Complex systems in geophysics: methods of research and prediction of their behavior

Authors

  • Serhiy Mykulyak S.I. Subbotin Institute of Geophysics, National Academy of Sciences of Ukraine, Kiev, Ukraine, Ukraine

DOI:

https://doi.org/10.24028/gj.v47i1.312874

Keywords:

complex system, earthquake, forecasting, artificial intelligence, neural networks

Abstract

Many natural and man-made systems have recently been considered and studied from the perspective of complex systems. Complex systems are systems formed by a large number of components that interact with each other, usually nonlinearly. As they evolve, complex systems can self-organize and acquire fundamentally new properties not inherent to the constituents.

This review focuses on geosystems, which are natural complex systems. Most part of the article highlight the properties of such complex geosystems as seismically active areas. Itconsiders the criteria by which systems can be classified as complex, their main properties, and possible methods of studying and predicting their behavior. The review analyzes various models for climate forecasts and models that describe seismic processes originating from the complex behavior of lithospheric subsystems (seismically active zones). Most phenomenological regularities that describe the statistical properties of earthquakes are large-scale, indicating the complexity of this system. Forecasting earthquakes remains the most important task for seismological research despite rather modest achievements. The intensity of research in this direction does not decrease, since the consequences of earthquakes for humanity are significant. The types of forecasts and models used for forecasting are analyzed. Special attention is paid to modern forecasting methods that use artificial intelligence. Various approaches for forecasting seismic events, their advantages, and disadvantages,as well as the difficulties that arise in forecasting tasks, are described. The science of complex systems is rapidly developing and it has great prospects for acquiring one of the most important tools for studying the surrounding natural environment and man-made artificial systems.

References

Aghdam, H.H., & Herav, E.J. (2017). Guide to convolutional neural networks. New York,

NY: Springer. https://doi.org/10.1007/978-3-319-57550-6.

Aminzadeh, F., Katz, S., & Aki, K. (1994). Adaptive neural nets for generation of artificial earthquake precursors. IEEE Transactions on Geoscience and Remote Sensing, 32(6), 1139—1143. https://doi.org/10.1109/36.338361.

Anderson, E.M. (1905). The dynamics of faulting. Transactions of Edinburgh Geoljgical Society, 8, 387—340.

Anthony, J.L. (2005). Influence of particle characteristics on granular friction. Journal of Geophysical Research: Solid Earth, 110(B8). https://doi.org/10.1029/2004jb003399.

Asim, K.M., Martínez-Álvarez, F., Basit, A., & Iqbal, T. (2017). Earthquakemagnitude prediction in Hindukush region using machine learning techniques. Natural Hazards, 85(1), 471—486. https://doi.org/10.1007/s11069-016-2579-3.

Asim, K.M., Moustafa, S.S., Niaz, I.A., Elawadi, E.A., Iqbal, T., & Martínez-Álvarez, F. (2020). Seismicity analysis and machine learning models for short-term low magnitude seismic activity predictions in Cyprus. Soil Dynamics and Earthquake Engineering, 130, 105932. https://doi.org/:10.1016/j.soildyn. 2019.105932.

Astuti, W., Akmeliawati, R., Sediono, W., & Salami, M.J.E. (2014). Hybrid technique using singular value decomposition (SVD) and support vector machine (SVM) approach for earthquake prediction. IEEE Journal of Selected Topics in Applied Earth Observations and Remote Sensing, 7(5), 1719―1728. https://doi.org/10.1109/JSTARS.2014.2321972.

Bach, B., Wissel, F., & Drossel, B. (2008). Olami-Feder-Christensen model with quenched disorder. Physical Review E, 77, 067101. https://doi.org/10.1103/PhysRevE.77.067101.

Baiesi, M. (2009). Correlated earthquakes in a self-organized model. Nonlinear Processes in Geophysics,16, 233—240. https://doi.org/10. 5194/npg-16-233-2009.

Bak, P., Tang, C., & Wiesenfeld, K. (1988). Self-organized criticality. Physical Review A, 38(1), 364—374. https://doi.org/10.1103/Phys RevA.38.364.

Bak, P., Christensen, K., Danon, L., & Scanlon, T.(2002).Unified scaling law for earthquakes. Physical Review Letters, 88(17), 178501. https://doi.org/10.1073/pnas.01258109.

Bakun, W.H., Aagaard, B., Dost, B., Ellsworth, W.L., Hardebeck, J.L., Harris, R.A., Ji, C., Johnston, M.J.S., Langbein, J., Lienkaemper, J.J., Michael, A.J., Murray, J.R., Nadeau, R.M., Reasenberg, P.A., Reichle, M.S., Roeloffs, E.A., Shakal, A., Simpson, R.W., & Waldhauser, F. (2005). Implications for prediction and hazard assessment from the 2004 Parkfield earthquake. Nature, 437, 969—974. https://doi.org/10.1038/nature04067.

Ball, P. (1999). The self-made tapestry: pattern formation in nature. Oxford: Oxford University Press, 296 p.

Banna, M.H.A., Taher, K.A., Kaiser, M.S., Mahmud, M., Rahman, M.S., Hosen, A.S.M.S., & Cho, G.H. (2020). Application of artificial intelligence in predicting earthquakes: state-of-the-art and future challenges. IEEE Access, 8, 192880―192923. https://doi.org/10.1109/ACCESS.2020.3029859.

Barés, J., Wang, D., Wang, D., Bertrand, T., O’Hern, C.S., & Behringer, R.P. (2017). Local and global avalanches in a two-dimensional sheared granular medium. Physical Review E, 96(5), 052902. https://doi.org/10.1103/Phys RevE.96.052902.

Barriere, B., & Turcotte, D.L. (1991). A scale-invariant cellular-automata model for distribited seismicity. Geophysical Research Letters, 18(11), 2011—2014. https://doi.org/10.1029/ 91GL02415.

Barriere, B., & Turcotte, D.L. (1994). Seismicity and self-organized criticality. Physical Review E, 49(2), 1151—1160. https://doi.org/10.1016/S0031-9201(98)00167-8.

Bar-Yam, Y. (2006). Engineering complex systems: multiscale analysis and evolutionary engineering. In D. Braha, A. Minai, Y. Bar-Yam (Eds.), Complex engineered systems. Understanding complex systems (pp. 22―39). Berlin, Heidelberg: Springer. https://doi.org/ 10.1007/3-540-32834-3_2.

Båth, M. (1965). Lateral inhomogeneities of the upper mantle. Tectonophysics, 2(6), 483—514. https://doi.org/10.1016/0040-1951(65)90003-X.

Bennett, C. (1988). Logical depth and physical complexity. In R. Herken, (Ed.). The universal Turing machine, a half-century survey (pp. 227—257). Oxford: Oxford Univ. Press.

Ben-Zion, Y., & Lyakhovsky, V. (2002). Accelerated seismic release and related aspects of seismicity patterns on earthquake faults. Pure and Applied Geophysics, 159(10), 2385—2412. https://doi.org/10.1007/s00024-002-8740-9.

Ben-Zion, Y., & Sammis, G.S. (2003). Characterization of fault zones. Pure and Applied Geophysics, 160, 677—715. https://doi.org/10. 1007/PL00012554.

Billi, A., & Storti, F. (2004). Fractal distribution of particle size in carbonate cataclastic rocks from the core of a regional strike-slip fault zone. Tectonophysics, 384, 115—128. https://doi.org/10.1016/j.tecto.2004.03.015.

Bretz, M., Zaretzki, R., Field, S.B., Mitarai, N., & Franco, N. (2006). Broad distribution of stick-slip events in Slowly Sheared Granular Media: Table-top production of a Gutenberg-Richter-like distribution. Europhysics Letters (EPL), 74(6), 1116—1122. https://doi.org/10.1209/epl/i2006-10048-2.

Brown, S.R., Scholz, C.H., & Rundle, J.B. (1991). A simplified spring-block model of earthquakes. Geophysical Research Letters, 18(2), 44—218. https://doi.org/10.1029/91GL00210.

Burridge, R., & Knopoff, L. (1967). Model and theoretical seismicity. Bulletin of the Seismological Sociaty of America, 57, 341—371. https://doi.org/10.1785/BSSA0570030341.

Carlson, J.M., & Langer, J.S. (1989). Properties of earthquakes generated by fault dynamics. Physical Review Letters, 62(22), 2632—2635. https://doi.org/10.1103/PhysRevLett.62.2632.

Ceva, H. (1995). Influence of defects in a coupled map lattice modeling earthquakes. Physical Review E, 52(1), 154—158. https://doi.org/10. 1103/PhysRevE.77.067101.

Ciamarra, M.P., De Arcangelis, L., Lippiello, E., & Godano, C. (2009). Granular failure: the origin of earthquakes? International Journal of Modern Physics B, 23(28-29), 5374—5382. https://doi.org/10.1142/S0217979209063699.

Cicerone, R.D., Ebel, J.E., & Britton, J., (2009). A systematic compilation of earthquake precursors. Tectonophysics, 476, 96―371. https://doi.org/10.1016/j.tecto.2009.06.008.

Corral, A. (2003). Local distributions and rate fluctuations in a unified scaling law for earthquakes. Physical Review E, 68, 035102. https://doi.org/10.1103/PhysRevE.68.035102.

Corral, A. (2004a). Long-term clustering, scaling, and universality in the temporal occurrence of earthquakes. Physical Review Letters, 92, 108501. https://doi.org/10.1103/Phys RevLett.92.108501.

Corral, A. (2004b). Universal local versus unified global scaling laws in the statistics of seismicity. Physica A, 340, 590—597. https://doi.org/10.1016/j.physa.2004.05.010.

Cover, T.M., & Thomas, J.A. (2006). Elements of information theory (2nd ed). New York, Chichester, Brisbane, Toronto, Singapore: Wiley-Blackwell, 748 p.

Daley, D.J., & Vere-Jones, D.(2002). An introduction to the theory of point processes. Vol. I: Elementary theory and methods (2nd ed). Berlin: Springer-Verlag, 471 p. https://doi.org/10. 1007/b97277.

Daniels, K.E., & Hayman, N.W. (2008). Force chains in seismogenic faults visualized with photoelastic granular shear experiments. Journal of Geophysical Research: Solid Earth, 113(B11), 1—13. https://doi.org/10.1029/2008 JB005781.

De Arcangelis, L., Godano, C., Grasso, J.R., & Lippiello, E. (2016). Statistical physics approach to earthquake occurrence and forecasting. Physics Reports, 628, 1—91. https://doi:10.1016/j.physrep.2016.03.00.

Dieterich, J.H., & Richards-Dinger, K.B. (2010). Earthquake Recurrence in Simulated Fault Systems. Pure and Applied Geophysics, 167, 1087—1104. https://doi.org/10.1007/s00024-010-0094-0.

Dominguez, R., Tiampo, K.F., Serino, C.A., & Klein, W. (2013). Scaling of earthquake models with inhomogeneous stress dissipation. Physical Review E, 87, 022809. https://doi.org/10.1103/PhysRevE.87.022809.

Dorostkar, O., Guyer, R.A., Johnson, P.A., Marone, C., & Carmeliet, J. (2017). On the role of fluids in stick-slip dynamics of saturated granular fault gouge using a coupled computational fluid dynamics-discrete element approach. Journal of Geophysical Research: Solid Earth, 122, 3689—3700. https://doi.org/10.1002/2017JB014099.

Engelder, J.T. (1974). Cataclasis and the generation of fault gouge. Geoogical Society of America Bulletin, 85, 1515―1522. https://doi.org/10.1130/0016-7606(1974)85<1515:CATGOF>2.0.CO;2.

Fan, J., Meng, J, Ludescher, J., Ludescher, J., Chen, X., Ashkenazy, Y. Kurths, J., Halvin, S., & Schellnhuber, H.J.(2021). Statistical physics approaches to the complex Earth system. Physics Reports, 896, 1―84. https://doi.org/10.1016/j.physrep.2020.09.005.

Ferdowsi, B., Griffa, M., Guyer, R.A., Johnson, P.A., Marone, C., & Carmeliet, J. (2013). Microslips as precursors of large slip events in the stick-slip dynamics of sheared granular layers: a discrete element model analysis. Geophysical Research Letters, 40(16). 4194—4198. https://doi.org/10.1002/grl.50813.

Florido, E., Asencio-Cortés, G., Aznarte, J.L., Rubio-Escudero, C., & Martínez-Álvarez, F. (2018). A novel tree-based algorithm to discover seismic patterns in earthquake catalogs. Computers & Geosciences, 115, 96—104. https://doi.org/:10.1016/j.cageo.2018.03.005.

Fraser, A.M., & Swinney, H.L. (1986). Independent coordinates for strange attractors from mutual information. Physical Review A, 33, 1134― 1140. http://dx.doi.org/10.1103/PhysRevA.33. 1134.

Fukushima, K. (1980). Neocognitron: A self-organizing neural network model for a mechanismof pattern recognition unaffected by shift in position. Biological Cybernetics, 36(4), 193—202. https://doi.org/10.1007/BF00344 251.

Gell-Mann, M., & Lloyd, S. (1996).Information measures, effective complexity, and total information. Complexity, 2, 44—52. https://doi. org/10.1002/(SICI)1099-0526(199609/10)2:1< 44::AID-CPLX10>3.0.CO;2-X.

Goes, S.D.B., & Ward, S.N. (1994). Synthetic seismicity for the San Andreas Fault. Annals of Geophysics, 37, 1495—1513. https://doi.org/ 10.4401/ag-4150.

Greiner, W. (2001). Quantum Mechanics: An Introduction (4th ed). Berlin: Springer, 485 p.

Gutenberg, B., & Richter, C. (1949). Seismicity of the Earth and associated phenomenon. Princeton, New York. NY: Princeton University Press, 273 p.

Hawking, S. (2000). I Think the Next Century Will Be the Century of Complexity. What Is Complexity? San JoséMercury News, 23 January 2000.

He, K., Zhang, X., Ren, S., & Sun, J. (2016). Deep Residual Learning for Image recognition. Proc. of the IEEE Conference on Computer Vision and Pattern Recognition (pp. 770―778).

Helmstetter, A., & Sornette, D. (2003). Bath law derived from the Gutenberg-Richter law and from aftershock properties.Geophysical Research Letters, 30(20), 2069. https://doi.org/10.1029/2003GL018186.

Hinton, G.E., Osindero, S., & Teh, Y-W. (2006). A fast learning algorithm for deepbelief nets. Neural Computation, 18(7), 1527—1554. https://doi.org/10.1162/neco.2006.18.7.1527.

Holovatch, Yu., Kenna, R., & Thurner, S. (2017). Complex systems: physics beyond physics. European Journal of Physics, 38, 02300. https://doi.org/10.1088/1361-6404/aa5a87.

Hong, S.-Y., Koo, M.-S., Jang, J., Kim, J.-E., Park, H., Joh, M.-S., Kang, J.-H., & Oh, T.-J. (2013). Anevaluation of the software system dependency of a global atmospheric model. Monthly Weather Review, 141(11), 4165—4172. https://doi.org/10.1175/MWR-D-12-00352.

Houdoux, D., Amon, A., Marsan, D., Weiss, J., & Crassous, J. (2021). Micro-slips in an experimental granular shear band replicate the spatiotemporal characteristics of natural earthquakes. Communication Earth & Environment, 2(1), 90. https://doi.org/10.1038/s43247-021-00147-1.

Huang, Y., Saleur, H., Sammis, C., & Sornette, D. (1998). Precursors, aftershocks, criticality and self-organized criticality. Europhysics Letters, 41(1), 43—48. https://doi.org/10.1209/epl/i1998-00113-x.

Huang, J.P., Wang, X.A., Zhao, Y., Xin, C., & Xiang, H. (2018). Large earthquake magnitude prediction in Taiwan based on deep learning neural network. Neural Network World, 2, 149—160. https://doi.org/10.14311/NNW. 2018.28.009.

Hulbert, C., Rouet-Leduc, B., Johnson, P.A., Ren, C.X., Rivière, J., Bolton, D.C., & Marone, C. (2019). Similarity of fast and slow earthquakes illuminated by machine learning. Nature Geoscience, 12, 69—74. https://doi.org/10.1038/s41561-018-0272-8.

Ito, K., & Matsuzaki, M. (1990). Earthquakes as self-organized critical phenomena. Journal Geophysical Research, 95(B5), 6853—6860. https://doi.org/10.1029/JB094iB11p15635.

Jagla, E.A. (2010). Realistic spatial and temporal earthquake distributions in a modified Olami-Feder-Christensen model. Physical Review E, 81, 046117. https://doi.org/10.1103/PhysRev E.81.046117.

Johnson, P., Savage, H., Knuth, M., Gomberg, J., & Marone, C. (2008). Effects of acoustic waves on stick—slip in granular media and implications for earthquakes. Nature, 451, 57—60. https://doi.org/10.1038/nature06440.

Johnson, P.A., Ferdowsi, B., Kaproth, B.M., Scuderi, M., Griffa, M., Carmeliet, J., Guyer, R.A., Le Bas, P-Y., Trugman, D.T., & Marone, C. (2013). Acoustic emission and microslip precursors to stick-slip failure in sheared granular material. Geophysical Research Letters, 40(21), 5627—5631. https://doi.org/10. 1002/2013GL057848.

Kazemian, J., Tiampo, K.F., Klein, W., & Dominguez, R. (2015). Foreshock and aftershocks in simple earthquake models. Physical Review Letters, 114, 088501. https://doi.org/10.1103/PhysRevLett.114.088501.

Kolmogorov, A.N. (1968). Three approaches to the quantitive definition of information. International Journal of Computer Mathematics, 2(1-4), 157―168. https://doi.org/10.1080/ 00207166808803030.

Külahcı, F., İnceöz, M., Doğru, M., Aksoy, E., & Baykara, O. (2009). Artificial neural network model for earthquake prediction with radon monitoring. Applied Radiation and Isotopes, 67(1), 212—219. https://doi.org/10.1016/j.apradiso.2008.08.0.

Ladyman, J., Lambert, J., & Wiesner, K. (2013).What is a complex system? European Journalfor Philosophy of Science, 3, 33—67. https://doi.org/10.1007/s13194-012-0056-8.

Lherminier, S., Planet, R., Levy ditVehel, V., Simon, G., Vanel, L., Maloy, K.J., & Ramos, O. (2019). Continuously sheared granular matter reproduces in detail seismicity laws. Physical Review Letters, 122, 218501. https://doi.org/10. 1103/PhysRevLett.122.218501.

Lloyd, S., & Pagels, H. (1988). Complexity as thermodynamic depth. Annals of Physics, 188, 186—213. https://doi.org/10.1016/0003-4916 (88)90094-2.

Lloyd, S. (2001). Measures of complexity: A nonexhaustive list. IEEE Control Systems Magazine, 21(4), 7—8. https://doi.org/10.1109/MCS.2001.939938.

Loveless, J.P., & Meade, B.J. (2011). Stress modulation on the San Andreas Fault by interseismic fault system interactions. Geology, 39(11), 1035—1038. https://doi.org/10.1130/G32215.1.

Maa, G., Meia, J., Gaoc, K., Zhaod, J., Zhoua, W., & Wanga, D. (2022). Machine learning bridges microslips and slip avalanches of sheared granular gouges. Earth and Planetary Science Letters, 579, 117366. https://doi.org/10.1016/j.epsl.2022.117366.

Mair, K., & Hazzard, J.F. (2007). Nature of stress accommodation in sheared granular material: Insights from 3D numerical modeling. Earth and Planetary Science Letters, 259(3-4), 469—485. https://doi.org/10.1016/j.epsl.2007. 05.006.

McCaffrey, R. (2005). Block kinematics of the Pacific-North America plate boundary in the southwestern United States from inversion of GPS, seismological, and geologic data. Journal of Geophysical Research, 110, B07401. https://doi.org/10.1029/2004JB003307.

Meade, B.J., & Hager, B.H. (2005). Block models of crustal motion in southern California constrained by GPS measurements. Journal of Geophysical Research, 110, B03403. https://doi.org/10.1029/2004JB003209.

Metzler, R., & Bar-Yam, Y. (2005).Multiscale complexity of correlated Gaussians. Physical Review E, 71(4), 046114. https://doi.org/10. 1103/physreve.71.046114.

Mignan, A., & Broccardo, M. (2020). Neural network applications in earthquake prediction (1994―2019). Meta-analytic insight on their limitations.Seismological Research Letters, 91(4), 2330—2342. https://doi.org/10.1785/ 0220200021.

Mirrashid, M. (2014). Earthquake magnitude prediction by adaptive neurofuzzy inference system (ANFIS) based on fuzzy C-means algorithm. Natural Hazards, 74(3), 1577—1593. https://doi.org/10.1007/s11069-014-1264-7.

Morgan, J.K., & Boettcher, M.S. (1999). Numerical simulations of granular shear zones using the distinct element method: 1. Shear zone kinematics and the micromechanics of localization. Journal of Geophysical Research: Solid Earth, 104(B2), 2703—2719. https://doi.org/10.1029/1998JB900056.

Morgan, J.K. (1999). Numerical simulations of granular shear zones using the distinct element method: 2. Effects of particle size distribution and interparticle friction on mechanical behavior. Journal of Geophysical Research: Solid Earth, 104(B2), 2721—2732. https://doi.org/10.1029/1998jb900055.

Mousavi, S.M., & Beroza, G.C. (2023). Machine learning in earthquake seismology. Annual Review of Earth and Planetary Sciences, 51, 105―129. https://doi.org/10.1146/annurev-earth-071822-100323.

Mousavi, S.M., Zhu, W., Sheng, Y., & Beroza, G.C. (2019). CRED: A Deep Residual Network of Convolutional and Recurrent Units for Earthquake Signal Detection. Science Report, 9, 10267. https://doi.org/10.1038/s41598-019-45748-1.

Moustra, M., Avraamides, M., & Christodoulou, C. (2011). Artificial neural networks for earthquake prediction using time series magnitude data or Seismic Electric Signals. Expert Systems with Applications, 38(12), 15032―15039. https://doi.org/10.1016/j.eswa.2011.05.043.

Mykulyak, S.V. (2018). Hierarchical block model for earthquakes. Physical Review E, 97, 062130. https://doi.org/10.1103/PhysRevE.97.062130.

Mykulyak, S., Kulich, V., & Skurativskyi, S. (2019a). Simulation of shear motion of angular grains massif via the discrete element method. In Z. Hu, S. Petoukhov, I. Dychka, M. He (Eds.), Advances in Intelligent Systems and Computing (pp. 74—81). Springer. https://doi.org/10.1007/978-3-319-91008-6_8.

Mykulyak, S.V., Polyakovskyi, V.O. & Skurativskyi, S.I. (2019b). Statistical Properties of Shear Deformation of Granular Media and Analogies with Natural Seismic Processes. Pure and Applied Geophysics, 176, 4309—4319. https://doi.org/10.1007/s00024-019-02209-0.

Mykulyak, S.V., Kulich, V.V., & Skurativskyi, S.I. (2021a). On the similarity of shear deformation of a granular massif and a fragmented medium in the seismically active area. Geofizicheskiy Zhurnal, 43(3), 161—169. https://doi.org/10. 24028/gzh.v43i3.236386.

Mykulyak, S.V., Polyakovskyi, V.O., & Skurativskyi, S.I. (2021b). Experimental study of shear deformation of the medium formed by the massif of ribbed grains. Geofizicheskiy Zhurnal, 43(2), 178—188. https://doi.org/10. 1002/grl.50813.

Nakanishi, H. (1990). Cellular-automaton model of earthquakes with deterministic dynamics. Physical Review A, 41, 7086—7089.https://doi.org/10.1103/PhysRevA.41.7086.

Nasuno, S., Kudrolli, A., Bak, A., & Gollub, J.P. (1998). Time-resolved studies of stick-slip friction in sheared granular layers. Physical Review E, 58(2), 2161—2171. https://doi.org/ 10.1103/physreve.58.2161.

Nicolis, G., & Nicolis, C. (2012).Foundations of complex systems: Emergence, information and prediction (2nd ed). Singapore: World Scientific Publishing, 384 p.

Ogata, Y. (1988). Statistical models for earthquake occurrences and residual analysis for point processes. Journal of the American Statistical Association, 83, 9—27. https://doi:10. 1080/01621459.1988.10478560.

Ogata, Y., (1992). Detection of precursory relative quiescence before great earthquakes through a statistical model. Journal of Geophysical Research: Solid Earth, 97(B13), 19845—19871. http://dx.doi.org/10.1029/92JB00708.

Olami, Z., Feder, H.J.S., & Christensen, K.(1992). Self-organized criticality in a continuous, nonconservative cellular automaton modeling earthquakes. Physical Review Letters, 68(8), 1244—1247. https://doi.org/10.1103/PhysRev Lett. 68.1244.

Panakkat, A., & Adeli, H. (2007). Neural network models for earthquake magnitude prediction using multiple seismicity indicators. International Journal of Neural Systems, 17(1), 13—33. https://doi.org/10.1142/S0129065707 000890.

Pandit, A., & Biswal, K.C. (2019). Prediction of earthquake magnitude using adaptive neuro fuzzy inference system. Earth Science Information, 12, 513—524. https://doi.org/10. 1007/s12145-019-00397-w.

Papachristos, E., Stefanou, I., & Sulem, J. (2023). A discrete elements study of the frictional behavior of fault gouges. Journal of Geophysical Research: Solid Earth, 128, e2022JB025209. https://doi.org/10.1029/2022JB025209.

Parisi, G.(1999). Complex systems: a physicist’s viewpoint. Physica A, 263, 557—564. https://doi.org/10.1016/S0378-4371(98)00524-X.

Pascanu, R., Gulcehre, C., Cho, K., & Bengio, Y. (2013). How to construct deep recurrent neural networks. Retrieved from https://arxiv.org/abs/1312.6026.

Pica Ciamarra, M., Lippiello, E., Godano, C., & de Arcangelis, L. (2010). Unjamming Dynamics: The Micromechanics of a Seismic Fault Model. Physical Review Letters, 104(23), 238001. https://doi.org/10.1103/PhysRevLett. 104.238001.

Pollitz, F.F. (2011). Epistemic uncertainty in California-wide synthetic seismicity simulations. Bulletin of Seismological Society of America, 101(5), 2481—2498. https://doi.org/10.1785/0120100303.

Ramos, O., Altshuler, E., & Maloy, K.J. (2006). Quasiperiodic events in an earthquake model. Physical Review Letters, 96, 098501. https://doi.org/10.1103/PhysRevLett.96.098501.

Rissanen, J. (1989). Stochastic complexity in statistical inquiry. Singapore: World Scientific, 188 p.

Rouet-Leduc, B., Hulbert, C., Lubbers, N., Barros, K., Humphreys, C.J., & Johnson, P.A. (2017). Machine learning predicts laboratory earthquakes. Geophysical ResearchLetters, 44, 9276—9282. https://doi.org/10.1002/2017GL0 74677.

Rundle, J.B. (1988). A physical model for earthquakes: 1. Fluctuations and interactions. Journal of Geophysical Research, 93(B6), 6237—6254. https://doi.org/10.1029/JB093iB06p062 37.

Rundle, P.B., Rundle, J.B., Tiampo, K.F., Martins, J.S.S., McGinnis, S., & Klein, W. (2001). Nonlinear network dynamics on earthquake fault systems. Physical Review Letters, 87(14), 148501. https://doi.org/10.1103/PhysRevLett. 87.148501.

Rundle, J.B., Rundle, P.B., Donnellan, A., & Fox, G. (2004). Gutenberg-Richter statistics in topologically realistic system-level earthquake stress-evolution simulations. Earth, Planet and Space, 56, 761—771. https://doi.org/10.1186/BF03353084.

Rundle, P.B., Rundle, J.B., Tiampo, K.F., Don nellan, A., & Turcotte, D.L. (2006). Virtual California: Fault model, frictional parameters, applications. Pure and Applied Geophysics, 163(9), 1819—1846. https://doi.org/10.1007/s00024-006-0099-x.

Rundle, J.B., Stein, S., Donnellan, A., Turcotte, D.L., Klein, W., & Saylor, C. (2021). The complex dynamics of earthquake fault systems: new approaches to forecasting and now casting of earthquakes. Reports on Progress in Physics, 84, 07680. https://doi.org/10. 1088/1361-6633/abf893.

Sammis, C., King, G., & Biegel, R. (1987). The kinematics of gouge deformation. Pure and Applied Geophysics, 125, 777—812. https://doi.org/10.1007/BF00878033.

Sayama, H. (2015). Introduction to the modeling and analysis of complex systems. New York, NY: Geneseo, 498 p.

Schellnhuber, H. (1999). Earth system’ analysis and the second Copernican revolution. Nature, 402, C19—C23. https://doi.org/10.1038/ 35011515.

Scholz, C.H. (2019). The mechanics of earthquakes and faulting (3nd ed). Cambridge, UK: Cambridge University Press, 512 p.

Serino, C.A., Tiampo, K.F., & Klein, W. (2011). New approach to Gutenberg-Richter scaling. Physical Review Letters, 106, 108501. https://doi.org/10.1103/PhysRevLett.106.108501.

Shcherbakov, R., Turcotte, D.L., & Rundle, J.B. (2015). Complexity and earthquakes.In G. Schubert, H. Kanamori (Eds.), Treatise on Geophysics (2nd ed) (pp. 627―653). Elsevier.

Shodiq, M.N., Kusuma, D.H., Rifqi, M.G., Barakbah, A.R., & Harsono, T. (2019). Adaptive neural fuzzy inference system and automatic clustering for earthquake prediction in Indonesia. JOIV: International Journal on Informatics Visualization, 3(1), 47—53. http://dx. doi.org/10.30630/joiv.3.1.204.

Sibson, R.H. (1977). Fault rock and fault mechanisms. Journal of the Geological Society, 133, 191―213. https://doi.org/10.1144/gsjgs. 133.3.0191.

Steffen, W., Sanderson, A., Tyson, P., Jаger, J., Matson, P., Оldfield, F., Richardson, K., Schellnhuber, H.-J., & Turner, B.L., Wasson, R.J. (2005). Global change and the earth system: A planet under pressure. Berlin, Heidelberg: Springer-Verlag. http://dx.doi.org/10.1007/b137870.

Steffen, W., Richardson, K., Rockström, J., Schellnhuber, H.J., Dube, O.P., Dutreuil, S., Lenton, T.M., & Lubchenco, J. (2020). Theemergence and evolution of Earth system science. Nature Reviews Earth & Environment, 1(1), 54—63. https://dx.doi.org/10.1038/s43017-019-0005-6.

Storti, F., Billi, A., & Salvini, F. (2003). Particle size distributions in natural carbonate fault rocks: insights for non-self-similar cataclasis. Earth and Planetary Science Letters, 206, 173―186. https://doi.org/10.1016/S0012-821X (02)01077-4.

Sultan, N.H., Karimi, K., & Davidsen, J. (2022). Sheared granular matter and the empirical relations of seismicity. Physical Review E, 105, 024901. https://doi.org/10.1103/PhysRevE. 105.024901.

Thurner, S., Hanel, R., & Klimek, P. (2018). Introduction to the Theory of Complex Systems.Oxford, UK: Oxford University Press.

Turcotte, D.L., Newman, W.I., & Shcherbakov, R. (2003). Micro and macroscopic models of rock fracture. Geophysical Journal International, 152(3), 718—728. https://doi.org/10.1046/j.1365-246X.2003.01884.x.

Turcotte, D.L., & Shcherbakov, R. (2006). Can damage mechanics explain temporal scaling laws in brittle fracture and seismicity? Pure and Applied Geophysics, 163, 1031—1045. https://doi.org/10.1007/s00024-006-0058-6.

Utsu, T. (1969). Aftershocks and Earthquake Statistics (1). Some Parameters, Which Characterize an Aftershock Sequence and Their Interrelations. Journal of the Faculty of Science, Hokkaido University, Series 7,Geophysic, 3(3), 129—195. Retrieved from http://hdl.handle.net/2115/8683.

Utsu, T. (1970). Aftershocks and Earthquake Statistics (2). Further Investigation of Aftershocks and Other Earthquake Sequences Based on a New Classification of Earthquake Sequences. Journal of the Faculty of science, Hokkaido University, Series 7, Geophysics, 3(4), 197—266. Retrieved from http://hdl.handle.net/2115/8684.

Wang, H., & Raj, B. (2017). On the Origin of Deep Learning. arXiv:1702.07800v4.

Wang, Y., Wang, Z., Cao, Z., & Lan, J. (2019). Deep learning for magnitude prediction in earthquake early warning. arXiv:1912.05531.

Ward, S.N. (1992). An application of synthetic seismicity in earthquake statistics: The Middle America Trench. Journal of Geophysical Research, 97(B5), 6675—6682. https://doi.org/ 10. 1029/92JB00236.

Yakovlev, G., Turcotte, D.L., Rundle, J.B., & Rundle, P.B. (2006). Simulation-based distributions of earthquake recurrence times on the San Andreas Fault system. Bulletin of Seismological Society of America, 96(6), 1995—2007. https://doi.org/10.1785/0120050183.

Zadeh, A.A., Barés, J., Socolar, J.E.S., & Behringer, R.P. (2019). Seismicity in sheared granular matter. Physical Review E, 99, 052902. https://doi.org/10.1103/PhysRevE.99.052902.

Zhou, W.-Z., Kann, J.-S., & Sun, S. (2017). Study on seismic magnitude prediction based on combination algorithm. Proc. of the 9th int. conf. on modelling, identification and control (ICMIC). Kunming, China (pp. 539―544). https://doi.org/:10.1109/ICMIC.2017.8321703.

Published

2025-02-21

How to Cite

Mykulyak, S. (2025). Complex systems in geophysics: methods of research and prediction of their behavior. Geofizicheskiy Zhurnal, 47(1). https://doi.org/10.24028/gj.v47i1.312874

Issue

Section

Articles