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RESEARCH PAPER

EARTH SCIENCE FRONTIERS Volume 14, Issue 1, January 2007 Online English edition of the Chinese language journal

Cite this article as: Earth Science Frontiers, 2007, 14(1): 193–206.

Received date: 2005-11-07. *Corresponding author: E-mail: [email protected] Copyright © 2007, China University of Geosciences (Beijing) and Peking University, Published by Elsevier B.V. All rights reserved..

Synergetics in Geology V.I. StAROSTIN*, A.S. SHCHERBAKOV, D.R. SAKYS Moscow State University, Leninskie Gory, Moscow 119992, Russia

Abstract: Synergetics as the general theory of self-organization, embraces a large class of natural phenomena and is not limited by the thermodynamic condition. The thermodynamic structure and thermal chaos are only one of the forms of polarity of existence. The structural self-organization proceeds in such a way that numerous fluctuations are formed at the beginning. Amplitudes of long-range correlations, which are small at first, increase when the system moves far away from the equilibrium. As a result, a single fluctuation, which embraces the entire system, emerges from a multitude of fluctuations. This thesis of synergetics describes the inorganic world by a completely different perspective. All classes of inorganic bodies, including geological ones, should be considered as mutants and products of the selection of mutants that have been realized in accordance with the Darwinian logical scheme. Nature is quite often but not always expressed in fractal forms, which is divided into the 'correct' and 'incorrect' ones. Example of correct fractal is crystalline lattices with their different-scale repeatability of elementary cell. Our planet is a natural fractal formation of the class incorrect fractals. Considering the subordination as a law of fraction structure, it is necessary to assume that lithosphere in both large and small configurations is also a fractal structure. Logically, the entire geological reality should represent a fractal product of synergetic self-organization of inorganic matter. The Earth represents a multistage convective system like the Benard's convective structure, in which convection at one level initiates convection at the next overlying level. The principle of structure-forming convection is manifested in both large and small scales. It constitutes, for example, the base of the theory of fluidization during the formation of mineral deposits that also includes other principles of synergetics. According to this theory, subsidence of sedimentary rocks is accompanied by the formation of fluid-saturated zones of dilatation. Fluids are represented by water-hydrocarbon components in the upper part and by water-carbonate and ore components in the lower part of the sedimentary section. Under the influence of increase in temperature with depth, the fluids are heated and the intraformation pressure is anomalously increased. Consequently, the heated fluids penetrate the higher levels of the section. The ascending fluids, which represent powerful heat carriers, realize the convective mechanism of significant additional heating of overlying sedimentary rocks and sharply accelerate their katagenetic transformation.

Key Words: synergetics; self-organization; thermodynamics

In contrast to other sciences, data of the birth of synergetics is reliably established. At the scientific conference in 1973, G. Haken made a report "Cooperative phenomena in strongly nonequilibrium aphysical systems". Haken noted that cooperative phenomena are observed in most of the different systems and environments. All phenomena such as phase transitions, autocatalytic reactions, dynamics of populations, astrophysical phenomena, social processes and even the origination and development of mode are examples of the joint cooperative synergetic phenomena. When they reach a certain boundary, the chaos of relationship between elements is immediately replaced by their structurally ordered relationship.

Any ensemble of elements is a self-organized and spontaneous self-arrangement of certain units of matter[1–5]. Processes of the cooperative self-organization take place by an unexplainable mysterious way. Elements act in a self-coordinated manner. There is no external control, and elements themselves decide the type of future structure. This is well demonstrated in the Taylor instability. The motion of liquid between coaxial cylinders was investigated in the experiment. The exterior cylinder is fixed, whereas the internal cylinder rotates. The liquid moves in a laminar regime at low rotation speed. At a certain threshold rotation speed, fluid structures oscillate with one or two frequencies. More complex structures can also be observed with an

V.I. STAROSTIN et al. / Earth Science Frontiers, 2007, 14(1): 193–206

oscillation frequency equal to 1/2, 1/4, 1/8, 1/16 of the main frequency. But how can one understand the following fact: at the critical threshold level, the chaos of water molecules ceases and each molecule tends to a certain point in space. How does any unit molecule of H2O know its unique place in the general structure?

Collectivity and coherence of the action of elements―emphasized Haken―are the key for understanding the synergetic self-assemblage of structures. Indeed, recrystallization of melt is followed by the collective organization of atoms in nodes of crystalline lattice of mineral. Magnetic moments are collectively arranged in the ferromagnetic matter, whereas molecule vortices in liquid or autocatalytic chemical reactions are self-arranged. Thus it can be confidently stated that cooperative arrangement and self-coordination is the general tool of structurization in any form of matter ranging from atomic units to social and intellectual matter.

1 Disequilibrium state and self-organization of medium

In addition to cooperative arrangement, the theory of synergetics includes another essential feature of the genesis of structuring, namely the nonequilibrium state of medium, i.e., such a state has to be constantly maintained by the input of external energy. The synergetic self-assemblage of structures takes place only when the energy flux drives out the system from the static state beyond the stability boundary. The statement, “the case of heat systems― beyond the boundary thermodynamic equilibrium” suggests at least four signs of self-organization[5–9]:

(1) Motion. This is natural. Self-organization of elements appears only in deep zones of the process.

(2) Open state of system. Classical thermodynamics investigated situations with heated gas in absolutely isolated vessel. New nonlinear thermodynamics do not consider ideal situations but consider real systems that are connected with the environment in terms of energy. Input of external energy is an essential condition of self-organization.

(3) Cooperative arrangement, coherence of the action of elements.

(4) Nonlinear thermodynamic situation. Nonequilibrium state implies the following. Both the

principles of thermodynamics are formulated for closed systems. According to the second principle, entropy increases in such system, and the whole system of its elements tends to equilibrium, i.e., the mean statistic distribution. Maximum entropy is maximum uncertainty and amorphous Brownian chaos in the relation of elements. Input of external energy leads to deviation from equilibrium. It not only suppresses the growth of entropy but also decreases the entropy. In this case, chaos in the system do

not disappear gradually. Only when the input of energy leads the system far beyond the equilibrium, the chaotic ensemble of elements is structurized in a stepwise manner.

The list of conditions of self-organization mentioned above suggests that the synergetics embraces only the thermal and thermodynamic processes, because the law of entropy growth is the second law of thermodynamics. However, it is not so.

The law of entropy growth was indeed first derived from the analysis of thermal processes. It was formulated by Clausivitz and was dismally interpreted soon after his death. In accordance with the law of entropy growth, thermal energy of any body is irretrievably dispersed. This is valid for any macroobject, as is for the whole Universe. The energy of stars and galaxies is dispersed and averaged in the cosmic refrigerator at some moment. The law of entropy growth leads to leveling of the difference in energy potentials in the Earth as well. Ultimately, all and any kind of processes will cease, and the Universe will come to standstill. At present, the development of synergetics has made clear as to why the above scenario did not occur. Synergetics has showed that the law of entropy growth, the demon of destruction, has an antipode defined as the principle of spontaneous structure genesis. This is a creative principle that provides the complication of matter in the Earth from the bio-inert form to the organic and intellectual ones.

To understand the deep essence of the theory of synergetics, it is necessary to know that, similar to the anti-entropic structure genesis, the entropic destruction is not limited by the class of thermodynamic phenomena. This is the partial invariant of world order, which appears and acts as difference of potentials in other fields of physics as well, similar to that in sciences of inorganic, organic, and socially organized matter. In addition, the theory of synergetic structure genesis with all logical bases of its essential principles was first constructed on the basis of the analysis of the thermodynamics of chemical processes.

As it is well known, the principles and mechanisms of the self-organization were distinctly formulated for the first time on the basis of autocatalytic chemical reactions by the Nobel laureate I. Prigogine, a descendant of Russian emigrants. I. Prigogine and G. Haken are the founders of synergetics, although they worked independently from each other. Therefore, Prigogine's theory is called "the theory of dissipative structures" rather than "synergetics" (this term was proposed by Haken). Its essence is simple [10–12].

2 Dissipative structures

Assume a system that intakes matter and energy. Under the action of energy flux, the system travels beyond the boundaries of the thermodynamic equilibrium. Beyond a


certain critical level, complex structures with spatiotemporal ordering appear in the system spontaneously, i.e., without exterior plan or control. The self-coordinated behavior of elements is based on the moment of matter activity-resonance excitation, which was not known previously. The essence of this phenomenon is clearly described in the book written by I. Prigogine and I. Stengers 'Order from disorder', in which transitional states of systems are considered[12]. The first state is the stable phase state (volume of gas, liquid, chemical reaction, laminar flow, etc.). It turned out that elements of system in equilibrium state behave independently, i.e., "each element ignores the remaining ones". Considering such passive behavior of particles, Prigogine called them hypnones, i.e., particles in a hypnotic sleeping state.

The transition to the nonequilibrium state excites the hypnones. The matter apparently wakes up. The particles are transferred to the resonance excitation state. A coherent connection, which is quite unfamiliar for their behaviour in equilibrium conditions, is established between them. In this case, the elements cease to become independent. Their integrated system behaves as if it is a reservoir of long-range forces. Although molecular (electromagnetic) interactions are short-range forces (they act over 10–8 cm), the system is such that each molecule gets information about the state of the whole system[11].

The structural self-organization proceeds in such a way that numerous fluctuations are formed in it at first. Amplitudes of long-range correlations are still small. They increase when the system goes far away from the equilibrium. As a result, a single fluctuation, which embraces the entire system, emerges from the multitude of fluctuations. According to Prigogine, this is the dissipative structure. The point where structure genesis takes place is called the bifurcation point. 'Bi' means two, i.e., division of the system, because it distinctly shows separation into chaos and ordering. The more substantial interpretation of this notion is as follows. The system can be located in three states at a critical point. One state is unstable, whereas other two states are stable. The system ultimately chooses one of the states for its further development. Thus, bifurcation takes place in the evolution of dissipative structures.

The bifurcation point has such a great meaning that it can be considered as the focus of the entire theory of self-organization. At the bifurcation point, just a chaotic ensemble of some units of matter cannot be observed. This is a dynamic group with numerous degrees of freedom. Here each fluctuation as united ensemble is a potentially preset construction that competes with other constructions. The relationship of fluctuations is a struggle of each fluctuation for the possibility of realization, i.e., for monopoly and reconstruction by suppressing all other fluctuations. As a matter of fact, this is the principle of system-structure

creation in nature. Probably, herein lies the mystery of creative potentials of a self-developing matter.

Two very important peculiarities of the dissipative structure genesis are discussed below. First, the generation of structures, more precisely, their specific nature depends on the material, conditions, and situations that are present initially in the system. For example, in the case of chemical dissipative structure, its parameters, spatiotemporal ordering and whole specifics depend on the concentrations of reagents, the accidental admixtures and also the form of walls of the vessel, in which the reaction occurs. In other words, chaos of fluctuations beyond the equilibrium state generates a structure, in which it determines the scale, symmetry type and spatiotemporal periodicity type (e.g., the Belousov-Zhabotinsky's 'chemical watches' reaction). The dissipative formation of the structure reflects internal conditions of origination. Exterior conditions are also superimposed upon them. The orientation of structure genesis on the external factors is characterized by excellent sensibility. Prigogine emphasizes that the system in a strongly nonequilibrium state begins to perceive exterior fields, for example, gravitational and magnetic fields of the Earth. The system responds even to intensity of the influence of light[11]. This supersensibility received a curious interpretation by our leading researchers of synergetics V.I. Arshinov and V.G. Budanov. They interpreted the super-sensibility of unstable systems to exterior forces as the response of each dissipative structure to the totality of phenomena in the Universe, i.e., their participation in all processes, including the human being as an observer of process[6].

Thus, the totality of factors in the medium is not just an exterior background of structure genesis. The entire process of synergetic self-organization represents a process of selection of structural configurations predetermined by the exterior conditions. This statement implies an important ideological and methodological thesis about the universality of the principle of natural selection. Prigogine writes: "The selection of dissipative structures in the evolution of inorganic objects turns out to be not just exterior analogue of the Darwinian selection. On the contrary, we deal with the phenomenon of a general trend for both organic and inorganic objects. Thus, the traditional rigorous discrimination of regularities in organic and inorganic matter is smoothed out". According to this approach, life ceases to resist the 'common' laws of physics. Today, physics has all bases to describe the structures as forms of adaptation to the exterior conditions[11]. This thesis of synergetics describes the inorganic world by a completely different perspective. Henceforth, all classes of inorganic bodies, including geological ones, should be considered not only as a natural fact but also as mutants and products of the selection of mutants that have been realized in accordance


with the Darwinian logical scheme. Thus, it is known that any unit of matter beyond the

boundary of thermodynamic equilibrium acquires the state of resonance excitation. Long-range forces of the correlation of elements participate in this case. Structure of the future object is created at the bifurcation point. The dissipative structure genesis follows the unstable regime, and numerous fluctuations are observed in the system. The system apparently fluctuates before the selection of its new evolution path. It is important for this state that numerous degrees of freedom are available. Resolution of this situation is predetermined by some influence of factors of the medium, which can be negligibly small in terms of energy potential.

As the probabilistic selection was understood and the system entered a certain path of development, the incident loses force. Until the next bifurcation point, the system will function in terms of determination. Originating at the bifurcation point, the new formation apparently forgets the probabilistic circumstances of its origination and develops even on the basis of laws corresponding to nature. The notion 'nature of system' means the specific type of its nonlinearity. In the general case, 'nonlinearity' means the absence of direct correlation between the interrelated phenomena. This is related to different degrees of competency of systems at different properties of components.

For example, the theory of dissipative structures suggests that the thermal flux in various parts of the system will scatter differently because of nonlinearity. Competitive relationships develop along the parameter of energy dissipation between nodes of the object. They include one dominant sector that draws the whole energy to itself, i.e., the thermodynamic situation includes one fast process that suppresses all of the remaining processes. We would like to again emphasize that the competition of thermal fluxes concerns only one partial case in the Prigogine's theory of dissipative structures. Synergetics as the general theory of self-organization embraces a large class of natural phenomena and is not limited by the thermodynamic situation, i.e., each phenomenon contains an invariant circumstance of competition, selection, and separation of the leading process. Such is the regime of wave selection in laser resonator, plasma state of matter, and chemical autocatalytic reactions.

In the biological evolution, the single choice of signs of evolutionary preference leads to the fact that the process of species evolution is characterized by acceleration. In the natural selection, forms appearing more rapidly and earlier than others succeed and are affirmed. This is the 'exacerbation regime' that is inherent to all nonlinear systems.

3 Exacerbation regime

The exacerbation regime is one of the key points in the theory of self-organization. Within the framework of synergetic process, this principle fulfils quite certain functions. First, the exacerbation regime provides the growth of a small body. It selectively intensifies a certain singular anomaly and transforms the small body into large one. Therefore, some small deviation (for example, reagent imprint) in the cycle of reactions acquires a dominating significance that can reprogram the entire chemical process. Second, the exacerbation regime determines the measure of sensitivity of an evolving system. In other words, the system remains analogous to itself up to a certain point. It suppresses the trend, deviations in the system, anomalies, and fluctuations. All of them are smoothed out without any traces. Such processes take place in nature, science, and culture. Third, and it is particularly important, the exacerbation regime determines the orientation of development paths. This means that only one exacerbation regime is possible because of the nonlinearity. Hence, any formation initially contains a program of the further development. That is, not any evolution path but only a certain path or spectrum of paths is possible for the specified observed phenomenon. This fact leads to the next synergetic phenomenon that represents a logical node in the theory of self-organization and is known as 'attractor'.

It is reasonable to interpret 'attractor' as an analogue of the law of entropy growth for open nonlinear systems or media. The law of entropy growth includes the obligatority of the motion of elements in an isolated system relative to equilibrium thermal chaos, i.e., the state of maximal entropy. Attractors of the evolution of open nonlinear systems also bear the obligatority of the motion of processes in a certain direction. Therefore, in the general case, the term 'attractor' corresponds to the future structure that obligatorily follows from the processes in the given nonlinear system. The concept 'attractor' is close to the concept 'purpose'. The term 'purpose' is interpreted in the wide (beyond the antropic) sense as the directionality of behaviour and the presence of final state. In other words, 'attractor' in the synergetics is understood as the future state of system that apparently attracts the possible trajectories of its motion in all types of their directions. On the other hand, on the basis of this fact, S.P. Kurdyumov, E.N. Knyazev[8] and other Russian synergeticists assume the possibility of determination from the future. The visual analogue of attractor is, for example, cone that attracts numerous trajectories and predetermines the process of evolution. Its psychological analogue can be the sum of obvious or hidden directions, features of character, and genetically inherited or acquired preferences that unconsciously force us to make unambiguous choice and create our own fate.


Finally, let us consider fractal or fractality, a key thesis of the synergetic concept of self-organization. The term 'fractality' means a general matter contained in the entire multitude of dissipative structures as the final result of synergetic process. Fractality is self-similarity or scale invariance. This means that a small fragment of structure in stereometry is similar and incorporated into the larger fragment. The latter fragment is similar to a larger configuration and so on up to the architecture of the entire object [13,14]. It has been established that nature is quite often but not always expressed in fractal forms. The fractals are divided into the 'correct' and 'incorrect' ones. Example of the correct fractal is crystalline lattices with their different-scale repeatability of elementary cell. The 'incorrect' fractals only show the trend of symmetric self-similarity. This is a type of idealized architectural invariance. Fractal formation is exemplified by the lung of human being, in which each bronchus bifurcates into small bronchial tubes. Configurations of tree branches, frost, banded clouds, and marine coasts are also fractal. The Norwegian coastline crosscut by fjords also represents the fractal structure with the scale reproducibility coefficient of 1.526.

Fractality is actively discussed in the literature. On the basis of spatial-topological side of self-similarity, one group of specialists on synergetics affirms that the fractality is not universal. Although it is manifested in tens of forms, fractality is episodic and local. Another group assumes that the fractal repeatability must be understood in a wider sense than the spatial invariance. The self-similarity can be manifested in the temporal periodicity of cyclic processes. For example, it can also be expressed in the rhythmic repeatability of properties of similar objects, as in the case of chemical elements in the Mendeleev Periodic Table. In this interpretation, fractal self-similarity is a common feature of natural structures. However, it is important that the fractality is an objective criterion of the parental synergetic process. It is also important that synergetics investigates the most different fields of scientific knowledge by means of fractality. In this sense, the modern relativist cosmology is a representative example.

It has been long ago affirmed in modern cosmology that the 'Big Bang' with the generation of cosmic matter is an energetically nonexpendable phenomenon. The meaning of well-known 'free breakfast' theory lies in that the formation of Megagalaxy is paid not by the energy, but by the entropy. The principle (synergetic) assessment of this phenomenon is found in works of Prigogine. He emphasizes that the origination of matter from an unstable physical vacuum is essentially analogous to phase transition. The transition itself is a result of the instability of vacuum caused by its internal fluctuations. Considering the synergetic development of ordered system of galaxy, Prigogine gives a comparison with the formation of Benard cells. Let us

remind its sense for the future discussion. Experiment of self-organization carried out by Benard is simple and convincing. A layer of mineral oil is poured onto the heated frying pan. Aluminium pieces are mixed up with oil for the sake of clarity. At first, the oil is at rest. However, heating of the zone between the upper and lower boundaries of the oil creates difference in temperature. The heated (hence, lighter) lower and the upper (heavier) oil layers tend to exchange places. Up to a certain moment, the internal motion of particles is damped by forces of viscosity. Then a convective flux appears at the critical difference of temperatures, and the oil layer is abruptly divided into hexagonal cells resembling the honeycomb[9].

The formation of hexagonal ordering, i.e., hexagonal stereometry of fractal is a means for the more effective dispersion of thermal energy. Cavities between the cells represent channels of dissipation. The dispersion of energy means entropy growth. Hence, the Benard structure appears as a result of sudden entropy growth. It means that the development of synergetic ordering is paid not by the energy, but by the entropy. This is also the case with the development of Metagalaxy. This is a 'free', i.e., energetically nonexpendable phenomenon. The origin of Universe, according to Prigogine, is a product of the giant explosion of entropy[12]. As for the type of its fractal ordering, answer to this question has been recently obtained. Metagalaxy is not chaotic. It was found that gravitational centres of the discovered 420 supergalaxies make up a cubic structure. Thus, the visible Universe is very primitive in terms of fractality.

4 Principles of synergetics in geology

Our planet is also probably a cosmic fractal. This is in accordance with the the well-developed theory of D. Gregory. He formulated several laws that reflect the mutual position of lands and oceans and showed that the body of planet has a spheroidal-octahedral configuration. Certainly, the octahedron of Earth is an approximate model. Actually, octahedron faces are not straight lines but are arc-shaped. In reality, convex segments of the surface of the Earth correspond to triangles. Besides, they are not ideally correct. But this does not rule out that our planet is a natural fractal formation of the class of 'incorrect' fractals. Taking into consideration the subordination as a law of fraction structure, it is necessary to assume that the lithosphere in both the large and small configurations is also fractal. Logically, the entire geological reality should represent a fractal product of synergetic self-organization of inorganic matter. This is confirmed by the numerical statistic analysis of planetary network of lineaments. This analysis leads to the following conclusions: (1) the system of at least Mesozoic and Cenozoic global tectonic structures has the symmetry of


correct polyhedrons; (2) lithospheric formations show three types of symmetry: tetrahedral, cubic, and icosahedral; (3) tetrahedral symmetry is best manifested in the mantle; (4) the position of lithospheric plates in the geological past was also geometrically ordered. Their rearrangement took place in a stepwise manner reflected in epochs of tectogenesis[15].

On the basis of numerous data, V.E. Khain concluded that our planet represents a multistage convective system like the Benard's convective structure, in which convection at one level provokes convection at the next overlying level[16].

It should be emphasized that the principle of structure-forming convection is manifested in both the large and small scales. It lies, for example, in the base of the theory of fluidization during the formation of mineral deposits that also include other principles of synergetics[17]. The theory of fluidization suggests that subsidence of sedimentary rocks is accompanied by the formation of fluid-saturated dilatation zones. Fluids are represented by water-hydrocarbon components in the upper part of the sedimentary section and by water-carbonate and ore components in the lower part. Under the influence of temperature increase with depth, fluids are heated and the intraformation pressure is anomalously increased. Consequently, the heated fluids penetrate the higher levels of the section. The ascending fluids, in turn, are powerful carriers of heat. They realize the convective mechanism of significant additional heating of overlying sedimentary rocks and sharply accelerate their katagenetic transformation. This is the mechanism of differentiation of the primary matter into the light petroliferous and heavy ore-bearing fractions [17]. It is not difficult to understand that we deal here with the bifurcational separation of process and exacerbation regime in the geological form. Let us present some more examples.

Cryology. It is well known that frozen ground has polygonal divisibility. This is simply referred to as self-similarity according to the convective mechanism. In fact, this mechanism does not differ from the classical Benard's cells. Their appearance is conditioned by the fast heating of ground as a result of the convection of ordered water in the subsurface layers. The only difference from the Benard's experiment lies in the fact that the warmer surface is at the top. Convection appears owing to the difference in heat content between cold and warm waters.

Volcanology. A good example of synergetic structures is cellular lava sheets. Hexagonal columns in basalts can reach a height of 20 m. Such correct divisibility is observed only near the surface, where the temperature difference is maximal. Mechanism of the formation of cellular basaltic fields corresponds to the same Benard's effect. Cells appear because of the necessity to rapidly dissipate the excess thermal energy. Contraction fractures serve as conduits of its release.

Structural geology. Vortex structures are an interesting geological phenomenon. It is assumed that spiral and conical structures are not accidental exotic features. Vortex-type structures are widespread in the lithosphere. Their nature is similar to that of structures in the Taylor's hydrodynamic experiment. The geological mechanism of their formation is as follows. Instability is caused by turbulence due to crystallization energy. In this process, the effect of long-range ordering and vertical self-organization of rock mass appears in rock near the critical point.

Geomorphology. Here, geometry of relief isolines is connected with the synergetic self-organization. Fractal dimensionality of river systems has been discussed in many studies. It turned out that the formation of the fractal river system is based on the principle of minimization of energy dissipation by the given system. Now, it has been established that the bifurcation of river systems follows the simple law of Harton who proposed to divide the river system into different segments designated by indices 1 (initial segment), 2 (segment formed after the confluence of two flows), and 3 (segment formed after the confluence of two double index flows). The ratio of the number of segments with two adjacent indices indicates the bifurcation division, which is always equal to 3. The hierarchic structure of flows indicates fractal properties of river systems and, hence, topographies, on the whole.

Geochemistry. The concepts of synergetics in the terms of chemical processes in lithosphere have been widely used in geochemistry for a long time. And this is understandable, because the whole theory of dissipative structures is based on the analysis of chemical processes of nonlinear thermodynamics that correspond to natural geological phenomena. Studies of modern geochemistry in this direction are discussed in[18].

Geotectonics. Cooperative self-organization in the development and structure of the Earth exists as an integral concept. It has been developed by V.E. Khain[16], Yu.M. Pushcharovsky[19], O.V. Petrov[20], P.A. Besprozvanny[15], and many other geologists. However, it is necessary to note that the earliest, primarily deductive-hypothetic investigation of this kind is linked with the name of the prominent geophysicist M.A. Sadovsky[21].

As early as 1979, Sadovsky proposed to consider the lithosphere as a system wherein the inhomogeneities in structures, substances, density etc, interact among each other. Lithosphere as a nonlinear system also includes another essential condition of spontaneous self-organization, namely, endogenic energy flux that continuously penetrates the lithosphere. According to Sadovsky, this typical synergetic situation necessarily produces a fractal dissipative structure of the planetary scale. He emphasized that geological synergetics is much more complicated than Prigogine's scheme of structure genesis. It includes such


factors as lithosphere vibration in a wide range of scales and frequencies: from thermal oscillations of atoms to motion of macrosystems including earthquakes and motions of continental plates. In accordance with the logics of synergetics, forces of long-range forces participating in the system infinitely increase the radius of coordinated behavior of lithospheric inhomogeneities. The effect of cooperative action is realized at all stages of the subordinated scale of its subsystems. Self-structuring at the upper stage is performed at the expense of analogous processes at the lower stage.

Sadovsky introduced a concept that enriches Prigogine's concept of self-organization concerning the role of deep faults in lithosphere: the deep faults are nothing but a zone of intense dissipation of thermal energy, and the formation of lithospheric structure is attributed to the formation of deep faults. The situation is exactly similar to that in the case of Benard's experiment. The formation of convective cells is a tool for improving the dissipation of energy that is released in faults on the surfaces of cells. The novel concept is that spontaneous structure genesis is not considered as the final step of synergetic phenomenon. This is only a tool, a method of adaptive behavior of system under changing conditions. The structured pattern of lithospheric blocks reflects the maximal, effective heat deflection process by an ordered network of deep faults. Faults themselves in this case represent a network of system-links of lithospheric blocks. This ultimately means that the Earth's lithosphere should be based on the principle of superposition. It should include the subordinated hierarchy of self-similar fractal configurations.

The heuristic value obtained in the studies of Sadovsky is primarily related to the concept of fractal self-organization of geological complexes. The situation that existed at that time was such that this aspect of synergetics began to be precisely incorporated in geology. An even higher significance is given to the concept of the role of 'long-range forces'. According to Sadovsky, these forces represent an essential core of the entire geological dynamics. Thanks to the pioneer works of Goryainov and Ivanyuk[7], this concept was included in geology only in the latest period. It should be noted that the investigation of these forces attracts special attention due to two reasons. First, because the object of attention is the Archaean history imprinted on the whole subsequent geology. Second, because here we almost obtain the clue for the applied methodological-reconnaissance level of analysis of phenomena.

Goryainov and Ivanyuk analyzed the plate tectonics theory from the point of view of synergetics and refined this theory in such a way that a completely new scenario of tectonic motions and folding is outlined. The cooperative nature of structuring serves as a reference system for the authors, which changes the logic of understanding tectogenesis within the framework of mobilistic and fixistic

concepts. Despite differences in the interpretation of tectonic structuring, both concepts are similar in one point: the formation of structures is a result of the passive response of crustal material to mantle perturbations. In such case, the structures have only regional (local) order that imprints the specific action field of forces and direction of the vector of their application.

The synergetic concept rules out restriction by the influence of linear energy of force. Any fold or fold zone is not a local-scale event but a small node in the general network of processes of cooperative self-organization. The fold zone is nothing but a fragment of dissipative structure based on the cooperative long-range forces. In the synergetic self-organization, folds as fragments of fractal structure genetically depend neither on the place of application nor on the orientation of these forces. Actually, they represent frozen autowaves without dislocation of matter during the network formation[7].

Thus, one can well see differences in the synergetic and mobilistic paradigms of geodynamics. The synergetic concept of self-organization affirms that the long-range order of elements appears at the bifurcation point. In this system, each subsystem or process is an organic part of the whole body and can be understood only through study of the whole body. Whereas according to the synergetic concept, the uncoordinated autonomous-local migration of lithospheric blocks is only an apparent process. Variations in coordinates of lithospheric structures independently of the integral dynamics of lithosphere are principally impossible[7]. This implies a novel interpretation of the Wilson cycle.

The Wilson cycle supposes extension and filling of the region at the early stage, with contraction and folding at the final stage. In the synergetics, system at the bifurcation point chooses a certain evolutionary path and cannot return to the initial position. In the geological context, this means that region at the bifurcation point chooses a developmental scenario that is best from the viewpoint of its stabilization under new conditions. It cannot return to the primary static form. Specifically, the region cannot experience both active extension and then active compression. In this context, the three-fold (according to some versions, four-fold) breakdown and amalgamation of Gondwana looks as a surrealistic plot. Evidently, amalgamation of a certain block should be accomplished in a single synergetic scenario. According to Goryainov and Ivanyuk, proponents of synergetics in geology, this scenario is as follows. At the first stage, thermal energy induces the formation of rifts with lateral basins. At the second stage, they are filled with sediments. Energy flux now becomes discrete. At the third stage, the rift valley is filled with volcano-sedimentary rocks. At the final stage, energy flux occurs. Breakthrough of energy at focal points induces shock perturbations. It is characteristic that a united fractal network, i.e., a network of


energy percolation or endogenic energy discharge is developed in earthquake centers. It is principally important that the network reveals the cooperative synergetic nature of process. This means that the network organizes formations of any age and of any genesis. This network contains the united ordering of sedimentary and magmatic rocks, old rock massifs, active island arcs, and new mid-oceanic ridges[7].

The process continues in the following manner. Folding, metamorphism, and final magmatism seal the percolation sutures, after which the percolation cell with the primary oceanic crust disappears. A new cell, always larger than the previous one, originates from its elements preserved on the old material. The cycle resumes and fixes the new system of suture rifts. The last cycle represents rift system of the modern world. One should emphasize that the model of energy percolation, which is in essence similar to the Benard experiment, represents the hierarchy of tectonospheric ensembles and reflects three characteristic peculiarities of tectonosphere: fractality of lithospheric complexes, coherence of the behavior of subsystems and structural homeostasis, and adaptation of ensembles to energy flux [7].

This synergetic model of tectonosphere is not only a theoretical construction. On the contrary, it is a pragmatic scheme that opens principally new possibilities for metallogenic constructions and concrete geological prognosis. This statement is supported by data on banded iron deposits.

It is known that ferruginous quartzites represent concentrated geology of the Precambrian. The entire analytical pathos of researchers is based on the thesis that the oldest (probably, younger as well) iron ore belts record the percolation network of endogenous energy discharge. Analyzing factual data, one can conclude that the oldest Archaean-Cenozoic percolation zone has a direct relation with the dynamics of processes associated with iron ore. Iron ore belts are products of the differentiation of the Earth's protomaterial according to the synergetic scenario under the influence of the endogenous energy flux. The available data show that the formation stages of new structures were accompanied by overlapping of the new iron ore formation with the previous one. Therefore, formations pertaining to different ages turn out to be regionally juxtaposed. Despite the difference in age, genesis and composition, all iron ore belts are mutually coherent and coordinated in the integral fold system. This can be the consequence of only a single process of structurization, i.e., synergetic cooperative self-organization.

Indeed, all iron ore deposits of the Baltic Shield are located along transformed faults of an ancient percolation network. The structure of deposits shows self-similarity and fractality of different scales. For example, the

Kola-Norwegian megablock has the shape of a falling drop. It includes 12 ferruginous quartzite deposits of the same drop-shaped form and symmetric-zonal structure. When iron ore beds are subdivided into smaller bodies, the initial order is always preserved. Such succession cannot be explained by lithological or stratigraphic factors. It should only be understood as the consequence of coherent self-organization of an initially homogeneous sequence under the influence of endogenous energy flux[7].

The presented material is far from exhausting the range of geological phenomena of cooperative self-organization. There are reasons to affirm that principles of self-organization are obeyed by the entire visible circle of geological structurization ranging from the mineral-crystal scale to the planetary-cosmic one. If so, we should address two pragmatic issues―the introduction of synergetics into geology and the efficiency of synergetic approach in this field.

It is known that the development of scientific knowledge as such has its own laws and principles. One of them states that any revolution in perception does not reject the factual material that served as basis for the previous paradigm[22]. It is just overloaded on the platform of a novel theoretical concept. This is so in the given case as well. The interpretation of geological phenomena of synergetic formation does not require any previously established fact. For example, the mobilistic concept and the traditional concept of Early Precambrian geodynamics are retained in geology. Only the understanding of Precambrian geodynamics is different.

Finally, the question of pragmatic side of the problem is considered. It is of course early to talk about the efficiency of synergetic approach because of its preliminary developmental stage in geology. However, we have already affirmed that synergetics has promoted some progress in the methodology of prognosis. Indeed, Archaean tectonic complexes are products of cooperative dynamics, representing a peculiar analogue of Benard's structures. This interpretation proved wrong the traditional understanding of processes of structurization and transportation effect on the formation of iron ore deposits based on the principle of passive accumulation of deformations. Now one should consider that the genesis of banded ferruginous formations is related to the endogenous energy discharge in the percolation network of transformed faults rather than the accumulation of sediments in basins near rifts and metasomatism of basic rocks. This implies a novel approach to the concept of metallogeny. Its essence is that ferruginous formations have no deep roots. Their formation is the prerogative of near-surface levels. The velocity of percolation energy discharge nonlinearly increases in such zones. In terms of synergetics, the exacerbation regime functions in such near-surface zones. The Archaean surface


precisely controls high-temperature processes of petrogenesis and mineragenesis in such a manner.

Principles of synergetics are particularly applicable to any metamorphosed formations of Precambrian ferruginous formations. The main structure-forming element in areas of their development is oval tonalite blocks combined with banded ferruginous complexes. In plan view, lenses of ferruginous formations are always curvilinear and grouped into compact subconformable lenses. The ore district, field, deposit, lode or its fragment makes up similar lens-shaped structures of lesser dimensions depending only on the scale of investigation. The main structural pattern of ore deposits does not become complicated, and they do not distort orthogonal fractures. This statement is inconsistent with the existing concepts about the crosscutting character of transverse faults (Fig. 1).

The sequential analysis of major elements in the structure and composition of Archaean-Proterozoic complexes revealed another fundamental peculiarity, namely, the compatibility of structure and composition of their constituents. At different-scale levels, the structure of productive section contains a systematic repetition of the same zonality. Each lens of ferruginous quartzites is surrounded by the following sequence: leptites biotite gneisses hornblende gneisses bodies, the larger the

melanocratic rocks and the thinner the ore-bearing section. All lenses have the shape of a falling drop. Their thick part in the section is oriented to the top. With increasing depth, the size of lenses decreases and the glomerate is scattered. Signs of boudinage are absent (Figs. 2 and 3).

The formation of the ensemble described above is related to endogenous energy flux that reached upper horizons along the planetary percolation network and formed the metamorphic appearance of rocks, as well as dikes and veins in the smaller network when the flux weakened. The concentration of energy flux per unit mass of substrate was sufficient for the 'rootless melting'. The most grandiose iron ore provinces formed in regions where the energy flux primarily led to the formation of greenstone rocks; medium-grade provinces formed in amphibolite-facies areas with high contents of acid rocks; low-grade provinces formed in the granulite-facies rocks with the maximal content of acid formations.

The synergetic approach in geological prognosis concerns not only iron ore deposits. The common feature of principles of self-organization allows us to extrapolate this concept to the metallogeny of other elements as well. This statement is also valid for the genesis of rootless gold ore deposits. Gold is released from volcano-sedimentary rock

Fig. 1 Lens-shaped arrangement of Archaean iron ore complexes of the KMA and Yilgarn block, western Australia (according to Gole, 1981). Tonalite lenses are outlined by gray colour, whereas ferruginous deposits and occurrences are shown by black


Fig. 2 Geological sketch of the Kirovogorsk deposit area (a), and longitudinal section of the Kirovogorsk deposit along profile A-B (b)

(Based on Goryainov and Ivanyuk, 2001)

Fig. 3 Examples of active intraore microblock dynamics in orebodies of the Kirovogorsk deposit[1]

（1）aluminous gneisses; (2) ferruginous quartzites; (3) ceramic pegmatites; (4) dolerites; (5) faults


along the same percolation network and scheme of exacerbation regime.

Complexity of the transition of theoretical geology to new paradigm is attributed to the fact that one cannot declaratively introduce synergetics as such. Evidently, we have to pass the period of 'adaptation' of ideas of synergetics in the context of geology. This means that the known set of principles of synergetics must become a skeleton (essential core) of geological constructions. From this follows the task of transformation and adaptation of conceptual apparatus of geology to concepts of synergetics. An even more difficult problem is the reconstruction of the traditional arsenal of geological methods in harmony with the methodological principles of synergetics. Of course, one cannot ignore the complexities of psychological character and the internal protest against assault on the classical geology. The only soothing fact is that the synergetic geology does not replace the classical geology. The nonlinear geology only advances and introduces achievements of the latest physics and mathematics into the geological perception.

However, we should not deceive people. Of course, the synergetic paradigm often (and in many cases) changes the theoretical fundamental bases. This can be illustrated by the Archaean geology. Actually, if Archaean tectonic ensembles are dominated by autowave folding (rather than passively induced folding, as is accepted), then the concepts of the dynamics of Archaean tectonosphere will be so strongly reformed that not a single type of tectonic reconstructions will be acceptable. Since the compositional zonality of Archaean complexes has no stratigraphic nature, the conventional structural approach―'higher-lower' means 'younger-older'―loses its traditional sense. The method of stratigraphic subdivision also loses force in relation to most part of Precambrian complexes.

From the point of view of synergetics, the concept of regional metamorphism―subsidence followed by rise―is also baseless. Now one should consider that both these processes are interrelated. According to the novel concept, any metamorphic complex is a single compositional-dynamic population of one age. Hence, traditional methods of reconstruction based on structural-metamorphic scales are simply incorrect. Similarly, the concepts of structural geology concerning the nature of folding in general are also not acceptable. From the point of view of synergetic cooperativeness of phenomena, folds are not consequences of the local action of strains. They are different-scale products of a wide range of processes of self-organization of the geological material. In other words, folds represent the really observed synergetic autowaves migrating during the inertial geological time. Alas, we should accept that the synergetic approach is not so harmless for the classical geology. Introduction of synergetics into geology is not just a

development of certain new paradigm. As a matter of fact, synergetics is not a paradigm at all, but a novel ideology in geological science. It introduces a novel research strategy that substitutes many classical fundamental principles.

5 Conclusions

Synergetics as the general theory of self-organization embraces a large class of natural phenomena and is not limited by the thermodynamic condition. The thermodynamic structure and thermal chaos are only one of the forms of polarity of existence. The structural self-organization proceeds in such a way that numerous fluctuations are formed at the beginning. Amplitudes of long-range correlations, which are small at first, increase when the system moves far away from equilibrium. As a result, a single fluctuation, which embraces the entire system, emerges from the multitude of fluctuations. This thesis of synergetics describes the inorganic world by a completely different perspective. All classes of inorganic bodies, including geological ones, should be considered not just as natural bodies but also as mutants and products of the selection of mutants that have been realized in accordance with the Darwinian logical scheme.

It has been established that nature is quite often but not always expressed in fractal forms. The fractals are divided into the 'correct' and 'incorrect' ones. Example of the correct fractal is crystalline lattices with their different-scale repeatability of elementary cell. The Earth is a natural fractal formation belonging to the class of incorrect fractals. If we consider the subordination as a law of fraction structure, it is necessary to assume that lithosphere in both large and small configurations is also a fractal structure. Logically, the entire geological reality should represent a fractal product of synergetic self-organization of inorganic matter.

Our planet represents a multistage convective system like the Benard's convective structure, in which convection at one level initiates convection at the next overlying level. The common features of principles of self-organization allow us to extrapolate the synergetic approach in geological prognosis to the metallogeny of many ore deposits (iron, gold, base metals, and so on). The principle of structure-forming convection is manifested in both large and small scales. It constitutes, for example, the base of the theory of fluidization during the formation of mineral deposits. According to this theory, subsidence of sedimentary rocks is accompanied by the formation of fluid-saturated zones of dilatation. Fluids are represented by water–hydrocarbon components in the upper part of the sedimentary section and by water-carbonate and ore components in the lower part. Under the influence of increase in temperature with depth, fluids are heated and the


intraformation pressure is anomalously increased. Consequently, the heated fluids penetrate the higher levels of the section. The ascending fluids as powerful heat carriers realize the convective mechanism of significant additional heating of overlying sedimentary rocks and sharply accelerate their katagenetic transformation. Thus, the primary matter is differentiated, for example, into the light petroliferous and heavy ore fractions.

References

[1] Winner N. Cybernetics. Moscow: Nauka, 1967. [2] Danilov Yu A, Kadomtsev B B. What is synergetics. In:

Nonlinear waves. Self-organization. Moscow: Nauka, 1983. [3] Kapitsa S P, Kurdyumov S P, Malenetsky G G. Synergetics and

prognoses of future. Moscow: Nauka, 2003. [4] Haken G. Synergetics. Moscow: Nauka, 1980. [5] Haken G. Synergetic hierarchy of instabilities in self-organizing

systems and constructions. Moscow: Nauka, 1985. [6] Arshinov V I, Budanov V G. Self-organization and science. In:

Experience of philosophical comprehension. Moscow: Nauka, 1994.

[7] Goryainov P M, Ivanyuk G Yu. Self-organization of mineral systems. Moscow: Synergetic principles of geological investigation, 2001.

[8] Knyazeva E N, Kurdyumov S P. Laws of the evolution and self-organization of complex systems. Moscow: Nauka, 1994.

[9] Klimantovich N Yu. Without formulas about the self-organization. Minsk: Vysshaya Shkola, 1986.

[10] Nikolas G, Prigogine I. Perception of the complex. Moscow: Mir, 1990.

[11] Prigogine I, Stengers I. Order from chaos. Moscow: Mir, 1986. [12] Prigogine I, Stengers I. Time, chaos, quant. Moscow: Mir,

1994. [13] Kunover R. Fractals and chaos in dynamic systems. Moscow:

Postmarket, 2002. [14] Smirnov B M. Physics of fractal clusters. Moscow: Nauka,

1991. [15] Besprozvanny P A, Borozdin E V, Bush V A. Numerical

analysis of ordered planetary network of lineaments. Izv Ross Akad Nauk, Fizika Zemli, 1994, (1): 57–65.

[16] Khain V E. Layering of the Earth and multistage convection as the basis of the genuine global geodynamic model. Dokl Akad Nauk SSSR, 1989, 308: 1437–1440.

[17] Sokolov B A, Starostin V I. Fluidal concept of the formation of mineral deposits (metal and hydrocarbon). In: Smirnov collection (Scientific-literary anthology). Moscow: Viniti, 1997.

[18] Letnikov F A. Synergetics of geological systems. Novosibirsk: Nauka Sib Div, 1992.

[19] Pushcharovsky Yu M, Sokolov S D. Nonlinear tectonics. In: Fundamental problems of general tectonics. Moscow: Nauchny Mir, 2001.

[20] Petrov O V. Nonlinear phenomena of thermogravitational instability and internal gravitational waves in the Earth. Dokl Ross Akad Nauk, 1992, 326: 506–509.

[21] Sadovsky M A. On natural lumpiness of rocks. Dokl Akad Nauk SSSR, 1979, 247: 1135–1142.

[22] Egorov D G. Change of paradigm in Earth sciences: from induction-actualistic to synergetic concept. In: Abstracts of papers of new ideas on Earth sciences, 2001. 38.

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