Quantitative correlation between geodynamic systems and geodynamic cycles of various ranks

Abstract

A concept of geodynamics of hierarchically subordinate geospheres developed by the author is briefly characterized. Geospheres of different ranks—(i) the Earth as a whole, (ii) the mantle and the crust, (iii) the upper mantle and the crust, (iv) the asthenosphere + the lithosphere, and (v) sedimentary cover—are successively enclosed in one another. Convective geodynamic systems of the respective ranks function in each of these geospheres. Such systems are composed of cells controlled by balanced arrangement of the tectonic flow and consisting, in turn, of domains of horizontal compression and horizontal extension alternating in chessboard order. The hierarchical organization of geodynamic systems implies that the domain of a lower rank (a larger scale) is simultaneously a system of a higher rank (a smaller scale). The interference of geodynamic systems of various ranks generates the entire spectrum of tectonic units of different scales, from the substantially continental Northern Hemisphere and the Indo-Atlantic segment of the Earth to small folds in orogenic belts. The geodynamic systems of various ranks reveal quantitative correlation with the hierarchical series of geodynamic cycles established by V.E. Khain [29]. The ratios of the thicknesses of the geospheres, where geodynamic systems of various ranks work, to the duration of the geodynamic cycle of the respective rank fall within a very narrow range of 0.45 ± 0.10 cm/yr. Therefore, this ratio may be regarded as an out-of-rank geodynamic constant that has dimensionality of velocity. Its formal physical meaning is a time-averaged rate of uplift of a minor elementary body of a geosphere from bottom to top during the geodynamic cycle. This rate may be deemed a characteristic velocity of the ascending convective flow in any of the aforementioned geospheres. The physical and geologic reality of this velocity is confirmed by realistic (within an order of magnitude) estimates of rates of continental drift and oceanic spreading deduced from this value. In contrast to the average velocity of tectonic flow, the average rate of deformation is variable and inversely proportional to the thickness of a geosphere of a respective rank. Not only does the thickness of a geosphere decrease with increasing rank but also the respective geodynamic system functions within more local areas. This is a specific realization of the abstract computer model of cascade convection in geospheres [24]. The increase in the deformation rate within increasingly local areas is a manifestation of the weak link effect. The essence of this effect is clearly demonstrated by a combination of extensive but slow ductile deformation and more local but faster brittle failure resulted from small-scale deformation in the Earth’s crust.