Fractal Hierarchies and the Historical Irreversibility of Geodynamic Processes

  • Oleg V. PetrovEmail author
Part of the Springer Geophysics book series (SPRINGERGEOPHYS)


The invariance of the revealed regularity in the spatial distribution of different-type hierarchies of the Earth’s gravitational instability structures throughout its geological history, along with the data discussed above on the distribution of mantle plumes and the sialic protocrust with respect to global structures such as G-hexagons in the eastern hemisphere and the L-hexagons in the western, confirms the emergence of these global structures, which determined the fundamental asymmetry of the Earth and divided it into the Indo-Atlantic and Pacific tectonic segments during the early Archean, simultaneously with the isolation of the liquid core, i.e. more than 3500 Ma. At the same time, paleogeodynamic reconstructions show that generational structures emerge during each subsequent stage of the Earth’s evolution, along with disordered instabilities. Moreover, these increasingly massive generational structures are presented predominantly by G-hexagon type in the eastern hemisphere and the L-hexagon type in the western. With the consideration of the relationship between the size and the stratification depth of the structures of gravitational instability, this means that with the course of geological time, the increasingly deep layers of the Earth’s crust and mantle became gravitationally unstable with respect to the underlying shells. From a physical point of view, the increase in the thickness of gravitationally unstable layers over time can easily be explained by the nonequilibrium cooling of the Earth through its surface, i.e., by external sinks of heat. With the increase in the size of the Earth’s gravitational instability structures, the associated tectonic regimes also change, ranging from fine-cellular intraplate (greenstone and granulite, protoaulacogenic and protogeosynclinal) to marginal-plate and global riftogenic regimes. In the terms of geodynamics, the horizontal component in the movement of the Earth’s crust becomes especially critical when the magnitude of its gravitational instability increases. The scale of its destruction increases, and a gradation from small-plate and intraplate tectonics to the tectonics of lithospheric plates can be observed.


  1. Danes Z.F. Mathematical formulation of saltdome dynamics. Geophysics. 1964; 29:414–424.CrossRefGoogle Scholar
  2. Selig F. A theoretical prediction of salt dome patterns. Geophysics. 1965; 30:633–643.CrossRefGoogle Scholar
  3. Biot M.A., Ode H. Theory of gravity instability with variable overburden and compaction. Geophysics. 1965; 30: 213–227.CrossRefGoogle Scholar
  4. Ramberg H. Instability of layered systems in the field of gravity, parts 1 and 2. Phys. Earth and Planet. Inter. 1968; 1:427–474.Google Scholar
  5. Ramberg H. Theoretical models of density stratification and diapirism in the Earth. J. Geophys. Res. 1972; 77:877–889.CrossRefGoogle Scholar
  6. Fletcher R.C. Application of a mathematical model to the emplacement of mantled gneiss domes. Am. J. Sci. 1972; 272:197–216.CrossRefGoogle Scholar
  7. Dziewonski A.M., Woodhouse J.H. Threedimensional Earth structure and mantle convection. Abstracts. 1989; 1(28th IGC):427–428.Google Scholar
  8. Nikolis G., Prigogine I. Samoorganizatsiya v neravnovesnykh sistemakh. Ot dissipativnykh struktur k uporyadochennosti cherez fluktuatsii. M.: Mir; 1979 [Nikolis G., Prigogine I. Self-organisation in nonequilibrium systems. From dissipative structures to ordering through fluctuations. M.: Mir; 1979 (In Russ.)].Google Scholar
  9. Prigogine I.R., Stengers I. Poryadok iz khaosa: novyi dialog cheloveka s prirodoi. Obshch. red. V.I. Arshinova, Yu.L. Klimontovicha i Yu.V. Sachkova. M.: Progress; 1986 [Prigogine I.R., Stengers I. Order out of chaos: Man’s new dialogue with nature. Ed. V.I. Arshinov, Yu.L. Klimontovich and Yu.V. Sachkov. M.: Progress; 1986 (in Russ.)].Google Scholar
  10. Nikolis G., Prigogine I. Poznanie slozhnogo. M.: Mir; 1990 [Nikolis G., Prigogine I. Exploring Complexity. M.: Mir; 1990 (In Russ.)].Google Scholar
  11. Kurdyumov S.P., Malinetskii G.G., Potapov A.B. Sinergetika - novye napravleniya. M.: Znanie. 1989; 11 [Kurdyumov S.P., Malinetskii G.G., Potapov A.B. Synergetics - new directions. M.: Znanie. 1989; 11 (In Russ.)].Google Scholar
  12. Ershov S.V., Malinvetskij G.G., Ruzmaikin A.A. A generalized twodisk dynamo model. Geophys. and Astrophys. Fluid. Dyn. 1989; 47:251–277.CrossRefGoogle Scholar
  13. Maruyama S., Kumazawa M., Kawakami S. Towards a new paradigm on the Earth’s dynamics. J. Geol. Soc. Japan. 1994; 100(1):1–3.CrossRefGoogle Scholar
  14. Stille H. Izbrannye trudy. M.: Mir; 1964. [Stille H. Selected works. M.: Mir; 1964 (in Russ.)].Google Scholar

Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Russian Geological Research Institute (VSEGEI)St. PetersburgRussia

Personalised recommendations