Ductile vs. Brittle Strain Localization Induced by the Olivine–Ringwoodite Transformation

Round 1

Reviewer 1 Report

This manuscript, Ductile vs Brittle Strain Localization Induced by the Olivine - Ringwoodite Transformation, submitted by Gasc et al. reports deformation experiments on Mg2GeO4-olivine, as an analog of Mg2SiO4 olivine. The authors synthesized sintered mixture of Mg2GeO4 (Ge-olivine) and MgGeO3 (Ge-pyroxene) as the starting materials, and performed the deformation experiments on the sample in Mg2GeO4 (Ge-spinel) P-T regime, so the role of olivine – ringwoodite transition on the rheological properties and its implications on deep earthquakes can be investigated by SEM-EBSD analysis and acoustic emissions, respectively. The results indicate the kinetics of olivine–ringwoodite phase transitions controlled by the temperature may play an important role in the formation of deep earthquakes. This manuscript fits the scope of Minerals and would be of interest to mineralogists and mineral physicists. I, therefore, recommend it for publication after addressing the following question: what are the motivation and effects of adding MgGeO3 (Ge-pyroxene) in the experiment? Why not the pure Mg2GeO4 system?

Author Response

I, therefore, recommend it for publication after addressing the following question: what are the motivation and effects of adding MgGeO3 (Ge-pyroxene) in the experiment? Why not the pure Mg2GeO4 system?

                The motivation stems from the density contrast between Ge-olivine and Ge-pyroxene (owing to a higher Ge/Mg ratio in pyroxene) which allows visualizing deformation in BSE mode in the SEM images. In that sense Ge-pyroxene is used as strain marker.

Other than that, effects are minimal. Proportions of Ge in the starting powder were adjusted so that a few percent of Ge-pyroxene would compose the final aggregate. The rheology of the aggregate therefore remains largely controlled by the mechanical properties of Ge-olivine, and in some cases, its transformation to Ge-spinel.

We added a few sentences to the methods section (2.1) to detail both of these aspects.

Reviewer 2 Report

 

This paper presents an experimental study of the mechanics of flow during the phase transition from olivine to spinel of Mg2GeO4.  The paper has a few interesting experiments of deformation with many interesting observations.  I feel that these observations are valuable and will be of interest to many scientists interested in this issue.  For this reason, I urge publication.

My issue with the paper lies in the vantage point that the authors project on the data and interpretation.  

1. They assert that transformational faulting is responsible for all of the deep earthquakes that aren't covered by brittle failure.  The enigma of deep earthquakes however, is 'why are there any earthquakes deeper than 50 km?'  So events at 100, 200, and 300 km depth are not caused by transformational faulting in the olivine to wadsleyite transformation at these depths.  Kinetic studies tend to limit the depth range of this transformation to depths much shallower than 700 km (see Mosenfelder et al, 2001, PEPI).  So the olivine transformation only can cover a small range of the deep events.  Perhaps, when we find a good reason for earthquake at 300 km depth, we will answer the question for all deep events.
2. Coincidence is not the same as causality.  The fact that acoustic emissions, faulting, and failure all coexist does not prove which one is the cause.  I am not convinced that we observe 'transformational faulting' in this data.  What does similar studies look like if spinel is the starting material?  Are there still AE?  Is there brittle failure?  The differential stress often equals or exceeds the pressure.  Surely, such conditions are not happening at 400 km depth.  How does this affect the conclusions?

It is all too easy to take our favorite model and use it to interpret all observations.  For example, the author claims that the reduction of seismicity at 350 km indicates the end of one mechanism and the beginning of a new one.  However, Mohiuddin and Karato show that the flow law in the mixed phase region indicates a dramatic decrease in strength.  Panasyuk, S. V., and B. H. Hager (1998) indicate a model with significant strength reduction in mixed phase regions.  Thus, maybe the reduction of seismicity is caused by the drop in ambient stress due to the relaxation by the phase transition.  Once the transformation is complete, then the old mechanisms ramp up the seismicity.  

I feel that the author's bias detracts from the importance of the paper.

 

 

 

Author Response

My issue with the paper lies in the vantage point that the authors project on the data and interpretation.

• They assert that transformational faulting is responsible for all of the deep earthquakes that aren't covered by brittle failure. The enigma of deep earthquakes however, is 'why are there any earthquakes deeper than 50 km?'  So events at 100, 200, and 300 km depth are not caused by transformational faulting in the olivine to wadsleyite transformation at these depths. 

We do not “assert that transformational faulting is responsible for all of the deep earthquakes that aren’t covered by brittle failure”. Since the reviewer does not refer to any specific paragraph, line or statement of our manuscript, this remark is particularly difficult to address. There is no denying that all deep earthquakes, in general, as in “deeper-than-50-km”, are somehow enigmatic. However, this paper very explicitly focuses on the deformation mechanisms related to the olivine-ringwoodite transformation, hence in the transition zone, and their possible relation to Deep-Focus Earthquakes, which occur by definition deeper than ~400 km. We rewrote a couple of statements in the introduction to address this issue and added a reference to make it clear that our focus is on DFEs specifically because in all slabs in which they occur, they are more numerous than earthquakes in the 200-300 km depth range:

“In addition, in slabs that do present DFEs, seismicity in the descending slab progressively decreases until depths of ~300 km and peaks again in the transition zone with DFEs [14]. This second burst of seismicity is somehow abnormal because it occurs at PT conditions that should preclude brittle failure.”

Kinetic studies tend to limit the depth range of this transformation to depths much shallower than 700 km (see Mosenfelder et al, 2001, PEPI).  So the olivine transformation only can cover a small range of the deep events.  Perhaps, when we find a good reason for earthquake at 300 km depth, we will answer the question for all deep events.

Several studies, including the one referred to by the reviewer here, have indeed used experimental kinetic data to model numerically and assess the metastable survival of olivine in the transition zone. Some of these studies found that it would be limited to the core of the fastest and oldest subducting slabs. To acknowledge this we added the following to the introduction of the manuscript, including the reference used by the reviewer:

“Some of these studies tend to limit the survival of metastable olivine to depths of 500-600 km in the core of the coldest and fastest subducting slabs (e.g., Tonga) (Mosenfelder et al., 2001; Rubie and Ross, 1994).”

However, subsequent studies have demonstrated that the transformation of olivine to wadsleyite and/or ringwoodite was very sensitive to both water and iron content, in addition to being exponentially sensitive –like any reaction– to temperature and equilibrium overstep (i.e., free Gibbs energy of reaction ΔG, see (Perrillat et al., 2016). All of these parameters combined make the extrapolation from lab to subduction time scales extremely difficult. Since then, the Mosenfelder 2001 model prediction was actually proven wrong in several instances where a metastable olivine wedge was observed by seismological data (Jiang et al., 2008; Kaneshima et al., 2007; Kawakatsu and Yoshioka, 2011; Shen and Zhan, 2020; Zhao, 2017). An explanation for the survival of metastable olivine in those cases was recently proposed by Ishii and Ohtani (Ishii and Ohtani, 2021) who showed that at the pressure and temperature conditions of the transition zone, dry olivine can coexist with hydrous phases. All of this was added to the introduction.

Furthermore, we do not believe, nor do we state, that transformational faulting is the only mechanism responsible for all of DFEs. In particular, regarding the largest DFEs that occur where a narrow metastable olivine wedge is expected (eg. the Chilean slab) the manuscript states that other mechanisms are likely at play. This is detailed in the second a paragraph of section 4.4 of the discussion to which we added this first sentence:

“However, transformational faulting might only explain a fraction of DFEs, particularly in cases where the MOW has a limited thickness. In that case, it might serve as a nucleation mechanism for the largest earthquakes.”

As well as a reference to possible DFE propagation by shear heating instabilities; “transformational faulting events nucleated in the MOW according to the model described above may propagate outside the MOW by other mechanisms, such as shear heating instabilities [19].”

 

• Coincidence is not the same as causality. The fact that acoustic emissions, faulting, and failure all coexist does not prove which one is the cause.  I am not convinced that we observe 'transformational faulting' in this data.

These comments are surprising and a bit baffling. In case there was a lack of clarity in the way the results were presented, we added a sentence regarding the degree of transformation at the beginning of the results section 3.1., so that mechanical and acoustic data can be related to the kinetics olivine-ringwoodite transformation. We also added a statement to clarify this issue by summarizing the mechanical and acoustic part of the results at the end of section 3.1.3.

In fact, not only does transformational faulting present compelling evidence in the present data set, it was also predicted to occur under these temperature and strain rate conditions by previous studies (Burnley et al., 1991; Schubnel et al., 2013). In a separate study, in press at Geology, we confirmed that transformational faulting occurs under a propitious ratio between transformation rate (controlled by temperature) and strain rate; see figure below. The main result from this figure is that the transformational faulting window corresponds to a slope of 1 in this log-log plot and that transformational faulting is observed here at transformation and strain rates both ~1000 times lower than for some of Burnley’s 1991 data. This concept is already summarized in Figure 17 and detailed in section 4.1. Transformational faulting was therefore expected in the present experiments. As pointed out by the reviewer, some of the experiments in our intermediate temperature range (600-700°C) show the “coincidence”, i.e., the concomitant occurrence, of faulting and AEs, characteristic of dynamic fault propagation; and most importantly a lack of ductility. It is not the case in the high temperature experiments where the samples are fully reacted (~840°C), nor is it the case at the lowest temperature where reaction is inhibited (~500°C). This is well illustrated by the results in figures 4 and 5. These mechanical and acoustic data together are a strong indication that it is the transformation that causes brittleness, faulting and results in large numerous AEs in the temperature range where kinetics are favorable, again as predicted by transformation-induced faulting theory.

     In addition, the microstructures show major evidence of faulting resulting from the unstable self-sustained of growth transforming regions in the intermediate temperature range. So, regarding the “causality”, there are actually entire paragraphs dedicated to it. Section 3.2.2 details the intimate relations found between transformation and strain localization, which go hand in hand in these samples. The analysis of AEs that follows in section 3.3 then shows that it is these growing spear-shaped regions that generate AEs, i.e., their growth is seismogenic. Finally, the model developed in the discussion (4.2.1) explains the causality (Figure 18). In short, the transformation first creates a weaker region that localizes shear strain and generates stress concentrations. Because of latent heat release the transformation is then boosted around this nucleus and proceeds preferentially where stress concentrations occur. The transforming region then evolves to sharper shapes due to feedbacks between stress and heat release. This results in an unstable growth that leads to dynamic rupture propagation. All of this is already detailed in the manuscript.

What does similar studies look like if spinel is the starting material?  Are there still AE?  Is there brittle failure? 

     Strictly speaking, no deformation experiments were performed on Ge-spinel as a starting material. But it is interesting to note that for experiments G15 and G43 kinetics were fast enough so that for most of the deformation Ge-spinel was the main constituent of these samples. These samples yielded either small AEs or none and deformed in a ductile way.

The differential stress often equals or exceeds the pressure.  Surely, such conditions are not happening at 400 km depth.  How does this affect the conclusions?

                It is true that samples deformed at such high stress are not representative of Earth conditions. However, the aim of the present work is to learn from the notable differences observed during deformation and eventual failure of the samples (as opposed to studies trying to establish constitutive flow laws of minerals, for instance). The fact that samples in the 500-700°C range become more brittle and generate more AEs with increasing temperature and decreasing strain rate is a very important result that helps us understand the complex relations between transformation, strain localization and faulting. A couple of sentences were added to acknowledge this in the discussion in section 4.1.

 

It is all too easy to take our favorite model and use it to interpret all observations.  For example, the author claims that the reduction of seismicity at 350 km indicates the end of one mechanism and the beginning of a new one.  However, Mohiuddin and Karato show that the flow law in the mixed phase region indicates a dramatic decrease in strength.  Panasyuk, S. V., and B. H. Hager (1998) indicate a model with significant strength reduction in mixed phase regions. 

                We are aware that the olivine-spinel phase transformation can induce a dramatic weakening. This was already mentioned in the introduction where the Mohiuddin reference used here was already cited. We have added the Panasyuk and Hager 1998 reference. These studies address the expected strength loss due to the phase transformation. However this transformation cannot be responsible for the “reduction of seismicity” mentioned by the reviewer for the reason that it does not simply occur “at 350 km” but is rather a continuous decreasing trend from lithospheric depths, as illustrated below by the figure from Zhan’s 2020 recent review. In fact, for most slabs by 300 km depth, seismicity has already almost shut down and does not reappear in the transition zone. Therefore, the olivine-spinel transformation cannot explain this seismicity reduction as it does not occur until depths of ~ 350 km, even for the coldest slabs where the olivine-spinel equilibrium is deflected towards shallower depths.

Thus, maybe the reduction of seismicity is caused by the drop in ambient stress due to the relaxation by the phase transition.  Once the transformation is complete, then the old mechanisms ramp up the seismicity.

The reviewer implies here that transformation induces weakening and that weakening necessarily results in aseismic deformation. In that case, DFEs in the transition zone would only occur in fully transformed ringwoodite mantle.

This is only true at the (small) scale of the transformed weakened region but at the larger scale, this stress relaxation implies stress enhancement on the adjacent –still strong– untransformed regions. Our study, confirms indeed that stress relaxation occurs during the transformation. However this mechanical weakening is absolutely compatible with brittle behavior and faulting. In section 4.2.1, the transforming regions that result in faulting and AEs are characterized as follows: “The locally enhanced kinetics attest of a relation between transformation, mechanical weakening and AEs.” “these transformation shear bands […] induce weakening due to the fine-grained reaction products partly constituting them”

Regions where this weakening occurs may be small and trigger failure in adjacent material similar to what has been suggested in Ferrand et al.’s (2017) study regarding serpentinite dehydration: “dynamic shear failure occurs primarily in strong olivine sub-volumes surrounded by weak, dehydrating antigorite clusters”

What our results suggest is that in most slabs, weakening accompanies the transformation without any earthquakes and strain probably localizes along ductile shear zones (our high-temperature samples are analogs to this scenario). However, in some “cold” slabs , i.e., with high thermal parameter, this weakening that first occurs locally at small scales propagates in an unstable way that leads to dynamic fault propagation at larger scales.

Author Response File: Author Response.pdf