Plume-ridge interactions: Ridge suction versus plate drag

Pang, Fengping; Liao, Jie; Ballmer, Maxim; Li, Lun

doi:https://doi.org/10.5194/se-2022-20

Preprints

https://doi.org/10.5194/se-2022-20

Preprints

16 Feb 2022

Status: this preprint was under review for the journal SE. A revision for further review has not been submitted.

Plume-ridge interactions: Ridge suction versus plate drag

Fengping Pang¹, Jie Liao^1,2,3, Maxim Ballmer⁴, and Lun Li^1,2,3 Fengping Pang et al.

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¹School of Earth Sciences and Engineering, Sun Yat-Sen University, Guangzhou 510275, China
²Guangdong Provincial Key Lab of Geodynamics and Geohazards, Guangzhou 510275, China
³Southern Marine Science and Engineering Guangdong Laboratory (Zhuhai), Zhuhai 519000, China
⁴Department of Earth Sciences, University College London, London, United Kingdom

Received: 10 Feb 2022 – Discussion started: 16 Feb 2022

Abstract. Mid-ocean ridges and mantle plumes are two attractive windows to allow us to get a glimpse of mantle structure and dynamics. Dynamical interaction between ridge and plume processes have been widely proposed and studied, particularly in terms of ridge suction. However, the effects of plate drag on plumes and plume-ridge interaction remains poorly understood. Quantification of suction versus plate drag between ridges and plumes remains absent. Here we use 2D thermomechanical numerical models to study the plume-ridge interaction, exploring the effects of (i) the spreading rate of ridge, (ii) the plume radius, and (iii) the plume-ridge distance systematically. Our numerical experiments suggest two different geodynamic regimes: (1) plume motion prone to ridge suction is favored by strong buoyant mantle plume and short plume-ridge distance, and (2) plume migration driven by plate drag is promoted by fast-ridge spreading rate. Our results highlight fast-spreading ridges exert strong plate dragging force, rather than suction on plume motion, which sheds new light on the natural observations of plume absence along the fast-spreading ridges, such as the East Pacific Rises.

Fengping Pang et al.

Status: closed (peer review stopped)

RC1:
'Comment on se-2022-20', Anonymous Referee #1, 09 Mar 2022

This paper investigates the controlling factors in deformation regimes caused by mantle plume-ridge interaction. Using 2-d numerical models, the authors studied effect of three parameters on resultant deformation regimes: (a) spreading rate, (b) plume-ridge distance and (c) plume radius. The outcomes of this study indicate that two different responses may result from plume-ridge interaction that are ridge suction and plate drag. The controlling factor has been proposed to be the competition between plate shearing and plume spreading, which depends on plume size, plume-ridge distance and the spreading rate of the mid-ocean ridge.

The subject of the paper is very interesting and is of broad interest. However, I have some concerns about the numerical models and the interpretations of their results on which the outcomes of this paper rely. I believe some corrections are required to improve the quality of the paper. Below I listed my comments and corrections which I hope will be helpful to raise the quality of the paper.

Main comments:

1) The language of the manuscript needs to be fully checked and revised by a professional editing service or a native speaker.

2) In this study, the relation between spreading rate and age of oceanic lithosphere is ignored. Usually, higher spreading rates create younger lithospheres at a constant distance. In this study, the authors assumed that the lithospheric age is constant near the side boundaries (50 Myr). As a result, by imposing some higher velocities near the side boundaries to simulate higher spreading rates, the lithosphere becomes under extension and since the ridge is the weakest point in the system the width of ridge changes (it is clearly seen in e.g., Figs 3e,4e and 5a-b); higher rates lead to wider ridges. Could the authors explain to what extend is this assumption realistic? I think the formation of cracks in the lithosphere is the consequence of this assumption.

3) In the abstract it is written “plume migration driven by plate drag is promoted by fast-ridge spreading rate.“ This is true only if the plume radii are small. For large plumes the rate of spreading is irrelevant (Fig. 6). This should be mentioned here and also in discussion and conclusions.

4) Usually decomposition melting of plume head causes the formation of a plateau above the plume head. Where do plateaus form in the models? I suggest that the authors add information about where plateaus form and how thick the crust is to the manuscript. The temporal evolution of plateaus is also interesting to be investigated.

5) Lines 20-22 : “Our results highlight fast-spreading ridges exert strong plate dragging force, rather than suction on plume motion, which sheds new light on the natural observations of plume absence along the fast-spreading ridges, such as the East Pacific Rises.“ As I indicated above this is true only if plume radii are smaller than 250 km (based on Fig. 6). This conclusion implies that plumes in the Pacific are smaller than those in Atlantic. Are there any observations supporting this? I’m interested in a discussion about this issue in the paper.

6) Looking at distribution of plumes and their sizes in Fig.9, one cannot see any correlation between plume size with plate drag and ridge suction. Can authors comment on that? Besides, in conclusion it is written: “The plume size, that is, the plume buoyancy flux, may play a critical role in controlling the connection between the two units, compared with distance and spreading rate.“ Why does plume size play important role compared to the two other factors? This is not discussed in the main text.

7) Line 413- 415 : “Based on a series of numerical modeling as well as geological and geophysical observations, we predict that mantle plumes in the Pacific Ocean are more likely to be dragged away by the spreading ridge. “ The authors emphasize on the fast spreading rate of Pacific ocean as a main factor for dragging plumes away from the ridges. I think the plume-ridge distance may be a main factor in this case; most of plume tails (shown as blue dots in Fig. 9a) in the Pacific ocean are located away from the ridges.

8) Line 145: Temperature of 2513 K is very high for temperature at 660 km. Considering adiabatic temperature gradient of 0.5 K km-1 and temperature of 1573 K at the base of lithosphere, temperature at the bottom of model should be ~1873 K.

9) Fig. 5: I expect the heat flux and melt are initially maximum in the area above the plume head. Then due to underplating of plume and its flowing towards ridge, the location of maximum heat flux and melt changes in time. That would be worth to show the evolution of heat flux and melt in time (similar to what is shown for surface topography in Fig. 3 and 4). For (5e-f): I suggest to show the results of plate drag model from ridge to some distances away from it , similar to what is shown in (c) and (d). I suspect that in plate drag due to imposing higher extension rate, the whole lithosphere is experiencing cracks and becomes extremely weak. Figure 5 shows the results in the early stage of deformation. Can authors provide a figure showing results at later stages?

10) I suggest to add a Table to the manuscript which describes the models, their description and their results. This helps with organising the peresntation of results in the manuscrip. For instance, in Figs 3-8 one can add the names of models to the figures and their captions.

Other comments:

Lines 13-15: These two sentences deliver the same message. Please remove one of them.

Line 36: What is Amsterdam?

Line 38: One should keep the sequence of figures in the text. Here, the authors first refer to Fig. 1b and later in the text to Fig. 1a. Please change the place of Fig1.b and Fig. 1a to be consistence with the sequence of referring to them in the text.

Line 38: “François et al., 2018“ is not in the references.

Line 44: Please refer here to Fig. 1a (As I proposed above this should be Fig. 1b in the new version of manuscript).

Lines 57-60: These are conclusions of this study and should be moved to the conclusions section.

Lines64-71: Figure Caption needs some modifications. The main message of Figure 1a is to show the location and number of plumes and their responses to plume-ridge interaction. But in the caption of Figure 1a it is written “Residual bathymetry of the ocean basins (Straume et al., 2019)“. The residual bathymetry is the background color which can be referred to at the end of description of Figure 1a (not in the first line). For the description of (c) I suggest: “ Sketches of ridge suction (top panel) and plate drag ( bottom panel) modes.“

Lines 76-77: “Colored boxes refer to the initial rock type, and corresponding newly formed molten rock types are also show in the rock boxes.” It is a bit confusing what are colored boxes and rock boxes. Please modify and clarify this part. It is good to indicate here that spreading rate was simulated by imposing half-spreading rate to the side boundaries as shown by yellow arrows in the figure.

Line 108: Replace “as” by “is” and insert “is” after C and phi.

Lines 136-138: It is not clear what this sentence mean. Please modify this sentence.

Lines 147-148: This is not consistence with cooling half space. The temperature of the oceanic lithosphere tends to change linearly with depth when lithosphere is very old (older than ~80 Myr).

Line 153: “An additional velocity is imposed on both sides of the ridge to represent the half spreading rate. “ Are they internal boundaries? Please explain more about it here; where are they and until which depth they extend.

Line 173: The significant surface uplift above the rising plume cannot be recognized in Figure 3a and b.

Line 181: “The mantle flow vertical velocity profiles“ It is a bit confusing. The profiles shown in Fig. 3f are the horizontal component of mantle velocities along two vertical profiles. Please rephrase this part and also explain the depths which were selected for these profiles. Are they from the surface till ~250 km depth?

Lines 186-187: “The overriding plate moves slower than the ponding plume, and hence actually slows down the spreading plume branches.“ It is not clear what the message of this sentence is. According to model setup, since plume is located on the left side of MOR, the overriding plate motion speeds up the plume flow towards left (since the plume flow and plate motion have the same direction) and slows down the flow in the right plume branch.

Lines 187-188: “Without suction effect from the spreading center, the left plume branch flows out much slower than the right branch.“ Similar to what I mentioned in my previous comment, I expect faster flow towards left.

Lines 190-194: Please add a brief description of reference model here (like Figure caption of Fig. 4). “topography evolutions along the flow path of selected snapshots.“ Does it mean surface topography at different times? Rephrase this sentence: “Solid, dash and dotted lines are the velocity profiles of plume branches 100 km aside the plume stem and plot in (f)“ Please add the scale of velocity vectors to the figures 3,4 and 5.

Line 199-201: This part refers to Fig. 5. One should keep the sequence of figures in the text. One cannot refer to Fig. 5 before explaining Fig. 4.

Line 211 : I suggest to modify this part and use the following sentence “except that in this mode a smaller plume (with radius of 100 km) interacts with a ”

Fig. 5: Black curve in Fig. 5e shows the plume head location. Please add a sentence in this regard to the figure caption.

Fig. 7: It is a very complicated figure. What do the upper panels of Fig. 7a-c stand for? They show the results at different times. Are the results shown in the lower panels of Fig. 7a-c showing the results at similar times as those shown in the upper panels? The scale of Fig. 7a-c is very small and one can hardly distinguish all the curves shown in the Figure. Please make the figure bigger. I suggest to move the legend of Fig. 7a ito the right side of Figure because Fig. 7b-c also shows the results of models with different plume-ridge distances. The colors of curves for different plume-ridge distances are very similar and hard to differentiate them from each other. I suggest to change the colors. What do “plume head stage- positive spreading out” and “plume tail stage- passive flow driven by plate” mean? How are buoyancy fluxes calculated?

Line 285: Tilted plume tail cannot be recognized in Fig. 7d. I suggest to show the plume tail materials with different color than yellow.

Lines 300-312: It is hard to understand this part. Please make it more understandable for readers.

Line 322: “with increasing spreading rate and off-axis distance“

Line 330: How does Fig. 8a indicate that fast-spreading ridge promotes plume dragging. In this figure, from three models with fast spreading rates two are representing ridge suction mode.

Fig. 8: What is the distance of plume-ridge in models shown in Fig. 8b-d? What do the dashed color curves in Fig. 8b stand for? Please explain them in the caption. The scale of figures are small. What does “plume head spreading“ in Figure 8d mean? What is the effect of plume size on shear force and overpressure difference?

Lines 340-347: It is not clear how shear force and pressure difference were calculated. Please re-write this part. Was the shear force calculated for the grids in the upper part of plume head or the whole plume head? The box of 50*50 km^2 in Fig. 8a is shown only for the plume head (and not for ridge center).

Lines 353-354: “However, without plume further supplies, the overpressure difference from the plume head to the spreading center decreases slowly with time (Fig. 355 8d).“ What does it mean?

Lines 360-361: “while all models gradually switch from ridge suction in the plume-head stage to dominant plate drag in the plume-tail stage“ Is it valid for all models or only those representing plate drag regime?

Figure 9: What do “MAR” and “EPR” stand for? Please explain them in the caption. How did the authors obtain the plume buoyancy flux (which indicate plume size) of hotspots shown in Fig. 9?

Citation: https://doi.org/10.5194/se-2022-20-RC1
- AC1: 'Reply on RC1', Fengping Pang, 24 May 2022
  
  Thanks for your comments. Please see the detailed replies in the Supplement pdf.
  
  Citation: https://doi.org/10.5194/se-2022-20-AC1
- AC3: 'latest reply on RC1', Fengping Pang, 27 May 2022
  
  Thanks for your comments. We have made further improvements to the reply letter, based on the AC1. Please see the latest detailed replies in the Supplement pdf.
  
  Citation: https://doi.org/10.5194/se-2022-20-AC3
RC2:
'Comment on se-2022-20', Anonymous Referee #2, 10 Mar 2022
This manuscript by Pang et al. presents results of a series of 2D numerical simulations of plume ridge interaction. The goal of this study is to assess the role of ridge suction versus ridge drag on the flow of spreading plume material toward or away from the ridge axis. Below I post several comments and suggestions that I hope the authors will consider to improve their manuscript.

Please revise the language using a professional editor or native speaker. There are many areas that may cause confusion as they are currently written.

Definitions: one of the major problems with this work at the moment is the lack of a definition of "ridge suction". Plate drag is reasonably well explained as the frictional force imposed upon the sub-lithospheric plume material, but ridge suction seems to be simply anything that causes plume material to travel toward the ridge. Currently, I have to infer this definition since no clear description is given and the quantitative assessment of ridge suction is a fractional number looking at the volume of plume material flowing toward and away from the ridge. If ridge suction is only asseses in this way, then this is inconsistent with the literature and should be retermed as ridgeward flow or something similar. Better, I believe the authors need to reasses their model results with a more consistent definition of ridge suction that can be quantitatively assessed.

In the abstract, the authors claim that plate drag has not been studied very much. However, I think this is perhaps an overly strong statement. There are several studies that incorporate the affect of plate motion (and the consequent drag) on plume spreading including Ribe et al. (1995); Ribe (1996); Ribe and Delattre (1998); Ito et al. (1997), Hall et al., 2003; 2004, etc. Each of these works (and others) incorporates the affects of plate drag on plume spreading in their calculations. I think the authors should be clear about what aspect of their work contributes something these other authors do not.

Model Comments:

In my opinion, for the scope of this work, the model used is overly complicated and in some respects inaccurate for a mid-ocean ridge setting. For example, the authors are examining the flow of mantle material beneath a lithosphere and have included a 1.5 km thick sediment layer across the model, but near ridge (especially fast ridges) there is little to no sediment. In fact, even along the slow-spreading MAR, 1.5 km of sediment does not occur along the ridge axis and, indeed not for a reasonable distance away.

Next, why is melting and heat flux useful for this study? Given the stated goal of the study to assess plume flow, I do not see (and it was not stated) why melting was useful or necessary. It is also unclear how the movement of melt throughout the system does or does not violate conservation of mass since you are working with an incompressible material and claming to add material beneath the crust after removing it from another location. Please justify the use of melting and melt movement/accumulation. Also, clearly state any affect this melt has on your model (viscosity? temperature structure?, density?, etc.)

Why do you need a plastic rheology? Given the scale of the problem you are workign on, is the added focusing of the ridge axis to a smaller number of grid cells necessary? I don't believe that the current models can answer this question given the problem I mention next.

Another issue is the lack of adjustment of the lithosphere for plate spreading rate. In other words, the ridge and lithosphere in the “fast spreading, ridge drag-dominated” cases do not appear to be in equilibrium before the plume is introduced. Looking that the compositional slices and temperature contours of the model in Figure 4, it appears that the sub-axial lithosphere is flattening out and a new, flatter lithosphere is forming without the initial half-space cooling structure (or with one that is in equilibrium with the faster spreading rate). This will alter the mantle flow field, the upslope topography of the ridge, and, potentially the location of the spreading ridge.

Thermal structure.

It is not clear to me how you arrive at a bottom boundary condition of 2513K when the base of the lithosphere has a Tmax = 1573. Since the base of the lithosphere is at ~100 km depth (Figure 1) and there is an imposed 0.5 K/km adiabatic temperature gradient, the max temperature at 660 km depth should be 1573 K + 560km*0.5K/km = 1853K. This is a big discrepancy that might imply a much hotter mantle than is realistic, which would likely have significant impacts on the results of this study.

How is the plume tail maintained? This is not clear or perhaps I missed it.

Results/Interpretation

The images in Figure 4 demonstrate a factor that may explain the affect of plume head size on ridgeward flow – the erosion of the lithosphere by the plume head. As pointed out by Kincaid et al., 1995 in their laboratory experiments, the formation of lithospheric levees can act to block plume flow. This appears to be happening here. Small plume heads eat into the lithosphere a bit, effectively create ridges (or levees) that are the same thickness as the plume material and halt its motion. Then, as the plate moves the plume material has no choice but to flow with the plate. In constrat, large plume heads push the lithosphere out of the way all the way to the ridge. Despite the significant ridgeward flow, I would argue that this has nothing to do with ridge suction, but the lithosphere rheology and plume buoyancy forces.

The claim of “tension cracks” seems to be based on the stresses in the model. These stresses reach maximums of + or – 3x10^-7 Pa (Figure 5), much too small to actually fracture of rock - especially near the surface, which typically has yield strengths many orders of magnitude larger. Is this a typo? If this should be + or – 3x10^7 Pa (i.e., 30 MPa) that seems very large and so I am left to question how tension cracks are justified here. However, I would note that I don't think these are essential for the results of this paper and fall into the over complication of the model for the state purpose of the modeling.

The role of ridge suction vs plate drag. I think the authors have glossed over some of the factors likely to contribute to the plume flow including the slope of the lithosphere and its role in guiding plume material up the slope, the buoyancy flux of the plume stem since this is not described by the plume radius definition here (which seems to describe the size of the plume head).

Much of the interpretation of these results hinge around spreading of the plume head, not the plume after it has established itself beneath the lithosphere. Many plume have been active for 10 Myr or more and the plume head will have greatly diminished or completely spread away by that time. Yet, these plume tails can still interact with ridges since ridges migrate and often approach plumes. How does the long term interaction look - after the plume head has dissappeared?

Related to 4., I don't think the authors should be claiming to assess plume radius, as this commonly is used to refer to the radius of the plume stem. Instead, I think the manuscript would be much clearer if the authors would state that they were varying the plume head radius.

Overall, I think the paper could use a significant overahaul and reassessment of the methodology and interpretation of the results. I hope that the authors will take the above as constructive criticisim and are able to improve their manuscript as plume spreading and its affect on the lithosphere is still a poorly understood topic. Below I add a few more specific comments.

Line 47-48 – I’m not clear as to what this statement has to do with the EPR sucking in plumes so that they do not appear near the ridge.

Line 52 – the use of the work “push” is inappropriate here and should be changed to “drag” or similar

Line 53 – I don’t think this sentence is needed as it is an opinion that does not bear on the rest of the paragraph.

Line 58 - The authors should reconsider how they phrase things – for example, “slow-spreading rate, short distance (small plume-ridge distances??), and large plume radii promote ridge suction,…” is an inaccurate statement – really, I think what the authors are trying to say is that these factors favor plumes being pulled toward ridges by ridge suction

Line 59 – maybe try a more careful wording – it is the fast plate motions associated with fast-spreading ridges that exert strong drag forces on plumes

Figure 1B what do the percents in the insets indicate? Is that percent of the total number of plumes, percent of the total number of interacting plumes, something else?

Figure 2 – this does not look like a half-space cooling model. Is this a plate cooling model or some modified half-space model? The half-space cooling model does not flatten like this.
Citation: https://doi.org/10.5194/se-2022-20-RC2
- AC2: 'Reply on RC2', Fengping Pang, 24 May 2022
  
  Thanks for your comments. Please see the detailed replies in the Supplement pdf.
  
  Citation: https://doi.org/10.5194/se-2022-20-AC2
- AC4: 'latest reply on RC2', Fengping Pang, 27 May 2022
  
  The comment was uploaded in the form of a supplement: https://se.copernicus.org/preprints/se-2022-20/se-2022-20-AC4-supplement.pdf
  
  Citation: https://doi.org/10.5194/se-2022-20-AC4

Status: closed (peer review stopped)

RC1:
'Comment on se-2022-20', Anonymous Referee #1, 09 Mar 2022

This paper investigates the controlling factors in deformation regimes caused by mantle plume-ridge interaction. Using 2-d numerical models, the authors studied effect of three parameters on resultant deformation regimes: (a) spreading rate, (b) plume-ridge distance and (c) plume radius. The outcomes of this study indicate that two different responses may result from plume-ridge interaction that are ridge suction and plate drag. The controlling factor has been proposed to be the competition between plate shearing and plume spreading, which depends on plume size, plume-ridge distance and the spreading rate of the mid-ocean ridge.

The subject of the paper is very interesting and is of broad interest. However, I have some concerns about the numerical models and the interpretations of their results on which the outcomes of this paper rely. I believe some corrections are required to improve the quality of the paper. Below I listed my comments and corrections which I hope will be helpful to raise the quality of the paper.

Main comments:

1) The language of the manuscript needs to be fully checked and revised by a professional editing service or a native speaker.

2) In this study, the relation between spreading rate and age of oceanic lithosphere is ignored. Usually, higher spreading rates create younger lithospheres at a constant distance. In this study, the authors assumed that the lithospheric age is constant near the side boundaries (50 Myr). As a result, by imposing some higher velocities near the side boundaries to simulate higher spreading rates, the lithosphere becomes under extension and since the ridge is the weakest point in the system the width of ridge changes (it is clearly seen in e.g., Figs 3e,4e and 5a-b); higher rates lead to wider ridges. Could the authors explain to what extend is this assumption realistic? I think the formation of cracks in the lithosphere is the consequence of this assumption.

3) In the abstract it is written “plume migration driven by plate drag is promoted by fast-ridge spreading rate.“ This is true only if the plume radii are small. For large plumes the rate of spreading is irrelevant (Fig. 6). This should be mentioned here and also in discussion and conclusions.

4) Usually decomposition melting of plume head causes the formation of a plateau above the plume head. Where do plateaus form in the models? I suggest that the authors add information about where plateaus form and how thick the crust is to the manuscript. The temporal evolution of plateaus is also interesting to be investigated.

5) Lines 20-22 : “Our results highlight fast-spreading ridges exert strong plate dragging force, rather than suction on plume motion, which sheds new light on the natural observations of plume absence along the fast-spreading ridges, such as the East Pacific Rises.“ As I indicated above this is true only if plume radii are smaller than 250 km (based on Fig. 6). This conclusion implies that plumes in the Pacific are smaller than those in Atlantic. Are there any observations supporting this? I’m interested in a discussion about this issue in the paper.

6) Looking at distribution of plumes and their sizes in Fig.9, one cannot see any correlation between plume size with plate drag and ridge suction. Can authors comment on that? Besides, in conclusion it is written: “The plume size, that is, the plume buoyancy flux, may play a critical role in controlling the connection between the two units, compared with distance and spreading rate.“ Why does plume size play important role compared to the two other factors? This is not discussed in the main text.

7) Line 413- 415 : “Based on a series of numerical modeling as well as geological and geophysical observations, we predict that mantle plumes in the Pacific Ocean are more likely to be dragged away by the spreading ridge. “ The authors emphasize on the fast spreading rate of Pacific ocean as a main factor for dragging plumes away from the ridges. I think the plume-ridge distance may be a main factor in this case; most of plume tails (shown as blue dots in Fig. 9a) in the Pacific ocean are located away from the ridges.

8) Line 145: Temperature of 2513 K is very high for temperature at 660 km. Considering adiabatic temperature gradient of 0.5 K km-1 and temperature of 1573 K at the base of lithosphere, temperature at the bottom of model should be ~1873 K.

9) Fig. 5: I expect the heat flux and melt are initially maximum in the area above the plume head. Then due to underplating of plume and its flowing towards ridge, the location of maximum heat flux and melt changes in time. That would be worth to show the evolution of heat flux and melt in time (similar to what is shown for surface topography in Fig. 3 and 4). For (5e-f): I suggest to show the results of plate drag model from ridge to some distances away from it , similar to what is shown in (c) and (d). I suspect that in plate drag due to imposing higher extension rate, the whole lithosphere is experiencing cracks and becomes extremely weak. Figure 5 shows the results in the early stage of deformation. Can authors provide a figure showing results at later stages?

10) I suggest to add a Table to the manuscript which describes the models, their description and their results. This helps with organising the peresntation of results in the manuscrip. For instance, in Figs 3-8 one can add the names of models to the figures and their captions.

Other comments:

Lines 13-15: These two sentences deliver the same message. Please remove one of them.

Line 36: What is Amsterdam?

Line 38: One should keep the sequence of figures in the text. Here, the authors first refer to Fig. 1b and later in the text to Fig. 1a. Please change the place of Fig1.b and Fig. 1a to be consistence with the sequence of referring to them in the text.

Line 38: “François et al., 2018“ is not in the references.

Line 44: Please refer here to Fig. 1a (As I proposed above this should be Fig. 1b in the new version of manuscript).

Lines 57-60: These are conclusions of this study and should be moved to the conclusions section.

Lines64-71: Figure Caption needs some modifications. The main message of Figure 1a is to show the location and number of plumes and their responses to plume-ridge interaction. But in the caption of Figure 1a it is written “Residual bathymetry of the ocean basins (Straume et al., 2019)“. The residual bathymetry is the background color which can be referred to at the end of description of Figure 1a (not in the first line). For the description of (c) I suggest: “ Sketches of ridge suction (top panel) and plate drag ( bottom panel) modes.“

Lines 76-77: “Colored boxes refer to the initial rock type, and corresponding newly formed molten rock types are also show in the rock boxes.” It is a bit confusing what are colored boxes and rock boxes. Please modify and clarify this part. It is good to indicate here that spreading rate was simulated by imposing half-spreading rate to the side boundaries as shown by yellow arrows in the figure.

Line 108: Replace “as” by “is” and insert “is” after C and phi.

Lines 136-138: It is not clear what this sentence mean. Please modify this sentence.

Lines 147-148: This is not consistence with cooling half space. The temperature of the oceanic lithosphere tends to change linearly with depth when lithosphere is very old (older than ~80 Myr).

Line 153: “An additional velocity is imposed on both sides of the ridge to represent the half spreading rate. “ Are they internal boundaries? Please explain more about it here; where are they and until which depth they extend.

Line 173: The significant surface uplift above the rising plume cannot be recognized in Figure 3a and b.

Line 181: “The mantle flow vertical velocity profiles“ It is a bit confusing. The profiles shown in Fig. 3f are the horizontal component of mantle velocities along two vertical profiles. Please rephrase this part and also explain the depths which were selected for these profiles. Are they from the surface till ~250 km depth?

Lines 186-187: “The overriding plate moves slower than the ponding plume, and hence actually slows down the spreading plume branches.“ It is not clear what the message of this sentence is. According to model setup, since plume is located on the left side of MOR, the overriding plate motion speeds up the plume flow towards left (since the plume flow and plate motion have the same direction) and slows down the flow in the right plume branch.

Lines 187-188: “Without suction effect from the spreading center, the left plume branch flows out much slower than the right branch.“ Similar to what I mentioned in my previous comment, I expect faster flow towards left.

Lines 190-194: Please add a brief description of reference model here (like Figure caption of Fig. 4). “topography evolutions along the flow path of selected snapshots.“ Does it mean surface topography at different times? Rephrase this sentence: “Solid, dash and dotted lines are the velocity profiles of plume branches 100 km aside the plume stem and plot in (f)“ Please add the scale of velocity vectors to the figures 3,4 and 5.

Line 199-201: This part refers to Fig. 5. One should keep the sequence of figures in the text. One cannot refer to Fig. 5 before explaining Fig. 4.

Line 211 : I suggest to modify this part and use the following sentence “except that in this mode a smaller plume (with radius of 100 km) interacts with a ”

Fig. 5: Black curve in Fig. 5e shows the plume head location. Please add a sentence in this regard to the figure caption.

Fig. 7: It is a very complicated figure. What do the upper panels of Fig. 7a-c stand for? They show the results at different times. Are the results shown in the lower panels of Fig. 7a-c showing the results at similar times as those shown in the upper panels? The scale of Fig. 7a-c is very small and one can hardly distinguish all the curves shown in the Figure. Please make the figure bigger. I suggest to move the legend of Fig. 7a ito the right side of Figure because Fig. 7b-c also shows the results of models with different plume-ridge distances. The colors of curves for different plume-ridge distances are very similar and hard to differentiate them from each other. I suggest to change the colors. What do “plume head stage- positive spreading out” and “plume tail stage- passive flow driven by plate” mean? How are buoyancy fluxes calculated?

Line 285: Tilted plume tail cannot be recognized in Fig. 7d. I suggest to show the plume tail materials with different color than yellow.

Lines 300-312: It is hard to understand this part. Please make it more understandable for readers.

Line 322: “with increasing spreading rate and off-axis distance“

Line 330: How does Fig. 8a indicate that fast-spreading ridge promotes plume dragging. In this figure, from three models with fast spreading rates two are representing ridge suction mode.

Fig. 8: What is the distance of plume-ridge in models shown in Fig. 8b-d? What do the dashed color curves in Fig. 8b stand for? Please explain them in the caption. The scale of figures are small. What does “plume head spreading“ in Figure 8d mean? What is the effect of plume size on shear force and overpressure difference?

Lines 340-347: It is not clear how shear force and pressure difference were calculated. Please re-write this part. Was the shear force calculated for the grids in the upper part of plume head or the whole plume head? The box of 50*50 km^2 in Fig. 8a is shown only for the plume head (and not for ridge center).

Lines 353-354: “However, without plume further supplies, the overpressure difference from the plume head to the spreading center decreases slowly with time (Fig. 355 8d).“ What does it mean?

Lines 360-361: “while all models gradually switch from ridge suction in the plume-head stage to dominant plate drag in the plume-tail stage“ Is it valid for all models or only those representing plate drag regime?

Figure 9: What do “MAR” and “EPR” stand for? Please explain them in the caption. How did the authors obtain the plume buoyancy flux (which indicate plume size) of hotspots shown in Fig. 9?

Citation: https://doi.org/10.5194/se-2022-20-RC1
- AC1: 'Reply on RC1', Fengping Pang, 24 May 2022
  
  Thanks for your comments. Please see the detailed replies in the Supplement pdf.
  
  Citation: https://doi.org/10.5194/se-2022-20-AC1
- AC3: 'latest reply on RC1', Fengping Pang, 27 May 2022
  
  Thanks for your comments. We have made further improvements to the reply letter, based on the AC1. Please see the latest detailed replies in the Supplement pdf.
  
  Citation: https://doi.org/10.5194/se-2022-20-AC3
RC2:
'Comment on se-2022-20', Anonymous Referee #2, 10 Mar 2022
This manuscript by Pang et al. presents results of a series of 2D numerical simulations of plume ridge interaction. The goal of this study is to assess the role of ridge suction versus ridge drag on the flow of spreading plume material toward or away from the ridge axis. Below I post several comments and suggestions that I hope the authors will consider to improve their manuscript.

Please revise the language using a professional editor or native speaker. There are many areas that may cause confusion as they are currently written.

Definitions: one of the major problems with this work at the moment is the lack of a definition of "ridge suction". Plate drag is reasonably well explained as the frictional force imposed upon the sub-lithospheric plume material, but ridge suction seems to be simply anything that causes plume material to travel toward the ridge. Currently, I have to infer this definition since no clear description is given and the quantitative assessment of ridge suction is a fractional number looking at the volume of plume material flowing toward and away from the ridge. If ridge suction is only asseses in this way, then this is inconsistent with the literature and should be retermed as ridgeward flow or something similar. Better, I believe the authors need to reasses their model results with a more consistent definition of ridge suction that can be quantitatively assessed.

In the abstract, the authors claim that plate drag has not been studied very much. However, I think this is perhaps an overly strong statement. There are several studies that incorporate the affect of plate motion (and the consequent drag) on plume spreading including Ribe et al. (1995); Ribe (1996); Ribe and Delattre (1998); Ito et al. (1997), Hall et al., 2003; 2004, etc. Each of these works (and others) incorporates the affects of plate drag on plume spreading in their calculations. I think the authors should be clear about what aspect of their work contributes something these other authors do not.

Model Comments:

In my opinion, for the scope of this work, the model used is overly complicated and in some respects inaccurate for a mid-ocean ridge setting. For example, the authors are examining the flow of mantle material beneath a lithosphere and have included a 1.5 km thick sediment layer across the model, but near ridge (especially fast ridges) there is little to no sediment. In fact, even along the slow-spreading MAR, 1.5 km of sediment does not occur along the ridge axis and, indeed not for a reasonable distance away.

Next, why is melting and heat flux useful for this study? Given the stated goal of the study to assess plume flow, I do not see (and it was not stated) why melting was useful or necessary. It is also unclear how the movement of melt throughout the system does or does not violate conservation of mass since you are working with an incompressible material and claming to add material beneath the crust after removing it from another location. Please justify the use of melting and melt movement/accumulation. Also, clearly state any affect this melt has on your model (viscosity? temperature structure?, density?, etc.)

Why do you need a plastic rheology? Given the scale of the problem you are workign on, is the added focusing of the ridge axis to a smaller number of grid cells necessary? I don't believe that the current models can answer this question given the problem I mention next.

Another issue is the lack of adjustment of the lithosphere for plate spreading rate. In other words, the ridge and lithosphere in the “fast spreading, ridge drag-dominated” cases do not appear to be in equilibrium before the plume is introduced. Looking that the compositional slices and temperature contours of the model in Figure 4, it appears that the sub-axial lithosphere is flattening out and a new, flatter lithosphere is forming without the initial half-space cooling structure (or with one that is in equilibrium with the faster spreading rate). This will alter the mantle flow field, the upslope topography of the ridge, and, potentially the location of the spreading ridge.

Thermal structure.

It is not clear to me how you arrive at a bottom boundary condition of 2513K when the base of the lithosphere has a Tmax = 1573. Since the base of the lithosphere is at ~100 km depth (Figure 1) and there is an imposed 0.5 K/km adiabatic temperature gradient, the max temperature at 660 km depth should be 1573 K + 560km*0.5K/km = 1853K. This is a big discrepancy that might imply a much hotter mantle than is realistic, which would likely have significant impacts on the results of this study.

How is the plume tail maintained? This is not clear or perhaps I missed it.

Results/Interpretation

The images in Figure 4 demonstrate a factor that may explain the affect of plume head size on ridgeward flow – the erosion of the lithosphere by the plume head. As pointed out by Kincaid et al., 1995 in their laboratory experiments, the formation of lithospheric levees can act to block plume flow. This appears to be happening here. Small plume heads eat into the lithosphere a bit, effectively create ridges (or levees) that are the same thickness as the plume material and halt its motion. Then, as the plate moves the plume material has no choice but to flow with the plate. In constrat, large plume heads push the lithosphere out of the way all the way to the ridge. Despite the significant ridgeward flow, I would argue that this has nothing to do with ridge suction, but the lithosphere rheology and plume buoyancy forces.

The claim of “tension cracks” seems to be based on the stresses in the model. These stresses reach maximums of + or – 3x10^-7 Pa (Figure 5), much too small to actually fracture of rock - especially near the surface, which typically has yield strengths many orders of magnitude larger. Is this a typo? If this should be + or – 3x10^7 Pa (i.e., 30 MPa) that seems very large and so I am left to question how tension cracks are justified here. However, I would note that I don't think these are essential for the results of this paper and fall into the over complication of the model for the state purpose of the modeling.

The role of ridge suction vs plate drag. I think the authors have glossed over some of the factors likely to contribute to the plume flow including the slope of the lithosphere and its role in guiding plume material up the slope, the buoyancy flux of the plume stem since this is not described by the plume radius definition here (which seems to describe the size of the plume head).

Much of the interpretation of these results hinge around spreading of the plume head, not the plume after it has established itself beneath the lithosphere. Many plume have been active for 10 Myr or more and the plume head will have greatly diminished or completely spread away by that time. Yet, these plume tails can still interact with ridges since ridges migrate and often approach plumes. How does the long term interaction look - after the plume head has dissappeared?

Related to 4., I don't think the authors should be claiming to assess plume radius, as this commonly is used to refer to the radius of the plume stem. Instead, I think the manuscript would be much clearer if the authors would state that they were varying the plume head radius.

Overall, I think the paper could use a significant overahaul and reassessment of the methodology and interpretation of the results. I hope that the authors will take the above as constructive criticisim and are able to improve their manuscript as plume spreading and its affect on the lithosphere is still a poorly understood topic. Below I add a few more specific comments.

Line 47-48 – I’m not clear as to what this statement has to do with the EPR sucking in plumes so that they do not appear near the ridge.

Line 52 – the use of the work “push” is inappropriate here and should be changed to “drag” or similar

Line 53 – I don’t think this sentence is needed as it is an opinion that does not bear on the rest of the paragraph.

Line 58 - The authors should reconsider how they phrase things – for example, “slow-spreading rate, short distance (small plume-ridge distances??), and large plume radii promote ridge suction,…” is an inaccurate statement – really, I think what the authors are trying to say is that these factors favor plumes being pulled toward ridges by ridge suction

Line 59 – maybe try a more careful wording – it is the fast plate motions associated with fast-spreading ridges that exert strong drag forces on plumes

Figure 1B what do the percents in the insets indicate? Is that percent of the total number of plumes, percent of the total number of interacting plumes, something else?

Figure 2 – this does not look like a half-space cooling model. Is this a plate cooling model or some modified half-space model? The half-space cooling model does not flatten like this.
Citation: https://doi.org/10.5194/se-2022-20-RC2
- AC2: 'Reply on RC2', Fengping Pang, 24 May 2022
  
  Thanks for your comments. Please see the detailed replies in the Supplement pdf.
  
  Citation: https://doi.org/10.5194/se-2022-20-AC2
- AC4: 'latest reply on RC2', Fengping Pang, 27 May 2022
  
  The comment was uploaded in the form of a supplement: https://se.copernicus.org/preprints/se-2022-20/se-2022-20-AC4-supplement.pdf
  
  Citation: https://doi.org/10.5194/se-2022-20-AC4

Fengping Pang et al.

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Short summary

Plume-ridge interaction is an intriguing geological process in plate tectonics. In this manuscript, we address the respective role of ridge suction vs plate drag in 2D thermomechanical models and compares the results with a compilation of observations on Earth. From a geophysical and geochemical analysis of Earth plumes and in combination with the model results, we propose that the absence of plumes interacting with ridges in the Pacific is largely caused by the presence of plate drag.


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