clarify this statement further. Furthermore, is this a finding, or a constraint of the model?\n12. Paragraph beginning line 146: This pgh can use reworking to clarify its content. The part beginning “from the 13 instances of…” conveys an important finding, but it is delivered after explaining why that might be the case, so it’s hard to follow. Also, are plumes being considered that do not get to the surface? That’s implied in line 151 with the plume reaching a “shallower depth.”\na. And how does plume viscosity matter here; if the ridge is being anchored, it’s presumably somehow related to the mantle’s viscosity/physical properties; what is the role of the plume’s viscosity in this system?\n13. Figure 6: Should label the India-Australia ridge.\n14. Line 176: What is the justification for the “most extensive plume products” mentioned here? Volume? This needs a citation at the minimum and ideally some graphic/explanation of how this is known, given how impactful this evidence could be for the argument laid out in this paper.\na. And why would a tilted plume result in more extensive plume products, wouldn’t more extensive material result from higher fluxes, not plume angle? Or is more widespread plume materials the appropriate description (as it’s described in the final paragraphs)?\n15. Line 185: I’m not so sure that the ratio between MORB and more enriched plume compositions reflects changes in the capacity of the plume to delivery more deeply sourced melt to the surface so much as on whether the plume is diluted by entrained upper mantle and/or depleted lower mantle material. The Zindler et al. (1979) reference predates a lot of research into this topic that has happened since; this warrants clarification/revisiting/updating.\na. Similarly, in the next sentence, stating that plume buoyancy flux plays a first-order control on the spread between depleted and enriched endmembers is also at the minimum an oversimplification, and really more of an inaccurate generalization.\n16. Line 190: the first 143Nd/144Nd should presumably be 87Sr/86Sr?\n17. It would really clarify this isotope argument to produce a simple timeline of the different isotopic ratios in samples, instead of the x-y isotope plots. It’s very hard to piece this together to understand the proposed pattern.\na. Also, why include N Atlantic Ridge (is that meant to be Australian?), or Pitcairn if they are ancillary to the story? Simpler would be better.\n18. The model could use clarification and simplification in how it’s explained. Is the idea that when the plume is anchoring the ridge, we should see more intermediate signatures along the two-component spectrum, but more plume-like signatures when the plume is on its own/ridge-free? (which is pretty much the basis of most plume-ridge interaction models that use geochemistry as the metrics)\na. If so, the PCA doesn’t add much to this; seems like you don’t need it here to test your hypothesis. PCA kind of muddies the water since the only focus is on PC1, which is just two-endmember mixing. What is involved in PC2, then, and why is it needed at all? Why not just use average plume and average MOR compositions (as is done in the binary isotope plots already)?\n19. Again, similar to point 18 as I try to work this out: If I am understanding the proposed isotopic mixing model, we should be seeing more ridge-like compositions first along the 90E ridge’s oldest samples, then a shift to more plume-like/intermediate signatures, then back again to ridge only for the youngest ones…right? This model could be conveyed much more clearly if that’s what it is; if not, then it definitely needs more explanation; the reliance on PCA to get the point across isn’t that effective. It would also be much more clearly conveyed in a simple graphic with time along one axis, as stated above, than forcing the reader to decipher it here by color (Figure 7).\na. Also, the model works ok for (a) and (b) in Figure 7 (Sr, Nd, Hf isotopic ratios), but it really doesn’t work well for either 206Pb/204Pb-208Pb/204Pb (c) (why don’t the younger samples get more MORB-like than they do, but stay closer to the plume composition?), and why do the older samples in the Sr-Pb system (d) not sit closer to N-MORB compositions? The model should work in all isotopic systems, but it doesn’t from what I can see, which calls it into question and warrants attention.\nb. Similarly, if this is an issue of going from ridge-only to plume/ridge mixing to ridge-only again, why are there so many inflection points in magma flux in Figure 9(b)? What happened to cause those complexities in the magma flux vs latitude (time) curve? Same question applies for the Walvis/Tristan analysis in the supplemental docs.\n20. Line 203: What’s “magma flux” referencing here? In the plume or the ridge, and how does it differ from buoyancy flux? I assume it’s MOR flux?\n21. Ok so maybe the issue I’m having is that the authors mean buoyancy flux/plume contribution to the ridge whenever it is mentioned, not in fact changing plume flux over time? If so, it took me until nearly the end of the paper to understand that nuance, despite careful reading. Some simple clarification early on to indicate that the study focuses on the RIDGE’s erupted products and the buoyancy flux of magma to the ridge (from both the conventional MOR upwelling plus or minus plume contributions) would probably sort out a lot of the potential for confusion. I’m sure it’s mentioned early on, but as someone who works on plumes, I definitely assumed that “buoyancy flux” referenced the PLUME’s buoyancy flux, not the flux of material to the MOR throughout this paper. My error if I missed it early on, but many people read papers far more quickly, so finding a way to make it bomb-proof what you are modeling early on in the paper would be great (just bear in mind that the use of “buoyancy flux” is most commonly and automatically attributed to the PLUME among plume researchers, not the supply to the ridge.\n22. Line 246: Really can’t follow what’s meant here as written. Could use clarification.\n23. Are there any implications of this model for the ocean islands and their compositions (and/or morphologies/sizes) being formed by the plume in a near-ridge environment?\n24. In general, the manuscript would benefit from a detailed proofread that focuses on clarifying sentences, finding a more systematic way to convey information via figures (it bounces around between figures quite a bit, which makes it frustrating to read), designing shorter paragraphs focused on single topics, and use of commas and other minor grammatical tools to help clarify sentences (e.g., line 146 needs a comma after “anchor” to make it read easily).", "reviewer_2": "I have reviewed the manuscript ’Spreading ridge migration enabled by plume-ridge de-anchoring’, by B. Mather and coauthors. This manuscript uses numerical models of viscous flow to draw conclusions about the dynamics of ridge migrations and the controls operated by ridge-plume interactions.\nThe topic of the study is one of interest and has the potential to advance tectonic reconstructions at the global scale. However, I would see this study more suited for a specialized outlet. In fact, the study revolves around analyses of model behavior upon changes of the input parameters. I fail to see a testable hypothesis that is rooted in specific observations, and that is tested against independent data and uncertainties. The study makes a comparison with SE Indian Ridge reconstructions, but to me this seems more a case of resemblance rather than prediction. This is not to say there is no merit in this study. Rather, that it does not make a convincing case for a paradigm shift in geological knowledge.\nBelow are a few points that authors may find useful:\nThat plate tectonics is primary driven by slab pull is a rather partial view: there is a significant body of work illustrating the relevance of controls on plate tectonics operated by pressure-drived mantle convection (for instance, the work of Lenardic, Richars and coauthors).\nSome of the statements that are key to the dynamics proposed in this study are based on other studies (ref. 2 for plume push, ref. 11 for slab pull) that contain proposals rather than tested hypotheses. This gives the impression that these are well established dynamics, which is not the case.\nA notion invoked at line 105 is that a strong plume can break the lithosphere. This statement should be backed up with either references (the past work of Roger Buck may be something to look at) or tests/calculations. For instance, can the push of a plume exceed the strength of oceanic lithosphere?\nWhat is the background color in fig. 4?\nDo velocities in fig. 6 come with uncertainties?"}, "author_response": "Thank you for providing us with reviews of our manuscript. We have significantly overhauled\nthe manuscript in line with the reviewers’ comments, and believe that the manuscript is much\nstronger as a result of this feedback. Please find a track-changes document attached to this\nsubmission where we have indicated all alterations to the manuscript compared to the original\nsubmission. Below is our point-by-point response to the reviews in blue.\nReviewer #1 (Remarks to the Author):\nThis manuscript addresses a topic that has been in need of attention for quite some\ntime. Considerable research has considered plume-ridge interaction from geochemical,\ngeophysical, and geodynamics perspectives, but those studies have not directly\naddressed the specific mechanism of how plumes interact with ridges and affect their\nmigration via anchoring/de-anchoring. The multidisciplinary approach taken by the\nauthors that combines geodynamic modeling with geochemistry to “ground truth” the\nmodeling is an effective one, for the most part, but not as clearly conveyed or applied as\nit could be in the manuscript, something easily addressed. The idea that plume flux into\na ridge system is a controlling factor in terms of how effectively a ridge can be anchored\nto a plume is an important concept to have identified in a systematic way. In short, I\nanticipate that this paper will be appreciated and referenced by many researchers\nworking on near-ridge plumes and near-plume ridges in the future.\nSome comments as I go through the manuscript:\n1. I am not a modeler, so I cannot assess the model details or methodology. That said,\nit would help readers like me who are not modelers to clarify a bit of the Results section.\nFor instance, why was a 323 Myr timespan chosen? At the most basic level, is this\nmodeling a generic spherical planet with Earth-like mantle convection or one that has\nsome of Earth’s characteristics (plates, plumes, etc.)? Stating this unequivocally up front\nwould eliminate some questions to those who are not in the modeling realm, and would\nhelp make this more friendly to the non-modeler.\nThe 323 Myr timespan was simply an arbitrary point at which to stop the\nnumerical simulation. All simulations need to balance model resolution with the\nnumber of timesteps, the numerical complexity of solving each timestep, and the\ncomputational resources available to run the simulation. A detailed explanation of\nthe choices of parameters, initial conditions, and rheological scaling is available\nin the methods section. We have also added some text to the results section to\nclarify some general details of the simulation. Importantly, we write, “the model\nproduces self-consistent plate-like behaviour and dynamic mantle plumes which\nreproduce plume excess temperatures, and buoyancy fluxes statistically\ncomparable to Earth observations” (lines 73-75).\n2. Figure 1 could use a bit more explanation in the caption of how the flux was modeled;\njust recapping it in a sentence in the caption would help make this a more\nunderstandable figure.\nWe have included a sentence in the Fig 1 caption explaining how plume\nbuoyancy flux was calculated, referencing the methods section for more details.\n3. Figure 2 would benefit from some explanation in the caption to indicate that it’s\neffectively showing 3 dimensions; at first it is confusing b/c it looks like it’s a bird’s eye\n(2D) view, but I think (?) that it’s meant to show the tilt in the plume conduit? If this is\nincorrect, then it supports my point that it’s a bit hard to know how to understand this\nfigure clearly. Same applies to the two animation clips.\nWe have added more shading to the plume conduits to improve the perception\nthat it is a 3D illustration. The core-mantle boundary (CMB) is now indicated on\nthe figure and the caption has been modified to clarify the illustrations are 3D.\n4. In Results (and in the model), is the plume flux changing in response to the\ninteractions with the ridge, or is it changing b/c it’s a generic plume lifetime that includes\nincreasing in intensity then waning flux as it goes extinct? What I’m trying to ask is\nwhether plume flux is tied to ridge motion in some way, because around line 94, the\npaper reads as though the flux is being documented, not pre-determined. I am sure I’ve\nmissed something here, but stating clearly (even if it's obvious to modelers) that you are\nor are not modeling the plume flux behavior would help. This section is written as\nthough the plume flux is a response to the model parameters, but I’m unclear if that’s\nthe case in reality. Again, if I missed something, apologies. NOTE: I think I sorted this\nout, see point 21…if that’s correct, some of these comments may not be as relevant; if\nthat’s NOT correct, then definitely things need to be clarified.\nThere is no forcing of plumes or plume buoyancy flux, rather we allow the plumes\nto evolve self-consistently within the simulation and track their characteristics\nthrough time (i.e. excess temperature, upwelling velocity, plume flux, etc.) Any\ninteraction between plumes and mid-ocean ridges occurs spontaneously within\nthe model. In line 75 we articulate this point more clearly, “From the long model\ntimespan of 323 Myr, we track the evolution of multiple mantle plumes and\nspreading ridges through time. There is no forcing of plume or spreading ridge\ndynamics which enables us to study feedbacks in constantly evolving plume-\nridge interactions.”\n5. Line 96: Is this meant to be Figure 2a or 3a? Seems confusing to be jumping to\nFigure 3 when the paper is mostly focused on Figure 2 here.\nFigure 3a is correct. The results section have now been split into more\nparagraphs which deal with one figure or concept to improve readability.\n6. Why does the spreading rate increase again (Figure 3g) once the plume has been\ndisconnected from the ridge? This seems counter-intuitive from a physical perspective\nand definitely needs to be discussed.\nIn cases where strong asymmetric forces are exerted on a plate pair, the\nspreading ridge bordering the spreading rate needs to increase to accommodate\nridge migration. In lines 151-153, we clarify this process: “The seafloor spreading\nrate increases from 2 to 8 cm/yr (Figure 3g) to accommodate rapid ridge\nmigration following a change in plate boundary forces associated with\nestablished far-field subduction zones (Figure S2f).”\n7. The Results section would be easier to follow if it were split into shorter, single-focus\nparagraphs, each dealing with one figure/phenomenon at a time.\nWe have split the results section into several smaller paragraphs to improve\nreadability.\n8. Line 113-114 how old is “older” seafloor? How much older can it be in a near-ridge\nplume system?\nAgreed. After re-reading this paper the age of oceanic seafloor appears to be\nless important than spreading rate. This has been rectified.\n9. Line 118: Within 1 Myr of what?\nThis has been rephrased to “The timescale of the ridge jump occurs within 1\nMyr…” to avoid confusion.\n10. Line 121: Need a “within” in front of 1000 km, and the “which” should be a “that”\nCorrected.\n11. Caption of Figure 4: Isn’t it kind of a given that “plumes that are active over a longer\ntimespan within the numerical model tend to have a larger buoyancy flux” or is that not\nthe case? Would be good to clarify this statement further. Furthermore, is this a finding,\nor a constraint of the model?\nIt is intuitive that stronger plumes should outlive weaker plumes, but to my\nknowledge this has not been demonstrated in previous research. This has been\nclarified in the caption. There is no constraint in the numerical model to enforce\nplume longevity. As stated in the results (lines 74-76): “The model produces self-\nconsistent plate-like behaviour and dynamic mantle plumes which produce plume\nexcess temperatures, and buoyancy fluxes comparable to Earth observations”.\n12. Paragraph beginning line 146: This pgh can use reworking to clarify its content. The\npart beginning “from the 13 instances of…” conveys an important finding, but it is\ndelivered after explaining why that might be the case, so it’s hard to follow. Also, are\nplumes being considered that do not get to the surface? That’s implied in line 151 with\nthe plume reaching a “shallower depth.”\nWe have moved this paragraph to the top of the section entitled “Ridge de-\nanchoring” since it provides general statistics on de-anchoring over 13 plume-\nridge interactions. From there we focus on one representative example of plume-\nridge de-anchoring discussing the geodynamic drivers for this phenomenon.\nShallower depth refers to how much the plume penetrates the overriding plate.\nIndeed, the plume reaches the surface. The statement considers the qualities of\nthe plume that localize deformation through thermal weakening. Increased\nupwelling velocity means more of the plume penetrates the overriding plate, and\nincreased temperature weakens the overriding plate. We have reworded this part\nto, “A stronger buoyancy flux equates to a greater upwelling velocity and higher\ntemperature. The former means the plume penetrates a shallower depth in the\noverriding plate and the latter results in lower viscosity. Both are weakening\nagents which maintain the localisation of deformation in the overriding plate\nwhich, when reduced, facilitates ridge migration.” (Lines 163-167).\na. And how does plume viscosity matter here; if the ridge is being anchored, it’s\npresumably somehow related to the mantle’s viscosity/physical properties; what is the\nrole of the plume’s viscosity in this system?\nPlume viscosity does not matter very much in terms of anchoring spreading\nridges. The plume viscosity in the numerical models is relatively low, so it does\nnot impart stresses on the overriding plate. Plumes act more through their\nthermal effect beneath the lithosphere, leading to its local thinning.\n13. Figure 6: Should label the India-Australia ridge.\nAdded.\n14. Line 176: What is the justification for the “most extensive plume products”\nmentioned here? Volume? This needs a citation at the minimum and ideally some\ngraphic/explanation of how this is known, given how impactful this evidence could be for\nthe argument laid out in this paper.\na. And why would a tilted plume result in more extensive plume products, wouldn’t more\nextensive material result from higher fluxes, not plume angle? Or is more widespread\nplume materials the appropriate description (as it’s described in the final paragraphs)?\nWe have removed this sentence on the focusing of plume products on the Indian\nplate from a tilted Kerguelen plume. This behavior is predicted only from the\nnumerical models and we have no way of knowing if the Kerguelen plume was\ntilted at 80 Ma during the formation of the Ninety-East Ridge. Magma production,\non the other hand, is focused on the Indian Plate, which is evidenced by the\nformation of the Ninety-East Ridge and relatively little magma production on the\nAustralian or Antarctic plates during from 80 to 43 Ma (Figure 6).\n15. Line 185: I’m not so sure that the ratio between MORB and more enriched plume\ncompositions reflects changes in the capacity of the plume to deliver more deeply\nsourced melt to the surface so much as on whether the plume is diluted by entrained\nupper mantle and/or depleted lower mantle material. The Zindler et al. (1979) reference\npredates a lot of research into this topic that has happened since; this warrants\nclarification/revisiting/updating.\nThe first-order observation that spreading ridge segments on or near hotspots\nexhibit geochemical evidence of mixing of plume and asthenosphere has been\nconfirmed over 50 years (since Schilling and co-workers). And bigger plumes\n(greater buoyancy) that are directly beneath or close to ridges have stronger and\nwider (along ridge) geochemical signatures than weaker or more distant plumes.\nDetails of how plume and asthenosphere mix (e.g. entrainment, depending on\nviscosity difference) and whether the plume delivers multiple components from\nthe lower mantle are interesting but secondary. Our simple assumption is that the\nKerguelen plume has delivered the same composition (that of the Kerguelen\nIsland, ~25 Ma volcanics) through time, that mixes variably with the\nasthenosphere (SEIR composition) depending on the buoyancy flux of the plume.\nThe correlation we see between isotopic compositions and magma flux (plume\nbuoyancy) is consistent with this.\na. Similarly, in the next sentence, stating that plume buoyancy flux plays a first-order\ncontrol on the spread between depleted and enriched endmembers is also at the\nminimum an oversimplification, and really more of an inaccurate generalization.\nWe agree that this is a simplification, but contend that it is an accurate one that\napplies generally to plume-ridge geochemical signatures.\nThe Kerguelen plume has an EM1 mantle source composition. Simplistically,\ngreater buoyancy flux = higher mantle temperatures, greater volumes of melting,\nand greater proportion of plume material in the mixing zone with ambient\nasthenosphere. So, the composition of the volcanic product should then be\ncloser to the plume composition. This ignores complexities such as possible\nentrainment of asthenosphere into plume, and any changes in the plume\nendmember composition with time, or multi-component plume compositions.\nHowever, such simple mixing is evident along spreading ridges e.g., Reykjanes\nRidge [Ito et al. 2003] and Galapagos Spreading Center [Schilling et al. 2003],\nand the extent is correlated with plume buoyancy (as indicated by volume of melt\nproducts). Geodynamic laboratory and modeling studies predict that the width\nover which plumes expand along the spreading ridge axis increases with plume\nflux and buoyancy, and decreases with plate spreading rate, plume viscosity, and\nplume-ridge separation.\n16. Line 190: the first 143Nd/144Nd should presumably be 87Sr/86Sr?\nYes, fixed.\n17. It would really clarify this isotope argument to produce a simple timeline of the\ndifferent isotopic ratios in samples, instead of the x-y isotope plots. It’s very hard to\npiece this together to understand the proposed pattern.\nThe distribution of isotopic compositions in bivariate plots are important to include\nto examine the variations between N-MORB and enriched plume end-members,\nbut we now also include isotopic compositions vs. latitude (a proxy for age) along\nthe Ninety-East Ridge.\na. Also, why include N Atlantic Ridge (is that meant to be Australian?), or Pitcairn if they\nare ancillary to the story? Simpler would be better.\nWe removed Pitcairn and the Australian-Antarctic Ridge fields from the isotopic\ncomposition plots (Figure 7). The fields we plot include the SE Indian Ridge (N-\nMORB), 24-25 Ma Kerguelen Archipelago basalts (Enriched Plume), Amsterdam-\nSt. Paul Islands, and Kerguelen Plateau basalts. These greatly simplify the\ninterpretation of geochemistry results.\n18. The model could use clarification and simplification in how it’s explained. Is the idea\nthat when the plume is anchoring the ridge, we should see more intermediate\nsignatures along the two-component spectrum, but more plume-like signatures when\nthe plume is on its own/ridge-free? (which is pretty much the basis of most plume-ridge\ninteraction models that use geochemistry as the metrics)\nWe say nothing about plume—ridge distance, only variable plume buoyancy flux.\nBetween 80 – 43 Ma, the plume is coupled to the 90E ridge. The changes in\nradiogenic isotope is due to variations in the plume buoyancy flux adding excess\nmaterial (measured by the magma production) which exhibit a more “enriched\nplume” signature.\na. If so, the PCA doesn’t add much to this; seems like you don’t need it here to test your\nhypothesis. PCA kind of muddies the water since the only focus is on PC1, which is just\ntwo-endmember mixing. What is involved in PC2, then, and why is it needed at all? Why\nnot just use average plume and average MOR compositions (as is done in the binary\nisotope plots already)?\nThank you for this suggestion. We have removed the principal component\nanalysis (PCA), revised the bivariate isotope analysis (Figure 7) and created new\nplots of Sr, Nd, Pb ratios as a function of latitude (along the 90E ridge). The PCA\nrequired that any rows with missing data be omitted from the analysis, which\nexcluded a considerable number of samples along the 90E ridge. Dropping this\nin favor of bivariate plots and isotope ratios plotted against latitude increases the\nnumber of samples we can include, which bolsters our comparison between\nmagma flux and radiogenic enrichment.\n19. Again, similar to point 18 as I try to work this out: If I am understanding the proposed\nisotopic mixing model, we should be seeing more ridge-like compositions first along the\n90E ridge’s oldest samples, then a shift to more plume-like/intermediate signatures,\nthen back again to ridge only for the youngest ones…right? This model could be\nconveyed much more clearly if that’s what it is; if not, then it definitely needs more\nexplanation; the reliance on PCA to get the point across isn’t that effective. It would also\nbe much more clearly conveyed in a simple graphic with time along one axis, as stated\nabove, than forcing the reader to decipher it here by color (Figure 7).\nRefer to the response above, and our response to point 21.\na. Also, the model works ok for (a) and (b) in Figure 7 (Sr, Nd, Hf isotopic ratios), but it\nreally doesn’t work well for either 206Pb/204Pb-208Pb/204Pb\nThis is because the isotopic compositions in (a) and (b) are more strongly\ncorrelated and dispersed. The dispersion in 206Pb/204Pb is not great so the\nrange in MORB-plume mixing is not as clear.\n(c) (why don’t the younger samples get more MORB-like than they do, but stay closer to\nthe plume composition?), and why do the older samples in the Sr-Pb system (d) not sit\ncloser to N-MORB compositions?\nThe older samples (higher plume buoyancy) should be closer to the plume\nendmember, which they are. The younger samples get more MORB-like which is\nconsistent with a waning plume prior to de-anchoring.\nThe model should work in all isotopic systems, but it doesn’t from what I can see, which\ncalls it into question and warrants attention.\nb. Similarly, if this is an issue of going from ridge-only to plume/ridge mixing to ridge-\nonly again, why are there so many inflection points in magma flux in Figure 9(b)? What\nhappened to cause those complexities in the magma flux vs latitude (time) curve? Same\nquestion applies for the Walvis/Tristan analysis in the supplemental docs.\nRefer to point 21.\n20. Line 203: What’s “magma flux” referencing here? In the plume or the ridge, and how\ndoes it differ from buoyancy flux? I assume it’s MOR flux?\nRefer to point 21.\n21. Ok so maybe the issue I’m having is that the authors mean buoyancy flux/plume\ncontribution to the ridge whenever it is mentioned, not in fact changing plume flux over\ntime? If so, it took me until nearly the end of the paper to understand that nuance,\ndespite careful reading. Some simple clarification early on to indicate that the study\nfocuses on the RIDGE’s erupted products and the buoyancy flux of magma to the ridge\n(from both the conventional MOR upwelling plus or minus plume contributions) would\nprobably sort out a lot of the potential for confusion. I’m sure it’s mentioned early on, but\nas someone who works on plumes, I definitely assumed that “buoyancy flux” referenced\nthe PLUME’s buoyancy flux, not the flux of material to the MOR throughout this paper.\nMy error if I missed it early on, but many people read papers far more quickly, so finding\na way to make it bomb-proof what you are modeling early on in the paper would be\ngreat (just bear in mind that the use of “buoyancy flux” is most commonly and\nautomatically attributed to the PLUME among plume researchers, not the supply to the\nridge.\nYes, we mean plume buoyancy flux which adds to the normal asthenosphere\nmelting beneath the spreading ridge, resulting in increased magma production\n(e.g. the Ninety-East Ridge). In detail, much of the combined melting will erupt at\nthe ridge, but there will be additional volcanic products adjacent to the ridge (e.g.,\nIceland).\nIn Nature, plume buoyancy flux is difficult to constrain at times older than the\npresent-day. It is this which motivates our analysis of magma production and\ngeochemistry along the Ninety-East Ridge so that we may better understand the\nrelative ‘strength’ of the Kerguelen plume through time. In particular, we explore\nwhether the Kerguelen plume was waning in the leadup to plume-ridge de-\nanchoring at 43 Ma, which we have demonstrated.\nThe geochemistry of the Ninety-East Ridge has been moved to follow the section\non magma production and we have removed the PCA analysis. This greatly\nimproves the flow of arguments and clarifies the important point that the input of\nthe Kerguelen plume adds excess, fusible material beneath the SE Indian ridge,\nwhich is manifested in the production of the Ninety-East Ridge from 80 to 43 Ma.\n22. Line 246: Really can’t follow what’s meant here as written. Could use clarification.\n“Interaction” should be “attraction”. This has been fixed.\n23. Are there any implications of this model for the ocean islands and their compositions\n(and/or morphologies/sizes) being formed by the plume in a near-ridge environment?\nWe have added the following sentence in line 236 “Following de-anchoring, the\nvolcanic products should switch from MORB to OIB systematics as intraplate\nvolcanism is established.”\n24. In general, the manuscript would benefit from a detailed proofread that focuses on\nclarifying sentences, finding a more systematic way to convey information via figures (it\nbounces around between figures quite a bit, which makes it frustrating to read),\ndesigning shorter paragraphs focused on single topics, and use of commas and other\nminor grammatical tools to help clarify sentences (e.g., line 146 needs a comma after\n“anchor” to make it read easily).\nWe have split large paragraphs in the results section into several smaller\nparagraphs that deal with one concept and one figure at a time to improve\nreadability. The manuscript has also been thoroughly checked for punctuation.\nReviewer #2 (Remarks to the Author):\nI have reviewed the manuscript ’Spreading ridge migration enabled by plume-ridge\nde-anchoring’, by B. Mather and coauthors. This manuscript uses numerical models of\nviscous flow to draw conclusions about the dynamics of ridge migrations and the\ncontrols operated by ridge-plume interactions.\nThe topic of the study is one of interest and has the potential to advance tectonic\nreconstructions at the global scale. However, I would see this study more suited for a\nspecialized outlet. In fact, the study revolves around analyses of model behavior upon\nchanges of the input parameters. I fail to see a testable hypothesis that is rooted in\nspecific observations, and that is tested against independent data and uncertainties.\nThe study makes a comparison with SE Indian Ridge reconstructions, but to me this\nseems more a case of resemblance rather than prediction. This is not to say there is no\nmerit in this study. Rather, that it does not make a convincing case for a paradigm shift\nin geological knowledge.\nOur study explores how plume-ridge interaction can influence plate boundary\nmigration through time. We show that the interactions between plumes and\nridges are modulated by plume buoyancy flux which can anchor plate boundaries\nin-place. We relate the findings from numerical models to examples from nature\nby examining the magmatic products of plume-ridge interactions. By analysing\nmagma production and radiogenic isotope variation along the Ninety East Ridge,\nwe reconstructed the changes in plume buoyancy flux of the Kerguelen plume to\nthe SE Indian Ridge. This adds support to our models of plume-ridge interactions\nwhich show that plumes of relatively low buoyancy flux are statistically correlated\nto spreading ridge migration. These predictions also hold for the Walvis Ridge in\nthe South Atlantic (Figure S4). Previous studies (mostly 2D) have examined\nplume-ridge interaction in a closed system, but our study is the first to examine\nself-consistent plumes and their interactions with constantly evolving plate\nboundaries. This has important implications for the evolution of plate boundaries,\nthe distribution of plume-related volcanism, and the reconstruction of ocean\nbasins through deep time.\nBelow are a few points that authors may find useful:\nThat plate tectonics is primary driven by slab pull is a rather partial view: there is a\nsignificant body of work illustrating the relevance of controls on plate tectonics operated\nby pressure-drived mantle convection (for instance, the work of Lenardic, Richars and\ncoauthors). Some of the statements that are key to the dynamics proposed in this study\nare based on other studies (ref. 2 for plume push, ref. 11 for slab pull) that contain\nproposals rather than tested hypotheses. This gives the impression that these are well\nestablished dynamics, which is not the case.\nIt is well accepted in the tectonics and geodynamics communities that slab pull\nand (to a lesser extent) plume push are primary drivers of plate motion. The\nreferences we have cited (ref. 1 for slab pull, ref. 2 for plume push) provide\ncompelling evidence for their respective roles in driving plate motion, which has\nbeen embraced by the scientific community as reflected by the high number of\ncitations. More recently, pressure-derived mantle convection (Lenardic),\nsimilar\nto mantle drag (Coltice), has been proposed as additional driving forces of plate\nmotion, although the magnitude of this force is poorly understood.\nThe mechanism proposed by Lenardic, Richards, and co-authors does not\ncontradict the evidence that slab pull and plume push forces drive plate motion.\nRather, they propose that asthenosphere flow velocities do not always align with\nthe direction and magnitude of plate motion. This line of questioning is tangential\nto the aims and outcomes of our study. We propose that strong plumes act as an\nanchor thereby impeding ridge migration. Whether plate motion is driven by slab\npull or pressure-driven mantle convection is of minor importance.\nA notion invoked at line 105 is that a strong plume can break the lithosphere. This\nstatement should be backed up with either references (the past work of Roger Buck\nmay be something to look at) or tests/calculations. For instance, can the push of a\nplume exceed the strength of oceanic lithosphere?\nIt is not the case that plumes push through oceanic lithosphere in the\ngeodynamic models we use. Rather, plumes are agents of thermal weakening.\nAs explained in lines 163-167: “A stronger buoyancy flux equates to a greater\nupwelling velocity and higher temperature. The former means the plume\npenetrates a shallower depth in the overriding plate and the latter results in lower\nviscosity. Both are weakening agents which maintain the localisation of\ndeformation in the overriding plate which, when reduced, facilitates ridge\nmigration.”\nWhat is the background color in fig. 4?\nThe blue color is a kernel density estimate based on the density of points. We\nhave updated the caption accordingly.\nDo velocities in fig. 6 come with uncertainties?\nUnfortunately, there are no uncertainties associated with this plate model due to\nthe qualitative nature of interrogating palaeomagnetic data to reconstruct plate\nmotions. However, since we reconstruct plate motions only back to 60 Ma, the\nvelocities are relatively well constrained by the seafloor magnetic anomalies\nwhich are preserved in seafloor of the Indian Ocean."}, {"round": 2, "reviewer_comments": {"reviewer_1": "The manuscript is significantly clearer and more impactful in this revised version. It reads smoothly and makes an admittedly somewhat circumstantial but intriguing case for the role of plumes in not only anchoring MORs but also in how de-anchoring from a plume can affect ridge migration rates to a significant extent. Some of the claims are not that well supported, particularly near the end of the manuscript where it gets especially speculative about the role of de-anchoring, plume force balancing, and increases (or not) in MOR migration rates. Still, these are interesting ideas that should be explored, so they seem appropriate to include in the paper. That said, finding just a bit more (even circumstantial) evidence to support some of these claims (such as more locations than just Tristan to support the plate forces balancing contention and its role in MOR migration rates once a ridge has been released from a plume’s anchor) would strengthen the ending of the paper.\nOverall, this manuscript lays out important ideas that connect MOR migration rates, plate tectonic dynamics, and plume-ridge interaction in thoughtful and insightful ways that are likely to be both referenced and used as ideas for future work in the field.\nSome minor comments:\n1. Helpful intro to the Results section. The first paragraph in the Results section reads more like it belongs in the end of the introduction, in some ways, as it sets the trajectory for the work in the paper.\n2. Super minor suggestion: use “that” when there is no comma in front of it, or add a comma in front of “which” when used. Not like this affects the science…\n3. I would be helpful to mention somewhere the range of fluxes of existing mantle plumes (the authors do for Hawaii, but no others), just for context for those unfamiliar with plume flux values.\n4. Figure 7: Why are there two decreases in enrichment level along the plume track? This model predicts enriched to more depleted to more enriched only, not the additional enriched/depleted cycle. It would be great to hear the authors’ perspectives on this additional cycle in the context of their proposed model.\n5. Small (1995) should really be cited (about ridge jumps owing to thermal influence of the plume on a ridge), given that it’s one of the earliest works that invoke this kind of model.\n6. Line 266: opening sentence could use clarification/refinement. Verb/subject agreement isn’t right, and “similar” needs definition (similar to each other, presumably). Also, what does “much” mean in “much more slowly?” And more slowly than when anchored, presumably? This could all use some qualification to make the use of the adjectives more precise. Minor issue that would clarify.\n7. Line 268: Again, “similar” refers to what exactly? Should be defined to be unambiguous. This whole paragraph is pretty speculative and poorly constrained (both as written and conceptually), and could use more precise language as well as referencing to support claims made in it.\n8. No hyphen for “in-place” in line 276.\n9. In general, the last few paragraphs get a bit too speculative and poorly constrained, and could benefit from reworking and stronger grounding in the scientific literature, to at least ground it in some corroborating evidence to support the claims (even if it’s circumstantial, more than is included here would help).", "reviewer_2": "Review Mather et al. 2024, Nature Communications\nIn this paper, the authors combine the results from a numerical model of mantle convection with geochemical data and insights from plate tectonic reconstructions to propose and quantify a new mechanism of plume-ridge interaction from ridge capture to de-anchoring. I really like that the authors used a range of methods and consider real-world implications of their work with a case study. I really enjoyed reading this paper! It’s really cool and overall it was quite clear!\nObviously, I did not see the first version of this manuscript and for some reason I couldn’t find the tracked changes file, but from reading the rebuttal letter, I gather that the authors made quite significant changes to the manuscript. I think that - with a few exceptions - most comments from the previous reviewers have been addressed satisfactorily. The manuscript reads well even though it is quite dense (a lot of information and findings in so few words!). The figures are really clear and beautiful. All in all, I think the paper is in quite a good shape.\nI still have a few comments about the results and implications of the study (see below) that perhaps require some additional paragraphs and additions to figures plus a bunch of minor textual comments for some last clarifications to the text. As such I recommend moderate revisions before this manuscript is ready for publication.\nPS: I received 2 versions of the manuscript: one that included the methods and one that didn’t. As a result, the line numbers are inconsistent in the latter parts of those two versions of the manuscript. So, when I refer to line numbers, I note the section of the paper as well, so you can hopefully find the line I am talking about across the different versions.\nMajor comments\n1. As far as I can discern, there is only 1 model used in this paper: model 2 from Arnould et al. 2020, which is then thoroughly analysed to sus out the details of plume-ridge interactions. Is that correct? Because at multiple instances in the paper, the term ‘numerical models’ is mentioned. For example, the section title in the methods “setup of whole mantle convection models” and line 388 in the caption of figure 1: “the numerical models”. This could lead the reader to believe that there are in fact multiple models, while that is not the case. So, there needs to be a thorough search throughout the manuscript to make sure the text only ever mentions 1 numerical model. As a further example that this can be easily misunderstood, I think this is something reviewer 2 picked up on, who references “analyses of model behaviour upon changes of the input parameters”, but as far as I can see, there are no input changes / parameter studies at all throughout this work. This is fine, but best to be careful with the formulation in the manuscript then.\n2. It would be useful and interesting to show the difference in plume buoyancy flux between ridge capture and ridge release for the 13 plume-ridge interactions in another boxplot in Figure 1 to show that the plume buoyancy flux systematically decreases (and by how much) between ridge capture and ridge release, because that info is not currently not available in the plot, but would really corroborate the narrative of your manuscript, right?\n3. Why do the plume buoyancy fluxes increase / decrease depending on their interaction with the ridge? Is that just the convection pattern? Or is there some other mechanism at play? What controls the plume buoyancy flux? It would be great if you could discuss that briefly.\nIn line with points 2 and 3, I guess what I am hinting at is that I think there is a kind of chicken-and-egg problem here: does the plume buoyancy flux decrease and therefore the ridge is free to de-anchor and move away? Or does the ridge migrate away and does this cause a reduction in plume buoyancy flux? I know you argue for the former explanation in this article and indeed the right panels of Figure 3 seem to support your conclusion, but this was only 1 of the 13 interactions between plumes and ridges and hence - presumably - 1 of 13 examples of ridge de-anchoring. So, is the explanation you propose always what you see in the model? Can you really reject the other hypothesis of the ridge moving away first and that causing a reduction in plume buoyancy flux? It would be great if you could add some discussion on this and show the results of the other (12) examples of ridge capture and ridge de-anchoring in the supplementary material for reference (analogous to Figure 3 perhaps).\n4. Since triple junctions seem to be formed during ridge capture and when the plume and ridge are coupled, I just wonder if this implies that these plume-ridge interactions are one of the main methods of forming a triple junction? Are all current triple junctions on the Earth fed by / on top of a plume for instance? And does this mean that triple junctions are by definition a temporary, transitional feature that only form through ridge capture? Do you see the formation of triple junctions for all of your 13 plume-ridge interactions? How long-lived are they, i.e., do they last for the entire duration of the ridge-plume coupling? These are many questions - I apologise - but they struck me while I was reading your paper, so it would be really cool if you could expand a bit on this / provide some discussion in the manuscript about this.\n5. I agree with reviewer 1 that Figure 8b and c and to an extent d (showing eNd against eHf; 208Pb/204Pb against 206Pb/204Pb; and 204Pb/204Pb against 87Sr/86Sr) are not convincing in showing that younger samples have a more N-MORB composition compared to older samples and hence do not convincingly corroborate the main idea of the paper. It might be very convincing to geochemists, but as a geodynamicist/seismologist, I was a bit underwhelmed. I know the authors wrote an explanation to the question of reviewer 1, explaining why it is expected that these isotope variations do not necessarily show this trend (because of less dispersion in the samples…? what does that mean exactly? and why is that?) but I did not pick up on this while reading the manuscript, so please make this more clear in the main text.\nModerate comments\n1. If I understand correctly, the ridge capture and ridge de-anchoring examples in Figures 2, 3, 5, S1 and across the text are actually from 2 different plume-ridge interactions. That is, 2 of the total of 13 mentioned in the text. It took me a while to figure this out and as a result I was initially quite confused why the left panels of Figure 3 don’t seamlessly transition into the right panels of Figure 3. Could you make this more clear in the manuscript?\n2. In the caption of Figure 1, you mention plume-ridge coupling. Am I to understand that that means “anchoring”? That is, the ridge being on top of the plume? Could you clarify this and/ or provide a definition for plume-ridge coupling?\nMinor comments\n1. Line 74 in the results: I agree with reviewer 1 that the model time of 323 Myr is oddly specific and invokes the idea that there might be some scientific relevance to this number. Perhaps adding the word “arbitrary” in front of “model timespan” would resolve this issue.\n2. Line 81 in the results: Should this be “within 1000 km of a ridge”?\n3. Line 319 in the methods: “by from” —> remove “by”\n4. Line 320 in the methods: “encircle” —> “encircles”\n5. Line 378 in the code availability: “is freely available” —> “are freely available”\n6. Line 379 in the code availability: “ET” —> “ETH”\n7. Line 397 in the caption of Figure 1: “begin” —> “begins”\n8. Caption Figure 2: Define the abbreviation “MOR” (and maybe also “MORB” in the text where you first use it. I know you write “spreading ridge basalts (MORB)”, but I always thought it stood for “mid-oceanic ridge basalts”. Would be good to clarify the origin of this abbreviation in the manuscript.\n9. Caption Figure 3: Could you make clear that there are 2 different y-axes in the left and right panels? Because it is very easy to assume at first glance that there are the same and it makes the comparison a bit difficult. Would it be possible to have the same y-axes for the panels? or maybe have that figure for comparison in the supplementary material?\n10.Line 430-431 in caption of Figure 3: It seems like this sentence should be moved down a bit. Perhaps in the explanation of panel d.\n11.Caption Figure 5: Please make it clear in the caption that the x-axes between the top and bottom panels differ, because one naturally wants to compare the two, but that actually doesn’t really work."}, "author_response": "We thank the editor and the reviewers for providing feedback on our manuscript. We believe this is a significant\nimprovement on our previous version and thank the reviewers for their helpful suggestions. Our responses to the\nreviewers’ comments below are highlighted in blue.\nReviewer #1\nThe manuscript is significantly clearer and more impactful in this revised version. It reads smoothly and makes an\nadmittedly somewhat circumstantial but intriguing case for the role of plumes in not only anchoring MORs but\nalso in how de-anchoring from a plume can affect ridge migration rates to a significant extent. Some of the claims\nare not that well supported, particularly near the end of the manuscript where it gets especially speculative about\nthe role of de-anchoring, plume force balancing, and increases (or not) in MOR migration rates. Still, these are\ninteresting ideas that should be explored, so they seem appropriate to include in the paper. That said, finding just\na bit more (even circumstantial) evidence to support some of these claims (such as more locations than just\nTristan to support the plate forces balancing contention and its role in MOR migration rates once a ridge has\nbeen released from a plume’s anchor) would strengthen the ending of the paper.\nOverall, this manuscript lays out important ideas that connect MOR migration rates, plate tectonic dynamics, and\nplume-ridge interaction in thoughtful and insightful ways that are likely to be both referenced and used as ideas for\nfuture work in the field.\nSome minor comments:\n1. Helpful intro to the Results section. The first paragraph in the Results section reads more like it belongs in the\nend of the introduction, in some ways, as it sets the trajectory for the work in the paper.\nThe first paragraph of the results section introduces the numerical model which frames the beginning of\nthe results section, so we think it is best to keep it where it is. Explaining the numerical model in detail\ndoes not seem relevant to the introduction. In the introduction we explain the motivation for this study\nand frame the ideas we explore later in the paper.\n2. Super minor suggestion: use “that” when there is no comma in front of it, or add a comma in front of “which”\nwhen used. Not like this affects the science…\nFixed.\n3. It would be helpful to mention somewhere the range of fluxes of existing mantle plumes (the authors do for\nHawaii, but no others), just for context for those unfamiliar with plume flux values.\nGood point. We now provide an upper and lower range of plume fluxes. The upper end being Hawaii\n(2,800 – 8,700 kg/s) and the lower end being Galapagos (1,000 – 1,800 kg/s) on lines 123-125.\n4. Figure 7: Why are there two decreases in enrichment level along the plume track? This model predicts\nenriched to more depleted to more enriched only, not the additional enriched/depleted cycle. It would be great to\nhear the authors’ perspectives on this additional cycle in the context of their proposed model.\nPlumes are dynamic and will exhibit varying buoyancy fluxes throughout their evolution. We attribute\nthese local decreases in enrichment along the plume track primarily to a small reduction in plume\nbuoyancy flux. Additional sources of variation may occur due to the entrainment of upper mantle into the\nupwelling plume or variations in plume source composition with time. We have added this in the text\n(222-223).\n5. Small (1995) should really be cited (about ridge jumps owing to thermal influence of the plume on a ridge),\ngiven that it’s one of the earliest works that invoke this kind of model.\nWe have included a reference to Small, 1995.\n6. Line 266: opening sentence could use clarification/refinement. Verb/subject agreement isn’t right, and “similar”\nneeds definition (similar to each other, presumably). Also, what does “much” mean in “much more slowly?” And\nmore slowly than when anchored, presumably? This could all use some qualification to make the use of the\nadjectives more precise. Minor issue that would clarify.\nWe have revised this sentence for clarity. It now reads, “If the balance of forces on each plate pair are\nsimilar to each other, then the spreading ridge would migrate much more slowly following plume-ridge\nde-anchoring than if the plate force balance was highly asymmetric.” (Lines 282-284)\n7. Line 268: Again, “similar” refers to what exactly? Should be defined to be unambiguous. This whole paragraph\nis pretty speculative and poorly constrained (both as written and conceptually), and could use more precise\nlanguage as well as referencing to support claims made in it.\nWe have revised this sentence for clarity. It now reads, “The Atlantic Ocean is not bounded by\nsubduction zones which indicates the balance of plate boundary forces along the Atlantic Ridge is\nrelatively similar to each other28.” (Lines 284-285). We have added a reference to Clennett et al 2023\n(ref 28) on assessing tectonic plate driving forces.\n8. No hyphen for “in-place” in line 276.\nRemoved.\n9. In general, the last few paragraphs get a bit too speculative and poorly constrained, and could benefit from\nreworking and stronger grounding in the scientific literature, to at least ground it in some corroborating evidence\nto support the claims (even if it’s circumstantial, more than is included here would help).\nWe have expanded the discussion around how plume-ridge de-anchoring facilitates ridge migration\ndepending on the force balance on each plate pair. We have added a reference to Clennett et al 2023\n(ref 28) on assessing tectonic plate driving forces. A new example is provided in the Easter plume –\nEast Pacific Rise de-anchoring, now discussed on lines 293-298.\nReviewer #3\nIn this paper, the authors combine the results from a numerical model of mantle convection with geochemical\ndata and insights from plate tectonic reconstructions to propose and quantify a new mechanism of plume-ridge\ninteraction from ridge capture to de-anchoring. I really like that the authors used a range of methods and consider\nreal-world implications of their work with a case study. I really enjoyed reading this paper! It’s really cool and\noverall it was quite clear!\nObviously, I did not see the first version of this manuscript and for some reason I couldn’t find the tracked\nchanges file, but from reading the rebuttal letter, I gather that the authors made quite significant changes to the\nmanuscript. I think that - with a few exceptions - most comments from the previous reviewers have been\naddressed satisfactorily. The manuscript reads well even though it is quite dense (a lot of information and\nfindings in so few words!). The figures are really clear and beautiful. All in all, I think the paper is in quite a good\nshape.\nI still have a few comments about the results and implications of the study (see below) that perhaps require some\nadditional paragraphs and additions to figures plus a bunch of minor textual comments for some last clarifications\nto the text. As such I recommend moderate revisions before this manuscript is ready for publication.\nPS: I received 2 versions of the manuscript: one that included the methods and one that didn’t. As a result, the\nline numbers are inconsistent in the latter parts of those two versions of the manuscript. So, when I refer to line\nnumbers, I note the section of the paper as well, so you can hopefully find the line I am talking about across the\ndifferent versions.\nMajor comments\n1. As far as I can discern, there is only 1 model used in this paper: model 2 from Arnould et al. 2020, which\nis then thoroughly analysed to sus out the details of plume-ridge interactions. Is that correct? Because at\nmultiple instances in the paper, the term ‘numerical models’ is mentioned. For example, the section title\nin the methods “setup of whole mantle convection models” and line 388 in the caption of figure 1: “the\nnumerical models”. This could lead the reader to believe that there are in fact multiple models, while that\nis not the case. So, there needs to be a thorough search throughout the manuscript to make sure the\ntext only ever mentions 1 numerical model. As a further example that this can be easily misunderstood, I\nthink this is something reviewer 2 picked up on, who references “analyses of model behaviour upon\nchanges of the input parameters”, but as far as I can see, there are no input changes / parameter\nstudies at all throughout this work. This is fine, but best to be careful with the formulation in the\nmanuscript then.\nIndeed, we use just one model corresponding to model 2 from Arnould et al. 2020. We interrogate that model\nto extract multiple instances of plume-ridge interaction. The text has now been modified to remove plurals to\navoid confusion.\n2. It would be useful and interesting to show the difference in plume buoyancy flux between ridge capture\nand ridge release for the 13 plume-ridge interactions in another boxplot in Figure 1 to show that the\nplume buoyancy flux systematically decreases (and by how much) between ridge capture and ridge\nrelease, because that info is not currently not available in the plot, but would really corroborate the\nnarrative of your manuscript, right?\nWe agree and have included another boxplot in figure 1 to show this. The caption has been updated to\nreflect the change. Thank you for the recommendation.\n3. Why do the plume buoyancy fluxes increase / decrease depending on their interaction with the ridge?\nIs that just the convection pattern? Or is there some other mechanism at play? What controls the plume\nbuoyancy flux? It would be great if you could discuss that briefly.\nWe measure the plume buoyancy flux over the entire depth range of the plume conduit (line 97-98). The\nbuoyancy flux we refer to in Figure 1 and 4 is the mean buoyancy flux from the core-mantle boundary to the\nsurface. While the buoyancy flux increases in the upper mantle upon ridge capture, because the upwelling\nvelocity increases in response to spreading (Figure 5d), our view is that changes in wholesale plume\nbuoyancy flux affects spreading ridges, not the other way around. We provide an extended discussion on\nthis point in the response to the comment below.\nIn line with points 2 and 3, I guess what I am hinting at is that I think there is a kind of chicken- and-egg problem\nhere: does the plume buoyancy flux decrease and therefore the ridge is free to de-anchor and move away? Or\ndoes the ridge migrate away and does this cause a reduction in plume buoyancy flux? I know you argue for the\nformer explanation in this article and indeed the right panels of Figure 3 seem to support your conclusion, but this\nwas only 1 of the 13 interactions between plumes and ridges and hence - presumably - 1 of 13 examples of ridge\nde-anchoring. So, is the explanation you propose always what you see in the model? Can you really reject the\nother hypothesis of the ridge moving away first and that causing a reduction in plume buoyancy flux? It would be\ngreat if you could add some discussion on this and show the results of the other (12) examples of ridge capture\nand ridge de-anchoring in the supplementary material for reference (analogous to Figure 3 perhaps).\nIndeed, we argue that the plume buoyancy flux decreases which allows the ridge de-anchor and migrate\naway from the plume. We reject the alternate hypothesis because in all of our 13 instances of plume-ridge\ninteraction, the buoyancy flux we refer to is the mean buoyancy flux from the core-mantle boundary to the\nsurface (Figures 1 and 4). This is important because if the ridge were to influence the buoyancy flux of the\nplume, it would need to perturb the buoyancy flux across the entire depth range of the plume conduit in the\nmantle. We acknowledge that the upwelling velocity of a plume undergoing de-anchoring decreases in the\nuppermost mantle, which brings down the plume flux. But this is would not reduce the mean plume flux\nsignificantly unless the buoyancy flux across the rest of the plume conduit was also reduced (an example of\nthis is shown in Figure 5g). Another line of evidence is that plume-ridge de-anchoring tends to occur after the\nplume buoyancy flux has substantially decreased. For instance, in Figure 1 the boxplot for ridge release\nshows a reduction in mean buoyancy flux within 20 Myr window of de-anchoring, and the right pane of Figure\n3 shows that de-anchoring only occurs when the buoyancy flux is already at a minimum. Therefore, we\nconclude it is the wholesale reduction of plume buoyancy flux which allows the ridge to de-anchor, not the\nother way around.\nWe have added additional text to the discussion to make this distinction clearer, “We contend that a\nreduction in plume buoyancy flux facilitates ridge migration and reject the counter argument that the\nmigration of a spreading ridge results in a reduction in plume buoyancy flux because (1) ridge migration\noccurs only after the plume buoyancy flux has substantially decreased, and (2) the plume buoyancy flux is\nreduced from the core-mantle boundary to the surface at the time of de-anchoring. A local decrease in\nbuoyancy flux within the upper mantle would be anticipated following plume-ridge de-anchoring, but this\nwould not significantly reduce the plume buoyancy flux across the entire plume conduit. We observe a\nwholesale reduction in the mean buoyancy flux in the leadup to ridge migration (Figure 1, 5h), which\nsuggests that waning plumes facilitate plume-ridge de-anchoring.” (lines 171-179).\n4. Since triple junctions seem to be formed during ridge capture and when the plume and ridge are\ncoupled, I just wonder if this implies that these plume-ridge interactions are one of the main methods of\nforming a triple junction? Are all current triple junctions on the Earth fed by / on top of a plume for\ninstance? And does this mean that triple junctions are by definition a temporary, transitional feature that\nonly form through ridge capture? Do you see the formation of triple junctions for all of your 13 plume-\nridge interactions? How long-lived are they, i.e., do they last for the entire duration of the ridge-plume\ncoupling? These are many questions - I apologise - but they struck me while I was reading your paper,\nso it would be really cool if you could expand a bit on this / provide some discussion in the manuscript\nabout this.\nWhile we do observe many triple junctions being fed by mantle plumes of high buoyancy flux in the\nnumerical models, we do not venture so far as to say that every triple junction must have been formed by a\nmantle plume, since our numerical models cannot capture the full complexity of plate boundary\nreorganisation that occurs on Earth. In the text we speculate on the association between high plume\nbuoyancy fluxes triple functions as follows, “High plume buoyancy flux may also be a key driver of triple\njunction formation, since a faster upwelling velocity and excess temperature will fragment the overriding plate\ninto smaller plates to accommodate more efficient plate motion.” (Lines 271-273). We thank the reviewer for\ntheir suggestion.\n5. I agree with reviewer 1 that Figure 8b and c and to an extent d (showing eNd against eHf;\n208Pb/204Pb against 206Pb/204Pb; and 204Pb/204Pb against 87Sr/86Sr) are not convincing\nin showing that younger samples have a more N-MORB composition compared to older\nsamples and hence do not convincingly corroborate the main idea of the paper. It might be\nvery convincing to geochemists, but as a geodynamicist/seismologist, I was a bit\nunderwhelmed. I know the authors wrote an explanation to the question of reviewer 1,\nexplaining why it is expected that these isotope variations do not necessarily show this trend\n(because of less dispersion in the samples...? what does that mean exactly? and why is\nthat?) but I did not pick up on this while reading the manuscript, so please make this more clear in\nthe main text.\nThe isotopic enrichment is consistent with the variation in plume buoyancy, although plume melt proportions\nmay not be the exclusive control on isotopic compositions (i.e., entrainment of upper mantle into upwelling\nplume mantle, variations in plume source composition with time). The Sr, Nd isotopes show a strong\ncorrelation, revealing mixing between N-MORB and enriched plume end-members, whereas the Pb isotopes\nexhibit a narrower range in values, so less powerful in tracking changes in plume melt proportions. We have\nshown all isotopic domains to be transparent with the data and complete in our analysis. Geochemists will\nnot be surprised by Figure 8.\nModerate comments\n1. If I understand correctly, the ridge capture and ridge de-anchoring examples in Figures 2, 3, 5, S1 and\nacross the text are actually from 2 different plume-ridge interactions. That is, 2 of the total of 13\nmentioned in the text. It took me a while to figure this out and as a result I was initially quite confused\nwhy the left panels of Figure 3 don’t seamlessly transition into the right panels of Figure 3. Could you\nmake this more clear in the manuscript?\nWe have modified the captions to make clear that we interrogate two different plume-ridge interactions.\n2. In the caption of Figure 1, you mention plume-ridge coupling. Am I to understand that that\nmeans “anchoring”? That is, the ridge being on top of the plume? Could you clarify this and/ or provide a\ndefinition for plume-ridge coupling?\nThe caption has been modified from “coupling” to “anchoring”. Essentially, they are the same, but we make\nthe point in the paper that plumes act as an anchor thereby impeding ridge migration (lines 161-162), thus\nwe adopt the terminology “anchoring” and “de-anchoring”.\nMinor comments\n1. Line 74 in the results: I agree with reviewer 1 that the model time of 323 Myr is oddly specific and\ninvokes the idea that there might be some scientific relevance to this number. Perhaps adding the word\n“arbitrary” in front of “model timespan” would resolve this issue.\nDone\n2. Line 81 in the results: Should this be “within 1000 km of a ridge”?\nFixed.\n3. Line 319 in the methods: “by from” —> remove “by”\nFixed.\n4. Line 320 in the methods: “encircle” —> “encircles”\nFixed.\n5. Line 378 in the code availability: “is freely available” —> “are freely available”\nFixed.\n6. Line 379 in the code availability: “ET” —> “ETH”\nFixed.\n7. Line 397 in the caption of Figure 1: “begin” —> “begins”\nFixed.\n8. Caption Figure 2: Define the abbreviation “MOR” (and maybe also “MORB” in the text where you first\nuse it. I know you write “spreading ridge basalts (MORB)”, but I always thought it stood for “mid-oceanic\nridge basalts”. Would be good to clarify the origin of this abbreviation in the manuscript.\nFixed.\n9. Caption Figure 3: Could you make clear that there are 2 different y-axes in the left and right\npanels? Because it is very easy to assume at first glance that there are the same and it makes the comparison a\nbit difficult. Would it be possible to have the same y-axes for the panels? or maybe have that figure for\ncomparison in the supplementary material?\nWe do not believe the change in scale is unclear. The y-axes have legible numbers that are on different\nscales. Nevertheless, we have added a note in the figure caption that points out to the reader that the y-\naxes have different scales.\n10. Line 430-431 in caption of Figure 3: It seems like this sentence should be moved down a bit. Perhaps in\nthe explanation of panel d.\nFixed.\n11. Caption Figure 5: Please make it clear in the caption that the x-axes between the top and bottom panels\ndiffer, because one naturally wants to compare the two, but that actually doesn’t really work.\nWe have now indicated the x-axes have different scales in the figure caption."}]

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