Cross-diffusion waves resulting from multiscale, multiphysics instabilities: application to earthquakes

Regenauer-Lieb, Klaus; Hu, Manman; Schrank, Christoph; Chen, Xiao; Clavijo, Santiago Peña; Kelka, Ulrich; Karrech, Ali; Gaede, Oliver; Blach, Tomasz; Roshan, Hamid; Jacquey, Antoine B.; Szymczak, Piotr; Sun, Qingpei

doi:https://doi.org/10.5194/se-12-1829-2021

Articles | Volume 12, issue 8

https://doi.org/10.5194/se-12-1829-2021

© Author(s) 2021. This work is distributed under
the Creative Commons Attribution 4.0 License.

Special issue:

Thermo-hydro-mechanical–chemical (THMC) processes in natural...

https://doi.org/10.5194/se-12-1829-2021

© Author(s) 2021. This work is distributed under
the Creative Commons Attribution 4.0 License.

Articles | Volume 12, issue 8

Research article

|

16 Aug 2021

Research article |

| 16 Aug 2021

Cross-diffusion waves resulting from multiscale, multiphysics instabilities: application to earthquakes

Klaus Regenauer-Lieb, Manman Hu, Christoph Schrank, Xiao Chen, Santiago Peña Clavijo, Ulrich Kelka, Ali Karrech, Oliver Gaede, Tomasz Blach, Hamid Roshan, Antoine B. Jacquey, Piotr Szymczak, and Qingpei Sun

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Final revised paper (published on 16 Aug 2021)
Preprint (discussion started on 29 Sep 2020)

Interactive discussion

Status: closed

AC: Author comment | RC: Referee comment | SC: Short comment | EC: Editor comment

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RC1: 'Comment to “Cross-diffusion waves as a trigger fo multiscale, multiphysics instabilities: Applications to earthquakes” by Regenauer-Lieb et al.', Angelo De Santis, 08 Mar 2021
- AC1: 'Reply on RC2', Klaus Regenauer-Lieb, 19 May 2021
RC2: 'Review 2', Anonymous Referee #2, 10 May 2021
- AC1: 'Reply on RC2', Klaus Regenauer-Lieb, 19 May 2021

Peer-review completion

AR: Author's response | RR: Referee report | ED: Editor decision

AR by Klaus Regenauer-Lieb on behalf of the Authors (20 May 2021) Author's response Author's tracked changes Manuscript

ED: Referee Nomination & Report Request started (20 May 2021) by Andre R. Niemeijer

RR by Anonymous Referee #3 (13 Jun 2021)

Suggestions for revision or reasons for rejection

GENERAL COMMENTS
This contribution builds on the Part I companion paper and applies the theory developed there to develop a new generic approach for illuminating the role that coupled THMC processes may play in triggering earthquake rupture (shear) instability through the generation of spatially and temporally organized spikes in field variables such as pore fluid pressure. The wider applications go far beyond the case of earthquake triggering, as complex THMC coupling and feedback processes, operating on different characteristic length and time scales, are clearly evident in the multiscale self-organization and self-similarity seen in geological structures and in geophysical observations. Since the approach followed is so fundamental, it is inevitable that the paper is rather generic in nature and that significant introductory/didactic material has to be presented. Nonetheless, I feel that the authors have responded very effectively to the criticisms levelled in the first round of the review procedure and have successfully focused the paper down more specifically on application to earthquake instability. I found the paper, along with Part I, a fascinating read, and am encouraged to see how the authors and their co-workers are exploring the exceedingly challenging topic of reaction-diffusion processes and Onsager-type cross-coupling between the corresponding thermodynamic force-flux relations. The paper will be quite abstract and unfamiliar for many readers. However, it is based on sound physical principles, is well explained, well-referenced and well-structured. It should be welcomed into the literature as providing a new and inspirational basis for quantitatively exploring the complexity of geological and geophysical reality. In my judgement, the manuscript is acceptable for publication, though I would suggest a few minor revisions for the sake of clarity and completeness, as detailed below. No further review is needed in my opinion.

DETAILED SUGGESTIONS
A) Abstract, line 11. “a rogue wave would appear as a sudden fluid pressure spike on the future fault plane”. This suggests that only faulting of intact rock is important or considered here, which is not the case. Best reformulate “future fault plane” to make clear that such a spike is most likely to trigger unstable slip on a pre-existing (near-critically stressed) fault. This might be worth emphasizing in the main body of the article also.
B) Lines 15-16. “Although the paper is formulated for earth sciences the approach constitutes a generic theory for any material and therefore lacks experimental evidence.” I do not see how this follows. Surely, the more general a theory is the more likely it would be that someone has found evidence for expression of some aspect of it. Perhaps drop the last 5 words? The issue of experimental evidence/validation is dealt with later, after all.
C) Lines 38-39. “The particles are subject to a pressure exerted by the solid matrix and the pressure of
the pore fluid”. Does this mean that only the hydrostatic component of (effective) stress supported by the solid is considered in the analysis? In general, deviatoric stresses would be accounted for too, of course, but if that is the case here, would it not be better to replace “pressure exerted by the solid matrix” with something like ‘thermodynamic force exerted by the stress supported by the solid matrix’?
D) Lines 179-183. I fully agree with the statement that is made here. However, I would advise adding a short qualifier making it clear that “initial” material and environmental heterogeneities at multiple scales, will tend to complicate the picture.
E) Lines 189-194. Quite a number of papers have been published on the structure and slip/seismogenic behaviour of faults in carbonate rocks, in nature and experiment, based on (quantitative) considerations of crystal plastic, diffusive and “superplastic” deformation mechanisms – and considering/reporting decarbonation more qualitatively. The recent papers by the Durham (e.g. De Paola 2015) and Utrecht (Chen, Verberne) groups come to mind, for example, as well as the somewhat broader work in a more rate-and-state framework by Aharanov and Scholtz. These mostly focus on feedback between shear/frictional heating and the above deformation (or asperity contact) mechanisms, rather than coupled reaction-diffusion in the present sense. Perhaps it is worth mentioning that the present type of model is not the only way of explaining localized fault structures in carbonates, or indicating how the approaches differ.
F) Line 331. What is meant here by “effective stress weakens”? Are the authors referring to a decrease in the effective (mean?) stress supported, i.e. to some measure of strength?
G) Lines 434-435. “In geomechanical laboratory experiments the solid matrix is known to respond to external forces by a nonlinear reaction commonly expressed in a power law”. Presumably a rheological law (power law creep) can be treated in the same way as a reaction rate description in the present treatment. Both are dissipative kinetic processes, of course, but it might be useful to clarify briefly whether both can be treated equivalently.
H) Equations 12. It would be helpful to many readers, I think, if a couple of lines could be added here to clarify what physical/chemical conditions the chosen parameters imply.

Referee Report: PDF

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ED: Publish subject to minor revisions (review by editor) (13 Jun 2021) by Andre R. Niemeijer

AR by Klaus Regenauer-Lieb on behalf of the Authors (14 Jun 2021) Author's response Author's tracked changes Manuscript

ED: Publish as is (15 Jun 2021) by Andre R. Niemeijer

ED: Publish as is (16 Jun 2021) by Susanne Buiter (Executive editor)

AR by Klaus Regenauer-Lieb on behalf of the Authors (17 Jun 2021) Manuscript

Short summary

This paper presents a trans-disciplinary approach bridging the gap between observations of instabilities from the molecular scale to the very large scale. We show that all scales communicate via propagation of volumetric deformation waves. Similar phenomena are encountered in quantum optics where wave collisions can release sporadic bursts of light. Ocean waves show a similar phenomenon of rogue waves that seem to come from nowhere. This mechanism is proposed to be the trigger for earthquakes.