| Citation: | Bing Li. Synchronization Theory and Tungsten-Polymetallic Mineralization Distribution in the Qianlishan-Qitianling Area, Southern Hunan. Journal of Earth Science, 2011, 22(6): 726-736. doi: 10.1007/s12583-011-0223-4
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In the 1970s, many nonlinear theories, such as the chaos and fractal theories, emerged. They are collectively called "nonlinear science." Nonlinear science reveals regularities in complex phenomena by studying complex objects from different angles. It has great significance and is changing people's traditional opinions (Nicokis, 1995). The earth is complex and has become the subject of research in modern geosciences, which study the earth and various geological phenomena from complex and nonlinear angles.
Synchronization is a universal phenomenon that occurs with the coupling of two or more nonlinear oscillators. It was discovered at the beginning of the modern scientific age by Huygens (Pikovsky et al., 2002; Rosenblum et al., 2001; Schäfer et al., 1998). In the 1960s, with the development of nonlinear theories, such as the chaos theory, the study of synchronization entered a new stage. The theories have been widely applied in many fields, such as engineering, medical science, ecology, electronics, information, laser, and solid physics (Wang et al., 2006; Pikovsky et al., 2002; Ims and Andreassen, 2000; Blasius et al., 1999; Sarnthein et al., 1998; Schäfer et al., 1998; Kocarev and Parlitz, 1996; Mirollo and Strogatz, 1990; Pecora and Carroll, 1990). However, their study and application in geosciences, especially in mineralization research, are still limited.
Southern Hunan is rich in mineral resources and complete ore types. It is currently under investigation in many studies. However, only a few of these are nonlinear.
In this article, areas with high mineral concentrations of nonferrous and rare metals, such as the metallogenic belt in southern Hunan or the Qianlishan-Qitianling area, were selected. Based on spacetime dualism, preliminarily studies were conducted and this article discusses the regional ore regularity and distribution patterns of wolfram polymetallic deposits in the Qianlishan-Qitianling area using the synchronization theory.
Southern Hunan lies in the middle of the famous Nanlin metallogenic belt, where geologic-tectonic conditions are complex and mineral resources are rich. Some nonferrous and rare metal resources, such as wolfram, tin, molybdenum, bismuth, lead, and zinc, are found in the area. We conducted the study in the Qianlishan-Qitianling area in southern Hunan located at 25º20'N-25º50'N and 112º30'E-113º30'E. It has one of the highest mineral concentrations of nonferrous and rare metals, and a metallogenic belt was earlier found in Nanling (Che et al., 2005). Moreover, medium-sized, large, medium-scale, and super-huge metal minerals were found in Shizhuyuan, Jinchuan-tang, Yejiwei, Xintianling, Xianghualing, and Huang-shaping. In 2008, a large tin-polymetallic deposit was found in Furong.
The Qianlishan-Qitianling research area has experienced many complicated tectonic movements in different stages and at varying degrees, accompanied by magmatic activities. Its center is located in the area where the Yangtze and the Cathaysian plates (the two major inland plates) converge and in the Chenzhou-Shaoyang strike-slip tectonomagmatic zone (Fig. 1). The main area of the strike-slip tectonic zone, which is made up of a fracture zone and intruded magma, is in the Chenzhou-Shaoyang region, extending in the NW direction to the Snowberg arc tectonic belt, but is out-side Yaogangxian of Hunan Province in the southeast. The Indo-Chinese-Yanshanian period is the research area's most important and most active period (Deng et al., 2003). During that period, a significant oreconducting structure developed in the area, controlling the distribution of ore fields with secondary structures controlling orebody shapes and scales.
The Yanling-Lanshan fault zone extends south-westward, from Yanling County to Lanshan and through Chenzhou, with both ends stretching out through the province. It has a syndepositional foreland basin fault originating from the Sinian period (Early Paleozoic), a deep and large fault from the Caledonian movement continuing until the Indo-Chinese-Yanshanian period, and a large-scale basement-cut fault with a long active period (Tang et al., 2007). Along the fault, an acid and ultra-acid magmatic belt with a curving arc developed, the top position of which projects southeastward, near Qitianling, in which the main phase of some magmatic bodies (e.g., Wangxianling) is Indo-Chinese and the rest are Yan-shanian (Deng et al., 2003).
The Chenzhou-Shaoyang fault zone extends northwestward, from Yaogangxian through Chenzhou to Dayishan. It extends northwestward to the snow-berg arc structure belt at the center of Hunan and extends southeastward to Guangdong (Tang et al., 2007). Indo-Chinese-Yanshanian is its important active period, causing the intrusion of intermediate-acid rocks from Guandimiao, Dayishan, etc. (Deng et al., 2003).
Magmatic rocks are widely distributed throughout southern Hunan and have complicated assortments, the majority of which are granite. Some are ba-sic basalt and diabase, and some are neutral, intermediate- acid diorites (Chen et al., 1979). A tectonic magmatic belt (NE direction), called the Yanling-Lanshan magmatic belt, lies in the Qianlishan-Qitianling area. The belt extends from Yanling through Baofengxian, Qianlishan, Qitianling, and Xianghualing to Jiuyi Mountain. In these areas, most magmatic rocks, such as those found in Qianli-shan, Qitianling, Xianghualing, and Jiufeng are Yan-shanian granites, although some of the rocks, such as those found in Wangxianling, are Indo-Chinese epoch granites (Liu et al., 2003).
The primary granitic bodies are found in Qitianling. The Qitianling granitic body is one of the representative rock bodies of Nanling granites, and is situated at the juncture of Chenzhou, Yizhang, and Guiyang, three counties south of Hunan Province. It is found at 112º44'E-113º00'E and 25º23'N-25º41'N. The whole rock body is sharply equiaxed. Its total disclosing area is about 520 km2 and its northeast edge is only 20 km from Chenzhou. Many nonferrous metal and rare metal deposits have been discovered not more than 40 km from Qitianling. Many of these deposits are of a large (super large) scale, such as the Shizhu-yuan tungsten tin deposit, the Yaogangxian tungsten deposit, the Huangshaping lead and zinc deposits, and the Xianghualing tin, lead, and zinc deposits. Nearby rock bodies were found to have Xintianling tungsten deposits, Caojia lead, and zinc deposits, among others. In Furong, a large tin deposit was discovered in a southcentral rock body. The age, cause, and minerali-zation correlativity of the Qitianling granite body remain as current subjects of study (Zhou, 2007).
In this region, magma activity is frequent and is characterized by multiple stages and multiple intru-sions (or eruptions). Yanshanian in southern Hunan has the most intrusions and the widest range of distri-bution. Moreover, it has many rock bodies and much magma, and it is characterized by high-intensity dif-ferentiation, a large quantity of nonferrous metal elements (i.e., W, Sn, Mo, Bi, Cu, Pb, Zn, and Sb), vola-tilized components, and very high mineral concentrations. The Yanshanian period is the most important period of nonferrous metal mineralization in the region (Liu et al., 2003).
Southern Hunan covers about 20% of the whole province. Ore types and minerals, including rare and nonferrous metals and rare ores (e.g., tungsten, tin, molybdenum, bismuth, lead, zinc, copper, antimony, mercury, gold, silver, cobalt, uranium, beryllium, niobium and tantalum, lithium, yttrium clan, and cerium clan), are found in this area. Dispersed elemental ores, such as cadmium, indium, germanium, and gallium, are also present. Ferrous metals (e.g., iron, manganese, and titanium) and nonmetal ores (e.g., sulphur, arsenic, phosphorus, boron, fluorite, potassium feldspar, graphite, and coal) have also been found in the area (Chen et al., 1979). The Qianlishan-Qitianling area, the study area, has one of the most important mineral-ized concentrations of rare and nonferrous metal ores.
Mineral resources found in the region, especially rare and nonferrous metals, are dominated by tungsten, tin, lead, and zinc. According to rough statistics (Che, 2005), there are close to a thousand types of nonfer-rous metal deposits (prospects), mainly located in several large ore fields in Huangshaping, Xianghualing, Xintianling, Yaogangxian, and Dongpo. The ore fields are distributed in the Yanling-Lanshan and Chenzhou-Shaoyang fault zones.
Different ore deposit types are found on both sides of the Yanling-Lanshan fault zone and polymet-allic deposits are found on the northwestern side. Lead and zinc mineralization elements are found in the Huangshaping ore fields. Tungsten and tin mineralization elements are found in several typical ore fields, including the Shizhuyuan super-large-scale ore fields, Yaogangxian large-scale ore fields, Xintianling large-scale ore fields, and Xianghualing large-scale ore fields (Che, 2005). The Shizhuyuan, Yaogangxian, and Xintianling fields are found at the junction of the Yanling-Lanshan and Chenzhou-Shaoyang fault zones.
The deposits mentioned above are mostly post-magmatic hydrothermal deposits in southern Hunan. Hydrothermal mineralization is a coupling process between the transport (e.g., flow and diffusion) and the chemical reaction of fluids in fractureporous rocks. A hydrothermal mineralization system can be approximately regarded as a "reaction-diffusion sys-tem" (Yu, 2006).
The interactions between fluids and surrounding rocks change the chemical concentrations of fluids and form chemical waves with different wave frequencies. Some components of the surrounding rocks are dissolved and mixed and transported with the fluids. Meanwhile, chemical waves propagate. New minerals are precipitated when the solubility of the composition of the new species is exceeded. Fluid-rock interactions continuously change the chemical concentrations of fluids and rocks, and cause the formation and propagation of chemical waves (Yu, 2006).
When chemical waves propagate in porous media, such as in surrounding rocks, partial synchronization takes place because of inter-coupling or perturbation (e.g., tectonic activity). Hence, chemical waves with coherence (coherent waves) are formed. The components of a coherent wave have specific mineral and elemental associations, and their wave velocities are uniform. Coherent waves with different components have different frequencies and wave velocities. This kind of spatiotemporal separation of the association of minerals and elements causes distribution regularities in mineral ores. To sum up, hydrothermal mineralization includes the production and propagation of chemical wave trains and involves spatiotemporal structural problems on their synchronization.
A chemical wave is a fluctuation phenomenon suggesting that spatial distribution patterns of macro-scopic variables (e.g., component concentrations, temperatures of the system, and average size of sediment particles) change over time. It is the coupling of chemical oscillators between the transport (e.g., diffusion) and the nonlinear reaction dynamic process (Xin, 1999). Oscillation is determined by the mechanism of the reaction dynamics of the internal system and is a spatiotemporally ordered structure (Xin, 1999).
Oscillation takes place so long as the potential energy curve is at its minimum (Zhao and Luo, 2004). In geological movement processes, the potential energies of particles are inevitably identical and at their minimum because of inequality in the geo-structural environment, among other reasons. Meanwhile, frac-tured porous structures are universal in rocks. An oreforming fluid's continuous exchange and reaction with its surrounding rocks, and its transport into the fracture pores of rocks cause changes in variables, such as density and temperature, and then produce perturbation in its movement process. According to the above, the perturbation produce chemical waves; therefore, this article concludes that chemical waves are ubiquitous.
A chemical wave is a kind of chemical oscillator. A temporal oscillator produces spontaneous spatial heterogeneity and produces a lasting spatial structure in an open system. This mechanism enables a chemi-cal wave to cover a wide area, with the chemical ma-terials distributed in a large area (Yu and Peng, 2009).
Reaction-diffusion is the most typical and the most basic interaction that not only displays the motion of a matter's spatiotemporal structure but also produces a chemical wave, making it the activity with the most abundant and most varied functions and be-haviors (Yu and Peng, 2009). Chemical waves induce changes in material density from the interaction be-tween the different chemical components of fluids, as well as from the interaction between fluids and a per-meable medium; this is the advantage of studying chemicals and their propagation, as well as their reaction and flow into a permeable medium, over common study methods (Yu and Peng, 2009).
Earth matter and its movement exist objectively and primarily. Geological processes involve the movement of earth matter and can neither be away from time nor be beyond space. The time evolutions of geological processes show certain regularity, also called temporal structures. Meanwhile, the space distributions of geological processes also show certain regularity, called spatial structures. Geological processes and spatiotemporal structures coexist, respond-ing to the mechanism and the spatiotemporal location of geological events. They are coupled with each other and are inseparable. Geological processes (the movement of earth matter) are primary. The close interrelation between geological processes and four-dimensional time-space forms of geological processes and spatiotemporal structures respond to the occur-rence, mechanism, and spatiotemporal location of geological events. Geological processes and spatio-temporal structures are the essence and core of all geological phenomena (Yu, 2006).
Time and space show the dualism of dialectical unity. The essence of the space-time dualism is the at-tribution of the unity of opposites, complementarities, and time-space correlations. Imagined and observed activities all boil down to the space location of the structural properties of a system. In short, the external facts shown by space and time are displayed by space (Yu, 2006).
In geology, the natural surface of any geological region is a true spatiotemporal curved surface of an earth matter, including the wave surface of a chemical wave that is formed from the reaction-transport process of metallogenic coupling. The movement history of earth matter shows congruence in the curved sur-faces of many chemical waves, and it is the comprehensive embodiment of geological processes and spa-tiotemporal structures in a particular region. Therefore, a complex mineralization system can be studied using spatiotemporal synchronization after observing and measuring the system's spatiotemporal profile, which is the response of chemical waves in a geological region (Yu and Peng, 2009).
Synchronization is an important frontier in con-temporary nonlinear science and its use dates back to the 17th century when the famous Dutch scientist Christiaan Huygens reported his observations on the synchronization of two pendulum clocks in 1673. The systematic study of this kind of phenomenon, experimentally as well as theoretically, was started by Ed-ward Appleton and Balthasar van der Pol in the 1920s (Rosenblum et al., 2001; Pikovsky et al., 2000). With the development of the chaos theory and its introduction into the synchronization theory in the 1960s up to the early 1980s, much work was poured into the study of synchronization. Although the modern study of synchronization is only more than twenty years old, its research and application have already expanded into such fields as electronics, information, lasers, solid physics, chaos control, and medical science.
The word "synchronization" is derived from a Greek word " ". In the classical sense, synchronization means adjustment of frequencies of periodic self-sustained oscillators due to a weak interaction (Rosenblum et al., 2001). Today, synchronization is defined as the phenomenon or process in which multiple periodic processes with different frequencies or phases achieve a common frequency (denoted as frequency entrainment) or common phase (denoted as phase locking) within a weak interaction or weak external perturbation.
Two oscillator objects achieve synchronization because of homogeneity or a stronger coupling or external force, that is, the whole behavior is identical; this is called "complete synchronization." Usually, because an oscillator system is not homogeneous within a system or is not evenly perturbed by an external force, it has a common frequency, while it keeps other properties (e.g., amplitude); this is called "phase synchronization" or "partial synchronization." Phase synchronization can be mathematically expressed as follows (Rybski et al., 2003; Rosenblum et al., 2001)
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where Φx(t) and Φy(t) are the corresponding functions of x and y systems, n and m are integers, δ represents the phase shift between both oscillators, and const is any positive finite number.
As previously mentioned, the movement history of earth matter shows the congruent spatiotemporal curved surfaces of many chemical waves, Then an oreforming process can be regarded as the synchro-nization process of the chemical waves of mineralization elements, orecontrolling and oretransporting elements in a reaction-transport process, and (quasi-)periodic variations of element contents are the reflections of chemical waves on spatiotemporal curved surfaces. Therefore, we may define the phase in the geochemistry dynamics of mineralization as the content of oreforming, orecontrolling, and oretransporting chemical elements related to miner-alization in geological spatiotemporal points, which constitute the spatiotemporal sequences of the element contents' periodic change by the positive and negative feedback of mineralization (Yu and Peng, 2009).
Here, the phase is not simply defined along with physics to provide a calculation method of the phase function. In fact, because the amplitude has no effect on the phase, angular velocity, ω=ω(t), is the only decisive factor of the phase. It is not easy to acquire the phase based on the physical definition, 
As can be known, the curve of the element con-tent after gridding is similar to Fig. 2. Starting from the first value that must be a peak, we seek the next adjacent peak (the second peak) and then consider the interval between the two peaks as a half cycle to cal-culate the phases according to the nonlinear formula of Fig. 2. Then starting from the second peak and con-tinuing this step, the phase increases by. We can calculate the phases of each element's chemical waves and so on.
The selected analytical samples were taken from stream-sediment samples on a 1 : 50 000 scale, with three to eight samples per squarethousand-meter den-sity: 16 028 samples are obtained. This article matches and analyzes metal oreforming elements, such as wolfram, tin, molybdenum, bismuth, lead, zinc, cop-per, and gold, and two kinds of orecontrolling and oretransporting elements, namely, fluorine and arse-nic.
The mutual synchronization in multiple oscillator systems is too complex, and few people have studied it so far. Therefore, only two kinds of related elements were selected to study their synchronization process in this article.
Wolfram and tin are closely related to fluorine, and can form stable complex compounds during mi-gration. However, lead, zinc, molybdenum, bismuth, copper, and gold generally form complex compounds when they migrate with sulphur (Liu, 1984). Arsenic is relatively richer in sulphide; hence, in this study, sulphur is replaced with arsenic and matched with lead or zinc. Therefore, the following eight analyzed element groups are established: W-F, Sn-F, Mo-As, Bi-As, Au-As, Cu-As, Pb-As and Zn-As.
According to the synchronization theory, the condition under which two oscillator systems synchronize is as follows
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Here, we consider the condition n=m=l, and assign a small appropriate number to the constant based on the phase difference curves. When any phase difference of the matched elements is smaller than the constant in a certain region, the region is regarded as the region af-ter synchronization or a possible mineralization region. On the basis of the corresponding value of the charac-teristics, the region is taken according to the length of the regional platform.
Geostatistics, founded and developed by the French professor G. Matheron in the early 1960s, studies natural phenomena with structure and ran-domicity in a spatial distribution, with space correlation (mineralized spatiotemporal structure) as the basis, regional variation as the core, and variation function as the tool (Yu and Peng, 2009).
Geochemistry studies the dual properties of structure and randomicity (Yu and Peng, 2009). In this study, we utilize geochemistry data on stream sediments in Hunan and the data containing oreforming spatiotemporal structures and distribution of geo-chemistry fields; hence, geostatistics is entirely appli-cable.
According to geostatistical theory, a mineralized phenomenon can be characterized using the spatial distribution of regional variations. The variation function shows incremental variance in regional variables and uses the formula, 2×γ(h)=var{Z(u+h)-Z(u)}. It is used to express changes in regional variations. In an actual process, fitting the experimental variation function with the spherical model allows the acquisition of some characters, such as the correlation of regional variations and the anisotropy of spatial fields. Analysis interpolation is then performed for the number of synchronized regional platforms. The analysis generates a spatiotemporal distribution chart of characteris-tic values of the regional platform after merging the data with an equal number of synchronization plat-forms for each spatiotemporal profile.
Figures 3-4 provide the analytical results of wolfram, tin, molybdenum, bismuth, lead, zinc, copper, and gold on a 1 : 50 000 scale. The characteristic value of the regional platform is the sign of the degree of maturation of the ore formation, so the chart actually represents the mineralization anomaly spatiotemporal distribution, and the arcs are anomalous regional boundaries that are illustrated below. But the characteristic value is different from the geochemical anomaly. The geochemical anomalies only include the content values and spatial locations, and are static; however, the characteristic values of the regional platform include the complete information of three aspects: mineralization, space and time, and can reveal the mechanism and onset of ore formation, which is the advantage of the synchronization method.
The chart shows that there are abundant minerals in the Shizhuyuan, Qitianling, Huangshaping, Furong, Jigongtan, Yaogangxian, and Xianghualing areas. It also shows that Furong and Jigongtan are prospective areas.
As previously mentioned, chemical waves attain coherence after synchronization and are thus called coherent waves. Coherent waves with different com-ponents have different velocities. These components have specific mineral and elemental associations, as well as uniform velocities within the same coherent wave. These coherent wave trains, because of their characteristics, form zone sequences with the excitation site of chemical waves as the center, according to their respective velocities. They subsequently form metallogenic zones. Kuramoto (1984) showed that the propagation of the spatiotemporal synchronization of chemical waves in reaction-diffusion systems forms target patterns (Yu, 2006). The target patterns are in fact metallogenic zones. The phase dynamics of the synchronization theory also shows that the shape of a geometry-dynamics-ordered structure, which is spontaneously revealed with the frequency synchronization or phase synchronization of chemical waves, is the nonlinear target pattern. On one side are incomplete partial annular sections, whereas on the other side are nearly closed or closed annular sections. The center of distribution is the site of the origin of the chemical waves, and is called the organizing center (Yu and Peng, 2009).
Often, studies involve the building of models. During the process of investigation, a certain scale is selected to show important and secondary factors, and ontological characteristics are consequently reduced. This is the so-called intermediate asymptotic principle (Kocarev and Parlitz, 1996).
Based on the two aspects mentioned, we draw the mineralization distribution regularity of each element (arc sections and closed annularity in Figs. 3-4). The mineralization centers of all elements are located on the Qitianling rock body, indicating that the Yansha-nian period is the main mineralization period and that the Qitianling rock body has close connections with mineralization. We must point out the accuracy and certainty of the boundary of target patterns using the mathematical method.
It is obvious that mineral distribution in the Qianlishan-Qitianling area in southern Hunan is responsible for the production, propagation, and synchronization processes of multiple compound chemi-cal wave trains in the geological system, which cause metallogenic zoning, with Qitianling as the center and the Yanshanian period as the main mineralization period.
Based on Figs. 3-4, there are large deposits of minerals near the Jiufeng rock body. Whatever results are gathered using the synchronization method after interpolation may be considered inaccurate because of missing data on Jiufeng (25º20'N-25º30'N and 113º15'E-113º30'E). The deviation is caused by data processing and the analytical method. At present, there is no better way to avoid such deviation.
The application of synchronization uses space-time dualism as the starting point, overcomes the weakness of traditional methods that neglect time information, and analyzes the regional mineralization regularity of the Qianlishan-Qitianling area in south-ern Hunan using a new viewpoint. The results confirm factual data, indicating that it is feasible to apply spa-tiotemporal synchronization theory in geology.
Three major conclusions may be drawn from the study. First, large mineral deposits are found in the Qianlishan-Qitianling area, the Yanshanian period is the main mineralization period, and the Qitianling rock body has close connections with mineralization.
Second, minerals in the Qianlishan-Qitianling area are responsible for the production, propagation, and synchronization processes of multiple compound chemical wave trains, which form metallogenic zones, with Qitianling as the center.
Lastly, this is a new attempt to study and explore regional mineralization regularity using the spatio-temporal synchronization theory. The study presents some ideas on regional mineralization regularity in the Qianlishan-Qitianling area.
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