Review of the paper “Thrusts control the thermal maturity of accreted sediments” by Mannu and co-authors, submitted to Solid Earth.

In this study, the authors use a thermo-mechanical numerical model to investigate the thermal evolution, and in particular the thermal maturity, within forming accretionary prisms. The numerical model represents a mantle-scale subduction model and thus includes a (more) sophisticated thermal and isostasy model compared to higher resolution but dynamically simpler wedge models. Based on the thermal model and parameters specifically adjusted to fit borehole data from the Nankai through, the vitrinite reflection parameter %R_0 is computed based on three different existing models. The main conclusion of their work is that the evolution of %R_0 within accretionary wedges is strongly affected by thrusting, which is also observed in vitrinite reflection data from a borehole from the Nankai Trough.

The general idea of the paper is intriguing and allows to interpret the temporal and spatial evolution of a parameter, here thermal maturity through vitrinite reflectance, that in field measurements remains one-dimensional. This implies that the strength of the work is its applicability to natural systems, which comes a bit short. Below, I comment on several points that in my opinion need improvement for the paper to be accepted. I also attach the pdf of the manuscript with individual comments. The main points circle around the introduction of the numerical model and the comparison to natural data. Furthermore, there are many small errors and lack of clarity throughout the manuscript and writing has to be improved.

Based on the comments below and in the attached pdf, and my general impression, I recommend major revision before reconsidering the paper.

I hope my comments are constructive and helpful

Best wishes, Jonas

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Major comments:

1) Model setup. The paper consists to >90% of modelling results and therefore needs a proper introduction of how the model was set up and how the different routines are implemented. As the present paper is ultra-short, I see no reason why not to extend the model setup section by a proper introduction of the numerical but also the %R_0 model.  For example move the model setup part of the Supp Mat to the main manuscript and show a general tectonic evolution of such a model including isotherms so that a reader that is not that familiar with geodynamic modelling can understand. Also better introduce the %R models and describe their differences. I personally would also have liked to see how %R is calculated to later better understand their differences (what is the temperature dependence etc.). Furthermore, there are some errors and ambiguities in the choices of parameters and the model description in the Supp Mat. First of all, décollement strength ranges from 2° to 22°, while internal wedge strength is unclear. Means, the wedge strength is defined by the faults, which after a strain of 1.5 have a friction angle of 15 or 20 (text and table differ). Furthermore, the tables itself are contradictory. Table 1 says décollement 0.03/0.08, which is nothing close to 22°, and sediment strength with a friction coefficient of 4.64, which is out of range. Table 2 gives friction angles that are not matching those parameters. Also, in the supplementary material, the equation for Mohr-Coulomb friction is wrong. I guess it should be Drucker-Prager (P in equation 9 is mean stress, not lithostatic stress as in the Mohr-Coulomb formulation), in this case missing a cos(phi) multiplied with cohesion. Otherwise one gets wrong geometric fault angles. I was also pretty lost with the sedimentation process. Although nicely introduced in the supplementary material, it remains enigmatic when only reading the manuscript.

2) Comparison to natural systems. The authors argue that the strength of the paper is its application to natural systems, but the paper only mentions one borehole to which it compares well. Since thermal parameters are implemented from that borehole that is not unexpected. Although the borehole data occupies a prominent position in this work, it is not really introduced. In my opinion, the paper would gain a lot of strength if it presented a proper section on comparison to previous work and natural examples on the topic. Also comparison to other numerical models that investigate thermal properties of shallow subduction zone dynamics is missing. For example Sepideh Pajang’s work in Solid Earth, as a counterpart to mantle-scale models (just an example).

3) Discussion. Large parts of the discussion are rephrasing the results and redundant. I think the discussion would benefit from a separation of subsections that focus on different topics, for example: Importance of thrusting on …., comparison to natural examples, comparison to previous work, and even implications for prospection or so, as it is mentioned to be of importance in the introduction.

Minor comments:

Besides the suggestions above, I commented directly into the attached pdf.

Review

General Comments

The article is a very dense, and compact summary of an extensive series of numerical experiments which broady speaking, make realtively realistic simulations of accretionary prism evolution. The models are “full cycle” with a standard, pre-subduction initiation, initial condition, a “natural-forced” subduction initiation (triggered by a pre-placed weak zone between the converging plates) and subsequent “conveyer belt” type subduction-accretion of sediments to the wedge from the oceanic plate. The accretion process is well-described by the mechanical model, which is extensively documented both here and in other publications, and is generally a robust method for tackling this problem. More simply put, the equations chosen conserve mass and momentum across all accretion and subduction related processes. They also have a rheology that produces a reasonable facsimile of the faulting process. This arises entirely “naturally” from the internal conditions of the model.

Development of faults in space and time during the evolution of the accretionary prism is quite critical for core material of the paper – the evolution of the thermal maturity of the wedge sediments. The paper neatly demonstrates a number of phenomena in this context.

Heat transfer through the evolving wedge is also a major component of the paper’s results.

From my point of view, perhaps the most significant and somewhat mysterious result is the overall increase in thermal maturity (given as an average value) for the system according to a) the strength of the décollement horizon on which the wedge forms and/or b) the amount of sedimentation on top of the growing wedge. However, the extensive quantification of material paths in the wedge the paper provides is also very interesting.

A few of the problems with the paper begin here. There is little discussion of the actual process of heat transfer. The paper focuses, perhaps understandably, but perhaps too much, on the mechanical evolution of the wedge and the different styles of thrusting that develop. Ultimately, the problem being tackled is one of an actively deforming wedge with heat being pushed into it from its base, as well as “advected” into it from the “side” (and also thermal blanketing from the top in the cases involving active sedimentation.) Perhaps this is a reasonable, physical analogy for what is happening (to a first order at least). The wedge material is being both heated up and also stirred or mixed with differing amounts of stirring/mixing depending on the wedge properties (effectively the strength of the décollement). When discussion of heat flow comes, it is only of local phenomena around individual faults. Whilst obviously important, this does not really capture the thermal behaviour of the model as a whole. The model actually implements radiogenic heat, shear heating, adiabatic heating, and of course, in general, advection. All of these different components of heat transfer/generation as well as the approximate conditions of the deeper, more stable parts of the system ought to be discussed. Instead, these phenomena are treated as side effects, subsumed to mechanical processes and ignored.

I understand the conclusions of the paper to show that somehow more sediment reaches greater depths in the stronger décollement models, hence leading to higher overall thermal maturity. I am not entirely sure why this doesn’t show up more clearly in the various figures presented (for me at least, this is not the case). I would also be interested in questions such as whether the total heat flux through the model – in other words, the total amount of heat energy pumped into the accretionary wedge as a whole – is greater in a case with higher average thermal maturity?

Nevertheless, another broad conclusion is that the model “can” be used as a predictive/interpretative tool for thermal maturity data (and potentially other things too) from accretionary prisms in general. This is, I think, largely true. One of the only caveats remaining, I am still not entirely sure why it (the model) makes the predictions it does. Being more clear about why/what exactly is happening would be very helpful. Another caveat. I think the authors believe they have already explained this, but I think there is another, less superficial, deeper level of explanation possible.

In terms of structure/text/figures, the article is reasonable. I have noted later that I would like to see 2 or 3 more “cartoon” type figures to help the reader better understand stuff in the text. Currently, it is very difficult to follow in places because concepts/terms are used without adequate definition. The English language usage is sometimes difficult to follow, and seems quite heterogeneous in quality. I have made a number of technical points in this regard too. It requires quite large improvements in places.

I think overall the paper represents a significant amount of work, of fundamentally high quality. However, it is currently difficult to understand in places. With some work and extra thought, it should be possible to change that.

Specific Comments

Whilst I’m satisfied the numerical model is a perfectly reasonable one, there is something I have noticed that needs to be pointed out. The equations used in the model represent all layers as viscous materials. Looking at the movies, which is the only place you would see it, there is quite clearly significant “flexing” of the two plates, in particular the oceanic subducting one. Of course, this cannot be “flexure”, since the material has no elastic strength. The problem this creates is that the décollement angle is being repeatedly modified by wedge growth primarily, but this is something that is coupled with and feeds back into, deformation and redistribution of mass of the overlying sedimentary wedge material. In simple terms, thinking of a critically tapered wedge, a change in basal angle changes the wedge surface angle. This is more complicated when there is a continuously varying basal angle below the wedge, as is assumed in the case of subducting oceanic plates for instance. In a time-dependent, viscous model, transient states will develop which will in turn drive some of the faulting. This isn’t necessarily a problem. However, the usual understanding of such a process is that there is probably some elastic support of wedge material. The viscous model will instead give a relatively fast evolution towards an Airy isostatic condition. There will probably be a difference between the two “basal surface geometries” that either model would predict. The (more) correct solution is likely to be one involving some elastic support. And so on. More generally, the “load” condition on the supporting substrate is a complicated thing, also influenced by the evolving thermal state of the subduction system. This point comes back to my earlier concern about the lack of discussion of the thermal evolution of the model.

Concerning the mechanical modelling, relatively little attention is paid to rates. The displacement rates on individual faults, as opposed to the overall convergence rate might be interesting to consider. That would be for the existing series of models. A further thought would be, what happens if the convergence rate changes? Is the change in thermal maturity broadly a linear function of rate or a non-linear one? This might be a bit much for one paper, as I have little feel for how difficult it is to set-up and run, although it would involve a fundamentally identical starting condition and simply run the convergence faster.

Concerning fault, rates and heat transfer. This is a combination of things, in a submarine wedge, that surely leads to groundwater flow and hydrothermal systems. This is turn would, in real systems modify temperature, heat flow and potentially long term thermal maturity. Again, the discussion of heat transfer in general could be added/extended substantially in this direction too.

The paper oscillates somewhat between generalised models to represent accretionary systems of different physical characteristics, and specific references to site(s) within the Nankai accretionary prism. Sometimes this makes it a bit confusing to know whether the model is actually simulating the Nankai, or whether these are general models simulating non-specific “type” examples of prisms. I would make this a bit clearer in the text in places.

line 159-161: I suspect that it isn't too difficult to get this degree of correspondence between a measured temperature profile and a calculated one, just based on top and bottom boundary conditions, reasonable total lithospheric thickness and reasonable thermal conductivity values, as well as any heat sources. Relatively small differences in temperature at these depths are actually already generally quite significant when considering a lithospheric geotherm.

Technical Corrections

line 23: support that – replace with “show that”.

line 26: must take account of the length and frequency

line 29: factual – replace with “measured”

line 67: propose subdividing these …

line 72-75: incomprehensible

paragraph lines 72-82: this paragraph introduces fundamental, existing concepts in understanding thermal and mechanical evolution of wedges. The verbal description is hard to impossible to follow. It seems to me a cartoon figure could help the reader enormously however.

line 99: not clear what this means, Do you mean that the geotherm is "fixed" and the model migrates through it? (Clearly not, because of the equations used). Then is it "better" because you have better surface and basal boundary conditions, or better thermal conductivity parameters or better ways of tracking their evolution or a combination of all 3 of these?

line 107-108: (English) – replace with “It is generally rare to have data on both thermal maturity and thermal conductivity from the same borehole. To our knowledge, the C0002 borehole in the Nankai accrretionary wedge in the Kumano forearc basin is the only place where this can be found in an accretionary wedge.”

line 111: this is quite a jump for anyone trying to follow what's going on. The "maarker" concept is due to an Eulerian formulation (fixed grid with stuff moving "through" it). Your model state is tracked by "markers" that you track as they migrate through the grid. You really need to explain this in the main text, and not just the supplement.

line 115: repetition of the sentence here.

line 119-120: “using data from the International Argo Program” (unless you mean the data was actually requested by you and then given to you, in which case, say "using data made available to us by the…)

lines 121-126: repeated/garbled sentences

line 144: This is a bit of an abrupt way to start the section. It sort of follows from the preceding one, but it would be nice to make it a bit smoother. For instance, In our models, subduction initiates at ....

Beyond that, the age of 0.1MYr - is it always at this moment and is that in any way significant?

line 156: In the preceding description of thrust sheet length, it isn't really obvious how this is measured. I assume it must be from a footwall cut off forwards, to the hanging wall cut off of the same unit? But I could be wrong. You must mean some particular geometric parameter here and it needs a bit more clearly defining. Also, the table alone is a bit of a stretch for readers. Figure 1 is not really clear enough to see what you are looking at when it concerns individual "faults" and "thrust sheets". Some sort of figure to show both how these lengths are defined/determined and where faults are present in the models (higher resolution needed) would be really helpful.

line 156: thrush – replace with “thrust”.

line 158: analogue

line 167: you need to show exactly what you mean by this. Where is your trench? Which way is "landward" in this case? Where is you forearc high? You haven't actually defined them anywhere else. These are key results overall in this paper. Some sort of cartoon figure to summarise them (thermal maturity trends only) would maybe help readers.

line 172: how do you define this horizon? Especially in an already deformed model? When you say "horizon" it has geological connotations, like a formation boundary or similar. But in the context you are using it here, it must be some sort of relatively flat (another problem, everything is curved with the plate) line that cuts through whatever it encounters. Again, a cartoon figure showing what is meant would be helpful, probably as an inset in fig. 2. The results themselves in fig 2 are very convincing! It would just be nice to get them in clear context.

line 173: attains the – replace with “reaches a”.

line 200: none of the top half m...etc. incomprehensible

line 218: As our models….

line 229-230: It isn’t clear what the advantages are that you mean!

line 230-233: doesn’t make sense. Is the resolution of your model too low or the others, or all of them?

line 234: “we are confident of the thermal maturity patterns of our models” – then I am very happy for you…but this also shouldn’t be written in this way in a paper…

line 238: how can your models “correlate” with a P-wave velocity!? They can surely only correlate with some parameters derived from P-wave velocities?

line 241: evolve over long time intervals

line 243: see specific comment. Are you sure of what you are saying about the model? Even if you are, the observation needs much more discussion/explanation than one line in the text and only being visible in the movies and there, without comment or annotation.

line 246-248: bad English.

line 249: the question is here, from what point on, and at what depth? Total depth is different for the different models. So is the width of the accretionary wedge. Fig 1 shows a large spread of results. Also quite evenly layered thermal maturity for low basal friction cases.

line 255-259: these are very “broad brush” statements dropped rather out of nowhere and just left there. They need far more serious discussion.

line 262: such as for.. (also this citation needs more context directly in the text).

line 293: contradictory

line 297: what do you mean by “crossover paths”?

line 300: what do you mean by “laminar paths”? In fluid mechanics we have laminar and turbulent flow. Is it something like that? Please define.

line 309: Many fossil “accretionary prism” deposits exist. They still show large areas of quite consistent bedding in many cases, suggesting relatively large chunks of these systems remain coherent, not chaotic. At least that was my impression. Perhaps these obserations are at a smaller scale than those implied in the models. In any case, fossil natural examples would be a useful citation in this context. What do they show in general? Are outcrops of them at a scale similar to what you model can show?

Fig 2: add cartoon inset figure (see specific comments)

Fig 3: this is not easy to read or understand. It probably needs better explanation. Moreover, this figure is key for the whole concept of “peridocity” in the paper’s results. Again, a cartoon explaining what/how periodicity is/arises would be helpful.

Fig 4: What is the colorbar scale on the right (Yn)?

Supplement

Fig S5: what are the length scales on this figure? What are the “Boreholes” and how can one wedge represent “Positions” from all the different models simultaneously?

Fig S7 – what is Yn?