Seismic and gravity constraints on plate flexure and mantle rheology along the whole Hawaiian-Emperor seamount chain

Domain: earth_science
Published: 2025-12-02
Editorial outcome: minor_revision

Abstract
The Hawaiian-Emperor seamount chain is a hotspot-generated intraplate volcanic chain that has yielded key constraints on the rigidity of Earth’s tectonic plates. However, previous studies have shown significant variability in the effective elastic thickness, T , a proxy for the long-term strength of the lithosphere, along the chain. While low T (10-20 km) at the Emperor Seamounts and high T (17-37 km) at the Hawaiian Ridge are expected because of their differences in volcano and plate age, the change between them appears abrupt and occurs in the vicinity of the bend in the chain. To investigate this variability, we estimated T along 3000 profiles - spaced 2 km apart along the chain - from gravity and flexure modeling, calibrated using constraints from deep seismic experiments carried out in 2018 and 2019. Here we show that, contrary to previous predictions, T changes gradually along the chain and that weak zones can exist within the interior of a large, otherwise rigid, plate and may, we speculate, facilitate the initiation of intra-oceanic subduction in response, for example, to changes in plate motion and eventually lead to their break-up.

Introduction
The Hawaiian-Emperor seamount chain (HESC) is a pre-eminent example of an intraplate hotspot-generated volcanic chain that has provided key constraints on the finite rotations of Earth’s tectonic plates as well as their long-term flexural rigidity. The pioneering studies of Vening Meinesz1 and Gunn2, for example, showed using gravity anomalies that the southeast end of the chain was regionally rather than locally isostatically compensated. Subsequent studies3,4 demonstrated the gravity anomalies could be explained by simple models in which the volcanoes that comprise the chain loaded a thin elastic or viscoelastic plate (i.e., a plate with a thickness that is small compared to the radius of curvature of flexure) with uniform thickness. Watts5 found differences along the chain with small values (10-20 km) of the effective elastic thickness, T, a proxy for the long-term strength of the lithosphere, at the Emperor Seamounts and large values (17–37 km) at the Hawaiian Ridge. Since the chain is underlain mostly by Cretaceous Normal Polarity oceanic crust and the Emperor Seamounts are significantly older than the Hawaiian Ridge, Watts5 proposed that T was a function of the age of the Pacific plate at the time of loading.

While subsequent forward modeling studies6–11 have generally confirmed these results, they reveal an abrupt change in T at the HESC bend (~48 Ma12), which is not expected from the volcano load (0-80 Ma12) and plate (83-121 Ma13) ages (Supplementary Fig. S1). Spectral studies based on the moving window admittance14 and wavelet15 techniques reveal more gradual changes at the bend. But the windows used by Kalnins and Watts14 are hundreds of km in width and so tend to smear out spatial variations in T. Wavelet techniques are spatially localized, but the T values resolved by Lu et al.15 are relatively high (~35 km) at the Emperor Seamounts and relatively low (~25 km) at the western Hawaiian Ridge, which are difficult to reconcile with previous results, including those of Kalnins and Watts14. Irrespective, previous forward modeling estimates of T beneath the HESC are consistently lower than those determined by previous workers for the same age of plate presently being subducted at the Circum-Pacific Trench-Outer Rise (CPTOR) (Supplementary Fig. S1).

Comparisons of observed and calculated T based on Yield Strength Envelope (YSE) profiles (referred to here as the ‘yield T’) show that the brittle law of Byerlee16 and the ductile flow laws of Goetze17,18, as well as other Low Temperature Plasticity (LTP) laws19,20 describe well the observed T deduced by Hunter and Watts21 in their inversion A1 at the CPTOR. These same laboratory-based laws, however, appear too strong at both the Emperor Seamounts22 and the Hawaiian Ridge23. There has therefore been a debate24 as to why the strength of the Pacific oceanic plate might differ between its interior and its boundary, and the role played by factors such as the timescales of loading, spatial differences in brittle and flow law parameters, or thermal rejuvenation and melt-assisted flexure.

The best observational constraint on flexure driven by volcanic loads is seismic data, which, unlike gravity or geoid data, have the potential to image the surfaces of flexure directly. Unfortunately, seismic constraints along the HESC are limited to a few single reflection and refraction transects. The earliest experiments25,26 used shots at sea and stations on land and revealed relatively thick oceanic crust (~15– ≥21 km) beneath Maui and Hawaii and relatively thin crust (~6–7.5 km) in flanking regions but no details of the transition between them. The first multichannel seismic experiment specifically designed to test flexure was carried out on board R/V Robert D. Conrad and R/V Kana Keoki in 1982 along 3 transects of the Hawaiian Ridge in the vicinity of Oahu27. The reflection data, which have recently been reprocessed28, continuously imaged the top of oceanic crust and Moho in the vicinity of Oahu. The refraction data resolved the velocity structure at 9 Expanding Spread Profile mid-points, which was used together with the free-air gravity anomaly to constrain the T and the flexure.

In 2018 and 2019 a multichannel seismic experiment was carried out along four 550-km-long transects of the HESC at Jimmu/Suiko guyot, Oahu/Kauai and Maui/Hawaii using a 15-km-long streamer and a 40-element airgun array on board R/V Marcus G. Langseth (thick red lines, Fig. 1). The refraction data29–32, which was acquired using 35 Ocean Bottom Seismometers, revealed the internal P-wave velocity structure of these seamounts and ocean islands, including the geometry of their high P-wave velocity (>6.5–7.0 km s−1) and dense cores (>2710–2972 kg m−3), the top of the pre-flexed oceanic crust in the flanking moats, and on Emperor Seamounts Line 1 and Hawaiian Ridge Lines 1 and 2 (Fig. 1) the bottom of the oceanic crust, or Moho, beneath the volcanic edifice. The reflection data33 has revealed spatial variations in regional crustal structure and thickness variations, Moho reflective characteristics, and the locations of buried oceanic fracture zones that intersect the HESC.

In this work, we use seismic constraints on the crust and mantle structure together with 2D and 3D forward gravity and flexure modeling to evaluate T on 3000 profiles spaced 2 km apart along a ‘trail’ that connects the summits along the HESC. We show here the results of the modeling and examine their implications for crustal structure, plate flexure, and the long-term rheology of the Pacific oceanic lithosphere.

Results
The main results of our modeling are 3000 estimates of T and a range of estimates for the densities of the root and moat infill. The degree to which the model predictions fit the observed free-air gravity anomaly data is shown in Supplementary Movies 1 and 2 and along 6 selected profiles of the HESC (Fig. 1, inset) in Fig. 2 for Model D and in Supplementary Fig. S2 for Model C. The Root Mean Square (RMS) difference between observed and calculated gravity anomaly has a well-defined minima (e.g., Supplementary Fig. S3) and ranges from 9.2–13.6 mGal and 7.8–13.0 mGal for Models D and C, respectively, which we consider excellent in the presence of observed free-air gravity anomalies that are in the range −100 to +300 mGal.

While the RMS differences for Models C and D are similar, they yield different densities for the load and root and moat infill. Model C is associated with peak load densities in the range 2764–2840 kg m−3 (Supplementary Fig. S4), consistent with previous estimates along the HESC. But, the root and moat infill densities for Model C are high and in the range 2450–3200 kg m−3. Model D, in contrast, is associated with moat infill densities in the range 2500–2725 kg m−3 (Fig. 2), which are generally consistent with previous studies along the HESC. But, the root infill densities in Model D appear low, at least for Jimmu, Ojin, Kure, and French Frigate Shoals. We explain these results as indicating that both models requires some increase in mass compared to ‘normal’ values: Model C achieves it through increasing the density of the infill, while Model D achieves it through a boost to the ‘driving’ load (i.e., the surface bathymetric load above the regional bathymetry), γ. Densities for the load and infill along the entire HESC are summarized in Supplementary Fig. S4.

Significantly, Models C and D yield similar results for T along the HESC (Supplementary Fig. S5b and Fig. 3a), the mean and RMS difference between them being 1.7 and 4.6 km, respectively. Both models reveal small T values at the Emperor Seamounts, relatively high values at the Hawaiian Ridge, and a T that varies gradually, not abruptly, on either side of the HEB. The increase towards the young end of the Hawaiian Ridge appear to occur independently of the age of the plate at the time of loading, which is constant at ~90 Ma, although seafloor ages are not well known in Cretaceous Normal polarity oceanic crust. Similar results were found by Watts et al.34 from a reciprocal admittance and Kalnins and Watts14 from a moving window admittance. In addition, the T values are compatible with previous forward modeling results at the central Emperor Seamount chain29 and the central Hawaiian Ridge35.

The comparison of our results with seismic data requires that we first use the T structure derived from the models to calculate the top and bottom (i.e., Moho) of the flexed oceanic crust. To do this, we subdivided the bathymetry along the HESC into 27 contiguous loads (Supplementary Fig. S6b) and computed the flexure associated with each load using the best-fit T derived from gravity modeling. Figure 3b (black lines) shows the ‘upstream’ flexure (i.e., the flexure in a direction opposite to that of load migration) associated with each load and the progressive flexure (thick red dotted line) obtained by summing the ‘upstream’ and the ‘downstream’ flexure (i.e., the flexure in the direction of load migration) based on the best fit T for Model D.

We justify our choice of Model D with a ‘load boost’ for the Emperor Seamounts because they are mainly guyots (Fig. 3c), so have lost a substantial amount of their summit region as the once ocean island was being reduced to sea level. The Hawaiian Ridge, in contrast, comprises more atolls and islands (Fig. 3c) than the Emperor Seamounts, and so we suspect less summit removal and hence less of a ‘load boost’ along this part of the HESC. There are guyots on the Hawaiian Ridge, and there is evidence of large-scale land sliding, which might justify some ‘load boost’. However, Supplementary Fig. S5b reveals little difference between the T along the Hawaiian Ridge derived from Model D with a ‘load boost’, γ, of 1.35 (or γ = 1.15) and Model C with γ = 1.00.

Figure 3c shows the ‘driving’ load (light blue shaded region), the calculated root infill (intermediate blue shaded region), and the calculated flexed oceanic crust (dark blue shaded region), obtained by summing the individual seamount and ocean island loads to the progressive flexure. We assumed in the calculation a uniform thickness for the flexed crust of 5.3 km and 6.0 km at the Emperor Seamounts and Hawaiian Ridge, respectively, based on seismic refraction data30–32. The figure shows that oceanic crust generally shallows along the Emperor Seamounts across the HEB towards Colahan and Hancock seamounts and then deepens along the Hawaiian Ridge towards Hawaii. Moho depths vary between ~12 and 18 km, with the shallowest depth to Moho between Colahan and Hancock and the deepest depth, not beneath Hawaii in the Hawaiian Ridge, as might be expected, but beneath Koko in the Emperor Seamounts. We attribute this to the relatively large size of the Koko Seamount and its emplacement on relatively young oceanic lithosphere that is mechanically weaker on long timescales than the older lithosphere that underlies Hawaii.

Figure 4 compares the P-wave velocity models of Xu et al.30, MacGregor et al.31 and Dunn et al.32 to an overlay of the multichannel seismic reflection data of Boston et al.33 along each 500- to 550-km-long ‘dip’ transects of the HESC (Fig. 1). There is a good general agreement between the observed seismic structure and the calculated top and bottom of the oceanic crust derived from progressive flexure and gravity modeling at Emperor Seamounts Line 1 and Hawaiian Ridge Line 2 (Thick dashed white lines, Fig. 4a, b). The agreement is not as close for Hawaiian Ridge Line 1 (Fig. 4c) despite our taking into account here of the contribution of both the flexure of the Cretaceous seamounts to the southwest of Hawaii, which formed at or near a mid-ocean ridge, and the difference in thickness of the oceanic crust, which is thinner north of Hawaii than it is to the south31. We consider the fit acceptable, however, given that the line transects the young end of the HESC and it is possible that isostatic equilibrium here is still not complete. For example, Hawaiian Ridge Line 1 intersects the ‘donut’ of earthquakes centered on Hawaii36, which indicates active deformation and an ongoing, dynamic response to volcanic loading rather than a static one, as we have assumed in the flexure modeling.

Irrespective, we believe the agreements in Fig. 4 to be close enough that we can, with some confidence, use the flexure due to the 27 contiguous loads, together with their T structure, to estimate the volume flux of the material that comprises the ‘driving’ load and the root and moat infill loads. Supplementary Fig. S7 shows, for example, that the Model D T structure overlaps previous T results based mainly on forward modeling in the Pacific Ocean, outside of the French Polynesia region, and Supplementary Fig. S8 shows that the volume flux estimates based on this T structure, the average density of the load and infill, and the age of the seamounts and ocean islands, generally agrees well with the previous estimates of Wessel37. The highest volume flux estimates are at Hawaii (~0.4 Ma) and the lowest values at Colahan and Hancock (~34–38 Ma), the main difference being the absence in our results of the peak identified by Wessel37 at ~12–14 Ma.

We have so far only considered surface loads in our modeling. There is evidence that oceanic crust underlying seamounts and ocean islands may also have been subject to subsurface (i.e., buried) loads such as those associated with magmatic underplating27 and intrusion38. The seismic data in Fig. 4 show, however, little evidence of magmatic underplating. Rather, the mantle that underlies flexed oceanic crust is remarkably homogeneous with regard to its P-wave velocity structure, suggesting little or no effect of large-scale underplating on either the gravity anomaly or flexure. In contrast, the seismic data reveal high velocity, dense, intrusive bodies within the core of the edifice that may act to boost the surface load. We address this here by using a 3D bathymetry-dependent load, for example, as used by Watts et al.22, based on the seismic P-wave velocity structure, where the density of the load can vary laterally between a seamount flank and its dense core, rather than assume a constant density load.

Methods
Modeling was carried out using the Fast Fourier Transform (FFT) for the flexure and a combined analytical and FFT method for the gravity anomaly. The first step was to isolate the volcanic loads that drive the flexure. This was achieved by selecting a 1200 × 1200 km window centered on the chain and applying an Optimal Robust Separator (ORS)37 filter to a SRTM15+V2.4 bathymetry grid65 and the V29.1 satellite-derived free-air gravity anomaly grid66. We found that a filter width of 346 km for the Emperor Seamounts and 450 km for the Hawaiian Ridge most satisfactorily isolated the regional bathymetry and gravity while at the same time maximized the amplitude of the load and the gravity anomaly associated with flexure. The correlation between the regional bathymetry and gravity anomaly at the young end of the HESC (Supplementary Fig. S6) is close such that the gravity to bathymetry ratio is ~21–27 mGal/km, similar to that derived by Watts67 and used by McKenzie68, suggesting that ORS filtering has removed much of the effect of the Hawaiian swell and its compensation. The difference in filter widths between the two chain segments was attributed by Watts et al.22 to the shorter wavelengths of flexural isostasy associated with the Emperor Seamounts than the Hawaiian Ridge.

Once isolated, the loads were used to calculate the flexure and gravity anomaly. Since sample ages69 and oceanic crustal ages based on magnetic anomaly identifications70 suggest the age of the lithosphere at the time of volcanic loading varies from ~32 Ma at Detroit Seamount to ~78 Ma at the Hawaiian-Emperor Bend (HEB) to ~90 Ma at Hawaii, it is likely that T varies spatially along the HESC. The Fast Fourier Transform (FFT) method of computing gravity71 and flexure52 usually assumes uniform T and so is strictly not applicable to such situations. We circumvent this limitation by computing 2D solutions based on the FFT for the top and bottom of the flexed oceanic crust for a wide range of elastic thickness, T values (from 0 [i.e., Airy isostasy] to 50 km in steps of 1 km) and determining the best-fitting T on 3000 closely spaced (2 km) profiles (Fig. 1, inset) using only data within a 1200 × 1200 km window centered on the chain (as was carried in the ORS analysis). This approach enabled T to be a free parameter that could be determined as a function of position along the chain.

The gravity anomaly, as previous studies have shown, is sensitive to the flexure as well as to the bathymetry and the densities assumed for the load, the root infill (defined here as the material that infills the flexure immediately beneath the volcanic load), and the flanking moat infill. We construct here a 3D bathymetry-dependent model in which the load density varies in depth within the volcanic edifice, similar to the model used by Wessel et al.72 at Jasper Seamount and Watts et al.73 at Jimmu Guyot. In both these examples, the density structure was constrained by the seismic P-wave velocity derived from active source seismic experiments30,74 using empirical relationships between P-wave velocity and density as summarized in Brocher75. The lowest density on the load flank and the highest density in the load core were specified on the basis of the P-wave velocity structure to be 2100 and 3020 kg m−3 respectively.

A number of these amounts along the HESC are guyots and so have been subject to significant amounts of mass wasting, including the loss of their summit through wave action. We use a ‘load boost’ to allow consideration of the mass missing (Supplementary Fig. S11) in the present-day bathymetry that may have contributed to the gravity anomaly and flexure at the time of volcanic loading. We present two models here: one in which the load density varies spatially with the bathymetry and there is a ‘load boost’, γ, of 1.35 (i.e., Model D73) and one in which the load density varies spatially and γ = 1.00 and so there is no ‘load boost’ (i.e., Model C73).

The remaining densities concern the material that infills the flexure in the flexural depressions flanking the seamounts and ocean islands (the moat infill) and the material that infills the flexure immediately beneath the load (the root infill). Since these densities may like T also vary along the HESC and are again not well determined by the limited seismic data we therefore also searched for them along each of the profiles.

The gravity anomaly calculation is the sum of contributions from the bathymetry, the load, infill and the flexed oceanic crust73. Of these contributions the load calculation was the most computer intensive since it involved calculating the 3D gravity effect of a series of stacked rectangular prisms76,77 (solid light blue line in Supplementary Fig. 12a). We performed this calculation using GMT’s gravprisms78 assuming that each stack of prisms extended down from the seafloor to a reference depth corresponding to the base of the bathymetric load of 6 km and 5 km for the Emperor Seamounts and Hawaiian Ridge respectively. We note that the gravity effect of the load only needed to be computed once for the referenced density variation, since we can simply multiply the resulting gravity anomaly by the Parker71 algorithm for other profiles, as the FFT of the gravity anomaly is a linear function of the density contrasts.

The final step is to compute the gravitational effect of the infill and the flexed oceanic crust. We will use 2D FFT-based solutions71 as implemented in GMT’s gravfft module. We used 2D because the surfaces of flexure are deep, and we found that the differences in the gravity anomaly between the 3000 profiles to be small. Here, in order to accurately include the flexural depression and the bulge, we create 7 different surfaces at different distances below the seafloor, each of which has a constant density contrast across it (Supplementary Fig. S12). Since we aim to be as exact as possible and because the FFT method is most stable when the density contrast is constant, we treat the different density contrasts related to the flexural compensation as separate interfaces.

Peer review rounds
[{"round": 1, "reviewer_comments": {"reviewer_1": "Review of “New seismic and gravity constraints on plate flexure and mantle rheology along the whole Hawaiian-Emperor seamount chain”.\nIn this manuscript, the authors investigated the elastic thickness of the Pacific Plate along the Hawaiian-Emperor seamount chain, using seismic and gravity observations as constraints. They evaluated the elastic thickness along 3000 profiles with a spatial interval of 2 km, and found that the elastic thickness along the seamount chain is generally consistent with those inferred for the weak zones at the seaward wall of circum-Pacific trenches, lower than those inferred for the interior of the Pacific Plate and the strong zones of the circum-Pacific trench outer rise. This finding is of interest to the broad audience of the Earth Science, as it helps constrain the plate rheology. It also provides a reliable estimation on the volume flux of the Hawaiian plume since the Cretaceous, which should provide some insights on the evolution of the Hawaiian plume.\nI support the publication of this manuscript after some minor revision. The manuscript is very well written with the figures very well illustrated. I enjoyed reading this manuscript. However, I must disclose that I am not an expert in plate flexure modeling. Therefore, I am not able to comment on the technical details, for example, whether it is a good approximation to use 2D elastic plate modeling despite the 3D nature of the islands on the Hawaiian-Emperor seamount chain, and whether the misfit between the modeled flexure and the seismically constrained flexure at Hawaiian Ridge Line 1 should be considered “acceptable”. It would be important to make sure that the manuscript is also reviewed by someone with such a background. I believe some of the novelty lies in the technical aspects and the thorough investigation using variable model parameters. Below I list some places that confuse me, which I hope can be helpful to make the manuscript more accessible to nonspecialists.\n1. When computing the loading, the density variations within the mantle lithosphere and below is not considered. There should be some thermal erosion caused by the plume. Additionally, at the Hawaiian Islands, the positive buoyancy of the mantle plume may also partially lift the lithosphere. I am wondering whether these density variations would affect the estimation of the elastic thickness, and how large the impact would be.\n2. The inference on plate rheology to me is the most important implication of this study. The authors have provided multiple alternative explanations, although most of them seem not satisfying to the authors. I am thinking if the distinct elastic thickness is related to the time scale of the loading processes. Is it possible to provide and compare the strain rates of the lithosphere when the plate bends at the trench versus when the plate flexures during magma loading at the HESC. Recent studies have also invoked grain size reduction during slab bending at the trench to account for the weakening of slab. I am wondering if grain size reduction could be a candidate for the thin elastic thickness at HESC.\n3. It would be nice to give a clear definition of the yield Te. I realize that it is calculated from the yield strength envelop, but I am not sure how this envelop is converted to a thickness, and which part of the envelop is considered mechanically strong.\nMinor issue: In Fig. 1, “Blue lines show the 83 and 121 Ma isochrons” seem to be missing.", "reviewer_2": "This study investigates the strength of the Pacific plate along the trail of seamounts associated with the Hawaiian hotspot. The authors make use of satellite derived gravity, bathymetry, and seismic experiments to develop new estimates of the strength of the Pacific plate along the chain of seamounts, taking into account many confounding factors in a thorough and detailed manner. The paper is well-written throughout, and the supporting animations in particular are valuable.\nMy main two concerns relate to points made in the summary, (1) that the new results contradict previous studies and (2) that the new results have significant implications for understanding subduction initiation. Detailed comments on both issues are provided below. My overall assessment is that the manuscript may be suitable for publication in Nature Communications if the authors can clarify these points and confirm the novelty and significance of the work.\nRegarding two of the points emphasized in the Summary:\n“The new results show that, contrary to previous predictions, Te changes gradually along the chain.....”\nThis phrase sets the expectation that the new results are revealing a flaw in current thinking, yet it is not clear to me from within the manuscript whether this is really the case. On line 52 we are told that many previous studies yield an abrupt change in Te at the HESC bend. The most recent of these studies is 1993. Many more recent studies (e.g. Kalnins and Watts, 2009; Lu et al, 2021) don’t show an abrupt change at the bend. Further, subsequent text in the ‘Results’ section states a broad agreement between the new results and some previous studies, so that in the end it is not clear how the new 2D profile model results are providing novel insights. I suggest the authors aim to clarify this point.\n“...weak zones can exist within the interior of a large, otherwise rigid, plate and may, we speculate, facilitate the initiation of intra-oceanic subduction in response, for example, to changes in plate motion and eventually lead to their break-up.”\nThis is an interesting idea, and I had the expectation that the main text would develop it further. However, only the paragraph beginning on line 465 touches on it again. There is a huge literature on subduction initiation that goes completely ignored, and at the least it would be useful for the authors to articulate how they imagine the interpreted weak zones to contribute to existing paradigms - either in a general sense, or making suggestions for specific examples in the recent past (see Gurnis et al, 2004; Lallemand and Arcay, 2021, and many others) where it is at least plausible that weak zones associated with hotspot trails were an important factor.\nA related question would be, does the new proposal make testable predictions that would be valuable to other communities. For example, there are many workers studying subduction initiation by mapping and sampling ophiolites, is the implication of this study that we might expect to see certain things in ophiolites interpreted to record some aspects of subduction initiation that is characteristic of weak zones associated with hotspot trails?\nFurther related question - what can we say about the nature of weak zones related to volcanic trails in general, as opposed to just the HESC specifically? For example, it should be possible to produce Te estimates for Louisville and other trails (or use existing ones), considering these could reveal something about whether such weak zones are likely to be common through Earth history or limited to only a subset of trails with Hawaii-like characteristics.\nRegarding writing style - I would suggest large sections of text need to be made more accessible for a Nature Communications article, given the target audience should be wider than (for example) GJI or JGR. Certain concepts such as the ‘upstream’ and ‘downstream’ flexure are introduced with little context and would require most readers to immediately go and read other sources for background for the text here to be understandable.\nRegarding uncertainty propagation - I think the authors have done a decent job of considering the many various choices and assumptions that must be made to arrive at Te estimates in this way. Nonetheless, the final presented values generally appear as a single line of best-fitting Te versus distance (e.g. Figure 3). We are therefore left to wonder how the magnitude of the variations in this series compares to the uncertainty associated with any or all of the choices at each step. For example, I could imagine that fitting for each profile could yield a range of possible fits that give some kind of confidence region, which together would give an envelope around the best-fitting curve. Of course this would also depend on some assumptions but I think it would be useful to illustrate the magnitude of such envelopes.\nOther technical comments:\nMissing some context, given that we need to understand what constitutes a ‘weak zone’ in the context of surrounding ‘normal’ oceanic lithosphere.\nI am surprised there is no mention of the work of Lu et al (2021), “What Controls Effective Elastic Thickness of the Lithosphere in the Pacific Ocean”, JGR. Full disclosure, I have no particular skin in the game in terms of contrasting interpretations, rather I just want to understand the origins of any contrasting ideas in the current literature. My impression is that the current submission brushes some issues under the carpet. Low Te at subduction zones seems to be a debated issue, yet the text glosses over this. The broader issue to me is that (in furtherance of comments made above) the results presented in the current submission are very much focussed on the HESC without much context (at least in terms of the figures). Consider for example in figure S9, we see plotted some estimated volume fluxes for the HESC with the Wessel (2016) estimates plotted for comparison. This is useful context (even though the flux is a relatively minor issue here. What I would like to see is a much better attempt to illustrate current ideas on Te within Pacific plate lithosphere (or better, oceanic lithosphere in general) with the new results for the HESC. While all the results appear to be reasonable in themselves, there is a large conceptual leap to the ‘significance for subduction initiation’ which needs to be bridged.\nFinal point, I wonder whether another factor not mentioned relates to the other hotspot trails on the Pacific plate which transect the HESC. For example, older trails transect the HESC (Shatsky, Hess, Musicians), we should expect these to also influence Te?", "reviewer_3": "This study investigates the lithospheric flexure and rheological properties of the Pacific plate along the Hawaiian-Emperor Seamount Chain (HESC) using gravity and seismic data constraints. The authors analyzed 3000 profiles spaced 2 km apart and applied 2D/3D forward modeling to estimate effective elastic thickness Te. Contrary to previous interpretations suggesting an abrupt change in Te at the Hawaiian-Emperor Bend (HEB) or kink, the study finds a gradual variation, with low Te at the Emperor Seamounts and high Te at the Hawaiian Ridge. The modeling incorporates recent seismic constraints and considers varying densities of volcanic loads and infill materials.\nResults indicate that Te correlates better with the 340–350°C oceanic isotherm, suggesting a mechanical, rather than thermal, weakening of the lithosphere due to volcanic loading. Comparisons with yield strength envelopes (YSE) based on brittle and ductile rheology show that traditional flow laws are too strong to explain the low observed Te. The findings imply that weak zones may exist within tectonic plate interiors, potentially preconditioning them for subduction initiation and plate break-up, offering insights into intraplate deformation and mantle dynamics.\nAfter reading the manuscript, I found several aspects that are either insufficiently explained or entirely omitted (specially quantification of parameters through the text), which the authors should address to better convince the reader. Most of these issues are minor, while others are of moderate. Below, I outline several key points:\nAbstract\n...... ” While low Te at the Emperor Seamounts and high Te at the Hawaiian Ridge are expected because of their differences in volcano and plate age,” .......\nHow are \"low\" and \"high\" Te defined in this context? Please provide quantitative values or ranges—otherwise, the terms remain subjective and open to interpretation.\n...”Te changes gradually along the chain”\nIt is stated that Te changes gradually from one value to another, but the specific values are not provided. Could you please clarify what X and Y are? Without this information, the statement remains vague.\nIntroduction and motivation\nLine 44. “thin elastic or viscoelastic plate with uniform”\nWhat exactly is meant by “thin” in this context? While elasticity theory assumes that Te is much smaller than the plate length, previous studies have reported specific ranges of Te values for the Hawaiian Ridge and Emperor Seamounts. This information should be clearly explained and acknowledged in the Introduction to provide proper context.\nLine 49. “Cretaceous Normal Polarity oceanic crust”\nThis explanation is clear and appropriate for geoscientists. However, since Nature Communications reaches a broader scientific audience, please consider adding the age range in parentheses—for example, “(121–83 Myr old)”—to provide clearer context for readers from other disciplines.\nLines 52-54: “While subsequent studies5-10 have generally confirmed these results, they reveal that Te changes abruptly at the HESC bend which is not expected from the volcano load and plate ages”\nThe bend appears more like a kink—an abrupt change in the Pacific Plate’s azimuth. When did this kink occur? According to Wessel & Kroenke (2008, JGR), it happened between 53.4 and 47.9 Ma. This fundamental detail should be clearly stated in the Introduction.\nFigure 1.\n• Some isochron values on the oceanic plate are missing. At a minimum, please include isochrons at 50 Myr intervals for better reference.\n• Additionally, key ages of the Hawaiian Ridge and Emperor Seamounts should be labeled. There are well-established geochemical and geochronological data available for several locations along the HE and ES chains thatwould help readers understand the age difference between the Pacific Plate and the seamounts. This would effectively illustrate the classical concept of “the age of the plate at the time of volcanic emplacement or loading,” which is critical for interpreting flexure.\nLines 122-123. “for example, with the Hawaiian swell while at the same time maximised the amplitude of the load (Supplementary Figure S2).”\nI'm not sure the Hawaiian swell signature can be dismissed a priori. McNutt & Bonneville (2000, G-Cubed) and Watts (Chapter 5, Flexure and Isostasy of the Lithosphere, 2nd ed.) highlight the significance of both buried and subsurface loads associated with underplating of anomalously thick crust. This anomalously thick crust is less dense than the surrounding mantle and generates buoyant stresses that contribute to swell formation.\nWhile the volcanic load—with its higher density contrast relative to seawater—likely plays a dominant role in downward flexure, the contribution of the buried load should not be overlooked. Its effect should be quantified, at least along profiles constrained by seismic models that provide density distributions and Moho geometry.\nAlthough I expect the results may not vary significantly due to the relatively high effective elastic thickness (Te) of approximately 20 km along the Hawaiian-Emperor Seamount Chain (HESC), this assumption needs to be tested explicitly along selected profiles and shown in Methods of Supporting Information.\nFigure 3c.\nAt first glance, this figure appears somewhat unrealistic. Typically, we would expect infill material to accumulate along the flanks of the oceanic ridge, adjacent to the seamount. However, Figure 4 shows that the volcanic edifice extends continuously from the flexed oceanic crust all the way to the core of the seamount. An exception is seen along the Vp model along Line 2, where infill material occupies approximately half of the elevated topography.\nThis raises the question: how different is the density of the volcanic edifice compared to that of the infill material? If the densities are similar, then Figure 3c could serve as a useful—though simplified—proxy for the system.\nThat said, it is important to recognize the limitations of the model. These include assumptions about uniform density, simplified geometry, and the omission of sediment compaction or lateral variations in lithology. Such simplifications may lead to discrepancies between the model output and the actual structure, particularly in areas where infill material dominates or where crustal flexure varies significantly.\nPlease explain the limitations and uncertainties of the model. It appears that a constant density is assumed for each material body, which may not reflect natural variability.\nFigure 4. Please clarify: were the dotted lines calculated using a constant or variable effective elastic thickness (Te)? What range of Te values best fits the data in panels (a), (b), and (c)? This information should be clearly specified in the figure caption.\nFigures 5 and 6. It is surprising that the “yield Te” is approximately twice as large as in the purely elastic model, even though Te(x) is allowed to vary and decrease in regions of high plate curvature in the elastic model. The yield Te—or more precisely, the yield strength envelope (YSE)—is known to depend on plate curvature, as shown in Figure 5, but it is also highly sensitive to several parameters: the strain rate (s ), activation energy (Q), the stress exponent in the ductile flow law (n), constant of the material (A), the friction coefficient (p), the fluid pore pressure ratio (A), and the thermal structure (T(z)). An explicit expression for the yield deviatoric stress should be included in the Supporting Information or Methods section. There are various formulations beyond the exponential laws, and the specific choice is critical for deriving a higher “yield Te” compared to the purely elastic model.\nLater, the authors mention that“...the brittle and ductile flow laws are too strong to explain the observed Te at the HESC...”. At this point in the manuscript, they should explicitly state the values of the critical parameters used (s , A, Q, p, n, and A), rather than waiting until Figure 6 to discuss the calibration of p, n, Q, and T(z) to match the observations.\nA few questions arise from this analysis:\n• Why was the thermal age modified? It is generally well constrained, except in specific regions affected by plume-related thermal rejuvenation.\n• What is the impact of decreasing s from 10-14 to 10-15 or 10-16 s-1? In fact, Hunter & Watts (2016) used s = 10-16 s-1. What strain rate was used in Figure 5c for the “strong” Pacific Plate?\n• What value of the fluid pore pressure ratio (A) was applied in the brittle portion of the YSE calculations?\n• In Figure 6 shows the variation of Q are shown, but it is unclear what value of A was used in the calculations.\nThe geological cause of the apparent plate weakening remains unclear. From the perspective of the YSE, is this weakening primarily attributed to changes in A and n, or to a lowers? Which factor is more likely responsible?\nFinally, it would be very helpful to include a brief sentence indicating the typical range of plate curvature values in outer-rise settings, and how these compare to those associated with flexure due to seamount loading.\nThe last sentence “... we speculate, facilitate intra-oceanic subduction in response, for example, to changes in plate motion and eventually lead to their break-up .....” is identical to the last sentence of the Summary/Abstract.\nAlthough this is a speculation, plate breakup is typically accompanied by thermal upwellings and extensional stresses. Could you elaborate a bit more on this speculation and clarify the underlying mechanisms you envision?\nComment: I agree with the authors that the weakening observed at both the HESC and CPTOR is primarily a consequence of mechanical loading rather than thermal processes. This suggests a role for spatial variations in the parameters governing both brittle and ductile deformation, as has been proposed.\nVideos.\nThe videos are very good and illustrative. However, the physical units on both the horizontal and vertical axes are missing."}, "author_response": "Department of Earth Sciences\nSouth Parks Road, Oxford, OX1 3AN\nIn the following, black font shows the comment/query of the Reviewers and Editor and the red\nfont our response.\nReviewer 1\nI support the publication of this manuscript after some minor revision. The manuscript is\nvery well written with the figures very well illustrated. I enjoyed reading this manuscript.\nWe are pleased the reviewer supports the publication of our paper and found our paper “very\nwell written....and illustrated”.\nHowever, I must disclose that I am not an expert in plate flexure modeling. Therefore, I am not\nable to comment on the technical details, for example, whether it is a good approximation to\nuse 2D elastic plate modeling despite the 3D nature of the islands on the Hawaiian-Emperor\nseamount chain,\nWe used both 2D and 3D modeling techniques. 2D modeling was used to calculate the gravity\nanomaly of the flexed top and base (i.e., Moho) of the oceanic crust (the main contributor to the\nnegative part of the gravity anomaly) along each profile. This was because the surfaces of flexure\nare deep (> 6 km), and we found little or no change in either the gravity anomaly or flexure\nbetween the 3000 closely spaced (2 km) profiles. 3D modeling was used, however, to calculate\nthe gravity effect of the load (the main contributor to the positive part of the gravity anomaly),\nthe flexures due to individual ocean island and seamount load clusters, the progressive flexure,\nand the curvatures of flexure.\nWe have made our choice of 2D and 3D techniques clearer in the revised text at the end of the\nGravity and Flexure Modeling section.\nand whether the misfit between the modeled flexure and the seismically constrained flexure at\nHawaiian Ridge Line 1 should be considered “acceptable”.\nWe consider the fit between the modeled flexure and the seismic data along Line 1 is “acceptable”\ngiven that this is the young end of the Hawaiian-Emperor Seamount Chain (HESC), and it is\npossible that isostatic equilibrium here is still not complete. For example, Line 1\nProfessor Tony Watts FRS - Professor of Marine Geology and Geophysics\nTel: +44(0)1865 272032 Fax: +44(0)1865 272072\nEmail: tony@earth.ox.ac.uk http://www.earth.ox.ac.uk/~tony/watts\n2\nintersects the ‘donut’ of earthquakes centered on the big island of Hawaii (Klein, 2016), which\nindicates active deformation and, possibly, a broken rather than a continuous elastic plate as we\nmodeled.\nWe have pointed this out and added the Klein reference in the revised caption to Figure 4.\nWhen computing the loading, the density variations within the mantle lithosphere and below is\nnot considered. There should be some thermal erosion caused by the plume. Additionally, at the\nHawaiian Islands, the positive buoyancy of the mantle plume may also partially lift the\nlithosphere. I am wondering whether these density variations would affect the estimation of the\nelastic thickness, and how large the impact would be.\nThe reviewer is correct in pointing out density variations in the mantle due, for example, to a\nmantle plume and its impact on the lithosphere were not directly considered in our study.\nHowever, Optimal Robust Separator (ORS) filters were applied to both the observed\nbathymetry and free-air gravity anomaly data in order to remove the relatively long-wavelength\neffect of a mantle plume and its impact on the lithosphere and isolate the relatively short-\nwavelength bathymetry and gravity anomaly associated with flexure.\nTo demonstrate this we added the ORS filtered free-air gravity anomaly to Supplementary Figure\nS2. The figure reveals a strong correlation between the ORS filtered bathymetry and gravity\nanomaly in the region of the Hawaiian swell. The maximum ORS filtered bathymetry and\ngravity anomaly on the swell crest is 0.99 km and 20.58 mGal, respectively which implies a\ngravity to bathymetry ratio of ~21 mGal km-1, similar to the value estimated by Watts (1976) of\n22 mGal km-1 and attributed by him to some form of convective upwelling in the mantle that\nsupports the swell.\nWe believe therefore that ORS filtering satisfactorily isolates the bathymetry and gravity\nanomaly associated with the mantle plume that is presently located beneath the youngest volcano\nin the HESC and so after subtraction from the observations will have little or no effect on our\nrecovery of Te.\nThe inference on plate rheology to me is the most important implication of this study. The\nauthors have provided multiple alternative explanations, although most of them seem not\nsatisfying to the authors. I am thinking if the distinct elastic thickness is related to the time\nscale of the loading processes.\nWe tested a number of possible causes of the weakening in the brittle and ductile fields,\nincluding reduction of the coefficient of friction, increasing the pre-exponential constant,\ndecreasing the activation energy, and decreasing the thermal age of the lithosphere. Of these we\nfound that the values of the coefficient of friction and thermal age required to explain the Te\nare unreasonably low and high respectively, although some combination of these parameters\nmaybe possible.\nWe believe that the cause of the weakening is mechanical, not thermal, and that it is most likely\nthe result of an increase in the pre-exponential constant, a decrease in the activation energy or\nsome combination of these parameters.\nnot considered significant along the HESC, except perhaps at the youngest end of the chain.\nThis is because the spread of sample ages suggests individual seamounts and ocean islands take at\nleast a few Myr to form and by this time relaxation is essentially complete.\nIs it possible to provide and compare the strain rates of the lithosphere when the plate bends at\nthe trench versus when the plate flexures during magma loading at the HESC. Recent studies\nhave also invoked grain size reduction during slab bending at the trench to account for the\nweakening of slab. I am wondering if grain size reduction could be a candidate for the thin\nelastic thickness at HESC.\nIt is possible to estimate the strain rate at a trench from the distance to the neutral surface in the\nflexed plate, the change in the curvature of flexure with distance, and the subduction velocity.\nFor example, Hunter (2015, PhD thesis) and Hunter & Watts (2016) derived strain rates of 10\n-15.1\nto s for circum-Pacific trenches. We believe that grain size reduction in the ductile layer\n10-16.3 -1\n(e.g. as described for example by Gerya et al. 2021 at trench – outer rises) could indeed be a\ncandidate for the weakness at the HESC and so we have added a reference to this process in the\nrevised text.\nIt would be nice to give a clear definition of the yield Te. I realize that it is calculated from the\nyield strength envelop(e), but I am not sure how this envelop(e) is converted to a thickness, and\nwhich part of the envelop(e) is considered mechanically strong.\nWe have better defined the yield Te where it is first mentioned in the Discussion section and\nadded a reference to Watts & Burov (2003), as suggested by the Reviewer.\nMinor issue: In Fig. 1, “Blue lines show the 83 and 121 Ma isochrons” seem to be missing.\nWe have added the missing blue lines, as suggested by the Reviewer.\nReviewer 2\nThis study investigates the strength of the Pacific plate along the trail of seamounts associated\nwith the Hawaiian hotspot. The authors make use of satellite derived gravity, bathymetry, and\nseismic experiments to develop new estimates of the strength of the Pacific plate along the chain\nof seamounts, taking into account many confounding factors in a thorough and detailed manner.\nThe paper is well-written throughout, and the supporting animations in particular are valuable.\nWe are pleased the Reviewer considers the paper “well-written throughout” and the supporting\nanimations “valuable”.\nMy main two concerns relate to points made in the summary, (1) that the new results contradict\nprevious studies and (2) that the new results have significant implications for understanding\nsubduction initiation. Detailed comments on both issues are provided below. My overall\nassessment is that the manuscript may be suitable for publication in Nature Communications if\nthe authors can clarify these points and confirm the novelty and significance of the work.\n4\n“The new results show that, contrary to previous predictions, Te changes gradually along the\nchain .... ” This phrase sets the expectation that the new results are revealing a flaw in current\nthinking, yet it is not clear to me from within the manuscript whether this is really the case. On\nline 52 we are told that many previous studies yield an abrupt change in Te at the HESC bend.\nThe most recent of these studies is 1993. Many more recent studies (e.g. Kalnins and Watts,\n2009; Lu et al, 2021) don't show an abrupt change at the bend.\nThe previous Te estimates along the HESC that are plotted in Supplementary Figure S1 have\nbeen compiled from publications during 1970 to 2021. They are mainly based on comparisons\nof observed geoid, gravity or seismic data to forward models of simple plate flexure along\nsingle profiles. They do not include values based on 3D spectral (e.g., admittance, wavelet)\nmethods. The reviewer is correct in pointing out that the Kalnins & Watts (2009) values, which\nwere derived using (moving) windows hundreds of km in width, do not show an abrupt change\nat the bend. However, as these authors point out, windows of this size tend to smear out spatial\nvariations in Te. They are therefore unlikely to resolve the abrupt change at the bend as seen in\nprevious forward modeling studies. The Lu et al. (2021) study, in contrast, uses fan wavelet\ntechniques, which potentially have better spatial resolution and do show a change at the bend in\nthe HESC. However, the change is from high values (~35 km) at the Emperor Seamounts to low\nvalues (~25 km) at the western end of the Hawaiian Ridge, which is opposite to that shown by\nthe previous forward modeling studies. The Lu et al. (2021) values are therefore difficult to\nexplain since the Emperor Seamounts were formed on much younger oceanic crust than the\nwestern end of the HESC.\nWe have therefore added a discussion of the Kalnins & Watts and Lu et al. results in the\nIntroduction and Motivation section, as suggested by Reviewer.\nFurther, subsequent text in the ‘Results' section states a broad agreement between the new\nresults and some previous studies, so that in the end it is not clear how the new 2D profile model\nresults are providing novel insights.\nWe hope the reviewer will agree that by adding the range of the previous studies, including the\nLu et al reference, and discussing some limitations of the Kalnins & Watts study that we have\nclarified the. uniqueness of our new 3000 estimates of Te along the whole HESC.\nI suggest the authors aim to clarify this point “...weak zones can exist within the interior of a large,\notherwise rigid, plate and may, we speculate, facilitate the initiation of intra-oceanic subduction in\nresponse, for example, to changes in plate motion and eventually lead to their break-up.” This is\nan interesting idea, and I had the expectation that the main text would develop it further. However,\nonly the paragraph beginning on line 465 touches on it again. There is a huge literature on\nsubduction initiation that goes completely ignored, and at the least it would be useful for the\nauthors to articulate how they imagine the interpreted weak zones to contribute to existing\nparadigms - either in a general sense, or making suggestions for specific examples in the recent\npast (see Gurnis et al, 2004; Lallemand and Arcay, 2021, and many others) where it is at least\nplausible that weak zones associated with hotspot trails were an important factor.\nWe are pleased the reviewer considers the weak zone at the HESC a potential site for\nsubduction initiation “an interesting idea”.\nexpanded our discussion to include reference to the works of Gurnis et al. (2004) and Lallemand\n& Arcay (2021). The latter reference is particularly relevant to this paper as it is one of a number\nthat posits that seamount chains or oceanic plateaus may initiate subduction. One of the\nexamples given in the study is the Afanasy Nikitin Seamount Chain in the Central Indian Ocean\nwhere there is evidence of both a weak zone (Paul et al. 1990) and intraplate deformation\n(Weissel et al. 1980).\nWe have therefore expanded the discussion on subduction initiation at the end of the Discussion\nsection, adding these references as suggested by the Reviewer.\nA related question would be, does the new proposal make testable predictions that would be\nvaluable to other communities. For example, there are many workers studying subduction\ninitiation by mapping and sampling ophiolites, is the implication of this study that we might\nexpect to see certain things in ophiolites interpreted to record some aspects of subduction\ninitiation that is characteristic of weak zones associated with hotspot trails?\nWe thank the reviewer for this interesting question. There are a number of cases of seamounts\nand ocean islands that have been described from within ophiolite sequences, for example, in\nOman, Turkey, Iran, China and the US. Some of these features have been attributed to mantle\nplumes, others to intraplate volcanism. The weak zone derived in this paper has a mechanical\norigin and is based on comparisons of the observed Te to the calculated Te based on data from\nexperimental rock mechanics. We do not know the elastic thickness of the seamounts and ocean\nislands that have been found within ophiolites. However, Watts et al. (2010) pointed out that\nseamounts and ocean islands that form on weak lithosphere are more likely to be accreted to the\nforearc, and as a consequence be preserved within ophiolites, while those formed on strong\nlithosphere are more likely to be carried down into the mantle on the subducting slab. Therefore,\nwe speculate that plume generated seamounts and ocean islands within ophiolites may have\neither a MORB or OIB geochemical ‘fingerprint’.\nAlthough the composition of seamounts and ocean islands is still not well known recent seismic\nstudies along the HESC suggest they comprise a dense core of mafic or ultra-mafic rocks that\nare draped by extrusive basalts of tholeiitic or alkalic composition, so mafic or ultra-mafic\n‘pods’ might also be expected within ophiolites.\nFurther related question - what can we say about the nature of weak zones related to\nvolcanic trails in general, as opposed to just the HESC specifically? For example, it should\nbe possible to produce Te estimates for Louisville and other trails (or use existing ones),\nconsidering these could reveal something about whether such weak zones are likely to be\ncommon through Earth history or limited to only a subset of trails with Hawaii-like\ncharacteristics.\nWe agree with the reviewer that it would useful to produce continuous Te estimates along other\nseamount chains such as Louisville Ridge. Indeed, we have just begun a study to estimate Te\nalong the northern and southern segments of this ridge and we hope to be able to report on these\nresults soon in a future paper.\naccessible for a Nature Communications article, given the target audience should be wider than\n(for example) GJI or JGR. Certain concepts such as the ‘upstream' and ‘downstream' flexure\nare introduced with little context and would require most readers to immediately go and read\nother sources for background for the text here to be understandable.\nWe agree with the Reviewer and so have provided better definitions of ‘upstream’ and\n‘downstream’ flexure where these terms are first mentioned, and have also tried to make the\nlanguage more accessible throughout the paper.\nRegarding uncertainty propagation - I think the authors have done a decent job of considering the\nmany various choices and assumptions that must be made to arrive at Te estimates in this way.\nNonetheless, the final presented values generally appear as a single line of best-fitting Te versus\ndistance (e.g. Figure 3). We are therefore left to wonder how the magnitude of the variations in\nthis series compares to the uncertainty associated with any or all of the choices at each step. For\nexample, I could imagine that fitting for each profile could yield a range of possible fits that give\nsome kind of confidence region, which together would give an envelope around the best-fitting\ncurve. Of course this would also depend on some assumptions but I think it would be useful to\nillustrate the magnitude of such envelopes.\nWe agree with the Reviewer and so have added a new figure to Supplementary, Figure S6, which\nshows details of the RMS minima for each of the profiles plotted in Figure 2. By assuming a\ntolerance parameter of 0.1, we estimate our Te recovery to be accurate to better than ± 2 km.\nOther technical comments:\nMissing some context, given that we need to understand what constitutes a ‘weak zone' in the\ncontext of surrounding ‘normal' oceanic lithosphere.\nI am surprised there is no mention of the work of Lu et al (2021), “What Controls Effective\nElastic Thickness of the Lithosphere in the Pacific Ocean”, JGR. Full disclosure, I have no\nparticular skin in the game in terms of contrasting interpretations, rather I just want to\nunderstand the origins of any contrasting ideas in the current literature. My impression is that\nthe current submission brushes some issues under the carpet. Low Te at subduction zones\nseems to be a debated issue, yet the text glosses over this.\nAs we responded to Reviewer 1, we have added references to both Kalnins & Watts (2007) and\nLu et al. (2021) which are spectral methods and therefore are not directly comparable to results\nbased on forward modeling of gravity and seismic data at individual seamounts and ocean\nislands. There is evidence, for example, that spectral results may smear spatial variations in Te as\nshown by Kalnins & Watts in the vicinity of the Hawaiian Ridge where the high Te associated\nwith the islands extends to the Musician Seamount cluster to the north and the Cook/Jagger\nSeamount cluster to the south, both of which formed at or near a MOR and so are associated with\nlow, not high, values of Te.\nWe are not aware of the debate referred to here by the Reviewer. The results of Hunter & Watts\n7\n(2016), for example, show that there is a low Te at subduction zones, but it is limited to the\nseaward wall of the trench where swath bathymetry data indicate bend faults and the curvature\nof flexure is greatest. Elsewhere, in the outer rise region, there is high Te, which they show are\nwell described by the depth to the 450oC oceanic isotherm based on plate cooling models.\nThe broader issue to me is that (in furtherance of comments made above) the results presented\nin the current submission are very much focussed on the HESC without much context (at least\nin terms of the figures). Consider for example in figure S9, we see plotted some estimated\nvolume fluxes for the HESC with the Wessel (2016) estimates plotted for comparison. This is\nuseful context (even though the flux is a relatively minor issue here. What I would like to see is\na much better attempt to illustrate current ideas on Te within Pacific plate lithosphere (or better,\noceanic lithosphere in general) with the new results for the HESC. While all the results appear to be reasonable in themselves, there is a large conceptual leap to the ‘significance for subduction initiationʼ which needs to be bridged.\nWe are pleased the reviewer found the comparison of the volume estimates along the HESC to\nprevious results in Figure S9 useful.\nWe agree with the Reviewer regarding also showing current ideas on Te within the Pacific plate\nand so have added a new figure in Supplementary, Figure S12. The figure compares our Model\nD results with previous Te estimates from the French Polynesia region and with other regions of\nthe Pacific Ocean. While our Model results are higher than those from the French Polynesia\nregion (or from seamounts and ocean islands that backtrack to the region) they overlap the\nestimates from other regions of the Pacific. These estimates are best fit (mean = 2.7 mGal, RMS\n= 6.1 mGal) by the depth to the 350oC oceanic isotherm, which is similar to the isotherm that\ndescribes our new Te results.\nWe have commented on this in the caption of Supplementary Figure S12.\nFinal point, I wonder whether another factor not mentioned relates to the other hotspot trails on\nthe Pacific plate which transect the HESC. For example, older trails transect the HESC\n(Shatsky, Hess, Musicians), we should expect these to also influence Te?\nWhen modeling we applied a mask on the observed bathymetry and gravity data so as to ensure\nwe only considered volcanic loads that could be attributed to the HESC. The Shatsky and Hess\nrises and the Musician Seamounts, which formed at or near a mid-ocean ridge, are associated\nwith low Te and are characterized by relatively short wavelength gravity anomalies and flexure.\nThey are therefore likely to have little or no impact on the gravity anomaly or flexure associated\nwith the HESC.\nReviewer 3\nAfter reading the manuscript, I found several aspects that are either insufficiently explained or\nentirely omitted (specially quantification of parameters through the text), which the authors\nshould address to better convince the reader. Most of these issues are minor, while others are of\nmoderate. Below, I outline several key points:\n........ ” While low Te at the Emperor Seamounts and high Te at the Hawaiian Ridge are expected\nbecause of their differences in volcano and plate age,” ...... How are \"low\" and \"high\" Te defined\nin this context? Please provide quantitative values or ranges—otherwise, the terms remain\nsubjective and open to interpretation....”Te changes gradually along the chain”.\nIt is stated that Te changes gradually from one value to another, but the specific values are not\nprovided. Could you please clarify what X and Y are? Without this information, the statement\nremains vague.\nWe have added the ranges of Te (from Supplementary Figure S1) in the abstract, as suggested by\nthe reviewer.\nIntroduction and motivation:\nLine 44. “thin elastic or viscoelastic plate with uniform”\nWhat exactly is meant by “thin” in this context? While elasticity theory assumes that Te is much\nsmaller than the plate length, previous studies have reported specific ranges of Te values for the\nHawaiian Ridge and Emperor Seamounts. This information should be clearly explained and\nacknowledged in the Introduction to provide proper context.\nWe mean here an elastic beam/plate with a thickness that is small compared to the radius of\ncurvature of flexure. We have pointed this out in the revised paper, as suggested by the\nReviewer.\nLine 49. “Cretaceous Normal Polarity oceanic crust”\nThis explanation is clear and appropriate for geoscientists. However, since Nature\nCommunications reaches a broader scientific audience, please consider adding the age range in\nparentheses—for example, “(121–83 Myr old)”—to provide clearer context for readers from\nother disciplines.\nWe have added the age range for the Cretaceous Normal Polarity oceanic crust (83-121 Ma), as\nsuggested by the Reviewer.\nLines 52-54: “While subsequent studies 5-10 have generally confirmed these results, they reveal\nthat Te changes abruptly at the HESC bend which is not expected from the volcano load and\nplate ages”\nThe bend appears more like a kink—an abrupt change in the Pacific Plateʼs azimuth. When did\nthis kink occur? According to Wessel & Kroenke (2008, JGR), it happened between\n53.4 and 47.9 Ma. This fundamental detail should be clearly stated in the Introduction.\nWe have added the approximate age (~48 Ma) of the bend and the reference to Wessel &\nKroenke (2008), as suggested by the Reviewer.\nFigure 1.\n9\n• Some isochron values on the oceanic plate are missing. At a minimum, please\ninclude isochrons at 50 Myr intervals for better reference.\nWe have added the missing isochron values to Figure 1, as suggested by the Reviewer. We have\nnot added the 50 Ma age contours, however, as we believe they would make the figure less clear\nand add little relevant information.\n• Additionally, key ages of the Hawaiian Ridge and Emperor Seamounts should be labeled.\nThere are well-established geochemical and geochronological data available for several\nlocations along the HE and ES chains that would help readers understand the age difference\nbetween the Pacific Plate and the seamounts. This would effectively illustrate the\nclassical concept of “the age of the plate at the time of volcanic emplacement or loading,” which\nis critical for interpreting flexure.\nWe have added key ages to Figure 1 and their references, as suggested by the Reviewer.\nLines 122-123. “for example, with the Hawaiian swell while at the same time maximised the\namplitude of the load (Supplementary Figure S2).”\nI'm not sure the Hawaiian swell signature can be dismissed a priori.\nWe agree with the Reviewer that we were perhaps a little too dismissive about removing the\neffects of swell formation. To address this we modified Supplementary Figure S2 to show the\nORS-derived free-air gravity anomaly in addition to the regional bathymetry. The figure shows\na close correlation and a ratio of between the regional gravity anomaly and bathymetry at the\nyoung end of the HESC of ~21-27 mGal km-1. This ratio is similar to one found by Watts (1976)\nand suggests that ORS filtering successfully removes the Hawaiian swell, which has been\ninterpreted to be supported by some form of convection in the mantle.\nWe have revised the text in the Flexure and Gravity modeling section to reflect this, as\nsuggested by the Reviewer.\nMcNutt & Bonneville (2000, G-Cubed) and Watts (Chapter 5, Flexure and Isostasy of the\nLithosphere, 2nd ed.) highlight the significance of both buried and subsurface loads associated\nwith underplating of anomalously thick crust. This anomalously thick crust is less dense than the\nsurrounding mantle and generates buoyant stresses that contribute to swell formation.\nWhile the volcanic load—with its higher density contrast relative to seawater—likely plays a\ndominant role in downward flexure, the contribution of the buried load should not be\noverlooked. Its effect should be quantified, at least along profiles constrained by seismic models\nthat provide density distributions and Moho geometry.\nWe agree with the Reviewer that in addition to surface loads there is evidence that the oceanic\ncrust upon which seamounts and ocean islands have been emplaced may have also been subject\nto sub-surface (buried) loads such as those associated with magmatic underplating.\nThe seismic data in Figure 4, however, show little evidence of magmatic underplating. Rather,\n10\nthe mantle that underlies the flexed oceanic crust is remarkably homogeneous with regard to its\nphysical properties.\nWe do not therefore see the need to consider the effects on the free-air gravity field (or the\nflexure) of magmatic underplating along the HESC.\nWe note though that the seismic data in Figure 4 reveal another possible sub-surface (buried)\nload in the form a high velocity, dense, body in the core the volcanic edifice. This is one of the\nreasons (the other being the need to account for the removal of load during guyot formation)\nwhy we used a bathymetry-dependent model based on the seismic P-wave velocity in which\ndensity varied from the flank of a seamount or oceanic island to its dense core, rather than using\na constant load density\nWe have added a paragraph on this discussion at the end of the Results section, as suggested by\nthe Reviewer.\nAlthough I expect the results may not vary significantly due to the relatively high effective\nelastic thickness (Te) of approximately 20 km along the Hawaiian-Emperor Seamount\nChain (HESC), this assumption needs to be tested explicitly along selected profiles and shown in\nMethods of Supporting Information.\nThe reviewer is correct in stating that the effect of buried loading may not vary significantly due\nto the relatively high Te along the HESC. The problem is testing it since the geometry of the\nburied load is not well defined in 3D. The only location where it may be tested is on Jimmu\nGuyot where there is an intersecting seismic dip and strike line. This was carried out at Jimmu\nin Watts et al. (2021) where the geometry of the buried load was defined by the 6 km/s refractor\non the strike and dip lines. We found using a process-oriented approach the gravity effect of the\nburied load to be strongly localized and the effect on the flexure was to increase the Te derived\nfrom only surface (bathymetric) loading from 14 km to 21 km. We note here that the Te derived\nfrom gravity modeling with a load boost (Model D), which we believe addresses a dense core,\nwas 18 km (Figure 2), which is in better agreement with the 21 km derived previously by Watts\net al. (2021).\nFigure 3c.\nAt first glance, this figure appears somewhat unrealistic. Typically, we would expect infill\nmaterial to accumulate along the flanks of the oceanic ridge, adjacent to the seamount.\nHowever, Figure 4 shows that the volcanic edifice extends continuously from the flexed\noceanic crust all the way to the core of the seamount. An exception is seen along the Vp\nmodel along Line 2, where infill material occupies approximately half of the elevated\ntopography.\nWe do not believe Figure 3c is unrealistic. This is because it is a strike line through the summits of\nseamounts and ocean islands that comprise the HESC, not a dip line. The material that infills the\nmoat, which includes volcanoclastic and material derived from mass wasting, is expected to\ncontinue into the lowermost flanks of the HESC, but would only be visible on a dip line, not a\nstrike line. The moat infill does not extend across the summits, although the physical properties of\nthis region, which comprise extrusive lavas and clastics that drape intrusive rocks, may well\n11\nresemble those of the moat infill. The HESC (light blue shaded region in Figure 3c) comprises\nthe surface ‘driving’ load, which in our calculations is determined directly from the bathymetry.\nThere is infill along the whole HESC, dubbed the root infill, which is the material that has\naccumulated within the flexure immediately beneath the ‘driving’ load.\nThis raises the question: how different is the density of the volcanic edifice compared to that of\nthe infill material? If the densities are similar, then Figure 3c could serve as a useful—though\nsimplified—proxy for the system.\nThe differences in density between moat infill and root infill are given in Figures 2 and\nSupplementary S6. In general, the moat infill density is somewhat less than the root infill\ndensity because the moat infill includes more volcanoclastics and mass wasting products\nderived from the volcanic edifices while the root infill includes more basaltic lavas associated\nthe initial shield building phase of seamount/ocean island growth. The load density is shown in\nSupplementary Figure S7.\nThat said, it is important to recognize the limitations of the model. These include assumptions about uniform density, simplified geometry, and the omission of sediment compaction or lateral variations in lithology. Such simplifications may lead to discrepancies between the model output and the actual structure, particularly in areas where infill material dominates or where crustal flexure varies significantly. Please explain the limitations and uncertainties of the model. It appears that a constant density is assumed for each material body, which may not reflect natural variability.\nWe agree with the reviewer. We have therefore added a new figure, Supplementary Figure S6,\nthat illustrates the uncertainties in recovering Te for the 6 selected profiles shown in Figure 2.\nThe uncertainty is better than about ±2 km, assuming a tolerance parameter of 0.1. We used here\na 3D bathymetry-dependent load density model for each seamount and oceanic islands of the\nHESC in which the load density varies with depth within the volcanic edifice. Then we modeled\nthe flexure using this 3D variable density load, and the gravity effect of the load was calculated.\nThe remaining moat infill and root infill densities may vary along the HESC and are not well\ndetermined by the limited seismic data we therefore made them uniform and searched for them\nalong each of the profiles. Moreover, we used a ‘load boost’ to allow consideration of the mass\nmissing that may have contributed to the gravity anomaly and flexure at the time of volcano\nloading.\nFigure 4. Please clarify: were the dotted lines calculated using a constant or variable effective\nelastic thickness (Te)? What range of Te values best fits the data in panels (a), (b), and (c)? This\ninformation should be clearly specified in the figure caption.\nThe white dashed lines in Figure 4 shows the calculated flexure assuming a constant Te as\ndetermined from the 2D gravity modeling along each of the 3000 profiles. We are not\nattempting to derive the Te that best fit the seismic data (this has already been undertaken in the\npapers by Xu et al., Dunn et al. and MacGregor et al..\nThe Te and density values used to construct the flexure in Figure 4 are listed in Supplementary\nTable S1 and the Te values in this table have been added to the caption of Figure 4, as suggested\n12\nby the Reviewer.\nFigures 5 and 6. It is surprising that the “yield Te” is approximately twice as large as in the\npurely elastic model, even though Te(x) is allowed to vary and decrease in regions of high plate\ncurvature in the elastic model. The yield Te—or more precisely, the yield strength envelope (YSE)—is known to depend on plate curvature, as shown in Figure 5, but it is also highly sensitive to several parameters: the strain rate(ε)̇ , activation energy (Q), the stress exponent in the ductile flow law (n), constant of the material (A), the friction coefficient (µ), the fluid pore pressure ratio (λ), and the thermal structure (T(z)).\nOur approach has been to take the classic experimental results of Goetze and Geotze & Evans\nand compare the ‘yield Te’ implied by their rheology to the Te derived from gravity modeling\nalong the HESC. We chose this rheology because it has been widely used in flexure studies and\nHunter & Watts (2016) suggested in their inversion “A1” that it worked well at subduction\nzones. We found, however, using the observed curvatures of flexure that the rheology was too\nstrong for the HESC and so the question was could we change the parameters in this rheology\nand fit the observed Te? To do this we tested the dependence of the ‘Yield Te’ Goetze and\nGeotze & Evans rheology on activation energy (Q , Q ), constant of the material (A ), friction\np d p\ncoefficient (µ), and thermal structure T(z). We chose these test parameters above the others\nf\nbecause they had been varied in previous studies (e.g. Zhong & Watts) and are probably the most\nuncertain of all parameters in the laboratory-derived rheological laws.\nAn explicit expression for the yield deviatoric stress should be included in the Supporting\nInformation or Methods section. There are various formulations beyond the exponential laws,\nand the specific choice is critical for deriving a higher “yield Te” compared to the purely elastic\nmodel.\nWe have included the expressions for the yield stress that we used in the new Supplementary\nTable S2, as suggested by the Reviewer.\nLater, the authors mention that “...the brittle and ductile flow laws are too strong to explain the\nobserved Te at the HESC...”. At this point in the manuscript, they should explicitly\nstate the values of the critical parameters used (ε̇, A, Q, µ, n, and λ), rather than waiting until\nFigure 6 to discuss the calibration of µ, n, Q, and T(z) to match the observations.\nWe have added the values of ε,̇ A\np\n, Q\np\nand Q\nd\n, and µ to the first line where it is stated that the\nrheological laws are too strong, as suggested by the Reviewer. Other parameters are listed in\nthe new Supplementary Table S2.\nA few questions arise from this analysis:\n• Why was the thermal age modified? It is generally well constrained, except in specific regions\naffected by plume-related thermal rejuvenation.\nThe thermal age was modified because it has recently been proposed (e.g. Pleus et al. 2020,\nGJI; Douglas et al. 2025, JGR) that the Pacific lithosphere may have been rejuvenated by the\nthermal effects of the Hawaiian hotspot or magma assisted flexure.\n13\n• What is the impact of decreasing ε ̇from 10-14 to 10-15 or10-16 s-1? In fact, Hunter & Watts\n(2016) used ε ̇= 10-16 s-1. What strain rate was used in Figure 5c for the “strong” Pacific Plate?\nWe selected ε̇ = 10 s-1 based on consideration of a) the duration of time it takes for a ‘typical’\n-14\nseamount or ocean island to form and b) the relaxation that takes place as the thickness of the\nlithosphere that supports a volcanic load decreases from its short-term (seismic?) thickness to its\nlong-term elastic thickness. For example, an Emperor seamount that took 2.7 Myr to form on 50\nMa oceanic lithosphere with a seismic thickness of 95 km and a Te of 14 km would be\nassociated with a strain rate of ε̇ = 10-14 s-1. Decreasing the strain rate to 10 s-1 or 10 s-1 for\n-15 -16\nthe same thermal age, seismic thickness and Te, however, would require a duration of seamount\nformation of 27 and 270 Myr respectively which are a factor of 10 and 100 times respectively\nlonger than normally considered. Similar results were obtained for a seamount in the Hawaiian\nRidge.\nIrrespective, we have tested the effects of decreasing the strain rate to the values used by Goetze\n(10-15 s-1) and & Watts (10-16 s-1). We found that decreasing the strain rate weakens the plate.\nHowever, the effect is small and in the case of an Emperor seamount the result would be a\nreduction in the ‘Yield Te’ by 1.5-3 km and 3-6 km for a strain rate of 10 s-1 and 10 s\n-15 -16 -1\nrespectively. Similar results were obtained for a seamount in the Hawaiian Ridge.\nWe have made these points clearer in the revised text and Supplementary Table S3.\nThe Te in Figure 5c for the “strong” Pacific plate is based on the depth to the 671-714oC oceanic\nisotherms which Hunter & Watts (2016) showed describe well the observed Te oceanward of the\nweak zone at deep-sea trenches. It is not dependent on a strain rate.\nWe have made this clearer in the revised caption to Figure 5.\n• What value of the fluid pore pressure ratio () was applied in the brittle portion of the YSE\ncalculations?\nWe assumed fluid-pore pressure = 0 which is the case for ‘dry’ conditions as used by Goetze.\n• In Figure 6 shows the variation of Q are shown, but it is unclear what value of A was used in\nthe calculations.\nThe value of the pre-exponential, A p , used in Figure 6b is 7.0 × 10-14 Pa -n s-1 and is from Goetze.\nNote that the variation of A in the figure show the factors (e.g. 1, 104, 108 and 1012) by which\np\nthis value has been increased. We made this clearer in the Figure 6b caption, as suggested by the\nReviewer.\nThe geological cause of the apparent plate weakening remains unclear. From the perspective of\nthe YSE, is this weakening primarily attributed to changes in A and n, or to a\nlower ε?̇ Which factor is more likely responsible?\nWe have shown in this paper that the rheological laws of Goetze and Evans & Goetze – and\n14\nprobably other LPT laws - are too strong to explain the observed Te variation along the HESC.\nThe Pacific plate underlying the HESC is therefore weaker than expected by these laboratory-\nderived rheological laws. The cause of this weakness is not clear, but we believe it to be a\nmechanical, not a thermal, one. We present evidence in Figure 6 that plausible increases in the\npre-exponential constant and decreases in the activation energy could account for the degree of\nweakness. Decreases in frictional coefficient or thermal age at the time of loading might also\nexplain the weakness but they imply parameter values such as <0.075 and 67-83%, respectively,\nto explain our observations. We do not believe that other factors that might weaken the lithosphere\nsuch as an increase in the pore-fluid pressure (say to hydrostatic conditions) or decreases in the\nstrain rate would be significant enough to explain the weakness. Therefore, we conclude that\nincreases in the pre-exponential constant, decreases in the activation energy or some combination\nof these parameters best account for the observed Te variation.\nFinally, it would be very helpful to include a brief sentence indicating the typical range of\nplate curvature values in outer-rise settings, and how these compare to those associated with\nflexure due to seamount loading.\nThe plate curvature values in circum-Pacific outer-rise settings are given in figure 6a of Hunter\n& Watts (2016) and are in the range 4.5 × 10-7 m-1 to 11.0 × 10-7 m-1. Comparisons of these\nvalues show them to be of the order or lower than the maximum positive curvatures along the\nEmperor Seamounts and generally higher than the maximum positive curvatures along the\nHawaiian Ridge.\nWe have added the range of outer rise curvatures to Figure 5a so that comparisons can be\nmade with the seamount and ocean island curvatures, as suggested by the Reviewer.\nThe last sentence “... we speculate, facilitate intra-oceanic subduction in response, for example,\nto changes in plate motion and eventually lead to their break-up ..... ” is identical to the last\nsentence of the Summary/Abstract.\nWe have modified the sentence at the end of the Discussion slightly, as suggested by the\nReviewer.\nAlthough this is a speculation, plate breakup is typically accompanied by thermal upwellings and\nextensional stresses. Could you elaborate a bit more on this speculation and clarify the\nunderlying mechanisms you envision?\nWe have expanded the discussion on this speculation at the end of the Discussion section, as\nsuggested by the Reviewer.\nComment: I agree with the authors that the weakening observed at both the HESC and CPTOR is\nprimarily a consequence of mechanical loading rather than thermal processes. This suggests a\nrole for spatial variations in the parameters governing both brittle and ductile deformation, as has\nbeen proposed.\nWe are pleased the Reviewer agrees with the cause of the weakening at both the HESC and\nCPTOR.\nThe videos are very good and illustrative. However, the physical units on both the horizontal and\nvertical axes are missing.\nWe are pleased the Reviewer found the videos instructive and have added the physical units on\nthe vertical axes, as suggested by the Reviewer.\nEditor\nYou will see that while the [reviewers] are interested in your study, they also raise concerns.\nThese include the discussion of previous results, the implications of subduction initiation, the\ninfluence of density variations within the mantle lithosphere and the limitations and uncertainties\nof the model.\nWe believe that we have now addressed all the concerns in our response to the Reviewers. In\nparticular, the discussion of previous results have been addressed in the “Introduction and\nMotivation” section in response to Reviewer 2, the implications of subduction initiation have\nbeen fully addressed in an expanded “Discussion” section in response to Reviewer 2, the\ninfluence of density variations within the mantle lithosphere have been addressed in the “Flexure\nand Gravity modeling” section in response to Reviewer 1 and the limitations and uncertainties of\nthe model have been addressed in the “Results” section and in Supplementary Figure S6 in the\nresponse to Reviewer 3.\nWe hope these responses to Reviewers 1-3 and the Editor are satisfactory and we look forward to\nhearing from you.\nDepartment of Earth Sciences\nSouth Parks Road, Oxford, OX1 3AN\nNCOMMS-25-18554A\n.\nIn the following, black font shows the comment of the Reviewers and red font our response.\nReviewer 1\nThe authors have well responded to my comments. I think the manuscript is more accessible to\nthe general audience now. I have no further comments.\nWe are pleased the reviewer found we “have responded well to (his/her) comments” and that\n(he/her) has no further comments.\nReviewer 2\nI have not much to add based on the revised manuscript. The authors have made a good attempt\nto respond to comments, just a few new issues:\nWe are pleased the reviewer found we “have made a good attempt to respond to (his/her)\ncomments”.\nFigure 5 and related text, paragraph 417: I would find it useful to make a more explicit\nconnection between the text and the two alternative green curves, provide a basic explanation for\nwhat the 'weak zone' and 'strong zone' curves are and why they are significant here.\nLine 437 - consider shortening sentence.\nWe have shortened the sentence by breaking it into two, as suggested by the reviewer.\nLine 511 - consider shortening sentence.\nWe have shortened the sentence by breaking it into two, as suggested by the reviewer.\nProfessor Tony Watts FRS - Professor of Marine Geology and Geophysics\nTel: +44(0)1865 272032 Fax: +44(0)1865 272072\nEmail: tony@earth.ox.ac.uk http://www.earth.ox.ac.uk/~tony/watts\nConsider the wording here, I suspect you mean to convey that these features are sites of\nweakness that may control where subduction initiates (driven by forcing from elsewhere). Rather\nthan being the driver themselves.\nWe have changed the wording, as suggested by the reviewer.\nReviewer 3\nThe authors have addressed my suggestions, and the manuscript is now much improved. I have\nno further requests.\nWe are pleased the reviewer found that we “addressed (his) suggestions, and the manuscript is\nnow much improved”.\nWe hope these responses to Reviewers 1-3 are satisfactory and we look forward to hearing from\nyou."}, {"round": 2, "reviewer_comments": {"reviewer_1": "The authors have well responded to my comments.\nI think the manuscript is more accessible to the general audience now.\nI have no further comments.", "reviewer_2": "I have not much to add based on the revised manuscript. The authors have made a good attempt to respond to comments, just a few new issues:\nFigure 5 and related text, paragraph 417:\nI would find it useful to make a more explicit connection betweent the text and the two alternative green curves, provide a basic explanation for what the 'weak zone' and 'strong zone' curves are and why they are significant here.\nLine 437 - consider shortening sentence.\nLine 511 - consider shortening sentence.\nLine 529: \"...seamount chains or oceanic plateaus may initiate subduction...\"\nConsider the wording here, I suspect you mean to convey that these features are sites of weakness that may control where subduction initiates (driven by forcing from elsewhere). Rather than being the driver themselves.", "reviewer_3": "The authors have addressed my suggestions, and the manuscript is now much improved. I have no further requests.\nEduardo Contreras-Reyes"}, "author_response": "Department of Earth Sciences\nSouth Parks Road, Oxford, OX1 3AN\nNCOMMS-25-18554A\n.\nIn the following, black font shows the comment of the Reviewers and red font our response.\nReviewer 1\nThe authors have well responded to my comments. I think the manuscript is more accessible to\nthe general audience now. I have no further comments.\nWe are pleased the reviewer found we “have responded well to (his/her) comments” and that\n(he/her) has no further comments.\nReviewer 2\nI have not much to add based on the revised manuscript. The authors have made a good attempt\nto respond to comments, just a few new issues:\nWe are pleased the reviewer found we “have made a good attempt to respond to (his/her)\ncomments”.\nFigure 5 and related text, paragraph 417: I would find it useful to make a more explicit\nconnection between the text and the two alternative green curves, provide a basic explanation for\nwhat the 'weak zone' and 'strong zone' curves are and why they are significant here.\nLine 437 - consider shortening sentence.\nWe have shortened the sentence by breaking it into two, as suggested by the reviewer.\nLine 511 - consider shortening sentence.\nWe have shortened the sentence by breaking it into two, as suggested by the reviewer.\nProfessor Tony Watts FRS - Professor of Marine Geology and Geophysics\nTel: +44(0)1865 272032 Fax: +44(0)1865 272072\nEmail: tony@earth.ox.ac.uk http://www.earth.ox.ac.uk/~tony/watts\nConsider the wording here, I suspect you mean to convey that these features are sites of\nweakness that may control where subduction initiates (driven by forcing from elsewhere). Rather\nthan being the driver themselves.\nWe have changed the wording, as suggested by the reviewer.\nReviewer 3\nThe authors have addressed my suggestions, and the manuscript is now much improved. I have\nno further requests.\nWe are pleased the reviewer found that we “addressed (his) suggestions, and the manuscript is\nnow much improved”.\nWe hope these responses to Reviewers 1-3 are satisfactory and we look forward to hearing from\nyou."}]

Decision letter