SYNERGETICS IN GEOLOGY
Starostin V.I., Shcherbakov A.S., Sakya D.R.
Moscow State University, Leninskie gory, Moscow, 119992 Russia
e-mail: star@geol.msu.ru
Abstract
Synergetics as the general theory of self-organization embraces a large class of natural phenomena and is not
limited by the thermodynamic situation. 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
goes far away from the 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 in a completely different
light. 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 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 of incorrect fractals. If we take into consideration the subordination as a
law of fraction structure, it is necessary to suppose that lithosphere in both large and small configurations is also a
fractal structure. Logically, the entire geological reality should represent a fractal product of synenergetic selforganization 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 of the sedimentary section and by water
- carbonate and ore components in the lower part. Under the influence of temperature increasing 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, which represent powerful heat carriers, realize the convective
mechanism of significant additional heating of overlying sedimentary rocks and sharply accelerate their katagenetic
transformation.
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 the
most different systems and environments. Phase transitions, autocatalytic reactions, dynamics of
populations, astrophysical phenomena, social processes and even the origination and
development of mode - all these phenomena are examples of the joint cooperative synergetic
phenomena. When they reach a certain boundary, the chaos of relationship between elements is
instantly replaced by their structurally ordered relationship.
Any ensemble of elements is a self-organized and spontaneous self-arrangement of certain
units of matter [3, 6, 8, 22, 23]. 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 so-called Taylor instability. The motion of liquid between coaxial cylinders was investigated
in the experiment. The exterior cylinder is fixed, whereas the internal cylinder rotates. At low
rotation speed, the liquid moves in a laminar regime. At a certain threshold rotation speed, fluid
structures oscillate with one or two frequencies. One can also see more complex structures with
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
to be chaos 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 to
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. Now one can confidently
state 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.
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 that has to be constantly maintained by the input of external energy. The synergetic selfassemblage of structures takes place only when the energy flux drives out the system from the
static state beyond the stability boundary. For the case of heat systems - beyond the boundary
thermodynamic equilibrium. This statement suggests at least four signs of self-organization [1, 4,
9, 10, 23]:
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 considers not ideal situations, but
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 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 disappears not 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 above list of conditions of self-organization suggests that synergetics embraces only
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 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 it clear why the above scenario
did not take place. Synergetics has revealed 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 bioinert form to
the organic and intellectual ones.
In order to understand the deep essence of the theory of synergetics, it is necessary to know
that, like the antientropic structure genesis, the entropic destruction is not limited by the class of
thermodynamic phenomena. The thermodynamic structure and thermal chaos are only one of the
forms of polarity of existence. This is the partial invariant of world order, which appears and acts
as difference of potentials in other fields of physics as well, like in sciences of inorganic, organic
and socially organized matter. It is another thing that the theory of synergetic structure genesis
with all logical bases of its essential principles was first constructed based on the analysis of the
thermodynamics of chemical processes.
As is well known, principles and mechanisms of self-organization were distinctly
formulated for the first time based on 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 [13, 15, 16].
Dissipative Structures
Suppose a system that intakes matter and energy. Under the action of energy flux, the
system goes beyond the boundaries of 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 behaviour of elements is based on the
previously unknown moment of matter activity - resonance excitation. The essence of this
phenomenon is sufficiently clearly described in the book written by I. Prigogine and I. Stengers
'Order from disorder', in which transitional states of systems are considered [16]. 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". Taking into mind such passive behaviour 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 alien 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 as if each molecule gets information about the
state of the whole system [15].
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 load that it can be considered the focus of
the entire theory of self-organization. At the bifurcation point, we see not just a chaotic ensemble
of some units of matter. 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.
Now let us discuss two very important peculiarities of the dissipative structure genesis.
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 the whole specifics
depend on concentrations of reagents, accidental admixtures and even 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 fantastic 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 [15]. This
supersensibility received a curious interpretation by our leading researchers of synergetics V.I.
Arshinov and V.G. Budanov. They interpreted the supersensibility 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 [1].
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 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. Now physics
has all grounds to describe structures as forms of adaptation to exterior conditions [15]. This
thesis of synergetics describes the inorganic world in a completely different light. Henceforth, all
classes of inorganic bodies, including geological ones, should be considered not just as a natural
fact but as mutants and products of the selection of mutants that have been realized in
accordance with the Darwinian logical scheme.
Thus, we know 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.
Since the probabilistic selection was realized and the system entered a certain path of
development, the incident loses force. Up to 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 owing to 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 scenario 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 win and are affirmed. This is the 'exacerbation regime' that is inherent to all nonlinear
systems.
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
(say, 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. By the way, based on this fact, S.P. Kurdyumov, E.N. Knyazev [9] 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 compel us to
make unambiguous choice and create our own fate.
At last, let us dwell on fractal or fractality, a key thesis of the synergetic concept of selforganization. The term 'fractality' means a general matter contained in the entire multitude of
dissipative structures as the final result of synenergetic 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 [11, 19]. 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 selfsimilarity. This is a type of idealized architectural invariance. Fractal formation is exemplified by
the lunge 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 a fractal structure with the scale
reproducibility coefficient of ~1.52@6.
Fractality is actively discussed in the literature. Based on spatial-topological side of selfsimilarity, 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 energy, but by
entropy. The principle (synenergetic) 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. Speaking about 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 vividness. At first, the oil is at rest.
However, heating of the zone between the upper and lower boundaries of the oil creates
temperature difference. The heated (hence, lighter) lower oil layers and the upper (heavier) ones
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 [10].
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 synenergetic ordering is
paid not by energy, but by 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 [16]. 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.
Principles of Synergetics in Geology
Our planet is also probably a cosmic fractal. This follows from 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. Of course, the
octahedron of Earth is an approximate model. Actually octahedron faces are not straight lines but
arc-shaped. In reality, convex segments of the Earth's surface 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. If we take into consideration the subordination as a law of
fraction structure, it is necessary to suppose that lithosphere in both large and small
configurations is also fractal. Logically, the entire geological reality should represent a fractal
product of synenergetic 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;
and (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 [2].
Based on 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 [21].
It should be emphasized that the principle of structure-forming convection is manifested in
both 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 [20]. 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 heat
carriers. 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 [20]. 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 nothing
else but 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 with ordered water convection in the subsurface layers. The only difference from the
Benard's experiment lies in that the warmer surface is at the top. Convection appears owing to
the difference between cold and warm waters.
Volcanology. A bright example of synenergetic structures are 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 a curious 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 selforganization. Fractal dimensionality of river systems has been discussed in many works. It
turned out that the fractal river system is formed by the principle of energy dissipation
minimization 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 makes up the bifurcation division that is
always equal to 3. The hierarchic structure of flows indicates fractal properties of river systems
and, hence, topographies, on the whole.
Geochemistry. Ideas of synergetics in the sense 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. Works in this direction of
modern geochemistry are discussed in [12].
Geotectonics. Idea of cooperative self-organization in the development and structure of the
Earth exists as an integral concept. It has been developed by V.E. Khain [21], Yu.M.
Pushcharovsky [17], O.V. Petrov [14], P.A. Besprozvanny [2], and many other geologists.
However, it is necessary to note for the sake of fairness that the earliest, primarily deductivehypothetic investigation of this kind is linked with the name of the prominent geophysicist M.A.
Sadovsky [18].
As long as 1979, Sadovsky proposed to consider the lithosphere as a system of interacting
inhomogeneities in structures, substances, density etc. 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 behaviour 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 expressed an idea that enriches Prigogine's concept of self-organization
concerning the role of deep faults in lithosphere: they are nothing else but a zone of intense
dissipation of thermal energy, while lithospheric structure is a consequence of their formation.
The situation is exactly like 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 novation lies in that spontaneous structure genesis is considered not as the final point
of synergetic phenomenon. This is only a tool, method of adaptive behaviour of system under
changing conditions. The structured pattern of lithospheric blocks reflects the maximal effective
method of heat deflection 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 of Sadovsky's works is primarily related to the idea of fractal selforganization of geological complexes. The historical situation was such that precisely this aspect
of synergetics began to be incorporated in geology. An even higher significance belongs 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 pioneer works of P.M. Goryainov and
G.Yu. Ivanyuk [4], 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 get almost the first key to the applied methodologicalreconnaissance level of analysis of phenomena.
Goryainov and Ivanyuk analyzed the plate tectonics theory from the position 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 for the authors as a reference
system that changes the logics 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 linear-energy impact 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 else but a fragment of dissipative
structure based on the cooperative long-range forces. In the synenergetic 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 [4].
Thus, one can well see differences in the synergetic and mobilistic paradigms of
geodynamics. The synenergetic 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 the whole body. In 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 [4]. This implies a new 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 evolution path and cannot return to the initial position. In the geological
context, this means that region at the bifurcation point chooses a development 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 first experience active extension and then equally
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 synenergetic 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 volcanosedimentary rocks. At the final stage, the energy flux gets focussed.
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 synenergetic nature of process. This means that the network organizes formations of
any age and genesis. This network contains the united ordering of sedimentary and magmatic
rocks, old rock massifs, active island arcs and new mid-oceanic ridges [4].
The process continues in the following way. Folding, metamorphism and final magmatism
seal the percolation sutures. Then, 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 the modern world rift system. 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 behaviour of subsystems and structural
homeostasis, and adaptation of ensembles to energy flux [4].
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 iron ore process. 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 of new
structural stages was accompanied by overlapping of the new iron ore formation on the previous
one. Therefore, different-age formations 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 transform faults of an
ancient percolation network. The structure of deposits shows different-scale self-similarity and
fractality. 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 [4].
The presented material is far form exhausting the range of geological phenomena of
cooperative self-organization. There are grounds 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 factological
material that served as basis for the previous paradigm [7]. It is just overloaded on the platform
of a new theoretical concept. This is so in the given case as well. The formation of synergetic
interpretation of geological phenomena does not require the sacrifice of any previously
established fact. For example, the mobilistic concept and the traditional concept of Early
Precambrian are retained in geology. Only the understanding of Precambrian geodynamics is
different.
Finally, the question of pragmatic side of the problem. It is of course early to speak about
the efficiency of synergetic approach because of its embryonic state in geology. However, we
can already affirm that synergetics 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 abolishes the traditional
understanding of processes of structurization and transportation effect of 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 transform faults rather than the accumulation of
sediments in basins near rifts and metasomatism of basic rocks. This implies a new approach in
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 controls high-temperature processes of
petrogenesis and mineragenesis precisely in such a way.
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 the combination of oval tonalite blocks 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 ArchaeanProterozoic 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 one and the same zonality. Each lens of
ferruginous quartzites is surrounded by the following sequence: leptites - biotite gneisses hornblende gneisses -- amphibolites - tonalites. The smaller the quartzite 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 glomerare is scattered. Signs of boudinage are absent (Figs. 2-4).
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; and 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
commonness 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 volcanosedimentary rocks along the same percolation
network and scheme of exacerbation regime.
Complexity of the transition of theoretical geology to new paradigm lies in 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 comforting idea is that the synergetic geology does not
destroy 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 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 the most
part of Precambrian complexes.
From the position of synergetics, the concept of regional metamorphism---subsidence
followed by rise--is also groundless. Now one should consider that both these processes are
interrelated. According to the new concept, any metamorphic complex is a single compositionaldynamic population of one age. Hence, traditional methods of reconstruction based on structuralmetamorphic scales are just incorrect. The same collapse waits for concepts of structural geology
concerning the nature of folding in general. From the position 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 in 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 new ideology in
geological science. It brings a new research strategy that painfully crosses out many classical
fundamental principles.
Conclusions
Synergetics as the general theory of self-organization embraces a large class of natural
phenomena and is not limited by the thermodynamic situation. 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 goes far away from
the 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 in a
completely different light. All classes of inorganic bodies, including geological ones, should be
considered not just 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.
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 of the class of incorrect fractals. If we take into consideration the
subordination as a law of fraction structure, it is necessary to suppose that lithosphere in both
large and small configurations is also a fractal structure. Logically, the entire geological reality
should represent a fractal product of synenergetic 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
commonness of principles of self-organization allows us to extrapolate the synergetic approach
in geological prognosis to the metallogeny of many ore deposits (iron, gold, base metals, and
others). 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 temperature increasing 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.
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Moscow, 1985.FIGURE CAPTIONS
Fig. 1. Examples of active intraore microblock dynamics in orebodies of the Kirovogorsk
deposit. (1) Aluminous gneisses; (2) ferruginous quartzites; (3) ceramic pegmatites; (4) dolerites;
(5) faults. Based on P.M. Goryainov, G.Yu. Ivanyuk, 2001.
Fig. 2. 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 colour.
Kursk
Gubkin
Belgorod
Fig. 3. Geological sketch of the Kirovogorsk deposit area. (1) Tonalites; (2) hornfelsized
amphibolites; (3) leucocratic gneisses; (4) ferruginous quartzites; (5) ceramic pegmatites; (6)
dolerites.
N
Fig. 4. Longitudinal section of the Kirovogorsk deposit along profile A-B. (1) Leucocratic
gneisses; (2) ferruginous quartzites; (3) ceramic pegmatites; (4) dolerites. Based on P.M.
Goryainov, G.Yu. Ivanyuk, 2001.