Topical problems of the formation of slow deformation waves and their connection with recent geodynamic (deformational) processes are discussed. It is shown that the term “diffusion of stresses (displacements, strains)” is ill defined from the standpoint of physics of transfer phenomena because in the case of diffusion, mass transfer takes place, whereas the wave processes transfer energy. It is noted that the existing models describing the “diffusion of stresses” are solved based on the mathematical formalism of heat conduction theory which relies on the phenomenon of energy transfer. It is demonstrated that applying the term “wave” to the “stress diffusion” processes is untenable because in the classical sense, wave processes describe undamped (sustained, continuous) oscillations propagating in a homogeneous medium at constant velocity. The processes describing the “diffusion of stresses” form strongly damped oscillations whose propagation velocity substantially decreases with time. As a mechanism corresponding to the wave canonical concepts, a model of autowave deformation processes is proposed that implement the relay-race transfer and successive re-initiation of deformation activity from a fault to a fault or from one activated segment of a fault to another segment. Problematic issues of identifying the slow deformation waves are discussed, and the recommendations are proposed for constructing a network of observation points for the in situ measurements of spatiotemporal migration of the Earth’s surface deformations. It is substantiated that the existence of slow deformation waves does not explain the entire observed spatiotemporal spectrum of recent movements of the Earth’s surface.
Similar content being viewed by others
REFERENCES
Andronov, A.A. and Chaikin, C.E., Theory of Oscillations, Princeton: Princeton Univ. Press, 1949.
Ben-Zion, Y. and Allam, A.A., Seasonal thermoelastic strain and postseismic effects in Parkfield borehole dilatometers, Earth Planet. Sci. Lett., 2013, vol. 379, pp. 120–126.
Bird, R.B., Stewart, W.E., and Lightfoot, E.L., Transport Phenomena, New York: Wiley, 1965.
Birger, B.I., Stress propagation in the Earth’s lithosphere, Izv. Akad. Nauk SSSR,Fiz. Zemli, 1989, no. 12, pp. 3–18.
Bornyakov, S.A., Salko, D.V., Seminskiy, K.Zh., Demberel, S., Ganzorig, D., Batsaykhan, Ts., and Togtokhbayar, S., Instrumental recording of slow deformation waves in the South Baikal geodynamic study site, Dokl. Earth Sci., 2017, vol. 473, no. 1, pp. 371–374.
Bott, M.H.P. and Dean, D.S., Stress diffusion from plate boundaries, Nature, 1973, vol. 243, no. 5406, pp. 339–341.
Bykov, V.G., Waves of activation in crustal faults, Tikhookean.Geol., 2000, vol. 19, no. 1, pp. 104–108.
Bykov, V.G., Prediction and observation of strain waves in the Earth, Geodyn. Tectonophys., 2018, vol. 9, no. 3, pp. 721–754.
Bykov, V.G., Development of sliding regimes in faults and slow strain waves, Fiz. Mezomekh., 2019, vol. 22, no. 4, pp. 39–46.
Carslaw, H.S. and Jaeger, J.C., Conduction of Heat in Solids, Oxford: Clarendon Press, 1959.
Courant, R. and Hilbert, D., Methods of Mathematical Physics,vol. II:Partial Differential Equations, New York: Wiley, 1966.
Dobrovol’skii, I.P., Matematicheskaya teoriya podgotovki i prognoza tektonicheskogo zemletryaseniya (Mathematical Theory of the Preparation and Forecasting of a Tectonic Earthquake), Moscow: FIZMATLIT, 2009.
Elsasser, W.H., Convection and stress propagation in the upper mantle, in The Application of Modern Physics to the Earth and Planetary Interiors, Runcorn, S.K., Ed., New York: Wiley, 1969, pp. 223–246.
Eshelby, J.D., Elastic inclusions and inhomogeneities, in Progress in Solid Mechanics, vol. 2, Sneddon, I.N. and Hill, R., Eds., Amsterdam: North Holland, 1961, pp. 89–140.
Frenkel’, Ya.I., Statisticheskaya fizika (Statistical Physics), Moscow–Leningrad: AN SSSR, 1948.
Ishii, H., Sato, T., Tachibana, K., Hashimoto, K., Murakami, E., Mishina, M., Miura, S., Sato, K., Takagi, A., Crustal strain, crustal stress and microearthquake activity in the northeastern Japan arc, Tectonophysics, 1983, vol. 97, nos. 1–4, pp. 217–230.
Izyumov, S.F. and Kuzmin, Yu.O., Study of the recent geodynamic processes in the Kopet-Dag region, Izv. Phys. Solid Earth, 2014, vol. 50, no. 6. pp. 719–731.
Kasahara, K., Earthquake Mechanics, Cambridge: Cambridge Univ. Press, 1981.
Kolmogorov, A.N., Petrovskii, I.G., and Piskunov, N.S., A study of the diffusion equation with increase in the amount of substance, and its application to a biological problem, Byull. Mosk. Gos. Univ.,Ser. A, 1937, vol. 1, no. 6, pp. 1–26.
Kuzmin, Yu.O., Recent geodynamics of the fault zones in sedimentary basins and earthquake preparation processes, in Prognoz zemletryasenii: Geodezicheskie metody issledovanii (Earthquake Forecasting: Geodetic Methods of Study), vol. 11, Moscow–Dushanbe: Donish, 1989, pp. 52–60.
Kuzmin, Yu.O., Deformation autowaves in fault zones, Izv. Phys. Solid Earth, 2012, vol. 48, no. 1. pp. 1–16.
Kuzmin, Yu.O., Recent geodynamics of the faults and paradoxes of the rates of deformation, Izv. Phys. Solid Earth, 2013, vol. 49, no. 5. pp. 626–642.
Kuzmin, Yu.O., Recent geodynamics of fault zones: faulting in real time scale, Geodinam.Tektonofiz., 2014, vol. 5, no. 2, pp. 401–443.
Kuzmin, Yu.O., Recent geodynamics of a fault system, Izv. Phys. Solid Earth, 2015, vol. 51, no. 4. pp. 480–485.
Kuzmin, Yu.O., Recent geodynamics of dangerous faults, Izv. Phys. Solid Earth, 2016, vol. 52, no. 5. pp. 709–722.
Kuzmin, Yu.O., Paradoxes of the comparative analysis of ground-based and satellite geodetic measurements in recent geodynamics, Izv. Phys. Solid Earth, 2017, vol. 53, no. 6. pp. 825–839.
Kuzmin, Yu.O., Recent anomalous deformation of the ground surface in fault zones: shear or tensile faulting?, Geodinam.Tektonofiz., 2018a, vol. 9, no. 3, pp. 967–987.
Kuzmin, Yu.O., Recent geodynamics of tensile faults, Izv. Phys. Solid Earth, 2018b, vol. 54, no. 6. pp. 886–903.
Kuzmin, Yu.O., Recent geodynamics: from crustal movements to monitoring critical objects, Izv. Phys. Solid Earth, 2019a, vol. 55, no. 1. pp. 65–86.
Kuzmin, Yu.O., Induced deformations of fault zones, Izv. Phys. Solid Earth, 2019b, vol. 55, no. 5. pp. 753–765.
Lykov, A.V. and Berkovskii, B.M., Konvektsiya i teplovye volny (Convection and Heat Waves), Moscow: Energiya, 1974.
Melosh, H.J., Nonlinear stress propagation in the Earth’s upper mantle, J. Geophys. Res., 1976, vol. 81, no. 32, pp. 5621–5632.
Mishchenko, E.F., Sadovnichii, V.A., Kolesov, A.Yu., and Rozov, N.Kh., Avtovolnovye protsessy v nelineinykh sredakh s diffuziei (Autowave Processes in Nonlinear Media with Diffusion), Moscow: FIZMATLIT, 2010.
Mukhamediev, Sh.A., Grachev, A.F., and Yunga, S.L., Nonstationary dynamic control of seismic activity of platform regions by mid-ocean ridges, Izv., Phys. Solid Earth, 2008, vol. 44, no. 1, pp. 9–17.
Nikolaevsky, V.N., Mechanics of geomaterials and earthquakes, in Science and Technics Results: Mechanics of Deformed Solid Body, vol. 15, Moscow: VINITI, 1983, pp. 149–230.
Paulson, A., Zhong, S., and Wahr, J., Modelling post-glacial rebound with lateral viscosity variations, Geophys. J. Int., 2005, vol. 163, pp. 357–371.
The Scientific Papers of James Clerk Maxwell, Niven, W.D., Ed., Cambridge: Cambridge Univ. Press, 1890.
Turcotte, D.L. and Shubert, G., Geodynamics, Cambridge: Cambridge Univ. Press, 2002.
Vasil’ev, V.A., Romanovskii, Yu.M., Yakhno, V.G., Avtovolnovye protsessy (Autowave Processes), Moscow: Nauka, 1987.
Whitham, G., Linear and Nonlinear Waves, New York: Wiley, 1974.
Zel’dovich, Ya.B., Barenblatt, G.I., Librovich, V.B., and Makhvelidze, G.M., Matematicheskaya teoriya goreniya i vzryva (Mathematical Theory of Combustion and Explosion), Moscow: Nauka, 1980.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Kuzmin, Y.O. Recent Geodynamics and Slow Deformation Waves. Izv., Phys. Solid Earth 56, 595–603 (2020). https://doi.org/10.1134/S1069351320040059
Received:
Revised:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1134/S1069351320040059