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.
the Creative Commons Attribution 4.0 License.
https://doi.org/10.5194/se-12-1829-2021
© Author(s) 2021. This work is distributed under
the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
Research article
| 
16 Aug 2021
Research article |
| 16 Aug 2021
| 16 Aug 2021
Cross-diffusion waves resulting from multiscale, multiphysics instabilities: application to earthquakes
School of Minerals and Energy Resources Engineering, UNSW, Sydney, NSW 2052, Australia
Manman Hu
Department of Civil Engineering, The University of Hong Kong, Hong Kong
Christoph Schrank
Science and Engineering Faculty, Queensland University of Technology, Brisbane, QLD 4001, Australia
Xiao Chen
School of Minerals and Energy Resources Engineering, UNSW, Sydney, NSW 2052, Australia
Santiago Peña Clavijo
School of Minerals and Energy Resources Engineering, UNSW, Sydney, NSW 2052, Australia
Ulrich Kelka
CSIRO, Deep Earth Imaging FSP, Kensington, Australia
Ali Karrech
School of Engineering, University of Western Australia, Crawley, WA 6009, Australia
Oliver Gaede
Science and Engineering Faculty, Queensland University of Technology, Brisbane, QLD 4001, Australia
Tomasz Blach
School of Minerals and Energy Resources Engineering, UNSW, Sydney, NSW 2052, Australia
Hamid Roshan
School of Minerals and Energy Resources Engineering, UNSW, Sydney, NSW 2052, Australia
Antoine B. Jacquey
Department of Civil and Environmental Engineering, Massachusetts Institute of Technology, Cambridge, MA, USA
Piotr Szymczak
Institute of Theoretical Physics, Faculty of Physics, University of Warsaw, Warsaw, Poland
Qingpei Sun
Department of Civil Engineering, The University of Hong Kong, Hong Kong
Related authors
Klaus Regenauer-Lieb, Manman Hu, Christoph Schrank, Xiao Chen, Santiago Peña Clavijo, Ulrich Kelka, Ali Karrech, Oliver Gaede, Tomasz Blach, Hamid Roshan, and Antoine B. Jacquey
Solid Earth, 12, 869–883, https://doi.org/10.5194/se-12-869-2021, https://doi.org/10.5194/se-12-869-2021, 2021
Short summary
Short summary
In this paper we expand on a recent discovery of slow cross-diffusion hydromechanical waves cast into a new concise reaction–diffusion equation for THMC coupling. If waves are excited through the THMC reaction terms unbounded reactions can be captured by inclusion of statistical information from the lower scale through nonlocal reaction–diffusion equations. These cross-diffusion coefficients regularize extreme earthquake-like events (rogue waves) through a new form of quasi-soliton wave.
Kathryn E. Elphick, Craig R. Sloss, Klaus Regenauer-Lieb, and Christoph E. Schrank
Solid Earth, 12, 141–170, https://doi.org/10.5194/se-12-141-2021, https://doi.org/10.5194/se-12-141-2021, 2021
Short summary
Short summary
We analysed a sedimentary rock package located in Castlepoint, New Zealand, to test the control of the tectonic setting on the observed deformation structures. In extension and contraction, we observed faults and small fault-like structures characterised by complex spatial patterns and a reduction in porosity and grain size compared with the host rock. With these properties, the structures are likely to act as barriers to fluid flow and cause compartmentalisation of the sedimentary sequence.
David Boutelier, Christoph Schrank, and Klaus Regenauer-Lieb
Solid Earth, 10, 1123–1139, https://doi.org/10.5194/se-10-1123-2019, https://doi.org/10.5194/se-10-1123-2019, 2019
Short summary
Short summary
Image correlation techniques have provided new ways to analyse the distribution in space and time of deformation in analogue models of tectonics. Here, we demonstrate how the correlation of successive time-lapse images of a deforming model allows calculating the finite displacements and finite strain tensor. We illustrate, using synthetic images, the ability of the algorithm to produce maps of the finite deformation.
James Gilgannon, Florian Fusseis, Luca Menegon, Klaus Regenauer-Lieb, and Jim Buckman
Solid Earth, 8, 1193–1209, https://doi.org/10.5194/se-8-1193-2017, https://doi.org/10.5194/se-8-1193-2017, 2017
Short summary
Short summary
We examine rocks from the middle crust to explore how fluids circulate and influence a rock’s response to larger-scale tectonic movements. A model is developed in which fluids deep in the Earth migrate to clusters of pores generated during those movements. We document how distinct pores form in a specific order in association with local changes in how quartz deforms. The porosity evolves out of the deformation, changing the rate the rock moved under tectonic forces.
Roi Roded, Einat Aharonov, Piotr Szymczak, Manolis Veveakis, Boaz Lazar, and Laura E. Dalton
Hydrol. Earth Syst. Sci. Discuss., https://doi.org/10.5194/hess-2023-307, https://doi.org/10.5194/hess-2023-307, 2024
Preprint under review for HESS
Short summary
Short summary
Common practices in water resources management and geothermal applications involve the injection of hot or cold water into aquifers. The resulting thermal changes may lead to chemical disequilibrium and consequent mineral dissolution/precipitation in the rock void-space. A mathematical model is developed to study the effects of such thermal-fluid injection on the evolution of water composition, aquifer porosity and permeability. The model is then applied to two important case studies.
Ulrich Kelka, Cericia Martinez, Carmen Krapf, Stefan Westerlund, Ignacio Gonzalez-Alvarez, Mark Pawley, and Clive Foss
Solid Earth, 13, 827–847, https://doi.org/10.5194/se-13-827-2022, https://doi.org/10.5194/se-13-827-2022, 2022
Short summary
Short summary
The insights of this study will help to improve our understanding on how to identify basement linear structures and how these lineaments could be related to surface lineaments or geology in the context of the Central Gawler Craton, South Australia. This contribution suggests a targeting concept for identifying the structural footprint of subsurface mineral systems by combining remotely sensed data corresponding to surface and subsurface features.
Klaus Regenauer-Lieb, Manman Hu, Christoph Schrank, Xiao Chen, Santiago Peña Clavijo, Ulrich Kelka, Ali Karrech, Oliver Gaede, Tomasz Blach, Hamid Roshan, and Antoine B. Jacquey
Solid Earth, 12, 869–883, https://doi.org/10.5194/se-12-869-2021, https://doi.org/10.5194/se-12-869-2021, 2021
Short summary
Short summary
In this paper we expand on a recent discovery of slow cross-diffusion hydromechanical waves cast into a new concise reaction–diffusion equation for THMC coupling. If waves are excited through the THMC reaction terms unbounded reactions can be captured by inclusion of statistical information from the lower scale through nonlocal reaction–diffusion equations. These cross-diffusion coefficients regularize extreme earthquake-like events (rogue waves) through a new form of quasi-soliton wave.
Kathryn E. Elphick, Craig R. Sloss, Klaus Regenauer-Lieb, and Christoph E. Schrank
Solid Earth, 12, 141–170, https://doi.org/10.5194/se-12-141-2021, https://doi.org/10.5194/se-12-141-2021, 2021
Short summary
Short summary
We analysed a sedimentary rock package located in Castlepoint, New Zealand, to test the control of the tectonic setting on the observed deformation structures. In extension and contraction, we observed faults and small fault-like structures characterised by complex spatial patterns and a reduction in porosity and grain size compared with the host rock. With these properties, the structures are likely to act as barriers to fluid flow and cause compartmentalisation of the sedimentary sequence.
David Boutelier, Christoph Schrank, and Klaus Regenauer-Lieb
Solid Earth, 10, 1123–1139, https://doi.org/10.5194/se-10-1123-2019, https://doi.org/10.5194/se-10-1123-2019, 2019
Short summary
Short summary
Image correlation techniques have provided new ways to analyse the distribution in space and time of deformation in analogue models of tectonics. Here, we demonstrate how the correlation of successive time-lapse images of a deforming model allows calculating the finite displacements and finite strain tensor. We illustrate, using synthetic images, the ability of the algorithm to produce maps of the finite deformation.
James Gilgannon, Florian Fusseis, Luca Menegon, Klaus Regenauer-Lieb, and Jim Buckman
Solid Earth, 8, 1193–1209, https://doi.org/10.5194/se-8-1193-2017, https://doi.org/10.5194/se-8-1193-2017, 2017
Short summary
Short summary
We examine rocks from the middle crust to explore how fluids circulate and influence a rock’s response to larger-scale tectonic movements. A model is developed in which fluids deep in the Earth migrate to clusters of pores generated during those movements. We document how distinct pores form in a specific order in association with local changes in how quartz deforms. The porosity evolves out of the deformation, changing the rate the rock moved under tectonic forces.
Mauro Cacace and Antoine B. Jacquey
Solid Earth, 8, 921–941, https://doi.org/10.5194/se-8-921-2017, https://doi.org/10.5194/se-8-921-2017, 2017
Short summary
Short summary
The paper describes theory and numerical implementation for coupled thermo–hydraulic–mechanical processes focusing on reservoir (mainly related to geothermal energy) applications.
H. Roshan, M. Young, M. S. Andersen, and R. I. Acworth
Hydrol. Earth Syst. Sci. Discuss., https://doi.org/10.5194/hessd-11-8167-2014, https://doi.org/10.5194/hessd-11-8167-2014, 2014
Manuscript not accepted for further review
Related subject area
Subject area: Tectonic plate interactions, magma genesis, and lithosphere deformation at all scales | Editorial team: Rock deformation, geomorphology, morphotectonics, and paleoseismology | Discipline: Geophysics
Cross-diffusion waves resulting from multiscale, multi-physics instabilities: theory
Klaus Regenauer-Lieb, Manman Hu, Christoph Schrank, Xiao Chen, Santiago Peña Clavijo, Ulrich Kelka, Ali Karrech, Oliver Gaede, Tomasz Blach, Hamid Roshan, and Antoine B. Jacquey
Solid Earth, 12, 869–883, https://doi.org/10.5194/se-12-869-2021, https://doi.org/10.5194/se-12-869-2021, 2021
Short summary
Short summary
In this paper we expand on a recent discovery of slow cross-diffusion hydromechanical waves cast into a new concise reaction–diffusion equation for THMC coupling. If waves are excited through the THMC reaction terms unbounded reactions can be captured by inclusion of statistical information from the lower scale through nonlocal reaction–diffusion equations. These cross-diffusion coefficients regularize extreme earthquake-like events (rogue waves) through a new form of quasi-soliton wave.
Cited articles
Aharonov, E. and Scholz, C. H.: The Brittle–Ductile Transition Predicted by a Physics-Based Friction Law, J. Geophys. Res.-Sol. Ea., 124, 2721–2737, https://doi.org/10.1029/2018JB016878, 2019. a
Aifantis, E. C.: Gradient Extension of Classical Material Models: From Nuclear and Condensed Matter Scales to Earth and Cosmological Scales, Springer Tracts in Mechanical Engineering, 1, 417–452, Springer, Zurich, https://doi.org/10.1007/978-3-030-63050-8_15, 2021. a, b, c
Alevizos, S., Poulet, T., and Veveakis, E.: Thermo-poro-mechanics of chemically active creeping faults. 1: Theory and steady state considerations, J. Geophys. Res.-Sol. Ea., 119, 4558–4582, https://doi.org/10.1002/2013JB010070, 2014. a
Amdreo-Valle, F., Mazon, J., Rossi, D., and Toledo-Molero, J.: Nonlocal Diffusion Processes, Mathematical Surveys and Monographs, 165, American Mathematical Society, Providence, Rhode Island, https://doi.org/10.1090/surv/165, 2010. a
Antonioletti, M., Biktashev, V. N., Jackson, A., Kharche, S. R., Stary, T., and Biktasheva, I. V.: BeatBox – HPC simulation environment for biophysically and anatomically realistic cardiac electrophysiology, PLOS ONE, 12, e0172 292, https://doi.org/10.1371/journal.pone.0172292, 2017. a, b, c, d
Ball, P.: Pattern Formation in Nature: Physical Constraints and Self-Organising Characteristics, Archit. Design, 82, 22–27, https://doi.org/10.1002/ad.1375, 2012. a, b
Balluffi, R. W., Allen, S. M., and Carter, W. C.: Kinetics of Materials, John Wiley & Sons Inc., Hoboken, https://doi.org/10.1002/0471749311, 2005. a
Barraclough, T. W., Blackford, J. R., Liebenstein, S., Sandfeld, S., Stratford, T. J., Weinländer, G., and Zaiser, M.: Propagating compaction bands in confined compression of snow, Nat. Phys., 13, 272–275, https://doi.org/10.1038/nphys3966, 2017. a, b, c
Berenstein, I. and Beta, C.: Spatiotemporal chaos arising from standing waves in a reaction-diffusion system with cross-diffusion, J. Chem. Phys., 136, 034 903, https://doi.org/10.1063/1.3676577, 2012. a, b
Biktashev, V. N. and Tsyganov, M. A.: Quasisolitons in self-diffusive excitable systems, or Why asymmetric diffusivity obeys the Second Law, Sci. Rep., 6, 30 879, https://doi.org/10.1038/srep30879, 2016. a
Brace, W. and Byerlee, J.: Stick-slip as a mechanism for earthquakes, Science, 153, 990–992, 1966. a
Braeck, S. and Podladchikov, Y. Y.: Spontaneous Thermal Runaway as an Ultimate Failure Mechanism of Materials, Phys. Rev. Lett., 98, 095 504, https://doi.org/10.1103/PhysRevLett.98.095504, 2007. a, b
Brechet, Y. and Estrin, Y.: Pseudo-portevin-le châtelier effect in ordered alloys, Scripta Mater., 35, 217–223, https://doi.org/10.1016/1359-6462(96)00126-1, 1996. a
Cavaleri, L., Barbariol, F., Benetazzo, A., Bertotti, L., Bidlot, J.-R., Janssen, P., and Wedi, N.: The Draupner wave: A fresh look and the emerging view, J. Geophys. Res.-Oceans, 121, 6061–6075, https://doi.org/10.1002/2016JC011649, 2016. a, b
Chester, F. M., Rowe, C., Ujiie, K., Kirkpatrick, J., Regalla, C., Remitti, F., Moore, J. C., Toy, V., Wolfson-Schwehr, M., Bose, S., Kameda, J., Mori, J. J., Brodsky, E. E., Eguchi, N., Toczko, S., Expedition 343, and 343T Scientists: Structure and Composition of the Plate-Boundary Slip Zone for the 2011 Tohoku-Oki Earthquake, Science, 342, 1208–1211, https://doi.org/10.1126/science.1243719, 2013. a
Coleman, B. D. and Gurtin, M. E.: Thermodynamics and the Velocity of General Acceleration Waves, in: Wave Propagation in Dissipative Materials, edited by: Coleman, B. D., Gurtin, M. E., Herrera R, I., and Truesdell, C., 83–104, Springer Berlin Heidelberg, 1965. a
Crampin, S. and Gao, Y.: The New Geophysics, Terra Nova, 25, 173–180, https://doi.org/10.1111/ter.12030, 2013. a
Crampin, S. and Gao, Y.: The physics underlying Gutenberg-Richter in the earth and in the moon, J. Earth Sci., 26, 134–139, https://doi.org/10.1007/s12583-015-0513-3, 2015. a, b
Dematteis, G., Grafke, T., Onorato, M., and Vanden-Eijnden, E.: Experimental Evidence of Hydrodynamic Instantons: The Universal Route to Rogue Waves, Phys. Rev. X, 9, 041 057, https://doi.org/10.1103/PhysRevX.9.041057, 2019. a
Di Giacomo, D., Engdahl, E. R., and Storchak, D. A.: The ISC-GEM Earthquake Catalogue (1904–2014): status after the Extension Project, Earth Syst. Sci. Data, 10, 1877–1899, https://doi.org/10.5194/essd-10-1877-2018, 2018. a
Dieterich, J.: Time-dependent friction in rocks., J. Geophys. Res., 377, 3690–3697, 1972. a
Dieterich, J.: Constitutive properties of faults with simulated gouge, in: Mechanical Behavior of Crustal Rocks, Geophys. Monogr. Ser., 24, edited by: Carter, N. L., Friedman, M., Logan, J. M., and Stearns D. W., https://doi.org/10.1029/GM024p0103, 1987. a
Dudley, J. M., Genty, G., Mussot, A., Chabchoub, A., and Dias, F.: Rogue waves and analogies in optics and oceanography, Nature Reviews Physics, 1, 675–689, https://doi.org/10.1038/s42254-019-0100-0, 2019. a
Durrleman, S., Boschetti, F., Ord, A., and Regenauer-Lieb, K.: Automatic detection of particle aggregation in particle code simulations of rock deformation, Geochem. Geophy. Geosy., 7, Q05006, https://doi.org/10.1029/2005GC001063, 2006. a
Eberhard, M., Savojardo, A., Maruta, A., and Römer, R. A.: Rogue wave generation by inelastic quasi-soliton collisions in optical fibres, Opt. Express, 25, 28 086, https://doi.org/10.1364/OE.25.028086, 2017. a, b, c
Einav, I. and Guillard, F.: Tracking time with ricequakes in partially soaked brittle porous media, Science Advances, 4, eaat6961, https://doi.org/10.1126/sciadv.aat6961, 2018. a, b
Elphick, K. E., Sloss, C. R., Regenauer-Lieb, K., and Schrank, C. E.: Distribution, microphysical properties, and tectonic controls of deformation bands in the Miocene subduction wedge (Whakataki Formation) of the Hikurangi subduction zone, Solid Earth, 12, 141–170, https://doi.org/10.5194/se-12-141-2021, 2021. a
Español, P. and Warren, P. B.: Perspective: Dissipative particle dynamics, J. Chem. Phys., 146, 150 901, https://doi.org/10.1063/1.4979514, 2017. a
Estrin, Y. and Kubin, L.: Spatial Coupling and Propagative Plastic Instabilities, 1, 395–450, John Wiley and Sons, United States, 1995. a
Evans, D. and Searle, D.: The fluctuation theorem, Adv. Phys., 51, 1529–1585, 2002. a
Fan, X. and Lin, M.: Multiscale multifractal detrended fluctuation analysis of earthquake magnitude series of Southern California, Physica A, 479, 225–235, https://doi.org/10.1016/j.physa.2017.03.003, 2017. a
Fisher, R. A.: The wave of advance of advantageous genes, Ann. Eugenic., 7, 355–369, https://doi.org/10.1111/j.1469-1809.1937.tb02153.x, 1937. a
Fitzgerald, B. W., Zarghami, A., Mahajan, V. V., Sanjeevi, S. K. P., Mema, I., Verma, V., El Hasadi, Y. M. F., and Padding, J. T.: Multiscale simulation of elongated particles in fluidised beds, Chem. Eng. Sci. X, 2, 100 019, https://doi.org/10.1016/j.cesx.2019.100019, 2019. a
Gomberg, J.: Slow slip phenomena in Cascadia from 2007 and beyond: a review, GSA Bulletin, 122, 963–978, https://doi.org/10.1130/B30287.1, 2010. a
Grigoli, F., Cesca, S., Rinaldi, A. P., Manconi, A., López-Comino, J. A., Clinton, J. F., Westaway, R., Cauzzi, C., Dahm, T., and Wiemer, S.: The November 2017 5.5 Pohang earthquake: A possible case of induced seismicity in South Korea, Science, 360, 1003, https://doi.org/10.1126/science.aat2010, 2018. a
Gu, J., Rice, J. R., Ruina, A. L., and Tse, S. T.: Slip Motion and Stability of a Single Degree of Freedom Elastic System with Rate and State Dependent Friction, J. Mech. Phys. Solids, 32, 167–196, 1984. a
Hanasoge, S., Agarwal, U., Tandon, K., and Koelman, J. M. V. A.: Renormalization group theory outperforms other approaches in statistical comparison between upscaling techniques for porous media, Phys. Rev. E, 96, 033 313, https://doi.org/10.1103/PhysRevE.96.033313, 2017. a, b
Hayward, K. S., Cox, S. F., Fitz Gerald, J. D., Slagmolen, B. J., Shaddock, D. A., Forsyth, P. W., Salmon, M. L., and Hawkins, R. P.: Mechanical amorphization, flash heating, and frictional melting: Dramatic changes to fault surfaces during the first millisecond of earthquake slip, Geology, 44, 1043–1046, https://doi.org/10.1130/g38242.1, 2016. a
Hobbs, B. and Ord, A.: Structural Geology: The Mechanics of Deforming Metamorphic Rocks, Elsevier, Oxford, https://doi.org/10.1016/B978-0-12-407820-8.00015-1, 2015. a
Hobbs, B., Ord, A., and Regenauer-Lieb, K.: The Thermodynamics of deformed metamorphic rocks: A Review, J. Struct. Geol., 33, 758–818, 2011. a
Hu, M., Veveakis, M., Poulet, T., and Regenauer-Lieb, K.: The Role of Temperature in Shear Instability and Bifurcation of Internally Pressurized Deep Boreholes, Rock Mech. Rock Eng., 50, 3003–3017, https://doi.org/10.1007/s00603-017-1291-2, 2017. a
Kanamori, H. and Brodsky, E. E.: The physics of earthquakes, Phys. Today, 54, 34–40, 2001. a
Kanamori, H., Anderson, D. L., and Heaton, T. H.: Frictional melting during the rupture of the 1994 Bolivian earthquake, Science, 279, 839–842, 1998. a
Kohlstedt, D. and Holtzman, B.: Shearing Melt out of the Earth: An Experimentalist's Perspective on the Influence of Deformation on Melt Extraction, Annu. Rev. Earth Pl. Sc., 37, 561–593, https://doi.org/10.1146/annurev.earth.031208.100104, 2009. a
Kondepudi, D. and Prigogine, I.: Modern Thermodynamics: From Heat Engines to Dissipative Structures, John Wiley and Sons, Chichester, 1998. a
Koronovsky, N. V., Zakharov, V. S., and Naimark, A. A.: Short-Term Earthquake Prediction: Reality, Research Promise, or a Phantom Project?, Moscow University Geology Bulletin, 74, 333–341, https://doi.org/10.3103/S0145875219040057, 2019. a, b
Luther, R.: Propagation of chemical reactions in space, J. Chem. Educ., 64, 740, https://doi.org/10.1021/ed064p740, 1987. a
Lyakhovsky, V., Zhu, W., and Shalev, E.: Visco-poroelastic damage model for brittle-ductile failure of porous rocks, J. Geophys. Res.-Sol. Ea., 120, 2179–2199, https://doi.org/10.1002/2014JB011805, 2015. a
Manning, J. R.: Cross terms in the thermodynamic diffusion equations for multicomponent alloys, Metall. Mater. Trans. B, 1, 499–505, https://doi.org/10.1007/BF02811561, 1970. a
Masuda, T., Akimoto, A. M., and Yoshida, R.: 5.1 – Self-Oscillating Polymer Materials, 219–236, William Andrew Publishing, Norwich , https://doi.org/10.1016/B978-0-323-37127-8.00013-3, 2016. a
Maugin, G. and Muschik, W.: Thermodynamics with internal variables, vol. WSS Nonlin. Sci. Ser. A, 27, 77–105, https://doi.org/10.1142/9789812796271_0004, 1999. a
Molotkov, I. A. and Vakulenko, S. A.: Autowave propagation for general reaction diffusion systems, Wave Motion, 17, 255–266, https://doi.org/10.1016/0165-2125(93)90005-Z, 1993. a, b, c
Monneau, R. and Patrizi, S.: Homogenization of the Peierls–Nabarro model for dislocation dynamics, J. Differ. Equations, 253, 2064–2105, https://doi.org/10.1016/j.jde.2012.06.019, 2012. a
Obara, K.: Nonvolcanic deep tremor associated with subduction in southwest Japan, Science, 296, 1679–1681, 2002. a
Oberst, S., Niven, R. K., Lester, D. R., Ord, A., Hobbs, B., and Hoffmann, N.: Detection of unstable periodic orbits in mineralising geological systems, Chaos, 28, 085 711, https://doi.org/10.1063/1.5024134, 2018. a
Ohnaka, M.: A constitutive scaling law and a unified comprehension for frictional slip failure, shear fracture of intact rock, and earthquake rupture, J. Geophys. Res.-Sol. Ea., 108, ESE 6–21, https://doi.org/10.1029/2000JB000123, 2003. a, b, c
Ohtani, M., Kame, N., and Nakatani, M.: Synchronization of megathrust earthquakes to periodic slow slip events in a single-degree-of-freedom spring-slider model, Sci. Rep., 9, 8285, https://doi.org/10.1038/s41598-019-44684-4, 2019. a
Ostoja-Starzewski, M.: Microstructural Randomness and Scaling in Mechanics of Materials, Chapman & Hall/CRC, London, New York, 2008. a
Paschotta, R.: Quasi-Soliton pulses, Wiley-VCH, 1st edition, Hoboken, 2008. a
Peregrine, D. H.: Water waves, nonlinear Schrödinger equations and their solutions, J. Aust. Math. Soc. B, 25, 16–43, https://doi.org/10.1017/S0334270000003891, 1983. a, b
Perzyna, P.: Fundamental problems in viscoplasticity, Adv. Appl. Mech., 9, 243–377, 1966. a
Poulet, T., Veveakis, E., Herwegh, M., Buckingham, T., and Regenauer-Lieb, K.: Modeling episodic fluid-release events in the ductile carbonates of the Glarus thrust, Geophys. Res. Lett., 41, 7121–7128, 2014a. a
Poulet, T., Veveakis, E., Regenauer-Lieb, K., and Yuen, D. A.: Thermo-poro-mechanics of chemically active creeping faults: 3. The role of serpentinite in episodic tremor and slip sequences, and transition to chaos, J. Geophys. Res.-Sol. Ea., 119, 4606–4625, https://doi.org/10.1002/2014JB011004, 2014b. a, b, c, d, e, f
Regenauer-Lieb, K., Veveakis, M., Poulet, T., Wellmann, F., Karrech, A., Liu, J., Hauser, J., Schrank, C., Gaede, O., and Fusseis, F.: Multiscale coupling and multiphysics approaches in earth sciences: Applications, Journal of Coupled Systems and Multiscale Dynamics, 1, 2330–152X/2013/001/042, https://doi.org/10.1166/jcsmd.2013.1021, 2013a. a, b, c
Regenauer-Lieb, K., Veveakis, M., Poulet, T., Wellmann, F., Karrech, A., Liu, J., Hauser, J., Schrank, C., Gaede, O., and Trefry, M.: Multiscale coupling and multiphysics approaches in Earth sciences: theory, Journal of Coupled Systems and Multiscale Dynamics, 1, 2330–152X, https://doi.org/10.1166/jcsmd.2013.1012, 2013b. a
Regenauer-Lieb, K., Hu, M., Schrank, C., Chen, X., Clavijo, S. P., Kelka, U., Karrech, A., Gaede, O., Blach, T., Roshan, H., and Jacquey, A. B.: Cross-diffusion waves resulting from multiscale, multi-physics instabilities: theory, Solid Earth, 12, 869–883, https://doi.org/10.5194/se-12-869-2021, 2021. a, b, c, d, e, f, g, h, i, j, k, l, m, n, o, p, q, r, s, t, u, v, w, x, y
Rice, J. R.: Heating and weakening of faults during earthquake slip, J. Geophys. Res., 111, B05311, https://doi.org/10.1029/2005JB004006, 2006. a, b
Rice, J. R., Lapusta, N., and Ranjith, K.: Rate and state dependent friction and the stability of sliding between elastically deformable solids, J. Mech. Phys. Solids, 49, 1865–1898, 2001. a
Rubinstein, J. and Sternberg, P.: Nonlocal reaction–diffusion equations and nucleation, IMA J. Appl. Math., 48, 249–264, https://doi.org/10.1093/imamat/48.3.249, 1992. a
Ruina, A.: Slip instability and state variable friction laws., J. Geophys. Res., 88, 10359–10370, 1983. a
Schulz, S. E. and Evans, J. P.: Mesoscopic structure of the Punchbowl Fault, Southern California and the geologic and geophysical structure of active strike-slip faults, J. Struct. Geol., 22, 913–930, https://doi.org/10.1016/S0191-8141(00)00019-5, 2000. a
Sethna, J. P.: Statistical Mechanics: Entropy, Order Parameters and Complexity, Oxford University Press, Great Clarendon Street, Oxford OX2 6DP, first edition, 2006a. a
Sethna, J. P., Dahmen, K. A., and Myers, C. R.: Crackling noise, Nature, 410, 242–250, 2001. a
Shaar, M. and Ghavanloo, E.: Nonlocal Mechanics in the Framework of the General Nonlocal Theory, Springer Tracts in Mechanical Engineering, 1, 95–122, Springer, Zürich, https://doi.org/10.1007/978-3-030-63050-8_3, 2021. a
Shrira, V. I. and Geogjaev, V. V.: What makes the Peregrine soliton so special as a prototype of freak waves?, J. Eng. Math., 67, 11–22, https://doi.org/10.1007/s10665-009-9347-2, 2010. a
Solli, D. R., Ropers, C., Koonath, P., and Jalali, B.: Optical rogue waves, Nature, 450, 1054, https://doi.org/10.1038/nature06402, 2007. a
Sornette, D.: Earthquakes: from chemical alteration to mechanical rupture, Phys. Rep., 313, 238–291, 1999. a
Sornette, D. and Ouillon, G.: Multifractal scaling of thermally activated rupture processes, Phys. Rev. Lett., 94, 038501, https://doi.org/10.1103/PhysRevLett.94.038501, 2005. a, b
Sornette, D. and Pisarenko, V.: Fractal plate tectonics, Geophys. Res. Lett., 30, 1105, https://doi.org/10.1029/2002GL015043, 2003. a
Stanley, H. E. and Meakin, P.: Multifractal phenomena in physics and chemistry, Nature, 335, 405–409, https://doi.org/10.1038/335405a0, 1988. a
Storchak, D. A., Di Giacomo, D., Bondára, I., Engdahl, E. R., Harris, J., Lee, W. H. K., Villaseñor, A., and Bormann, P.: Public release of the ISC-GEM Global Instrumental Earthquake Catalogue (1900-2009), Seismol. Res. Lett., 84, 810–815, https://doi.org/10.1785/0220130034, 2013. a
Storchak, D. A., Di Giacomo, D., Engdahl, E. R., Harris, J., Bondár, I., Lee, W. H. K., Bormann, P., and Villaseñor, A.: The ISC-GEM Global Instrumental Earthquake Catalogue (1900–2009): Introduction, Phys. Earth Planet. In., 239, 48–63, https://doi.org/10.1016/j.pepi.2014.06.009, 2015. a
Sun, Q. and Manman, M.: Animation of Figure 6, available at: https://tinyurl.com/sz783szy, last access: 30 July 2021. a
Sun, Q., Hu, M., and Regenauer-Lieb, K.: FDM simulation of Turing-, Hopf-, Quasi-soliton instabilities, Mendeley Data [code], v2 https://doi.org/10.17632/9mkcsbk78x.2, 2021a. a
Towers, I. and Jovanoski, Z.: Application of rational Chebyshev polynomials to optical problems, ANZIAM J., 50, 60–74, https://doi.org/10.21914/anziamj.v50i0.1396, 2008. a
Tse, S. T. and Rice, J. R.: Crustal Earthquake Instability in Relation to the Depth Variation of Frictional Slip Properties, J. Geophys. Res.-Solid, 91, 9452–9472, 1986. a
Tsyganov, M. A. and Biktashev, V. N.: Classification of wave regimes in excitable systems with linear cross diffusion, Phys. Rev. E, 90, 062912, https://doi.org/10.1103/PhysRevE.90.062912, 2014. a, b, c
Tsyganov, M. A., Biktashev, V. N., Brindley, J., Holden, A. V., and Genrikh, R. I.: Waves in systems with cross-diffusion as a new class of nonlinear waves, Physics-Usp+, 50, 263, https://doi.org/10.1070/pu2007v050n03abeh006114, 2007. a
Turiel, A., Pérez-Vicente, C. J., and Grazzini, J.: Numerical methods for the estimation of multifractal singularity spectra on sampled data: A comparative study, J. Comput. Phys., 216, 362–390, https://doi.org/10.1016/j.jcp.2005.12.004, 2006. a, b
Vanag, V. K. and Epstein, I. R.: Cross-diffusion and pattern formation in reaction–diffusion systems, Phys. Chem. Chem. Phys., 11, 897–912, https://doi.org/10.1039/B813825G, 2009. a, b, c
Vardoulakis, I.: Thermo-poro-mechanics of rapid fault shearing, pp. 63–74, Springer Berlin Heidelberg, Berlin, Heidelberg, https://doi.org/10.1007/3-540-44424-6_5, 2001. a, b, c
Vasil'ev, V. A.: Autowave processes in distributed kinetic systems, Sov. Phys. Uspekhi, 22, 615–639, https://doi.org/10.1070/PU1979v022n08ABEH005591, 1979. a
Veveakis, E., Poulet, T., and Alevizos, S.: Thermo-poro-mechanics of chemically active creeping faults: 2. Transient considerations, J. Geophys. Res.-Sol. Ea., 119, 4583–4605, https://doi.org/10.1002/2013JB010071, 2014. a
Ward, C. B., Kevrekidis, P. G., and Whitaker, N.: Evaluating the robustness of rogue waves under perturbations, Phys. Lett. A, 383, 2584–2588, https://doi.org/10.1016/j.physleta.2019.05.030, 2019. a
Wiemer, S. and Wyss, M.: Mapping the frequency-magnitude distribution in asperities: An improved technique to calculate recurrence times?, J. Geophys. Res.-Sol. Ea., 102, 15115–15128, 1997. a
Yang, J.: Nonlinear Waves in Integrable and Non-integrable Systems, Society for Industrial and Applied Mathematics, USA, 2010. a
Zaiser, M. and Hähner, P.: Oscillatory Modes of Plastic Deformation: Theoretical Concepts, Phys. Status solidi B, 199, 267–330, https://doi.org/10.1002/1521-3951(199702)199:2<267::AID-PSSB267>3.0.CO;2-Q, 1997. a, b, c, d
Zakharov, V., Dias, F., and Pushkarev, A.: One-dimensional wave turbulence, Phys. Rep., 398, 1–65, https://doi.org/10.1016/j.physrep.2004.04.002, 2004. a, b
Zuev, L. and Barannikova, S.: Plastic Flow Macrolocalization: Autowave and Quasi-Particle, Journal of Modern Physics, 1, 1–8, https://doi.org/10.4236/jmp.2010.11001, 2010. a, b
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.
This paper presents a trans-disciplinary approach bridging the gap between observations of...
