Natural-science concepts of rotational movements and the ‘lumpy’ structure of medium are reviewed with a focus on key aspects. Through using torsional traps for hunting and «implementing» mechanical torque for ignition, Homo sapiens developed to man. Vortex movements «impregnated» in spiral structures of shells and torsional movements of toothy whales and fish were intuitively perceived by man as major stable movements of the environment. Based on the above, the ancient philosophy established the concept of the uniform world represented by atomic («noncuttable») structure of medium and vortex movements of ether. Based on conclusive arguments stated by R. Dekart, H. Helmgolz, Lord Kelvin and others within the framework of classical physics and in the first half of the 20th century by scientists in quantum physics and cosmogony, both «quantum structure» («lumpiness») and rotation («vorticity») are integral features of matter – space – time throughout the whole range from elementary particles to galaxies and galactic clusters.

Nowadays researchers in natural sciences, particularly in the Earth sciences, call attention again to the problem of structure of matter and its movements. In the 1920s, Chinese geologist Li Siguang established fundamentals of vortex geodynamics. In the second half of the 20th century, Li Siguan’s concepts were developed by geologists O.I. Slenzak and I.V. Melekestsev. Geologist A.V. Peive, mechanic L.I. Sedov and physicist M.A. Sadovsky put forward a concept of block structure of the geo-medium (geological and geophysical medium) and proposed a justified assumption that such blocks can move by own torque. This method of movement is confirmed by results of geological and tectonophysical studies, as well as instrumental geophysical measurements obtained from a variety of stations and focal zones of strong earthquakes. Many researchers, including W. Elsasser and V.N. Nikolaevsky, develop fundamentals of nonlinear wave mechanics of the geo-medium, admitting rotational movements of blocks. According to М.V. Stovas, V.Е. Khain and other researchers, rotation of the planet around its axis is of critical importance for understating the origin of geodynamic movements.

Based on the review of results from the previous comprehensive geological and geophysical studies, a conclusion is made on the torque origin of rotating block geo-medium which is termed as Peive–Sedov–Sadovsky medium. Analyses of migration of earthquake foci and volcanic eruptions and movements of edges of tectonic plates provided grounds to design a principally new model, and this rotational model is described in the present publication. Blocks and plates interacting with each other in the model are interrelated by long-range elastic fields which comprise a uniform planetary geodynamic medium, i.e. ‘self-consistent’ state of the geo-medium. Briefly reviewed are data about vortex geological structures and rotary motions of blocks and plates; such data have been detected and recorded in abundance in a variety of geophysical fields. It is stressed that similar, in principle, vortex movements / flows are solutions of the well known Dirichlet–Dedekind–Riemann problem of rotating and gravitating liquid drop that is the problem of the Earth’s equilibrium shape. According to the proposed rotational model, geodynamic solutions of the rotational model combine geodynamic flows in the solution of the problem of the Earth’s equilibrium shape and geologic-geophysical vortex structures and movements on the Earth’s surface in one and the same class of phenomena. It is proposed to apply such solutions for establishing a new geological paradigm – new torque (and/or wave / vortex) geodynamics.

Correlation between archaeological ruins and geological observations show that the region of the port city of Caesarea in central Israel has been stable during the last 2000 years. This stability, and the low range of the diurnal tidal variations of sea level, attributes global climatic significance to the reconstructions of various sea levels during several clear archaeological time-frames. It seems that while 2000 years ago sea level, and therefore also climate, was similar to the present one. Sea level was higher in the VII–VIII Centuries AD, and the climate was probably warmer, and sea level was lower, and the climate colder, in the ХII–ХIII Centuries AD. Consequently it is suggested that the presumption that the present global climatic warming in anthropogenic requires strong supporting evidence. On the other hand, the link between recent heavy damages to coral reefs and the anthropogenic activities that caused the rise in atmospheric CO2 content seems quite likely.

A new method is proposed to define piecewise continuous fields of velocity gradients of recent horizontal movements of the Earth’s crust from spatially discrete data on horizontal velocities of such movements. The method is designed to identify spatial inhomogeneities in the field of horizontal strain rates (e.g., zones of localized deformation and boundaries between areas with different strain rates) in considerable detail. It is applied to determine the field of horizontal velocity gradient in the region of the Central Asian GPS network which covers vast territories of the Kyrgyz Tien-Shan and Pamirs mountain ranges, the T arim depression, and the Kazakh Shield (Fig. 1). Calculations are based on GPS survey data obtained at 308 sites from 1995 to 2006 (Fig. 4). The resolution of the proposed method is increased by using a triangulation grid which is much denser than a conventional one (Fig. 2 and 3). As a result, point x on the surface under study is covered by several triangles rather than one (Fig. 5). Strain characteristics at point x are calculated by weighted summation of corresponding characteristics in the cover triangles. Thus, for each point we estimate spin tensor W, which defines angular velocity ω, and components of horizontal strain rate tensor E. These components provide for direct calculation of orientation of principal axes and invariants of E, i.e. maximum stretching E1, maximum shortening E2, velocity divergence E=E1+E2, and maximum shear rates Γ=⎪E1−E2⎪/2 (Fig. 6 to 11). The calculated values are presented in maps which demonstrate that spatial distribution of such values is highly inhomogeneous. Regions with increased values of kinematic characteristics mentioned above stand out sharply against the background. At the same time, spatial distribution of the kinematical characteristics in the Tien Shan region is quite regular: zones of increased absolute values of E2 are mainly oriented in the ENE direction, while the NNW orientation dominates in zones of increased values of E1.

The paper describes seismicity of Kamchatka for the period of 2008 and presents 2D distribution of background seismicity parameters calculated from data published in the Regional Catalogue of Kamchatka Earthquakes. Parameters under study are total released seismic energy, seismic activity A10, slope of recurrence graph γ, parameters of RTL, ΔS and Z-function methods, and clustering of earthquakes. Estimations of seismicity are obtained for a region bordered by latitude 50.5–56.5N, longitude 156E–167E, with depths to 300 km. Earthquakes of energy classes not less than 8.5 as per the Fedotov’s classification are considered. The total seismic energy released in 2008 is estimated. According to a function of annual seismic energy distribution, an amount of seismic energy released in 2008 was close to the median level (Fig. 1). Over 2/3 of the total amount of seismic energy released in 2008 resulted from three largest earthquakes (МW ≥ 5.9). About 5 percent of the total number of seismic events are comprised of grouped earthquakes, i.e. aftershocks and swarms. A schematic map of the largest earthquakes (МW ≥ 5.9) and grouped seismic events which occurred in 2008 is given in Fig. 2; their parameters are listed in Table 1. Grouped earthquakes are excluded from the catalogue. A map showing epicenters of independent earthquakes is given in Fig. 3. The slope of recurrence graph γ and seismic activity A10 is based on the Gutenberg-Richter law stating the fundamental property of seismic process. The recurrence graph slope is calculated from continuous exponential distribution of earthquakes by energy classes. Using γ is conditioned by observations that in some cases the slope of the recurrence graph decreases prior to a large earthquake. Activity A10 is calculated from the number of earthquakes N and recurrence graph slope γ. Average slopes of recurrence graph γ and seismic activity A10 for the area under study in 2008 are calculated; our estimations give evidence that the year of 2008 was not anomalous in terms of seismicity. Based on 2D distribution of recurrence graph slope γ, it is possible to locate an area of lower values of γ in the southern part of the Kamchatka seismic zone (Fig. 4). Data on maps of normalized variation of γ for 2007–2008 and 2006–2008 (Fig. 5) confirm statistical importance of γ reduction through the last three years in the given area. Maps of 2D distribution of seismic activity A10 are constructed for 2008 and the perdiod from 1962 to 2008; values of seismic activity A10 that are normalized to the average annual seismic activity are also mapped (Fig. 6). In 2008, increased values of A10 were observed at the southern part of the Avachinsky gulf and at the northern part of the Kamchatka gulf, as well as in the northern water area of Bering Island. The anomalous behavior of parameters RTL, ΔS and clustering of earthquakes may have predictive character [Sobolev, 2000]. Negative values of RTL-parameter correspond to seismic quiescence; increasing areas of seismic ruptures ΔS correspond to foreshock activation; clustering of earthquakes can evidence that activation tends to accumulate at a future main rupture location. For 2008, three zones of seismic quiescence were defined by data (Fig. 7). For estimation points with maximum modular values of RTL (marked by the Roman numerals in Fig. 7), RTL time curves are constructed for each of the above mentioned zones (Fig. 8); they provide for defining durations of anomalies and degrees of manifestation. A map of variations of seismic rupture areas ΔS (Fig. 9) shows that seismic activity of 2008 was mainly manifested at the southern part of the Kamchatka seismic zone. In 2008, most of the earthquake clusters varying in energy also occurred in the southern part of Kamchatka (Fig. 10). The northern chain of clusters is located at the border of the developing seismic anomaly, as defined by RTL parameter. Similar to RTL technique, an objective of the Zfunction method is to reveal seismic quiescence periods as temporary anomalies of seismic process in specific areas [Wyss, Habermann, 1988] The Z-function method reveals a zone wherein seismic rates decreased by a factor of 8 during 2008 (see a dashed-line contour in Fig. 11); the given zone is partially coincident with the southern anomaly defined by RTL parameter. The curve showing time dependence Z(t) through 12 months confirms statistical significance of seismic quiescence in the given area (Fig. 12). It should be noted that epicenters of the three largest earthquakes of 2008 occurred at the areas of seismic quiescence that are revealed by both methods (see Fig. 7 and 11). Earthquake timing is shown by arrows on corresponding time curves (see Fig. 8 and 12). Taking into account that a number of indicators, which can potentially have predictive character, are well correlated in space and time, there are grounds to conclude that seismic danger is increased in the southern part of the Kamchatka seismic zone and the Kamchatka Gulf region.

Three-dimensional space-time diagrams of «logarithm of total energy released by earthquakes» parameter, lgEsum are constructed for regions with stable concentrations of earthquake epicenters in Cis-Baikal region for a period from 1964 to 2002. Based on analyses of such diagrams, areas of slow migration of seismic activity are defined. Estimated are distances, time and velocities of slow migration in the range of the first kilometers – first dozen of kilometers per year.

Procedures of seismic data projection and construction of 3D diagrams are described in brief. A general scheme including contours of projection areas is proposed for the Pribaikalie (Fig. 1).

Three space-time diagrams are presented as examples of application of the above mentioned procedures. They are constructed for the Middle and Southern Baikal basins and the western part of the NE flank of the Baikal rift system (Fig. 2). Integrated analytical results are presented for all the diagrams which record earthquake migration within the Baikal rift system.

We also present a scheme of the zone of slow migrations ranked by dominating velocities (Fig. 3) and a diagram of the migration velocity range. We consider possible causes of slow migration of seismic activity at variable velocities: (1) slow deformation waves spreading in the crust, and (2) independent propagation of the deformation front along active faults.

Regulations of migration of strong earthquakes can be useful for definition of timelines and locations of future strong seismic events.

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.

Members of editorial board and readers of «Geodynamic & Tectonophysics» deeply grieve about unlimited death of a member of editorial board the professor Jack Angelier and express the intimate condolence to his family, friends and colleagues.