APPLICABILITY OF SIMILARITY CONDITIONS TO ANALOGUE MODELLING OF TECTONIC STRUCTURES

The publication is aimed at comparing concepts of V.V. Belousov and M.V. Gzovsky, outstanding researchers who established fundamentals of tectonophysics in Russia, specifically similarity conditions in application to tectonophysical modeling. Quotations from their publications illustrate differences in their views. In this respect, we can reckon V.V. Belousov as a «realist» as he supported «the liberal point of view» [Methods of modelling…, 1988, p. 21–22], whereas M.V. Gzovsky can be regarded as an «idealist» as he believed that similarity conditions should be mandatorily applied to ensure correctness of physical modeling of tectonic deformations and structures [Gzovsky, 1975, pp. 88 and 94].

Objectives of the present publication are (1) to be another reminder about desirability of compliance with similarity conditions in experimental tectonics; (2) to point out difficulties in ensuring such compliance; (3) to give examples which bring out the fact that similarity conditions are often met per se, i.e. automatically observed; (4) to show that modeling can be simplified in some cases without compromising quantitative estimations of parameters of structure formation.

(1) Physical modelling of tectonic deformations and structures should be conducted, if possible, in compliance with conditions of geometric and physical similarity between experimental models and corresponding natural objects. In any case, a researcher should have a clear vision of conditions applicable to each particular experiment.

(2) Application of similarity conditions is often challenging due to unavoidable difficulties caused by the following: a) Imperfection of experimental equipment and technologies (Fig. 1 to 3); b) uncertainties in estimating parameters of formation of natural structures, including main ones: structure size (Fig. 4), time of formation (Fig. 5), deformation properties of the medium wherein such structures are formed, including, first of all, viscosity (Fig. 6), ultimate strength, and tectonic stresses which caused formation of such structures (Fig. 7).

(3) A way to overcome the above mentioned difficulties can be found through awareness of the fact that physical similarity conditions are often met per se, i.e. automatically observed due to linear relationships between similarity coefficients (Fig. 8). For example, decreasing the viscosity of the equivalent material will result in corresponding decrease of time required for deformation of the given model, all other conditions being equal. Moreover, it is possible to use this similarity condition, i.e. an equation in one unknown, not only to select a required equivalent material, but also to quantitatively estimate the natural parameter in the given condition.

(4) Another way to overcome the above mentioned difficulties is simplification of modeling in cases when it is required to obtain qualitative results without any quantitative evaluations of parameters of structure formation (Figures 9 to 14). This necessitates development of fundamentally new criteria of similarity for modelling. For instance, it can be absence or presence of the original (pre-deformational) structuring of the geological medium that is preconditioned by previous deformation processes of self-organization of the givem medium. Possibilities of simulation of the selforganization shall be the subject of our future study. It is also needed to elaborate new similarity criteria for modeling of hierarchically subordinate geodynamic systems and structural parageneses. So far it has been accepted that simulations of the kind should be conducted on the principle of selectivity (separate simulation), established by M.V. Gzovsky [1975], such as, for example, separate simulation of folding and cleavage.

Having his own experience of 40+ years in experimental tectonics, the author addresses his views to young researchers, who are apprehensive about the need to ensure compliance with similarity conditions in physical modeling of tectonic deformations and structures, and to those members of editorial boards and reviewers of scientific journals who believe that authors should mandatorily declare such compliance. As a result, it is not uncommon that, striving to declare that this requirement is observed, an author saturates his/her papers with complicated equations which do not reflect the actual compliance with similarity conditions and thus become a mere demonstration of the author’s erudition in mathematics.

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