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ISSN 0145 8752, Moscow University Geology Bulletin, 2015, Vol. 70, No. 4, pp. 305­313. © Allerton Press, Inc., 2015. Original Russian Text © N.V. Koronovskii, A.A. Naimark, V.S. Zakharov, G.V. Bryantseva, 2015, published in Vestnik Moskovskogo Universiteta. Geologiya, 2015, No. 4, pp. 40­48.

On the Geological and Physical Mechanisms of Natural Processes in Dynamic Geology Problems
N. V. Koronovskii, A. A. Naimark, V. S. Zakharov, and G. V. Bryantseva
Department of Geology, Moscow State University, Moscow, Russia e mail: koronovsky@rambler.ru, fnaim@ya.ru, vszakharov@yandex.ru, bryan@geol.msu.ru
Received March 30, 2015

Abstract--The applicability of the abstract physical mechanisms in studies of concrete geological processes is considered. It is shown that "nongeological" theoretical models are an important component of the initial axiomatics in solving the fundamental and applied problems of dynamic geology. The discussed "simple" mechanisms adequately explain the complex deterministic­chaotic dynamics of nonlinear processes related to tectonic faulting and the unpredictability of geocatastrophes in a coarsely discrete fractal medium. Keywords: geological and physical mechanisms, fractal geomedium, deterministic­chaotic dynamics, tec tonic faulting DOI: 10.3103/S0145875215040067

INTRODUCTION The most important problem of dynamic geology as applied to reconstructing geological processes is revealing the mechanisms of these processes. Mecha nisms cannot be either observed under real and labo ratory conditions or inferred directly from empirical data; they are a priori set theoretical models that can be verified experimentally and then, in the case of pos itive results, used as the basis of prediction and recon structive interpretations of other facts. However, the validity and efficiency of such an approach in scientific knowledge of reality is often dis puted by geologists and they sometimes reject it. These doubts and rejection are based on the confidence that geology is a very specific branch where "...a theoretical approach hypnotizes and paralyzes inquisitiveness and unorthodox creativity in research...," while "...objec tively collected and properly generalized data suggest the correct interpretation" (Frolov, 2004, p. 104). "...The main error is simplification, viz., reducing complex geological phenomena, processes, and prob lems to simple mechanical or physical ones" (Frolov, 2004, p. 8), while "the main aim... is to construct the real history instead of a theoretical one..." (Frolov, 2004, p. 88). Several questions arise: how reasonable are these statements; how and why are the mechanisms of "complex" geological and "simple" mechanical and physical processes revealed; what is the true role of experimental facts and theoretical models; what are the requirements for these models; and how can the adequateness of such a model be validated?

DYNAMIC GEOLOGY: FROM OBSERVATION TO HYPOTHESIS, FROM DESCRIPTION TO MECHANISM The geological tradition implies that consideration of the progress and results of any research always starts from factual data: field observations and laboratory experiments. The quality of these factual data plays a large and sometimes even a crucial role in both result ing and a priori estimates of works. If some consider able set of maps, sections, descriptions, or analytical data is absent or seems to be insufficient, the conclu sions are believed to be doubtful or neglected. How ever, even the most complete and detailed observations do not lead to geological predictions and reconstruc tions, which also require understanding how different natural environments originate and evolve and how some events are prepared and occur in these environ ments. By observing, analyzing, and interpreting the sizes, configurations, compositions, and inner structures of geological bodies, as well as the amplitudes and orien tations of dislocations, and defining their ranking, typological, and age relationships, geologists make conclusions about intensity and spatiotemporal vari ability, as well as the individual and joint roles that are played by different factors, i.e., about the causes of concrete geological processes in certain areas. The resulting descriptions (examples can be found in almost every publication on geology) are the qualita tively or quantitatively expressed ideas on geological mechanisms (GMs). Nevertheless, geologists believe that this is an insuffi cient argument. According to (Zhukov, 1978, p. 62), "...genetic models of geology are too far from what the

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Let us give some typical simple examples and brief notes on them, on the basis of (Vadkovskii and Zakharov, 2002; Zakharov, 2011) where very detailed and strict descriptions can be found. Example 1: Stick­Slip Periodic Horizontal Shears of a Block along a Fault This is an old object of theoretical and experimen tal tectonophysical simulation. Let us consider the system dynamics (Fig. 1) that is usually used when studying friction (a block on a moving belt). A block of mass m is attached by a spring of stiffness k to a fixed base; this block lies upon the horizontal belt of a con veyor that moves at a constant velocity. Dry frictional force acts between the belt and the block; this force depends on their relative velocities, adds energy to the system, and excites vibrations in the block. The dry friction law is nonlinear: at an increase in the relative velocity, the friction coefficient is reduced and then becomes constant, while at a further increase in veloc ity it can grow again (Osnovy..., 2001). The body is dragged by the belt ("tectonic force") from the equi librium position, while this translational motion is impeded by the spring, which tears the body from the belt when the elastic force exceeds the frictional force. At some moment, the velocities of the body and belt become equal, friction abruptly increases, the body "sticks" to the belt, and both objects begin to move together until the next tearing off episode. Such a behavior is called stick­slip. The block executes strictly periodic but nonharmonic oscillations with a frequency that is close to the eigen frequency (Fig. 2a). In the phase diagram (Fig. 2b), the body positions are marked in the phase space, whose coordinates are dis placement and velocity (x and V, respectively). The horizontal part of the diagram refers to the stick phase. According to the modern concepts, such a mechanism of frictional self oscillations causes earthquakes (Burr idge and Knopoff, 1967). The main point here is dry friction, i.e., friction at rest should exceed slipping
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Fig. 1. The physical mechanism of alternating sign hori zontal slips of a block along a fault, after (Vadkovskii and Zakharov, 2002) (hereinafter, the explanations of the fig ures are in the text).

term mechanism means; they do not fit... the require ments of applied geology." At the same time, "...with all of its imperfections, inability to explain, and non constructiveness, genetic geology has always been and still remains the fundamental... component of the Earth Sciences" (Zhukov, 1978, p. 62). This is the rea son that geologists want to know "physical mecha nisms" (PMs) in addition to GMs. It is supposed that if a PM is based, analogous to a GM, on the results of field and experimental studies, it would take into account, if not all, at least the most significant (in the geological sense) factors that control the processes under study, on the one hand. On the other hand, if such a mechanism is a "physical" one, it will provide more fundamental and rigorously substantiated expla nations on "how a process really takes place" and hence more accurate and valid predictions and recon structions, compared to extrapolations of empirical geological data. Naturally, physicists are involved in these cases. However, after evaluating the ideas of physicists on a problem geologists often experience "failed expecta tions," e.g., the solution to the PM of seismogenic tec tonic faulting is more or less extensive commentary on figures that show a board with plummets on it, which are joined by springs to each other, and an upper board that moves in parallel to the lower one.
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friction and the friction force should decrease with the growth of velocity, while the shape of the respective function is not very significant. Example 2: Irregular Horizontal Seismogenic Stick­Slips along a Fault The dynamics of the model that is considered in the first example seems to be too simple to describe seis motectonic process, because all of the block's tearing off episodes (i.e., model earthquakes) occur on a strictly periodic and therefore predictable basis. However, the addition of a second block to the system (Fig. 3a) fun damentally changes the behavior of the system (Tur cotte, 1997). Here, kc, k1 = k2 = k is the stiffness of the springs that model the elastic coupling forces between the springs and the leading block and F1 and F2 are the forces of nonlinear dry friction that act on the bases of the first and second blocks. The blocks in the system interact in such a way that the motion of one block can cause the slip of another and vice versa. Depending on the values of the governing parameters (the stiffness of the springs, the friction coefficient, the velocity of the leading block), both periodic and chaotic (unpredict able) regimes are possible in the system. Figure 3b pre sents the phase pattern of such a system in displace ment coordinates (x1, x2) in the chaotic oscillation mode. Thus, a self oscillating system that consists of only two blocks with nonlinear dry friction demon strates chaotic behavior. A larger number of elements will obviously complicate the system dynamics. Example 3: Stick­Slip Seismogenic Horizontal Slips of a Block System Along a Fault In this case, the manner in which oscillations of different periods and amplitudes and abrupt seis mogenic slips occur is represented by a system of
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blocks that are coupled with each other and lie on the surface (Fig. 4a) and that move at a constant velocity. Elastic forces from the adjacent blocks act on each block, as well as the viscous drag force of the medium and the dry friction force from the underlying surface. Surges in the velocities of particular blocks cause slips of the adjacent ones and these disturbances fade with time. The time at which each slip occurs and the sign of the slip are unpredictable. Slips are not preceded by some behavior. An arbitrary small change in the initial
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conditions does not lead to a qualitative change in the behavior of the blocks, but the sequence of slips in time becomes completely different (Fig. 4b). Many varied models that were developed based on the approach of R. Burridge and L. Knopoff (1967) have been proposed. Turcotte (1997) considered the 2D version of the model (Fig. 5a): it demonstrates so called self organizing criticality (SOC) behavior (Bak and Tang, 1989). The results of its dynamics simula tion are widely used to explain the peculiarities of seis mic process. A hierarchic version (Fig. 5b) of the Burr idge­Knopoff model also exists (Schmittbuhl et al., 1996). Example 4: Stick­Slip Seismogenic Vertical Slips of a Block System Along a Fault In the model of piedmont zones, a system of blocks that are confined by subvertical faults and are relatively weakly coupled with each other is close to equilibrium (Koronovskii and Zakharov, 2000). Each block touches and interacts with the adjacent ones and with one large block of the rising orogen (Fig. 6a). The oro gen, in its order, involves the adjacent blocks in rising due to frictional forces, whose nonlinearity highly complicates the pattern of motion of the blocks. Along with variations that are determined by the eigen fre quency of each block, nonperiodic oscillations with a longer characteristic period (which is different by more than an order of magnitude compared to that of the eigen frequency related variations) occur about one, two, or sometimes three equilibrium positions, with unpredictable switches between them (Fig. 6b). Particular blocks demonstrate relatively independent behavior; adjacent blocks are involved in switches in both the same and the opposite directions. The blocks are sometimes grouped during joint oscillations and then separate. Small changes in the parameters of velocity and friction alter the behavior of each block, but a general regime of determined chaos remains.

ON ABSTRACTION AND THE "NONGEOLOGICAL" CHARACTER OF PHYSICAL MECHANISMS According to (Zhukov, 1978), a mechanism explains why and how some process originates and evolves. In the methodology of natural sciences, explanation of some phenomenon means that this phenomenon occurs due to the effect of the relevant (in our case, physical) law. The only way to do this is to consider the studied geological process as a physical one, i.e., where physical bodies interact in physical fields. This is what we see in the models that are described above. The main differences between PMs from GMs are (a) formality, (b) a strict set of initial and boundary conditions, and (c) reduction of various concrete geological bodies, dislocations, and forces, which all interact in accord with the commonly accepted mechanical laws, to very general physical abstractions. These simplifications make theoretical physical­mechanical models illogical: they can hardly be compared to GMs where the maximum numbers of acting factors that are empirically taken into account are combined with the respective empir ical estimates of their influences. However, PMs are more basic and universal and therefore can be ade quately applied in a larger number of real cases com pared to GMs. What are the opinions of practicing geologists on these theoretical models? Experienced geologists who search for and document the finest details in the struc ture and distribution of seismodislocations of different types and scales, and compare the peculiarities of their distribution within rock complexes of different com positions and age tend to consider the simple schemes that were presented above as being silly. Such a scien tist cannot connect these abstractions, on the one hand, and the facts (rejected observation results, or any other directly investigated structural geological features that might be related to ruptures and earth quakes), which are all the basis of all geological con structions, on the other hand. Instead of the obvious
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and primary necessity to analyze the geological data, such a scientist interprets these schemes as theorizing divorced from concrete natural settings and then, from the viewpoint of these abstract schemes, a pre con ceived analysis of the factual data that are the basis of the scientist's view. As a result, the effective predic tions and recommendations that might be expected are replaced by conclusions about the chaotic charac ter and unpredictability of what geology is supposed to obtain reliably using physics. In his order, a physicist cannot understand both why the proposed scheme is not accepted as a mechanism and what a PM is in geologist's opinion, to say nothing about the necessity of detailed field descriptions of concrete dislocations. The above discussion illustrates and explains, per haps in a slightly exaggerated manner, the divorce between the hypothetical­deductive methodology of scientific research in physics and the traditional geo logical ideas regarding the methodology of geological research. The intuitive (and objectively reasonable) attempts of geologists to determine the PMs of some geological processes fail because of the vagueness of both the term PM and how and for what purpose the stated problem should be solved.
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Geologists do not argue against possible "pessimis tic" and even "agnostic" conclusions when following a proposed physical model. However, the validity of initial assumptions of this kind and the adequacy of these abstract models of geological reality seem erro neous. Geologists believe that models do not take some essential properties of simulated processes into consideration; this leads to the unpredictability of pro cesses. A "nongeological" character is seen the most often in excessive general simplification, as well as in the insufficient volume and details of the necessary observation and experimental data. They do not real ize that "...in any theoretical research, basic (genetic) and applied (prediction) constructions in geology are essentially logical..." (Zhukov, 1978, p. 63). It has also been noted (Egorov, 2004) that geology prefers "objec tive" descriptions of reality, regardless any "preset" genetic scheme that allegedly impedes the unbiased selection of structural facts, which, in their order, should be the basis to infer a genetic theory. However, in fact, "...most geological theories are formulated as genetic concepts... The predominance of the genetic approach in the Earth Sciences is caused by the fact that the real research procedures in geology, analogous to any other natural science field, are based on the hypothetical­
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deductive research method (regardless of the opinions of some methodologists and practical researchers in Earth Sciences)" (Egorov, 2004, pp. 77­78). In the light of the preceding remark of D.G. Egorov, it may seem that rejection of abstract physical models by geologists is only a declarative following of tradition and that this does not affect real work. However, the hypothetical­ deductive methodology (instead of the traditional inductive­empirical logic) is used in geology rather intuitively and "unconsciously," if it is used at all; hence, efficiency is considerably affected. ON THE HYPOTHETICAL CHARACTER OF PHYSICAL MECHANISMS How convincing are the conclusions about geolog ical processes if they were inferred from knowledge of the physical mechanisms of these processes? If unpre dictability manifests itself even in the simplest physical mechanisms that are "far from geological reality," then why should the much more complex "real" sys tems be predictable; hence, the doubts that are related to model simplification are eliminated. The existence of reliable precursors of geological catastrophes means that these precursors can be revealed; in other words, anomalies in some parameters before strong and haz ardous events should contrast (in terms of scale and intensity) with those that are related to weak events with no hazard. However, this is hardly probable with the coarsely discrete self similarity of the geomedium and can be illustrated by the absence of clear steps in earthquake recurrence plots: these curves are log­log plots that follow the Gutenberg­Richter law (Sadovskii and Pisarenko, 1991). The only truth in the characteristics of physical models that are constructed by geologists is that these models are indeed theoretically constructed. Such a construction starts by definition not from the analysis of concrete experimental facts but with the selection of the initial axiomatic statements. These axiomatic statements are general ideas, which are, however, well founded and commonly accepted, and are relevant to the problem as well: observational generalizations and physical laws with logical implications. The theoreti cally possible versions of how the studied process could originate and evolve are inferred; this is also done in accord with logic, but with a more or less full account (depending on the problem character) of the concrete conditions in the study area. However, in natural sciences, even if the initial axiomatic state ments are true and the conclusions are logically cor rect, these versions are no more than hypothesis that require experimental verification. The arguments against the verified hypothesis (but not those for it) are of special importance, because if there are arguments against it then the hypothesis must be corrected. This leads us to a question: what are the facts that geologists readily accept and what are the facts that are not accepted?

ON EXPERIMENTAL AND THEORETICAL FACTS To start this section and to follow up on the ques tion in the previous section, are the structural parageneses and tectonic stress fields that are revealed and the structural and sedimentation stages that are identified in any concrete area facts that geologists would accept? The answer is often yes, e.g., V.S. Burt man (1978, p. 27) stated that it is necessary that the following facts agree between each other: the presence of a stationary network of faults in four­six directions; consistent pattern of slips on them (occurrence in cer tain epochs); and possible rotations of continents and their parts to any angle. According to (Rebetskii and Alekseev, 2014, p. 29), it follows from the analysis of the stress state in the Earth's crust within Pamir "...that the maximum compression stress that acts ver tically in the High Pamir crust is larger than one that acts horizontally in the crust in the nearest vicinity. This means that horizontal compression is not a factor that leads to the present uplifted state of Pamir." According to (Frolov, 2004, pp. 59­61), the obvious geological evidence that contradicts the statements of plate tectonics includes newly formed marginal seas at the eastern edges of the Asian and Australian conti nents, jointly with the expressed tendency to conti nental plate destruction by oceanic plates; oceanward thinning of the Precambrian or Paleozoic geosyncline basement of most island arcs, which were therefore founded on the continental crust; the duration of heating of the continental crust by mantle diapirs, massive riftogenesis, and taphrogenesis; trapp basalts on the bottoms of oceanic basins, with large areas of continental and shallow water deposits at the base of the respective sedimentary covers. Discussing the advantages of the traditional factual method of con structing geological history (in contrast to the theoret ical method, this provides a "solid factual framework" for paleogeographic reconstructions), V.T. Frolov emphasized that reconstructions that are made by this method are not strictly verifiable, not defensible, and nonfalsifiable, but they are probabilistically feasible (Frolov, 2004, p. 72). It is obvious that all of the mentioned structural geodynamic and geohistorical settings and events can not be found directly as facts in the framework of an experiment; they resulted from complex and ambigu ous interpretations of what was observed in nature, but was not classified or defined or named by nature itself. Thus, the so called factual conclusions in quotes that were cited above are in fact interpretations of the earlier interpretations of what was seen and described. Even in the simplest descriptions (limestone, anticline fold, and thrust) allegedly pure empirical facts are insepara ble from interpretation. Again, they are not fragments of reality proper that were "objectively and reliably" documented (such documenting is impossible), but were introduced into research in the form of some per son's ideas about reality (and therefore a priori not
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absolutely objective and reliable). If these fragments are both experimentally founded and introduced into the system of theoretical ideas, they are considered as theoretical facts. In the early 20th century, the French theoretical physicist P. Duhem (1906) introduced the term "theo retical fact" into science (however, this term is uncon ventional and even strange to geologists). P. Duhem believed that our observations are not a direct percep tion of reality, but capture some part of this reality, which can be perceived by our senses; an experiment is both an observation of facts and their interpretation on the basis of commonly accepted theories, therefore the essence of experience is connected to concrete reality via multiple and complex theoretical links. Physical experience and the simple statement of a fact are abso lutely different concepts. Theoretical interpretation provides a more detailed and deeper insight into phe nomena compared to ordinary common sense. In its order, a theoretical fact in exact sciences is a group of theoretical (mathematical) data that replace a con crete fact in one's thoughts and calculations. In the natural sciences, the term theoretical fact has been used for a long time, but in a wider sense, viz., the observation or experimental data that are assimi lated by some theoretical concept (Chernyak, 1986). It is accepted in the modern methodology of science that there are no facts that are free from sense and understanding. The role of theoretical interpretation can be seen in any observation, measurement, or experiment. MECHANISMS AND THE PROBLEM OF THE PREDICTABILITY OF GEOLOGICAL PROCESSES Thus, what conclusions can be made if we use the oretical facts? What are mechanisms in general, and what are geological and physical mechanisms in par ticular? According to (Zhukov, 1978, p. 63), in the natural sciences, ideas about the essence of natural phenomena are expressed in an abstract concept of their mechanism; a mechanism is a system of a finite number of factors that are interrelated in certain way and control the course and result of a respective pro cess (or at least they allow the course and result to be predicted). As a cause of a phenomenon, a mechanism is not an object itself, but a model of the interaction between objects. Hence, the problems of geological science can be reduced to the construction of some formalized mechanisms of natural phenomena, in particular, on the basis of physical models. The word "physical" in the geological context usu ally means something real, in contrast to something imaginary. In the more strict sense, it refers not to physics as a whole, but to its branch that studies phys ical reality. Finally, the scientific meaning of physical reality, after (Filosofskii..., 1989, p. 693), is a system of theoretical objects that characterizes the unobservable
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essence of phenomena by means of physical theories. This is the difference between the physical and objec tive realities: the latter does not depend on any theory. Hence, geological mechanisms should reflect geo logical reality from the viewpoint of theoretical geo logical ideas. However, due to the fact that these ideas are highly undeveloped, the respective models are detailed and concrete (i.e., adequate to particular cases); this does not provide founded solutions of fun damental geological problems, in contrast to physical models; e.g., according to (Frolov, 2004), the factual geohistory is composed of sequential layers, magmatic bodies, and other structural units. Being recognized and interpreted in the historical sense, these units are arranged to form a sequence of stages or a continuous process with the features of succession and inherit ance; they make up a factual framework. However, as was mentioned above, V.T. Frolov argued that these constructions are not strictly verifiable, not defensible, and nonfalsifiable. One alternative is physical­geological or geo logic­physical models (depending on the dominating aspects); these models are being developed. The latter can consider the results of empirical geological research, while the latter consider the important (for the problem being solved) properties of concrete geo logical processes and are based chiefly on fundamental physical (mechanical) ideas. Both these models are "dynamic systems" (this term is applied when the rate of change in variables that characterize the system state depends on the variables proper). The mathematical expression of dynamic systems consists of equations or equation systems that describe the changes of variables and their derivatives with time. In these equations, the set parameters do not depend on time and the set func tions link variables and parameters. One example of the simplest geological­mechani cal models is the mentioned schemes with weighs and springs. Their cognitive value and geological character are illustrated primarily by the fact that these models simulate the fundamental natural features of mutual displacements of geological blocks, as well as the deterministic and chaotic, irregularly punctuated, and irreversible character of block movements. The con clusion that follows from this is the fundamental unpredictability of the place, time, and magnitude of particular tearing off events of rough edges of different scales on the fault plane during these displacements. Below are concepts for which theoretical facts and experimental facts are not necessary (at the present state of knowledge) in order to validate them; in addi tion, contradictions to these theoretical facts are sin gular and random (Naimark, 1998, 2003; Koronovskii and Naimark, 2012, 2013). (1) Seismicity, which is a direct manifestation of tectonic faulting under the conditions of subcritical stress of geomedium structures in a fractal and coarsely discrete pattern.
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(2) The mentioned process is nonlinear and bifur cating and reflects the deterministic­chaotic opera tion of highly nonequilibrium tectonodynamic sys tems, which are extremely sensitive to the finest varia tions in the initial conditions. On the path from microfracturing to the occurrence of a main seis mogenic fault, multiple bifurcations occur; due to the finite accuracy of setting the initial conditions, each theoretically possible trajectory of the further develop ment at each bifurcation is unpredictable. (3) Each faulting episode generates cascades of secondary, tertiary, etc. faults; this unpredictably alters the structure and local stress fields of higher orders; therefore, it changes the conditions under which later faults will form. Overlaps of intra and inter rank sizes of dislocations and dynamic anomalies impede the valid identification of the scales and ages of these objects. (4) The operation of a seismotectonic system in the form of multiple self similar, spontaneous, irregular, and hierarchically subordinate cycles removes the problem of the unambiguous classification of the gen eral system behavior (deterministically or probabilisti cally predictable or absolutely disordered). The prob lem of distinguishing the deterministic­chaotic behavior in the general scheme arises instead: within some volume and on some scale level, spatial zones and time intervals (phases) are sought that are charac terized by predictability with the relevant conditions of predicting some seismic potential parameters. (5) Constrained slips, reconstructions of stresses and weak zones, and unavoidable turning of blocks of different sizes in an open, highly nonequilibrium, and deeply hierarchical tectonodynamic system cannot remain as the theoretical scheme of kinematic and age resolution of slips under a uniform load (this scheme is assumed on the basis of the continuous medium model). For multiple splitting of a set volume, the for mation of each following macrosplit is accompanied by secondary strengthening of earlier fractures; these fractures lose the ability to make a secondary slip. CONCLUSIONS Abstract and nongeological physical mechanisms are a necessary and important component of the initial axiomatics when solving dynamic geology problems, in particular, when predicting the preparation, occur rence, and aftermath of a seismogenic tectonic fault ing. It follows that any natural macrofracture can form directly in an initially quasicontinuous medium. At the pre destruction stage, such a medium unavoidably becomes a coarsely discrete fractal one. Multiple micro and meso fractures occur in the medium and surround the resultant macro fracture; they are more or less "scattered" under a bulk distributed load, while they are localized in a multidirectional in plane load (cut).

If any fracture network set in a model quasicontin uous block is not self organized, it will unavoidably distort the course and the results of subsequent defor mation and destruction which, in their order, depend strongly on the finest difference between the model and natural structures. In a real self structured medium, fractures take a load, respond to it, and mutually concur while growing in very different ways; this occurs due to the model irreproducibility of the features of multiple intercepts, joints, and crosses by finer fractures of different ranks that occurred at the early pre destruction stages. Depending on the small est variations in morphology, arrangement, and kine matics of these intercepts, joints, and crosses (and therefore depending on the unpredictable reconstruc tions of stress fields of different ranks), these deforma tions and motions, and thus the orientation, arrange ment, and size of the resultant macrofracture, will be highly unstable and irreproducible in the repeated experiments. Any complication of a model structure in order to provide a better fit between the experimental results and the observations in geological reality will not reject, but rather additionally validate the fundamen tal statements and the conclusions that follow from them in the present paper. REFERENCES
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Translated by N. Astafiev

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Vol. 70

No. 4

2015